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drawer barnatan is a professor of pure

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mathematics at the university of toronto

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previously specializing in not theory

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and more recently specializing in finite

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type invariants and kavanaugh homology

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we touch on quantum field theory's

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connection to not theory how to learn

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mathematics in general we also touch on

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ed witton as jorah barnatan's advisor

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for his phd was edwitten and drawer

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gives some anecdotes about eric

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weinstein as while eric was pursuing his

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phd drawer served as an informal advisor

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to eric at harvard professor barnatan

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taught a course in linear algebra that i

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took while i was at the university of

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toronto although i was a terrible

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student and i regret that i skipped the

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majority of his classes because he had

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an exceedingly intuitive approach for

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example there are vector space axioms

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can i i do and they seem extremely

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disconnected from any reason or

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motivation so what the professor would

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do would be before introducing a

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particular abstraction he would say

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imagine seven times a vector instead of

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imagine a times a vector and then

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generalize it which gave the abstraction

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some concreteness for those new to this

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channel my name is kurt jaimungal i'm a

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filmmaker with a background in math and

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physics dedicated to explicating what

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are called theories of everything from a

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mathematical physics perspective but

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also the possible connections

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consciousness has to the fundamental

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laws of nature provided these laws exist

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at all and are knowable to us this

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particular podcast isn't one to be

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listened to or at least you can but

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you're going to be frustrated as what's

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being referred to are one-dimensional

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objects embedded in a three-dimensional

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space in some configuration and the

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verbal description leaves much to be

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desired if you're listening to this on

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spotify or itunes i recommend you click

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the link in the description and follow

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along you can also download a pdf of the

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written notes from this podcast in the

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description as well there are a couple

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sponsors of today's podcast the first is

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podcast from his early days the second

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standard model is based on u1 cross su-2

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going to patreon.com kurtjimungle

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there's also a crypto address and a

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paypal address if that's more up your

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alley i now do this full time and the

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regardless i'm grateful for your

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viewership again that's patreon.com

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kurtjmungle

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c-u-r-t-j-a-i-m-u-n-g-a-l thank you and

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enjoy i actually had you as a professor

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i hope you didn't suffer too much

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that my favorite aspect of the course

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was that you would use the word seven

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you give an example of a number so you'd

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say a certain field number times a

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vector well let's call it seven so seven

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times a vector would be so-and-so you

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know it can get to extremes right you

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may end up doing things like uh

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the limit

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of uh e to the minus seven uh seven goes

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to infinity

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uh is equal to whatever it is zero right

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anyway yes

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what's your field of research

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uh not theory

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and

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from a very algebraic perspective

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and

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related

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algebra things

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it used to be

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uh

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much more not theory and quantum field

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theory and it slowly slowly moved to to

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being much more algebraic and their

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relationship with quantum field theory

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became more and more remote

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okay what's the relationship let's

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forget about the remoteness what's the

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close relationship between not theory

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oh it's a bit hard to

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explain and somewhat surprising and

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that's why that's why it took a long

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time to discover

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let me give you

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two answers

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that are

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somewhat unrelated and

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one answer is that quantum field theory

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and

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note theory is surprisingly also about

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the motion of particles

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so

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uh you know let's draw a simple minded

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knot

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uh

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so by the way is this a visible

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skin yeah okay so here is a simple

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it's actually the so-called trefoil knot

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but uh

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well whatever it is

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uh now uh what you can do

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is you can

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uh so it's living in in r3

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and uh i could set up my coordinates

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so that

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uh

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this coordinate will be called t maybe

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you want to call it z

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but you know i like to call it t at uh

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right now and the two coordinates here

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are x and y

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and then i can slice this knot

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at

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uh equal time

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uh slices so basically i uh

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draw a plane

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which leaves at some fixed height

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so at an equal in an equal time plane

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and slice the knot and then the slice is

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four points

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and as i move these points

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in time

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points move

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and they actually do a little lovely

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dance

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and

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uh the dance is as follows so if we call

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these points uh

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a

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b

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c and d

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then they start at a certain position

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a b

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c and d

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right

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and then

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as i move

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uh

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well you can see that c and b trade

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places so they play a dance they somehow

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dance around each other

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uh

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goes

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after a little while they trade places

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so you have

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a c

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sorry a

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uh

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c b

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d

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so

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uh again you will have a a b

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a c d and if you move a little further

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again they trade places so you'll have a

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c b d

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and then something funny happens

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uh

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points

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uh

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well points well by this time this is

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point b is over here and point c is over

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here

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what happens is that point c moves

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towards point d

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and points a more moves to points point

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b

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and they coincide

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and

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when they coincide they annihilate each

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other because if you look at the plane

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which is above

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the

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uh

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you no longer see any point so what

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happens next is that these points move

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towards each other these points move to

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each other they meet and bang they

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annihilate and after that there is an

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empty set

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and in fact i started a tight

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uh at a certain height had i started

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below i start with the empty set

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and instead of annihilation of pairs

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you get a creation of pairs so a pair of

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points get created here and a pair of

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points get created here and then they

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perform this nice dance

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so this was this particular note but the

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same story is true for every note every

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note can be written as a certain dance

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of points

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in which uh sometimes pairs

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get created sometimes pair meet and

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annihilate each other and in between

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these times they all dance

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anyway uh

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physics in general is about the motion

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of particles and it's not too surprising

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that there is a relationship

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physics also sees things like creation

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and annihilation of pairs of particles

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and i mean so again it's not so

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surprising

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but this is very very very loose

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gee the other explanation i can give you

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is even more loose

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uh

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but even but but in some sense

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more

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um

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uh well okay maybe you've heard

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that quantum mechanics is related to

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path integrals

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so

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uh you know in classical mechanics

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uh

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you know if a path goes from point a to

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point b

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sorry if a particle goes from point a to

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point b

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it goes along a specific path

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um

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probability of going uh from a to b and

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you compute this probability

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by doing a certain

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integral

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over the space of all paths

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so the particle or

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i mean again even even my interpretation

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of quantum mechanics here is a bit loose

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because interpreting quantum mechanics

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is a very hard thing

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but with this loose interpretation you

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sum over all probabilities of going this

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way or that way or that way

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or that way and by adding up all these

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probabilities or more precisely

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integrating over the space of all of

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those probabilities or more precisely

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phase factors or

291
00:11:52,629 --> 00:11:51,200
amplitudes

292
00:11:55,030 --> 00:11:52,639
uh you

293
00:11:58,870 --> 00:11:55,040
you can compute the probability of going

294
00:11:59,990 --> 00:11:58,880
from a to b that's quantum mechanics

295
00:12:01,750 --> 00:12:00,000
now

296
00:12:06,230 --> 00:12:01,760
uh

297
00:12:07,910 --> 00:12:06,240
quantum field theory it's essentially

298
00:12:10,470 --> 00:12:07,920
the same except the integrals are more

299
00:12:13,829 --> 00:12:10,480
complicated but the point is that

300
00:12:18,389 --> 00:12:13,839
already these integrals

301
00:12:20,150 --> 00:12:18,399
are not like integrals over rn

302
00:12:24,629 --> 00:12:20,160
right rn

303
00:12:28,389 --> 00:12:24,639
is uh the collection of n tuples of

304
00:12:32,629 --> 00:12:28,399
points a1 up to a n

305
00:12:34,949 --> 00:12:32,639
so a point in rn is determined by n

306
00:12:37,750 --> 00:12:34,959
real numbers

307
00:12:40,470 --> 00:12:37,760
whereas a function the space we are

308
00:12:42,710 --> 00:12:40,480
integrating over now

309
00:12:43,829 --> 00:12:42,720
is the space of all functions and a

310
00:12:46,710 --> 00:12:43,839
function

311
00:12:49,190 --> 00:12:46,720
is determined by infinitely many real

312
00:12:50,949 --> 00:12:49,200
values you need to know the value of the

313
00:12:52,470 --> 00:12:50,959
function here the value of the function

314
00:12:54,389 --> 00:12:52,480
here the value of the function here the

315
00:12:56,470 --> 00:12:54,399
value of the function here so to

316
00:12:58,870 --> 00:12:56,480
determine a function you need to know

317
00:13:01,509 --> 00:12:58,880
infinite infinitely many

318
00:13:06,550 --> 00:13:01,519
uh real numbers

319
00:13:07,310 --> 00:13:06,560
so the integral that you end up doing is

320
00:13:11,350 --> 00:13:07,320
not

321
00:13:13,750 --> 00:13:11,360
157 style sorry now i'm using a

322
00:13:17,269 --> 00:13:13,760
toronto style language or it's not one

323
00:13:20,230 --> 00:13:17,279
variable calculus in integral which is

324
00:13:23,509 --> 00:13:20,240
again one variable

325
00:13:26,069 --> 00:13:23,519
uh integral it's not this

326
00:13:28,069 --> 00:13:26,079
it's not second year calculus when you

327
00:13:30,310 --> 00:13:28,079
do n variable

328
00:13:33,990 --> 00:13:30,320
uh integrals

329
00:13:37,350 --> 00:13:34,000
it's infinite dimensional so infinitely

330
00:13:39,189 --> 00:13:37,360
many variables integration this is what

331
00:13:40,629 --> 00:13:39,199
we need

332
00:13:41,829 --> 00:13:40,639
okay

333
00:13:42,790 --> 00:13:41,839
so

334
00:13:47,829 --> 00:13:42,800
uh

335
00:13:53,430 --> 00:13:50,310
ended up developing

336
00:13:56,790 --> 00:13:53,440
a bag of techniques for computing

337
00:13:58,870 --> 00:13:56,800
infinite dimensional integrals

338
00:14:00,389 --> 00:13:58,880
and what these techniques are is a whole

339
00:14:03,829 --> 00:14:00,399
different story

340
00:14:05,910 --> 00:14:03,839
but uh but quantum field theory ended up

341
00:14:07,030 --> 00:14:05,920
doing this

342
00:14:08,470 --> 00:14:07,040
and then

343
00:14:10,389 --> 00:14:08,480
uh

344
00:14:13,189 --> 00:14:10,399
it turns out

345
00:14:15,590 --> 00:14:13,199
that infinite dimensional integrals are

346
00:14:17,910 --> 00:14:15,600
useful to topology

347
00:14:20,069 --> 00:14:17,920
so so the the the

348
00:14:22,629 --> 00:14:20,079
the way that quantum field theory

349
00:14:25,030 --> 00:14:22,639
becomes useful in topology is indirect

350
00:14:26,710 --> 00:14:25,040
it's not that the quantum field theory

351
00:14:28,870 --> 00:14:26,720
itself

352
00:14:30,949 --> 00:14:28,880
is useful

353
00:14:33,110 --> 00:14:30,959
even this is a lie because sometimes the

354
00:14:35,509 --> 00:14:33,120
quantum field theory itself is useful

355
00:14:38,230 --> 00:14:35,519
but but the main path by which quantum

356
00:14:39,430 --> 00:14:38,240
filter becomes useful to topology

357
00:14:40,389 --> 00:14:39,440
is not

358
00:14:45,670 --> 00:14:40,399
uh

359
00:14:48,310 --> 00:14:45,680
field theory developed a bag of

360
00:14:51,829 --> 00:14:48,320
techniques and this bag of techniques

361
00:14:55,990 --> 00:14:54,550
anyway why are infinite dimensional

362
00:14:58,790 --> 00:14:56,000
integrals

363
00:15:00,069 --> 00:14:58,800
useful to topology

364
00:15:03,430 --> 00:15:00,079
um

365
00:15:04,949 --> 00:15:03,440
the answer is again a bit

366
00:15:06,389 --> 00:15:04,959
uh

367
00:15:08,949 --> 00:15:06,399
complicated

368
00:15:13,110 --> 00:15:08,959
but let me try to summarize it

369
00:15:15,110 --> 00:15:13,120
so let me bring a knot here's a knot

370
00:15:16,310 --> 00:15:15,120
okay great

371
00:15:21,590 --> 00:15:16,320
uh

372
00:15:25,350 --> 00:15:21,600
why not picking what i'm showing you is

373
00:15:28,150 --> 00:15:27,110
a note

374
00:15:30,470 --> 00:15:28,160
is

375
00:15:38,150 --> 00:15:35,269
an equivalence class of such curves so

376
00:15:40,470 --> 00:15:38,160
this is a curve if i deform it a bit

377
00:15:43,509 --> 00:15:40,480
it's still a curve but it's considered

378
00:15:45,749 --> 00:15:43,519
the same knot if i deform it some more

379
00:15:47,829 --> 00:15:45,759
it's still a curve but it con but but

380
00:15:50,310 --> 00:15:47,839
but but it's the same not

381
00:15:53,590 --> 00:15:50,320
so a knot is not a single curve but an

382
00:15:56,069 --> 00:15:53,600
equivalent class of curves

383
00:15:59,749 --> 00:15:56,079
now suppose you want

384
00:16:03,110 --> 00:15:59,759
quantities that are associated to notes

385
00:16:04,470 --> 00:16:03,120
you want to be able to tell notes apart

386
00:16:05,910 --> 00:16:04,480
so you need

387
00:16:08,470 --> 00:16:05,920
quantities

388
00:16:10,550 --> 00:16:08,480
uh that would be computable from the

389
00:16:12,150 --> 00:16:10,560
knot and that you would use them to tell

390
00:16:14,150 --> 00:16:12,160
the notes apart

391
00:16:17,389 --> 00:16:14,160
okay

392
00:16:19,030 --> 00:16:17,399
now it's very easy to compute

393
00:16:22,629 --> 00:16:19,040
quantities

394
00:16:25,189 --> 00:16:22,639
that are associated with curves

395
00:16:29,110 --> 00:16:25,199
so if you have a curve

396
00:16:32,790 --> 00:16:29,120
uh you can measure its how much it bends

397
00:16:35,509 --> 00:16:32,800
so the radius of of the bending

398
00:16:38,230 --> 00:16:35,519
okay again these things have technical

399
00:16:39,509 --> 00:16:38,240
names the curvature maybe the torsion

400
00:16:42,150 --> 00:16:39,519
there are various

401
00:16:43,590 --> 00:16:42,160
names for for various quantities you can

402
00:16:44,870 --> 00:16:43,600
associate with

403
00:16:47,430 --> 00:16:44,880
curves

404
00:16:51,030 --> 00:16:47,440
so you know i can look at the maximal

405
00:16:53,030 --> 00:16:51,040
curvature of this knot of this curve and

406
00:16:55,269 --> 00:16:53,040
the maximal curvature will be the place

407
00:16:57,910 --> 00:16:55,279
where it turns the most and that's

408
00:17:00,710 --> 00:16:57,920
probably around here for this particular

409
00:17:03,269 --> 00:17:00,720
curve around here okay

410
00:17:06,630 --> 00:17:03,279
now um

411
00:17:09,590 --> 00:17:06,640
uh but that quantity is a quantity which

412
00:17:12,630 --> 00:17:09,600
is associated with curves

413
00:17:14,710 --> 00:17:12,640
it's a useless as a quantity for not

414
00:17:16,710 --> 00:17:14,720
it's useless as a quantity for knots

415
00:17:19,350 --> 00:17:16,720
because if we're talking about not you

416
00:17:22,470 --> 00:17:19,360
know i could deform it and the maximal

417
00:17:25,590 --> 00:17:22,480
curvature could go somewhere else

418
00:17:26,789 --> 00:17:25,600
could change could grow could shrink

419
00:17:27,990 --> 00:17:26,799
could differ

420
00:17:31,430 --> 00:17:28,000
right

421
00:17:32,789 --> 00:17:31,440
so the way to get quantities that are

422
00:17:34,630 --> 00:17:32,799
associated

423
00:17:36,230 --> 00:17:34,640
with knots

424
00:17:37,590 --> 00:17:36,240
rather than with

425
00:17:41,669 --> 00:17:37,600
curves

426
00:17:44,310 --> 00:17:41,679
is to integrate over the space of all

427
00:17:47,270 --> 00:17:44,320
geometries

428
00:17:50,470 --> 00:17:47,280
so instead of picking the quantity for a

429
00:17:51,990 --> 00:17:50,480
specific geometric manifestation of the

430
00:17:54,390 --> 00:17:52,000
knot

431
00:17:57,909 --> 00:17:54,400
you integrate over the space of all

432
00:18:00,750 --> 00:17:57,919
geometries and then the result will be a

433
00:18:03,510 --> 00:18:00,760
a quantity associated with the note

434
00:18:04,789 --> 00:18:03,520
unfortunately the examples are very very

435
00:18:07,990 --> 00:18:04,799
hard

436
00:18:10,230 --> 00:18:08,000
so you know the the famous example the

437
00:18:13,430 --> 00:18:10,240
example that uh

438
00:18:15,510 --> 00:18:13,440
got written uh well one of the examples

439
00:18:18,789 --> 00:18:15,520
that got written very very famous in

440
00:18:22,390 --> 00:18:18,799
topology or among mathematicians is the

441
00:18:26,950 --> 00:18:22,400
so-called chern simon's theory

442
00:18:31,590 --> 00:18:26,960
uh or chen simon's quantity which is um

443
00:18:35,430 --> 00:18:31,600
uh so uh in itself some integral so you

444
00:18:38,470 --> 00:18:35,440
integrate over r3

445
00:18:40,710 --> 00:18:38,480
so the quantity itself is a finite

446
00:18:45,110 --> 00:18:40,720
dimensional integral

447
00:18:48,070 --> 00:18:45,120
right so you integrate over r3 something

448
00:18:50,789 --> 00:18:48,080
called the churn simon's form

449
00:18:52,470 --> 00:18:50,799
uh which is something called which is a

450
00:18:54,630 --> 00:18:52,480
wedge d a

451
00:18:55,590 --> 00:18:54,640
plus two thirds

452
00:18:58,470 --> 00:18:55,600
uh

453
00:19:00,710 --> 00:18:58,480
a wedge a wedge a

454
00:19:03,029 --> 00:19:00,720
whatever that is but this is you know

455
00:19:05,750 --> 00:19:03,039
related to stuff appearing in second

456
00:19:08,710 --> 00:19:05,760
year uh multivariable calculus in the

457
00:19:10,630 --> 00:19:08,720
most advanced versions okay so wedge

458
00:19:13,669 --> 00:19:10,640
products and differential forms and

459
00:19:16,950 --> 00:19:13,679
exterior derivatives and stuff like that

460
00:19:20,190 --> 00:19:16,960
then you take this quantity and you

461
00:19:22,230 --> 00:19:20,200
multiply it by i multiply by k

462
00:19:25,510 --> 00:19:22,240
exponentiate it

463
00:19:29,510 --> 00:19:25,520
multiply by another quantity the

464
00:19:32,150 --> 00:19:29,520
so-called holonomy along the note of a

465
00:19:34,390 --> 00:19:32,160
whatever that is so i'm throwing names

466
00:19:36,070 --> 00:19:34,400
because i really have no choice because

467
00:19:38,710 --> 00:19:36,080
giving the precise definition is a

468
00:19:41,430 --> 00:19:38,720
matter for a graduate class yeah okay

469
00:19:45,909 --> 00:19:41,440
and this is the quantity that you

470
00:19:49,270 --> 00:19:45,919
associate with a geometric note

471
00:19:51,830 --> 00:19:49,280
and then to get an invariant of notes or

472
00:19:53,510 --> 00:19:51,840
to get a quantity associated with the

473
00:19:55,990 --> 00:19:53,520
not itself

474
00:19:59,270 --> 00:19:56,000
you integrate it

475
00:20:01,350 --> 00:19:59,280
over the space of all such a's and i

476
00:20:03,110 --> 00:20:01,360
didn't really tell you what these a's

477
00:20:04,549 --> 00:20:03,120
are but it's an infinite dimensional

478
00:20:05,350 --> 00:20:04,559
space

479
00:20:08,149 --> 00:20:05,360
so

480
00:20:10,710 --> 00:20:08,159
uh i guess i haven't really answered

481
00:20:13,909 --> 00:20:10,720
your question by giving an example but i

482
00:20:16,549 --> 00:20:13,919
just told you the examples are hard

483
00:20:19,110 --> 00:20:16,559
okay anyway um

484
00:20:20,630 --> 00:20:19,120
well they're hard but they're exactly of

485
00:20:21,430 --> 00:20:20,640
the nature

486
00:20:24,149 --> 00:20:21,440
that

487
00:20:26,710 --> 00:20:24,159
physics knows how to study

488
00:20:27,909 --> 00:20:26,720
or that quantum field theory developed

489
00:20:31,510 --> 00:20:27,919
techniques

490
00:20:34,149 --> 00:20:31,520
to study and so one can study it using

491
00:20:37,590 --> 00:20:34,159
quantum field theory techniques and get

492
00:20:39,750 --> 00:20:37,600
all sorts of um

493
00:20:42,310 --> 00:20:39,760
well

494
00:20:45,270 --> 00:20:42,320
quantities relevance to not relevant to

495
00:20:46,950 --> 00:20:45,280
not the so-called jones polynomial is an

496
00:20:48,710 --> 00:20:46,960
example and then there are many other

497
00:20:50,950 --> 00:20:48,720
examples

498
00:20:53,510 --> 00:20:50,960
are there any relationships between not

499
00:20:55,029 --> 00:20:53,520
theory and gravity so general relativity

500
00:20:56,789 --> 00:20:55,039
let's say

501
00:21:00,870 --> 00:20:56,799
um

502
00:21:05,350 --> 00:21:02,549
i'm not an expert

503
00:21:06,390 --> 00:21:05,360
the answer is yes

504
00:21:11,830 --> 00:21:06,400
uh

505
00:21:13,590 --> 00:21:11,840
i told you i've actually moved away from

506
00:21:15,190 --> 00:21:13,600
that subject

507
00:21:17,270 --> 00:21:15,200
what got you interested in not theory

508
00:21:19,110 --> 00:21:17,280
originally

509
00:21:21,110 --> 00:21:19,120
this subject

510
00:21:24,710 --> 00:21:21,120
so mainly you were interested in physics

511
00:21:25,590 --> 00:21:24,720
well okay i was a math undergrad

512
00:21:28,390 --> 00:21:25,600
uh

513
00:21:33,270 --> 00:21:31,590
during my time as an undergrad and then

514
00:21:36,230 --> 00:21:33,280
a master's student in tel aviv

515
00:21:39,029 --> 00:21:36,240
university i never finished the masters

516
00:21:41,430 --> 00:21:39,039
i moved on to doing my phd in in

517
00:21:43,830 --> 00:21:41,440
princeton but during my time as a

518
00:21:46,070 --> 00:21:43,840
master's student in in

519
00:21:49,029 --> 00:21:46,080
in tel aviv i got more and more

520
00:21:49,909 --> 00:21:49,039
interested in in physics

521
00:21:52,390 --> 00:21:49,919
and

522
00:21:54,390 --> 00:21:52,400
uh there's just wonderful mathematics

523
00:21:56,310 --> 00:21:54,400
inside physics so i got interested in

524
00:21:57,669 --> 00:21:56,320
physics and the fundamental question of

525
00:21:59,990 --> 00:21:57,679
physics right

526
00:22:03,350 --> 00:22:00,000
what are the basic laws of the universe

527
00:22:05,590 --> 00:22:03,360
i mean you can't ask a better question

528
00:22:07,669 --> 00:22:05,600
so i got more and more interested in

529
00:22:10,310 --> 00:22:07,679
physics and decided to do my phd in

530
00:22:13,430 --> 00:22:10,320
mathematical physics

531
00:22:18,070 --> 00:22:13,440
and i ended up uh working with ed

532
00:22:20,230 --> 00:22:18,080
wheaton uh who who is a very famous

533
00:22:23,990 --> 00:22:20,240
physicist or mathematical physicist or

534
00:22:27,270 --> 00:22:24,000
mathematician depending whom you ask

535
00:22:30,950 --> 00:22:27,280
and um

536
00:22:32,310 --> 00:22:30,960
uh and originally my interest was in

537
00:22:33,590 --> 00:22:32,320
physics

538
00:22:36,070 --> 00:22:33,600
or you know

539
00:22:37,990 --> 00:22:36,080
my aim was to do things that was rather

540
00:22:40,070 --> 00:22:38,000
were relevant to physics

541
00:22:41,750 --> 00:22:40,080
somehow that's not what happened you

542
00:22:42,789 --> 00:22:41,760
know at the end you don't choose your

543
00:22:47,990 --> 00:22:42,799
career

544
00:22:48,789 --> 00:22:48,000
you know so uh

545
00:23:09,430 --> 00:22:48,799
i

546
00:23:12,549 --> 00:23:09,440
turned out that that was relevant to

547
00:23:14,870 --> 00:23:12,559
something called finite type invariants

548
00:23:16,950 --> 00:23:14,880
and i thought i had new things to say

549
00:23:20,070 --> 00:23:16,960
about finite typing variance and that's

550
00:23:20,830 --> 00:23:20,080
completely and not theoretic subject

551
00:23:22,070 --> 00:23:20,840
so

552
00:23:22,950 --> 00:23:22,080
i uh

553
00:23:34,870 --> 00:23:22,960
i

554
00:23:38,070 --> 00:23:34,880
about and that paper or two became 10

555
00:23:39,750 --> 00:23:38,080
years with several paper many papers and

556
00:23:41,430 --> 00:23:39,760
many results and

557
00:23:43,350 --> 00:23:41,440
and

558
00:23:45,430 --> 00:23:43,360
you know

559
00:23:47,510 --> 00:23:45,440
and then a chinese meeting led me to yet

560
00:23:49,830 --> 00:23:47,520
another subject and you know

561
00:23:51,269 --> 00:23:49,840
what was the other subject it led you to

562
00:23:53,590 --> 00:23:51,279
um

563
00:23:56,390 --> 00:23:53,600
well no the next subject after finite

564
00:23:58,549 --> 00:23:56,400
typing variance was juvano homology

565
00:24:02,549 --> 00:23:58,559
anyway you don't choose what you do you

566
00:24:03,669 --> 00:24:02,559
you know you you at most uh try to steer

567
00:24:04,470 --> 00:24:03,679
it

568
00:24:06,870 --> 00:24:04,480
but

569
00:24:07,990 --> 00:24:06,880
it steers you much more than you steer

570
00:24:09,909 --> 00:24:08,000
it

571
00:24:12,870 --> 00:24:09,919
like the subject do you have an

572
00:24:13,990 --> 00:24:12,880
intuitive explanation for people who

573
00:24:17,190 --> 00:24:14,000
let's say they're at the second year

574
00:24:23,350 --> 00:24:17,200
level what is a homology

575
00:24:27,750 --> 00:24:24,630
it's a tough

576
00:24:29,990 --> 00:24:27,760
a very tough uh

577
00:24:32,070 --> 00:24:30,000
question

578
00:24:35,350 --> 00:24:32,080
because

579
00:24:36,470 --> 00:24:35,360
it's many things or it's related to many

580
00:24:40,470 --> 00:24:36,480
things

581
00:24:41,830 --> 00:24:40,480
and i could answer it in in many levels

582
00:24:44,310 --> 00:24:41,840
um

583
00:24:46,630 --> 00:24:44,320
you know

584
00:24:49,430 --> 00:24:46,640
uh let me

585
00:24:50,549 --> 00:24:49,440
let me give you a summary answer

586
00:24:51,830 --> 00:24:50,559
sure okay

587
00:24:55,669 --> 00:24:51,840
so

588
00:25:05,029 --> 00:25:00,630
there are two ways to describe objects

589
00:25:09,990 --> 00:25:05,039
you can describe them implicitly

590
00:25:10,990 --> 00:25:10,000
by telling what equations they satisfy

591
00:25:12,710 --> 00:25:11,000
or

592
00:25:15,750 --> 00:25:12,720
explicitly

593
00:25:18,230 --> 00:25:15,760
by constructing all of them

594
00:25:19,110 --> 00:25:18,240
let me give you the simplest example

595
00:25:20,950 --> 00:25:19,120
so

596
00:25:22,950 --> 00:25:20,960
uh consider

597
00:25:25,830 --> 00:25:22,960
the unit circle

598
00:25:28,549 --> 00:25:25,840
sorry i kind of care about the points of

599
00:25:32,230 --> 00:25:28,559
the unit circle so here is the unit

600
00:25:34,870 --> 00:25:32,240
circle in the x y plane and here is a

601
00:25:38,470 --> 00:25:34,880
point x y

602
00:25:40,630 --> 00:25:38,480
the implicit description of the circle

603
00:25:41,430 --> 00:25:40,640
so the implicit

604
00:25:44,630 --> 00:25:41,440
is

605
00:25:46,710 --> 00:25:44,640
by writing an equation which the points

606
00:25:49,510 --> 00:25:46,720
have to satisfy and everybody knows what

607
00:25:53,269 --> 00:25:49,520
the equation is the equation is x

608
00:25:56,390 --> 00:25:53,279
squared minus sorry plus y squared minus

609
00:25:57,830 --> 00:25:56,400
1 is equal to 0.

610
00:25:58,710 --> 00:25:57,840
okay

611
00:26:00,870 --> 00:25:58,720
uh

612
00:26:02,630 --> 00:26:00,880
but there is also an explicit

613
00:26:05,590 --> 00:26:02,640
description

614
00:26:07,990 --> 00:26:05,600
and again i'm not sure which one is

615
00:26:11,430 --> 00:26:08,000
why the naming is such but it it doesn't

616
00:26:14,630 --> 00:26:11,440
really matter namely i can construct all

617
00:26:17,669 --> 00:26:14,640
the points of the paper of the circle

618
00:26:18,870 --> 00:26:17,679
and the construction is you set x is

619
00:26:25,909 --> 00:26:18,880
equal to

620
00:26:31,350 --> 00:26:27,110
okay

621
00:26:34,070 --> 00:26:31,360
now this is the general

622
00:26:36,549 --> 00:26:34,080
a general feature in mathematics that

623
00:26:39,269 --> 00:26:36,559
many things can be described either be

624
00:26:42,789 --> 00:26:39,279
constructed that's the explicit

625
00:26:43,669 --> 00:26:42,799
or be defined by an equation

626
00:26:45,830 --> 00:26:43,679
now

627
00:26:48,230 --> 00:26:45,840
if you uh

628
00:26:50,310 --> 00:26:48,240
restrict your attention to linear

629
00:26:53,669 --> 00:26:50,320
algebra

630
00:26:55,990 --> 00:26:53,679
if you you you do the same thing but in

631
00:26:56,950 --> 00:26:56,000
linear algebra

632
00:26:57,750 --> 00:26:56,960
then

633
00:26:59,909 --> 00:26:57,760
uh

634
00:27:01,990 --> 00:26:59,919
the situation is that you have some

635
00:27:02,950 --> 00:27:02,000
space in the middle maybe it's a vector

636
00:27:09,029 --> 00:27:02,960
space

637
00:27:10,870 --> 00:27:09,039
describe things

638
00:27:13,269 --> 00:27:10,880
actually i'm not sure why i'm drawing it

639
00:27:15,029 --> 00:27:13,279
curve because the curve because if it's

640
00:27:17,909 --> 00:27:15,039
linear algebra i should be drawing it

641
00:27:19,430 --> 00:27:17,919
straight but anyway you want to describe

642
00:27:23,029 --> 00:27:19,440
things

643
00:27:24,549 --> 00:27:23,039
and there are two ways to describe them

644
00:27:26,549 --> 00:27:24,559
one way

645
00:27:28,230 --> 00:27:26,559
is by saying

646
00:27:30,630 --> 00:27:28,240
these things

647
00:27:32,470 --> 00:27:30,640
well you construct a map into another

648
00:27:37,029 --> 00:27:32,480
space

649
00:27:39,190 --> 00:27:37,039
and you say these things are the things

650
00:27:41,830 --> 00:27:39,200
in the kernel

651
00:27:43,269 --> 00:27:41,840
of this map so i don't know what let's

652
00:27:44,710 --> 00:27:43,279
call this map

653
00:27:46,630 --> 00:27:44,720
fi

654
00:27:51,430 --> 00:27:46,640
and these things

655
00:27:57,029 --> 00:27:52,549
and then

656
00:28:03,750 --> 00:28:00,950
so this is the implicit description

657
00:28:06,630 --> 00:28:03,760
this is you describe the things by an

658
00:28:08,710 --> 00:28:06,640
equation and and then there is also the

659
00:28:11,669 --> 00:28:08,720
explicit description so you have yet

660
00:28:15,590 --> 00:28:11,679
another vector space and you have a map

661
00:28:18,789 --> 00:28:15,600
let's call it let's call it psi

662
00:28:20,070 --> 00:28:18,799
and you say the things here

663
00:28:22,389 --> 00:28:20,080
that are

664
00:28:23,830 --> 00:28:22,399
well the good things like the points of

665
00:28:27,029 --> 00:28:23,840
the circle

666
00:28:30,149 --> 00:28:27,039
are the image of psy

667
00:28:32,870 --> 00:28:30,159
so you say these are the things that are

668
00:28:34,789 --> 00:28:32,880
the image of psy

669
00:28:37,350 --> 00:28:34,799
okay and this corresponds to the

670
00:28:39,909 --> 00:28:37,360
explicit view

671
00:28:44,310 --> 00:28:39,919
you construct the things you present

672
00:28:47,190 --> 00:28:44,320
them as an image via some operation

673
00:28:52,630 --> 00:28:49,830
coming from some you know maybe

674
00:28:55,269 --> 00:28:52,640
some smaller dimensional space

675
00:28:58,549 --> 00:28:56,830
uh so

676
00:29:01,029 --> 00:28:58,559
okay

677
00:29:05,430 --> 00:29:01,039
here's a funny thing so

678
00:29:08,389 --> 00:29:05,440
if your construction is reasonable

679
00:29:11,990 --> 00:29:08,399
then everything you construct

680
00:29:14,549 --> 00:29:12,000
solves the equations

681
00:29:16,070 --> 00:29:14,559
in other words everything in the image

682
00:29:19,750 --> 00:29:16,080
of psy

683
00:29:20,870 --> 00:29:19,760
is contained in the kernel of phi

684
00:29:23,510 --> 00:29:20,880
so

685
00:29:25,430 --> 00:29:23,520
once you have a situation like this you

686
00:29:27,830 --> 00:29:25,440
know that you're going to have that the

687
00:29:33,510 --> 00:29:27,840
image of psy

688
00:29:39,190 --> 00:29:36,789
and in fact if you're constructing the

689
00:29:42,549 --> 00:29:39,200
exact same things

690
00:29:45,909 --> 00:29:42,559
then the image of i will be equal

691
00:29:48,470 --> 00:29:45,919
to the kernel of i not just contained

692
00:29:52,310 --> 00:29:48,480
okay and then you will be saying that

693
00:29:55,430 --> 00:29:52,320
the situation is exact

694
00:29:57,269 --> 00:29:55,440
things got exactly the things that

695
00:30:00,710 --> 00:29:57,279
you've constructed are the things that

696
00:30:03,110 --> 00:30:00,720
you described by the equations

697
00:30:06,789 --> 00:30:03,120
but that's not always the case

698
00:30:09,590 --> 00:30:06,799
sometimes you have equations defining

699
00:30:12,470 --> 00:30:09,600
something and you want to know did i

700
00:30:17,269 --> 00:30:12,480
construct all the solutions

701
00:30:20,149 --> 00:30:17,279
so sometimes this inclusion is strict

702
00:30:24,789 --> 00:30:20,159
and then you want to measure

703
00:30:27,510 --> 00:30:24,799
by how much or how much did you fail

704
00:30:29,510 --> 00:30:27,520
so how much did you not construct

705
00:30:31,830 --> 00:30:29,520
everything and that's exactly the

706
00:30:34,470 --> 00:30:31,840
difference between the kernel of phi and

707
00:30:37,350 --> 00:30:34,480
the image of psy and in linear algebra

708
00:30:39,029 --> 00:30:37,360
the difference is quotient so you take

709
00:30:42,149 --> 00:30:39,039
the quotient space

710
00:30:44,870 --> 00:30:42,159
and this is the so-called homology

711
00:30:48,830 --> 00:30:44,880
so somehow homology measures

712
00:30:52,630 --> 00:30:51,269
uh uh

713
00:30:54,470 --> 00:30:52,640
how

714
00:30:55,669 --> 00:30:54,480
good

715
00:30:57,029 --> 00:30:55,679
are

716
00:31:00,950 --> 00:30:57,039
your

717
00:31:06,149 --> 00:31:03,350
did you construct everything or did you

718
00:31:08,630 --> 00:31:06,159
leave some stuff out

719
00:31:10,710 --> 00:31:08,640
is the kernel the implicit the

720
00:31:13,110 --> 00:31:10,720
description this

721
00:31:14,789 --> 00:31:13,120
does it contain more things and then

722
00:31:17,669 --> 00:31:14,799
you've constructed

723
00:31:20,389 --> 00:31:17,679
so somehow homology measures how good

724
00:31:22,230 --> 00:31:20,399
are your constructions and this is true

725
00:31:24,070 --> 00:31:22,240
in general

726
00:31:26,870 --> 00:31:24,080
uh

727
00:31:30,830 --> 00:31:26,880
and and and then there are lots and lots

728
00:31:32,870 --> 00:31:30,840
and lots and lots of specific examples

729
00:31:33,990 --> 00:31:32,880
uh and

730
00:31:36,549 --> 00:31:34,000
uh

731
00:31:38,789 --> 00:31:36,559
to some extent it's a bit of magic i'm

732
00:31:40,389 --> 00:31:38,799
not sure i i can give you a really good

733
00:31:43,909 --> 00:31:40,399
explanation

734
00:31:48,710 --> 00:31:43,919
why there are so many examples and why

735
00:31:51,430 --> 00:31:48,720
so much of mathematics uh end up

736
00:31:56,710 --> 00:31:54,149
having close relationships with with

737
00:31:59,110 --> 00:31:56,720
with uh with homology maybe this is a

738
00:32:01,269 --> 00:31:59,120
partial explanation so

739
00:32:02,950 --> 00:32:01,279
basically you always want to measure how

740
00:32:03,830 --> 00:32:02,960
good is what you've done

741
00:32:05,269 --> 00:32:03,840
so

742
00:32:07,350 --> 00:32:05,279
are you able to talk about what co

743
00:32:09,669 --> 00:32:07,360
homology is and then homology's

744
00:32:11,909 --> 00:32:09,679
relationship to co homology or is that a

745
00:32:13,990 --> 00:32:11,919
whole other can of worms it's another

746
00:32:17,509 --> 00:32:14,000
kind of forms but

747
00:32:19,990 --> 00:32:17,519
in some sense it's not interesting

748
00:32:21,190 --> 00:32:20,000
in in some philosophical sense it's not

749
00:32:27,990 --> 00:32:21,200
interesting

750
00:32:32,230 --> 00:32:30,789
it's essentially the same

751
00:32:34,230 --> 00:32:32,240
so

752
00:32:37,190 --> 00:32:34,240
the difference between a homology and

753
00:32:39,590 --> 00:32:37,200
co-homology more than anything else is a

754
00:32:41,590 --> 00:32:39,600
difference of conventions whether your

755
00:32:42,950 --> 00:32:41,600
map goes from left to right or from

756
00:32:46,549 --> 00:32:42,960
right to left

757
00:32:54,310 --> 00:32:49,590
from this

758
00:32:56,789 --> 00:32:54,320
very imprecise perspective there's

759
00:32:58,710 --> 00:32:56,799
really no difference

760
00:33:00,389 --> 00:32:58,720
professor what do your average days look

761
00:33:03,029 --> 00:33:00,399
like for example do you wake up at the

762
00:33:04,630 --> 00:33:03,039
same time do you drink the same type of

763
00:33:06,149 --> 00:33:04,640
do you drink coffee and it has to be

764
00:33:08,149 --> 00:33:06,159
this particular type of coffee do you

765
00:33:11,350 --> 00:33:08,159
eat a certain breakfast what does it

766
00:33:14,950 --> 00:33:11,360
look like paint the drawer picture

767
00:33:14,960 --> 00:33:18,870
well i'm a lazy bum

768
00:33:22,830 --> 00:33:19,909
and

769
00:33:26,070 --> 00:33:22,840
i'm a believer in the

770
00:33:29,350 --> 00:33:26,080
um you know there was at some point a

771
00:33:31,909 --> 00:33:29,360
revolution right before that uh people

772
00:33:34,470 --> 00:33:31,919
used to work seven days a week uh 12

773
00:33:36,789 --> 00:33:34,480
hours a day or maybe with a short break

774
00:33:38,870 --> 00:33:36,799
on sunday morning

775
00:33:39,990 --> 00:33:38,880
depending which culture you came from i

776
00:33:43,110 --> 00:33:40,000
suppose

777
00:33:45,190 --> 00:33:43,120
and then at some point there was this uh

778
00:33:46,070 --> 00:33:45,200
workers right uh

779
00:33:47,350 --> 00:33:46,080
uh

780
00:33:50,830 --> 00:33:47,360
revolution

781
00:33:54,870 --> 00:33:50,840
and somehow the working week shrunk to

782
00:33:56,630 --> 00:33:54,880
uh 40 hours a week or so like five days

783
00:33:58,149 --> 00:33:56,640
of eight hours

784
00:34:01,750 --> 00:33:58,159
hours a day right

785
00:34:04,870 --> 00:34:01,760
and i'm essentially a believer in that

786
00:34:08,310 --> 00:34:04,880
uh and furthermore i'm a lazy bum so

787
00:34:11,669 --> 00:34:08,320
during my eight hours of work a day

788
00:34:12,629 --> 00:34:11,679
five days a week i take coffee breaks i

789
00:34:15,909 --> 00:34:12,639
uh

790
00:34:16,869 --> 00:34:15,919
you know browse the web i cheat

791
00:34:18,069 --> 00:34:16,879
uh

792
00:34:21,430 --> 00:34:18,079
um

793
00:34:22,869 --> 00:34:21,440
but anyway you know i wake up at 6 30 i

794
00:34:29,990 --> 00:34:22,879
uh

795
00:34:32,869 --> 00:34:30,000
check my email do all sorts of

796
00:34:36,629 --> 00:34:32,879
unimportant things then uh

797
00:34:39,270 --> 00:34:36,639
around nine usually i start uh working

798
00:34:40,790 --> 00:34:39,280
i work until five or so i'm sorry i'm

799
00:34:44,389 --> 00:34:40,800
very dull

800
00:34:49,430 --> 00:34:47,030
and then i try to have fun for the rest

801
00:34:51,669 --> 00:34:49,440
of the day whatever that may be might be

802
00:34:53,030 --> 00:34:51,679
during the pandemic it was it is a bit

803
00:34:56,629 --> 00:34:53,040
harder

804
00:34:58,950 --> 00:34:56,639
and then on the weekends i try to go

805
00:35:01,510 --> 00:34:58,960
biking hiking

806
00:35:03,270 --> 00:35:01,520
puddling

807
00:35:05,430 --> 00:35:03,280
mostly things that don't have to do with

808
00:35:07,510 --> 00:35:05,440
work i'm lying a little bit because

809
00:35:09,510 --> 00:35:07,520
occasionally there is a reason to work

810
00:35:11,910 --> 00:35:09,520
on the weekend and occasionally i do

811
00:35:14,630 --> 00:35:11,920
have a meeting with somebody like i have

812
00:35:16,870 --> 00:35:14,640
an australian collaborator so often our

813
00:35:20,109 --> 00:35:16,880
meetings are in the evenings

814
00:35:23,030 --> 00:35:20,119
so i mean i'm i i've given you an

815
00:35:25,030 --> 00:35:23,040
idealized uh story the truth is a little

816
00:35:27,349 --> 00:35:25,040
different is you know

817
00:35:29,750 --> 00:35:27,359
varies when you're working from nine to

818
00:35:31,670 --> 00:35:29,760
five how much of that time is spent

819
00:35:34,150 --> 00:35:31,680
thinking versus reading someone else's

820
00:35:36,710 --> 00:35:34,160
paper versus answering departmental

821
00:35:39,190 --> 00:35:36,720
emails and requests like what is work

822
00:35:41,349 --> 00:35:39,200
because work obviously for a professor

823
00:35:42,630 --> 00:35:41,359
you have to teach you also have to do

824
00:35:45,349 --> 00:35:42,640
research there's

825
00:35:47,510 --> 00:35:45,359
perhaps 10. work is all of that and it

826
00:35:51,430 --> 00:35:47,520
depends on the season so

827
00:35:55,030 --> 00:35:51,440
basically when i teach two courses

828
00:36:00,710 --> 00:35:57,750
there's basically fall spring and summer

829
00:36:03,670 --> 00:36:00,720
you know fall semester spring semester

830
00:36:05,910 --> 00:36:03,680
and summer okay

831
00:36:07,990 --> 00:36:05,920
in the fall in the spring i teach either

832
00:36:10,550 --> 00:36:08,000
two or one course per semester in the

833
00:36:13,349 --> 00:36:10,560
summer i don't teach

834
00:36:14,470 --> 00:36:13,359
so when i teach two courses per semester

835
00:36:15,430 --> 00:36:14,480
that's

836
00:36:18,870 --> 00:36:15,440
almost

837
00:36:21,430 --> 00:36:18,880
have

838
00:36:22,390 --> 00:36:21,440
uh goes into that

839
00:36:25,109 --> 00:36:22,400
uh

840
00:36:27,670 --> 00:36:25,119
and the rest goes into the regular

841
00:36:30,230 --> 00:36:27,680
meetings that i have to keep

842
00:36:32,150 --> 00:36:30,240
so i have several graduate students that

843
00:36:34,390 --> 00:36:32,160
i work with several collaborators and

844
00:36:35,670 --> 00:36:34,400
i'm trying to keep weekly meetings with

845
00:36:37,750 --> 00:36:35,680
them

846
00:36:40,550 --> 00:36:37,760
so there is a certain amount of like

847
00:36:42,550 --> 00:36:40,560
weekly meetings that i have to keep

848
00:36:45,349 --> 00:36:42,560
when i teach one course

849
00:36:47,829 --> 00:36:45,359
uh i have some breathing room and when i

850
00:36:50,550 --> 00:36:47,839
teach nothing namely during the summer

851
00:36:52,390 --> 00:36:50,560
then a higher proportion goes into

852
00:36:54,630 --> 00:36:52,400
research

853
00:36:55,750 --> 00:36:54,640
even in the summer the proportion is not

854
00:36:57,990 --> 00:36:55,760
very high

855
00:37:00,150 --> 00:36:58,000
firstly is your ideal situation to

856
00:37:01,589 --> 00:37:00,160
simply be a research professor i know

857
00:37:03,589 --> 00:37:01,599
some professors

858
00:37:05,670 --> 00:37:03,599
don't they treat teaching as an aside

859
00:37:10,950 --> 00:37:05,680
they don't particularly like to do it

860
00:37:17,910 --> 00:37:12,950
well

861
00:37:25,270 --> 00:37:20,150
i mean

862
00:37:33,430 --> 00:37:27,510
um

863
00:37:39,430 --> 00:37:36,870
is to support teaching

864
00:37:42,790 --> 00:37:39,440
even the research is so that i will

865
00:37:43,589 --> 00:37:42,800
remain in shape

866
00:37:49,349 --> 00:37:43,599
and

867
00:37:51,349 --> 00:37:49,359
remain in shape so you know if if i do

868
00:37:52,230 --> 00:37:51,359
research i am able to

869
00:37:54,150 --> 00:37:52,240
uh

870
00:37:55,430 --> 00:37:54,160
teach graduate students how to do

871
00:37:57,910 --> 00:37:55,440
research

872
00:37:59,430 --> 00:37:57,920
and then they are

873
00:38:01,510 --> 00:37:59,440
become

874
00:38:05,589 --> 00:38:01,520
stronger mathematicians and can teach

875
00:38:09,030 --> 00:38:05,599
mathematics better so so so so so i even

876
00:38:12,150 --> 00:38:09,040
see researchers mostly uh supporting

877
00:38:16,230 --> 00:38:13,190
so

878
00:38:18,230 --> 00:38:16,240
i definitely wouldn't say that i see

879
00:38:19,750 --> 00:38:18,240
everything as research right i mean

880
00:38:23,109 --> 00:38:19,760
research

881
00:38:25,829 --> 00:38:23,119
again teaching is very significant

882
00:38:28,069 --> 00:38:25,839
well that's the theory

883
00:38:29,910 --> 00:38:28,079
in practice

884
00:38:32,230 --> 00:38:29,920
um

885
00:38:34,790 --> 00:38:32,240
you know waking up every morning and

886
00:38:36,870 --> 00:38:34,800
preparing your class and this marathon

887
00:38:38,230 --> 00:38:36,880
of teaching where you have to prepare

888
00:38:39,670 --> 00:38:38,240
your class

889
00:38:41,990 --> 00:38:39,680
uh you

890
00:38:44,310 --> 00:38:42,000
teach you feel

891
00:38:47,510 --> 00:38:44,320
terrible about the things you missed

892
00:38:49,670 --> 00:38:47,520
during class you don't even have time to

893
00:38:51,829 --> 00:38:49,680
digest it and you have to get ready for

894
00:38:54,150 --> 00:38:51,839
the next class already

895
00:38:55,190 --> 00:38:54,160
so uh

896
00:38:57,670 --> 00:38:55,200
you know

897
00:39:00,069 --> 00:38:57,680
it's very hard

898
00:39:02,950 --> 00:39:00,079
i mean people who haven't done that

899
00:39:06,950 --> 00:39:02,960
don't appreciate how it how hard it is

900
00:39:07,910 --> 00:39:06,960
but it's emotionally very very difficult

901
00:39:12,390 --> 00:39:07,920
and

902
00:39:16,870 --> 00:39:14,790
you have no idea how much i i'm i'm

903
00:39:21,589 --> 00:39:16,880
looking forward to the break so it's not

904
00:39:25,910 --> 00:39:22,950
you know i

905
00:39:27,990 --> 00:39:25,920
when i teach i want out

906
00:39:30,550 --> 00:39:28,000
do you find that to be true even if it's

907
00:39:33,190 --> 00:39:30,560
an undergraduate course the reason i ask

908
00:39:35,589 --> 00:39:33,200
this is that i imagine as a professor

909
00:39:37,270 --> 00:39:35,599
the undergraduate material you could

910
00:39:39,190 --> 00:39:37,280
teach with your pinky you don't have to

911
00:39:40,310 --> 00:39:39,200
think much about it because you first of

912
00:39:43,030 --> 00:39:40,320
all you've mastered it second you've

913
00:39:45,109 --> 00:39:43,040
taught it for years and years i do not

914
00:39:46,630 --> 00:39:45,119
teach the same class

915
00:39:47,589 --> 00:39:46,640
for years

916
00:39:49,829 --> 00:39:47,599
like

917
00:39:50,950 --> 00:39:49,839
i think the maximum i've ever repeated

918
00:39:54,230 --> 00:39:50,960
the class

919
00:39:56,390 --> 00:39:54,240
uh was like three years

920
00:39:57,430 --> 00:39:56,400
so it's not

921
00:40:02,630 --> 00:39:57,440
but

922
00:40:03,589 --> 00:40:02,640
uh you always have to prepare

923
00:40:06,150 --> 00:40:03,599
uh

924
00:40:08,550 --> 00:40:06,160
you always blunder i always blunder

925
00:40:13,349 --> 00:40:08,560
maybe perfect people don't

926
00:40:17,589 --> 00:40:15,190
here and there and then i have to figure

927
00:40:19,030 --> 00:40:17,599
out ways out

928
00:40:22,150 --> 00:40:19,040
i always

929
00:40:25,109 --> 00:40:22,160
find new things to do new ways to do

930
00:40:27,190 --> 00:40:25,119
things i always um

931
00:40:29,829 --> 00:40:27,200
even when i repeat but essentially but

932
00:40:32,710 --> 00:40:29,839
most of the time i don't repeat

933
00:40:36,710 --> 00:40:32,720
and the material is sometimes hard you

934
00:40:41,109 --> 00:40:39,750
and even when it's not hard

935
00:40:44,950 --> 00:40:41,119
so you know

936
00:40:47,349 --> 00:40:44,960
on day one of the class

937
00:40:52,550 --> 00:40:47,359
you teach of a linear algebra class you

938
00:40:59,910 --> 00:40:55,430
i obviously know these axions

939
00:41:02,390 --> 00:40:59,920
right i i obviously um

940
00:41:04,550 --> 00:41:02,400
when i see a vector space

941
00:41:07,430 --> 00:41:04,560
i know it

942
00:41:10,630 --> 00:41:07,440
when i when when you give me a vector

943
00:41:12,950 --> 00:41:10,640
space i know what to do with it

944
00:41:15,349 --> 00:41:12,960
but that's not the same thing

945
00:41:17,589 --> 00:41:15,359
as getting up in front of a class and

946
00:41:18,550 --> 00:41:17,599
listing the axioms

947
00:41:21,349 --> 00:41:18,560
and

948
00:41:24,150 --> 00:41:21,359
making sure that you haven't forgotten

949
00:41:26,790 --> 00:41:24,160
one small axiom somewhere

950
00:41:28,950 --> 00:41:26,800
or that you phrase them perfectly so

951
00:41:31,990 --> 00:41:28,960
that even people who have never seen

952
00:41:33,670 --> 00:41:32,000
these things before will understand

953
00:41:36,390 --> 00:41:33,680
um

954
00:41:39,829 --> 00:41:36,400
so i mean even day one of a very basic

955
00:41:41,270 --> 00:41:39,839
class uh requires preparation

956
00:41:42,710 --> 00:41:41,280
we're gonna talk about mathematical

957
00:41:45,190 --> 00:41:42,720
techniques

958
00:41:46,470 --> 00:41:45,200
in fact i believe when we emailed you

959
00:41:48,630 --> 00:41:46,480
said you don't like the emphasis on

960
00:41:50,790 --> 00:41:48,640
theorems and proofs you like

961
00:41:52,230 --> 00:41:50,800
well we can talk about that later

962
00:41:54,309 --> 00:41:52,240
as for

963
00:41:55,750 --> 00:41:54,319
teaching techniques i'm curious what

964
00:41:58,870 --> 00:41:55,760
have you gleaned what have you found to

965
00:42:01,349 --> 00:41:58,880
be productive and perhaps even some

966
00:42:03,670 --> 00:42:01,359
behaviors you find to be unproductive

967
00:42:07,270 --> 00:42:03,680
that you see other people other teachers

968
00:42:11,270 --> 00:42:09,750
i mean there is so much

969
00:42:13,270 --> 00:42:11,280
uh

970
00:42:14,390 --> 00:42:13,280
you know starting from

971
00:42:19,510 --> 00:42:14,400
com

972
00:42:22,069 --> 00:42:19,520
make sure that you're heard

973
00:42:25,109 --> 00:42:22,079
right if the classroom is large and you

974
00:42:27,270 --> 00:42:25,119
speak without a microphone

975
00:42:29,109 --> 00:42:27,280
uh people in the back are not going to

976
00:42:31,190 --> 00:42:29,119
hear you and then

977
00:42:33,910 --> 00:42:31,200
they're not going to follow

978
00:42:36,710 --> 00:42:33,920
uh make sure that you can be seen

979
00:42:39,510 --> 00:42:36,720
so if you write with a tiny you know if

980
00:42:40,870 --> 00:42:39,520
you write tiny letters with a faded

981
00:42:42,309 --> 00:42:40,880
chalk

982
00:42:46,950 --> 00:42:42,319
uh

983
00:42:48,710 --> 00:42:46,960
the class is a failure no matter what

984
00:42:50,870 --> 00:42:48,720
you say

985
00:42:52,150 --> 00:42:50,880
and then there are uh higher level

986
00:42:56,550 --> 00:42:52,160
things and

987
00:42:58,710 --> 00:42:56,560
basically everything should be motivated

988
00:43:01,349 --> 00:42:58,720
so you know i mentioned the first class

989
00:43:03,910 --> 00:43:01,359
of a linear the first class uh in a

990
00:43:07,510 --> 00:43:03,920
linear algebra course

991
00:43:09,510 --> 00:43:07,520
okay so you can give by uh you can give

992
00:43:12,710 --> 00:43:09,520
by this class

993
00:43:15,430 --> 00:43:12,720
by saying uh you can start this class by

994
00:43:18,990 --> 00:43:15,440
saying let f be

995
00:43:21,990 --> 00:43:20,870
essent

996
00:43:23,510 --> 00:43:22,000
v

997
00:43:24,950 --> 00:43:23,520
is

998
00:43:28,230 --> 00:43:24,960
called

999
00:43:30,710 --> 00:43:28,240
a vector space if

1000
00:43:33,430 --> 00:43:30,720
and then you can write property you know

1001
00:43:35,910 --> 00:43:33,440
operations and properties and you know

1002
00:43:37,190 --> 00:43:35,920
you write item number one to item number

1003
00:43:44,550 --> 00:43:37,200
15

1004
00:43:47,510 --> 00:43:44,560
like alpha times beta times a vector

1005
00:43:49,589 --> 00:43:47,520
you know whatever so one of the axioms

1006
00:43:53,990 --> 00:43:49,599
of a vector field

1007
00:43:55,349 --> 00:43:54,000
okay of a vector sorry a vector space

1008
00:43:58,390 --> 00:43:55,359
uh

1009
00:44:00,390 --> 00:43:58,400
and then the question arises why

1010
00:44:03,910 --> 00:44:00,400
and who cares

1011
00:44:05,829 --> 00:44:03,920
right right okay so if you start your

1012
00:44:08,710 --> 00:44:05,839
class this way

1013
00:44:09,829 --> 00:44:08,720
people aren't going to like it so before

1014
00:44:13,910 --> 00:44:09,839
this

1015
00:44:16,230 --> 00:44:13,920
there has to be a a little section

1016
00:44:18,069 --> 00:44:16,240
i don't know here

1017
00:44:21,190 --> 00:44:18,079
where you explain

1018
00:44:27,349 --> 00:44:24,630
well for such and such reasons we care

1019
00:44:31,270 --> 00:44:27,359
about vector spaces so there has to be

1020
00:44:34,470 --> 00:44:32,230
okay

1021
00:44:37,430 --> 00:44:34,480
and uh

1022
00:44:40,550 --> 00:44:37,440
and that's true

1023
00:44:42,230 --> 00:44:40,560
not only in the first class of the first

1024
00:44:43,910 --> 00:44:42,240
um

1025
00:44:47,270 --> 00:44:43,920
uh

1026
00:44:49,430 --> 00:44:47,280
of a linear algebra of course it's true

1027
00:44:51,990 --> 00:44:49,440
in every class whenever you say

1028
00:44:53,670 --> 00:44:52,000
something there has to be a reason

1029
00:44:55,990 --> 00:44:53,680
and the people who

1030
00:44:59,109 --> 00:44:56,000
um

1031
00:45:00,950 --> 00:44:59,119
who are listening to you uh

1032
00:45:04,309 --> 00:45:00,960
should know that you've thought about it

1033
00:45:06,150 --> 00:45:04,319
should know that you

1034
00:45:07,670 --> 00:45:06,160
that you're telling them these things

1035
00:45:08,870 --> 00:45:07,680
for a reason

1036
00:45:09,750 --> 00:45:08,880
okay

1037
00:45:12,710 --> 00:45:09,760
and

1038
00:45:13,910 --> 00:45:12,720
uh that's often omitted

1039
00:45:16,790 --> 00:45:13,920
it's often

1040
00:45:19,109 --> 00:45:16,800
too easy to just follow the definitions

1041
00:45:21,270 --> 00:45:19,119
in the theorems and never say what

1042
00:45:23,190 --> 00:45:21,280
they're good for

1043
00:45:25,030 --> 00:45:23,200
and um

1044
00:45:29,030 --> 00:45:25,040
and not only you should say these things

1045
00:45:29,040 --> 00:45:34,230
likewise when you write a proof uh

1046
00:45:38,950 --> 00:45:37,589
it's often easy to

1047
00:45:41,589 --> 00:45:38,960
well to

1048
00:45:43,030 --> 00:45:41,599
to so i mean often there is a picture

1049
00:45:47,589 --> 00:45:43,040
behind that proof

1050
00:45:49,750 --> 00:45:47,599
the proof is telling some story and you

1051
00:45:52,550 --> 00:45:49,760
and you want the picture of that story

1052
00:45:55,349 --> 00:45:52,560
in the minds of the students

1053
00:45:57,270 --> 00:45:55,359
but but but but it's often too easy to

1054
00:45:59,670 --> 00:45:57,280
reduce it to a

1055
00:46:02,470 --> 00:45:59,680
list of formulas

1056
00:46:03,990 --> 00:46:02,480
or a list of statements so a higher

1057
00:46:06,230 --> 00:46:04,000
level thing is to make sure that

1058
00:46:07,990 --> 00:46:06,240
everything is motivated

1059
00:46:10,710 --> 00:46:08,000
what else what's another higher level

1060
00:46:12,950 --> 00:46:10,720
aspect of teaching

1061
00:46:15,349 --> 00:46:12,960
that you find is a common mistake among

1062
00:46:18,150 --> 00:46:15,359
the teachers that you see

1063
00:46:23,190 --> 00:46:20,950
i think maybe this is the biggest

1064
00:46:25,510 --> 00:46:23,200
not showing the motivation clearly

1065
00:46:28,470 --> 00:46:25,520
enough

1066
00:46:30,790 --> 00:46:28,480
and by the way

1067
00:46:33,750 --> 00:46:30,800
uh

1068
00:46:37,349 --> 00:46:33,760
that's part of the reason why research

1069
00:46:39,109 --> 00:46:37,359
is a necessary part of teaching

1070
00:46:41,670 --> 00:46:39,119
because

1071
00:46:47,670 --> 00:46:45,430
you have to know the motivation

1072
00:46:51,270 --> 00:46:47,680
you know you can say

1073
00:46:53,670 --> 00:46:51,280
vector spaces are a great thing

1074
00:46:57,109 --> 00:46:53,680
unless you've actually worked with them

1075
00:46:59,589 --> 00:46:57,119
unless you've actually seen them used

1076
00:47:02,870 --> 00:46:59,599
so maybe vector spaces are good and are

1077
00:47:04,069 --> 00:47:02,880
easy enough so that you can um

1078
00:47:05,910 --> 00:47:04,079
uh

1079
00:47:07,990 --> 00:47:05,920
um

1080
00:47:10,069 --> 00:47:08,000
you know by third year you understand

1081
00:47:12,790 --> 00:47:10,079
why you why you learned about them in

1082
00:47:17,589 --> 00:47:15,190
but if you want to be able to say

1083
00:47:19,670 --> 00:47:17,599
something intelligent about homology you

1084
00:47:22,829 --> 00:47:19,680
have to have used it

1085
00:47:25,510 --> 00:47:22,839
the only way to use it is in research

1086
00:47:27,030 --> 00:47:25,520
so uh

1087
00:47:29,030 --> 00:47:27,040
uh

1088
00:47:33,670 --> 00:47:29,040
so that's what i meant by you have to be

1089
00:47:35,190 --> 00:47:33,680
in shape being in shape also means

1090
00:47:38,950 --> 00:47:35,200
remember what

1091
00:47:41,109 --> 00:47:38,960
what can be done with these things

1092
00:47:42,390 --> 00:47:41,119
do you find that you're more creative as

1093
00:47:44,790 --> 00:47:42,400
you get older

1094
00:47:50,790 --> 00:47:44,800
or that your creativity peaked at a

1095
00:47:55,190 --> 00:47:52,950
i you

1096
00:47:57,190 --> 00:47:55,200
you know i i wish i could answer the

1097
00:47:59,430 --> 00:47:57,200
truth is that

1098
00:48:04,069 --> 00:47:59,440
i don't really remember

1099
00:48:09,270 --> 00:48:06,790
it's very hard to remember myself at any

1100
00:48:11,270 --> 00:48:09,280
other age

1101
00:48:13,349 --> 00:48:11,280
so i mean certainly

1102
00:48:15,910 --> 00:48:13,359
um

1103
00:48:18,470 --> 00:48:15,920
i have matured

1104
00:48:21,829 --> 00:48:18,480
so the little i can remember from 20 or

1105
00:48:22,630 --> 00:48:21,839
30 years ago um

1106
00:48:30,309 --> 00:48:22,640
is

1107
00:48:38,069 --> 00:48:34,069
i'm more systematic perhaps

1108
00:48:45,109 --> 00:48:41,030
am i smarter am i more creative am i

1109
00:48:46,150 --> 00:48:45,119
stupider am i less creative i'm not sure

1110
00:48:47,750 --> 00:48:46,160
what do you mean when you say you're

1111
00:48:48,950 --> 00:48:47,760
more systematic now can you give an

1112
00:48:52,549 --> 00:48:48,960
example of how you would look at a

1113
00:49:01,190 --> 00:48:52,559
certain problem now or solve it versus

1114
00:49:06,230 --> 00:49:03,750
and also a sub question do you see being

1115
00:49:08,309 --> 00:49:06,240
systematic as a good thing or do you see

1116
00:49:10,790 --> 00:49:08,319
there being innovation in being

1117
00:49:12,309 --> 00:49:10,800
disorganized or creativity embedded

1118
00:49:16,790 --> 00:49:12,319
there

1119
00:49:25,349 --> 00:49:16,800
no systematic is generally better

1120
00:49:31,030 --> 00:49:26,549
much

1121
00:49:32,790 --> 00:49:31,040
more into the low hanging fruits

1122
00:49:36,790 --> 00:49:32,800
so

1123
00:49:39,910 --> 00:49:38,150
but

1124
00:49:45,510 --> 00:49:39,920
[Music]

1125
00:49:45,520 --> 00:49:50,470
i'd uh

1126
00:49:54,470 --> 00:49:52,950
like wait for opportunities and and then

1127
00:49:56,829 --> 00:49:54,480
use them

1128
00:50:02,470 --> 00:49:59,109
uh and

1129
00:50:07,270 --> 00:50:05,190
now it's much more i have a long-term

1130
00:50:08,150 --> 00:50:07,280
goal

1131
00:50:12,950 --> 00:50:08,160
uh

1132
00:50:16,470 --> 00:50:12,960
a theory of something

1133
00:50:18,870 --> 00:50:16,480
you know your your your uh

1134
00:50:21,750 --> 00:50:18,880
podcast is a theory of everything right

1135
00:50:24,390 --> 00:50:21,760
i just want a theory of something

1136
00:50:27,430 --> 00:50:24,400
so i want a theory of something because

1137
00:50:29,349 --> 00:50:27,440
i i feel for various reasons that it

1138
00:50:30,549 --> 00:50:29,359
ought to be there

1139
00:50:31,080 --> 00:50:30,559
and then i

1140
00:50:32,230 --> 00:50:31,090
um

1141
00:50:34,549 --> 00:50:32,240
[Music]

1142
00:50:35,589 --> 00:50:34,559
worked very hard

1143
00:50:38,069 --> 00:50:35,599
on

1144
00:50:40,950 --> 00:50:38,079
well very hard to my standards i already

1145
00:50:43,910 --> 00:50:40,960
admitted being a bomb so um

1146
00:50:44,870 --> 00:50:43,920
you know i i worked at least for a long

1147
00:50:49,030 --> 00:50:44,880
time

1148
00:50:52,150 --> 00:50:49,040
uh trying to find that theory

1149
00:50:54,630 --> 00:50:52,160
you know even assist even even at a very

1150
00:50:55,430 --> 00:50:54,640
at a much lower level

1151
00:50:56,309 --> 00:50:55,440
uh

1152
00:51:00,470 --> 00:50:56,319
so

1153
00:51:03,910 --> 00:51:01,349
uh

1154
00:51:05,750 --> 00:51:03,920
you know so you know math theorems and

1155
00:51:09,270 --> 00:51:05,760
proofs were

1156
00:51:11,349 --> 00:51:09,280
pressed into my brain was essentially an

1157
00:51:13,829 --> 00:51:11,359
external process right so i went to

1158
00:51:15,910 --> 00:51:13,839
classes and people pushed theorems into

1159
00:51:17,030 --> 00:51:15,920
my brain

1160
00:51:19,670 --> 00:51:17,040
and

1161
00:51:25,990 --> 00:51:20,829
some of

1162
00:51:28,790 --> 00:51:26,000
them seemed like complete formalities

1163
00:51:34,309 --> 00:51:31,990
a sequence of deductions

1164
00:51:36,870 --> 00:51:34,319
uh that i could have that i could

1165
00:51:39,430 --> 00:51:36,880
memorize and i could

1166
00:51:43,670 --> 00:51:39,440
verify

1167
00:51:46,790 --> 00:51:43,680
but were essentially created by aliens

1168
00:51:47,990 --> 00:51:46,800
you know i i had no idea how they came

1169
00:51:51,109 --> 00:51:48,000
to be

1170
00:51:52,230 --> 00:51:51,119
right in some theorems

1171
00:51:53,670 --> 00:51:52,240
uh

1172
00:51:54,790 --> 00:51:53,680
immediately

1173
00:51:57,270 --> 00:51:54,800
uh

1174
00:51:59,190 --> 00:51:57,280
became a picture i immediately

1175
00:52:01,030 --> 00:51:59,200
understood

1176
00:52:03,030 --> 00:52:01,040
uh

1177
00:52:08,230 --> 00:52:03,040
that

1178
00:52:11,109 --> 00:52:08,240
geometric reality

1179
00:52:13,349 --> 00:52:11,119
okay describe

1180
00:52:14,790 --> 00:52:13,359
i i i i could see the intuition behind

1181
00:52:16,390 --> 00:52:14,800
the proof

1182
00:52:17,990 --> 00:52:16,400
it's not always geometric though it's

1183
00:52:19,990 --> 00:52:18,000
just you see the internet necessarily

1184
00:52:22,470 --> 00:52:20,000
geometric i mean but i could see somehow

1185
00:52:24,870 --> 00:52:22,480
the motivation the the the i i could

1186
00:52:27,270 --> 00:52:24,880
imagine how the proof was discovered

1187
00:52:29,910 --> 00:52:27,280
i think i i i would get the feeling that

1188
00:52:31,910 --> 00:52:29,920
i understood the proof and there and and

1189
00:52:34,069 --> 00:52:31,920
that was essentially a dichotomy some

1190
00:52:37,270 --> 00:52:34,079
pictures some proofs

1191
00:52:39,190 --> 00:52:37,280
or some concept were of that type

1192
00:52:42,710 --> 00:52:39,200
made by aliens

1193
00:52:44,829 --> 00:52:42,720
and pushed into my brain by professors

1194
00:52:50,230 --> 00:52:44,839
and other

1195
00:52:53,349 --> 00:52:50,240
um uh concepts theorems proofs whatever

1196
00:52:56,390 --> 00:52:53,359
were clearly intuitive and made sense

1197
00:52:58,950 --> 00:52:56,400
and and i understood them

1198
00:53:01,270 --> 00:52:58,960
uh and that was it that was the world

1199
00:53:04,870 --> 00:53:01,280
there was this and there were those

1200
00:53:07,109 --> 00:53:04,880
and then sometime later in second year i

1201
00:53:09,750 --> 00:53:07,119
actually did my ba very very very

1202
00:53:12,069 --> 00:53:09,760
quickly so uh basically

1203
00:53:13,910 --> 00:53:12,079
i did it in essentially two years

1204
00:53:15,750 --> 00:53:13,920
so when i say second year you should

1205
00:53:18,470 --> 00:53:15,760
compare it maybe with year three and

1206
00:53:22,309 --> 00:53:18,480
four of um most students

1207
00:53:23,990 --> 00:53:22,319
so somewhere later in late in my studies

1208
00:53:27,589 --> 00:53:24,000
i realized

1209
00:53:30,630 --> 00:53:27,599
that if i think harder

1210
00:53:34,069 --> 00:53:30,640
about the theorems that

1211
00:53:35,349 --> 00:53:34,079
uh or the concepts that appear to be

1212
00:53:37,829 --> 00:53:35,359
alien

1213
00:53:40,870 --> 00:53:37,839
then sooner or later

1214
00:53:43,109 --> 00:53:40,880
i see the picture behind them sooner or

1215
00:53:43,910 --> 00:53:43,119
later i realize

1216
00:53:44,950 --> 00:53:43,920
uh

1217
00:53:46,790 --> 00:53:44,960
that

1218
00:53:47,750 --> 00:53:46,800
i i'm able to move them to the other

1219
00:53:53,109 --> 00:53:47,760
class

1220
00:53:56,950 --> 00:53:53,119
and and and um

1221
00:53:58,069 --> 00:53:56,960
and understand it and understood

1222
00:54:01,349 --> 00:53:58,079
and

1223
00:54:02,549 --> 00:54:01,359
it

1224
00:54:09,829 --> 00:54:02,559
so

1225
00:54:12,549 --> 00:54:09,839
i may learn it from a book that

1226
00:54:15,030 --> 00:54:12,559
describes it as a formula

1227
00:54:18,150 --> 00:54:15,040
okay and then i'll struggle to see the

1228
00:54:20,470 --> 00:54:18,160
intuition behind the formula

1229
00:54:23,510 --> 00:54:20,480
and so even at that level it's it's

1230
00:54:27,990 --> 00:54:23,520
something that took learning

1231
00:54:33,670 --> 00:54:31,109
again when i got to the university

1232
00:54:36,069 --> 00:54:33,680
you know when i when i was in first year

1233
00:54:38,950 --> 00:54:36,079
i took classes and i got good gr good

1234
00:54:42,150 --> 00:54:38,960
grades in in in all of them

1235
00:54:46,230 --> 00:54:43,670
and nevertheless

1236
00:54:51,190 --> 00:54:48,470
there was a point where

1237
00:54:53,270 --> 00:54:51,200
where things became better where where i

1238
00:54:55,990 --> 00:54:53,280
realize i can actually

1239
00:54:58,549 --> 00:54:56,000
understand everything

1240
00:55:00,069 --> 00:54:58,559
and not just repeat everything

1241
00:55:01,750 --> 00:55:00,079
and that came later

1242
00:55:03,829 --> 00:55:01,760
what does that process of finding the

1243
00:55:05,430 --> 00:55:03,839
intuition behind let's say a formula

1244
00:55:07,349 --> 00:55:05,440
that before you

1245
00:55:10,069 --> 00:55:07,359
previously simply had to memorize as

1246
00:55:12,150 --> 00:55:10,079
handed down from the gods or the aliens

1247
00:55:14,470 --> 00:55:12,160
what does that process look like the

1248
00:55:16,069 --> 00:55:14,480
process of finding the intuition does it

1249
00:55:17,750 --> 00:55:16,079
look like

1250
00:55:20,870 --> 00:55:17,760
i'm sure it's a variety of these but

1251
00:55:23,190 --> 00:55:20,880
does it majorly look like you copy it

1252
00:55:24,549 --> 00:55:23,200
down with the pen and paper precisely

1253
00:55:26,549 --> 00:55:24,559
and then you draw arrows and you say

1254
00:55:28,870 --> 00:55:26,559
okay so what's an example of this what's

1255
00:55:30,549 --> 00:55:28,880
a counter example of this or is it you

1256
00:55:32,710 --> 00:55:30,559
go on a bike ride and you keep thinking

1257
00:55:34,630 --> 00:55:32,720
about it what does that process look

1258
00:55:37,109 --> 00:55:34,640
like perhaps it would be edifying if you

1259
00:55:39,589 --> 00:55:37,119
took a specific example but if you can't

1260
00:55:42,309 --> 00:55:39,599
then just give the broad strokes

1261
00:55:45,910 --> 00:55:44,069
you know what it what does it look like

1262
00:55:48,390 --> 00:55:45,920
from the outside from the outside it

1263
00:55:51,270 --> 00:55:48,400
looks like i'm sitting on my chair and

1264
00:55:52,710 --> 00:55:51,280
staring into the into infinity

1265
00:55:54,710 --> 00:55:52,720
right or

1266
00:55:57,750 --> 00:55:54,720
sitting on my balcony and looking at the

1267
00:55:57,760 --> 00:56:16,230
what does it look like inside

1268
00:56:16,240 --> 00:56:32,549
it's very hard to answer without

1269
00:56:38,470 --> 00:56:35,109
without going through specific examples

1270
00:56:40,870 --> 00:56:38,480
and the specific examples are

1271
00:56:43,030 --> 00:56:40,880
far too complex or i i don't know if

1272
00:56:45,270 --> 00:56:43,040
they are far too complex but they fit in

1273
00:56:48,470 --> 00:56:45,280
a math class

1274
00:56:50,630 --> 00:56:48,480
and the other thing is um

1275
00:56:52,630 --> 00:56:50,640
you will never see these examples in my

1276
00:56:55,190 --> 00:56:52,640
classes because when i teach something i

1277
00:56:56,470 --> 00:56:55,200
try to motivate it

1278
00:56:59,349 --> 00:56:56,480
okay

1279
00:57:01,510 --> 00:56:59,359
so you will not see the alternative

1280
00:57:04,630 --> 00:57:01,520
okay you will see the motivated way of

1281
00:57:08,150 --> 00:57:04,640
explaining uh uh the

1282
00:57:12,789 --> 00:57:08,160
implicit function theorem or the uh

1283
00:57:15,589 --> 00:57:12,799
change of variables formula for multi

1284
00:57:21,270 --> 00:57:15,599
integrals right you'll see the motivated

1285
00:57:24,829 --> 00:57:23,030
i will not be showing you the

1286
00:57:27,430 --> 00:57:24,839
unmotivated

1287
00:57:29,349 --> 00:57:27,440
formulas for you much of the time when

1288
00:57:32,789 --> 00:57:29,359
it's difficult for you to understand a

1289
00:57:34,150 --> 00:57:32,799
proof or a theorem or concept is it

1290
00:57:42,710 --> 00:57:34,160
most of the time because it was

1291
00:57:47,030 --> 00:57:45,109
well the intuition is not explained

1292
00:57:50,390 --> 00:57:47,040
often

1293
00:57:54,549 --> 00:57:50,400
so in textbooks

1294
00:57:54,559 --> 00:58:06,829
often the intuition is not explained

1295
00:58:10,549 --> 00:58:08,549
now

1296
00:58:12,309 --> 00:58:10,559
some intuition is just getting used to

1297
00:58:15,270 --> 00:58:12,319
the concepts

1298
00:58:18,630 --> 00:58:15,280
so sometimes intuition is not is not

1299
00:58:22,390 --> 00:58:20,470
it's just playing around until you're

1300
00:58:23,829 --> 00:58:22,400
used to it

1301
00:58:24,870 --> 00:58:23,839
you know

1302
00:58:27,190 --> 00:58:24,880
uh

1303
00:58:30,470 --> 00:58:27,200
you've just landed in a foreign city

1304
00:58:31,589 --> 00:58:30,480
you've just landed in athens

1305
00:58:33,430 --> 00:58:31,599
uh

1306
00:58:37,109 --> 00:58:33,440
your hotel

1307
00:58:39,670 --> 00:58:37,119
is two kilometers from the acropolis

1308
00:58:40,950 --> 00:58:39,680
uh you got there at night you wake up in

1309
00:58:42,630 --> 00:58:40,960
the morning you want to go to the

1310
00:58:43,990 --> 00:58:42,640
acropolis

1311
00:58:47,030 --> 00:58:44,000
you

1312
00:58:49,990 --> 00:58:47,040
punch acropolis into google maps

1313
00:58:52,230 --> 00:58:50,000
and google maps tells you

1314
00:58:54,069 --> 00:58:52,240
you know go left go right go straight go

1315
00:58:56,390 --> 00:58:54,079
left go right and here's the cro

1316
00:58:58,950 --> 00:58:56,400
acropolis okay you follow the

1317
00:59:02,069 --> 00:58:58,960
instructions

1318
00:59:05,510 --> 00:59:02,079
you didn't learn atoms

1319
00:59:07,990 --> 00:59:05,520
you've learned the way to the acropolis

1320
00:59:10,230 --> 00:59:08,000
uh to learn athens

1321
00:59:12,870 --> 00:59:10,240
uh

1322
00:59:15,990 --> 00:59:12,880
in the afternoon after the acropolis you

1323
00:59:17,910 --> 00:59:16,000
have to wander around

1324
00:59:20,870 --> 00:59:17,920
uh and then you have to continue

1325
00:59:23,270 --> 00:59:20,880
wandering around for the next two weeks

1326
00:59:26,950 --> 00:59:23,280
and then maybe you're starting to have a

1327
00:59:29,670 --> 00:59:26,960
grasp of what athens is

1328
00:59:31,589 --> 00:59:29,680
so there is similar

1329
00:59:33,589 --> 00:59:31,599
there is something similar in in

1330
00:59:36,789 --> 00:59:33,599
mathematics

1331
00:59:38,950 --> 00:59:36,799
okay or in science or in fact in every

1332
00:59:42,470 --> 00:59:38,960
field of learning okay i mean but in

1333
00:59:44,870 --> 00:59:42,480
mathematics you know um

1334
00:59:46,630 --> 00:59:44,880
uh you don't

1335
00:59:48,309 --> 00:59:46,640
uh

1336
00:59:56,789 --> 00:59:48,319
learn

1337
00:59:58,390 --> 00:59:56,799
most interesting result result in a

1338
01:00:01,589 --> 00:59:58,400
certain field

1339
01:00:04,309 --> 01:00:01,599
you haven't learned the field

1340
01:00:07,109 --> 01:00:04,319
okay you've just learned and especially

1341
01:00:09,109 --> 01:00:07,119
if you if you follow the directions by

1342
01:00:10,870 --> 01:00:09,119
somebody else

1343
01:00:12,870 --> 01:00:10,880
okay

1344
01:00:14,390 --> 01:00:12,880
the learning happens if you wander

1345
01:00:16,230 --> 01:00:14,400
around later

1346
01:00:18,230 --> 01:00:16,240
and in a way you have to do it on your

1347
01:00:20,710 --> 01:00:18,240
own

1348
01:00:22,470 --> 01:00:20,720
right this this wandering around so

1349
01:00:25,430 --> 01:00:22,480
wandering around in mathematics means

1350
01:00:26,150 --> 01:00:25,440
you experiment you change the conditions

1351
01:00:34,069 --> 01:00:26,160
you

1352
01:00:40,950 --> 01:00:34,079
situations

1353
01:00:45,190 --> 01:00:43,030
well so i mean

1354
01:00:47,750 --> 01:00:45,200
like part of tourism you do with a tour

1355
01:00:49,990 --> 01:00:47,760
guide and part of an and a part you have

1356
01:00:56,470 --> 01:00:50,000
to do on your own on your own

1357
01:00:56,480 --> 01:01:02,069
uh so so so so some part of uh

1358
01:01:09,109 --> 01:01:04,549
being systematic if you wish is doing

1359
01:01:12,630 --> 01:01:09,119
this on my own thing in a systematic way

1360
01:01:15,190 --> 01:01:12,640
okay this realization that i can just

1361
01:01:18,309 --> 01:01:15,200
jump into a topic by

1362
01:01:19,589 --> 01:01:18,319
following somebody's guidance

1363
01:01:22,789 --> 01:01:19,599
i i

1364
01:01:26,630 --> 01:01:22,799
i must sit down and think and ask myself

1365
01:01:30,309 --> 01:01:26,640
many many many many more questions and

1366
01:01:34,230 --> 01:01:30,319
go on side tracks and until until it's

1367
01:01:38,470 --> 01:01:36,470
now in this example

1368
01:01:40,950 --> 01:01:38,480
let me let me see if i'm understanding

1369
01:01:42,390 --> 01:01:40,960
it correctly let's say athens athens the

1370
01:01:44,390 --> 01:01:42,400
city and then you have the acropolis

1371
01:01:45,589 --> 01:01:44,400
which is a landmark so that's almost

1372
01:01:47,430 --> 01:01:45,599
like a landmark theorem and then the

1373
01:01:48,549 --> 01:01:47,440
directions are the proof and the steps

1374
01:01:49,829 --> 01:01:48,559
to get there

1375
01:01:51,349 --> 01:01:49,839
would you say and you're saying the

1376
01:01:52,789 --> 01:01:51,359
learning comes from the wandering would

1377
01:01:55,510 --> 01:01:52,799
you say that when you first land in

1378
01:01:57,109 --> 01:01:55,520
athens you should wander or should you

1379
01:01:58,470 --> 01:01:57,119
learn the major landmarks and the

1380
01:02:00,549 --> 01:01:58,480
directions to get there perhaps

1381
01:02:02,230 --> 01:02:00,559
forgetting the directions you just get

1382
01:02:04,870 --> 01:02:02,240
yourself there so that you see what the

1383
01:02:06,630 --> 01:02:04,880
landmarks are like later you wonder the

1384
01:02:08,309 --> 01:02:06,640
analogy would be you learn the major

1385
01:02:09,670 --> 01:02:08,319
theorems and then later you try and get

1386
01:02:11,589 --> 01:02:09,680
the intuition by playing around with

1387
01:02:15,190 --> 01:02:11,599
them or do you play from the get-go i

1388
01:02:17,430 --> 01:02:15,200
mean there has to be a bit of both

1389
01:02:20,069 --> 01:02:17,440
uh basically you know if you land in

1390
01:02:23,270 --> 01:02:20,079
athens and start wondering randomly you

1391
01:02:26,470 --> 01:02:23,280
end up you may end up wandering randomly

1392
01:02:29,029 --> 01:02:26,480
in a completely uninteresting direction

1393
01:02:31,270 --> 01:02:29,039
plus there is a fear factor

1394
01:02:32,870 --> 01:02:31,280
and you know you may feared about

1395
01:02:35,270 --> 01:02:32,880
neighborhoods

1396
01:02:37,829 --> 01:02:35,280
interesting but but but but there

1397
01:02:39,670 --> 01:02:37,839
actually is an analog an analogy in

1398
01:02:40,950 --> 01:02:39,680
mathematics or

1399
01:02:45,910 --> 01:02:40,960
it

1400
01:02:48,870 --> 01:02:45,920
things and the guidance

1401
01:02:50,950 --> 01:02:48,880
can help you overcome the fear but maybe

1402
01:02:53,430 --> 01:02:50,960
fear is not the right way i mean think

1403
01:02:55,270 --> 01:02:53,440
that you have to explore atoms when when

1404
01:02:57,190 --> 01:02:55,280
it's dark

1405
01:02:59,589 --> 01:02:57,200
okay so you simply don't know which way

1406
01:03:01,589 --> 01:02:59,599
to go you just land

1407
01:03:03,750 --> 01:03:01,599
you know i tell you think about vector

1408
01:03:05,589 --> 01:03:03,760
spaces you have no idea what good

1409
01:03:08,789 --> 01:03:05,599
questions to ask are what are the good

1410
01:03:12,630 --> 01:03:09,750
and

1411
01:03:17,670 --> 01:03:14,150
[Music]

1412
01:03:19,670 --> 01:03:17,680
so you need guidance

1413
01:03:21,349 --> 01:03:19,680
or else you will be stuck in one

1414
01:03:23,430 --> 01:03:21,359
neighborhood and never realize that

1415
01:03:25,990 --> 01:03:23,440
there is more than that

1416
01:03:27,829 --> 01:03:26,000
but you know after the guidance took you

1417
01:03:31,829 --> 01:03:27,839
from here to there

1418
01:03:37,510 --> 01:03:34,870
go back and explore and explore more and

1419
01:03:40,630 --> 01:03:37,520
explore more and until you until it's a

1420
01:03:42,549 --> 01:03:40,640
solid and not just a single path

1421
01:03:44,950 --> 01:03:42,559
so you have to do your own finding path

1422
01:03:48,710 --> 01:03:44,960
integral over the space of mathematical

1423
01:03:50,069 --> 01:03:48,720
ideas there is a bit of that yes

1424
01:03:53,430 --> 01:03:50,079
what's your greatest strength as a

1425
01:03:56,549 --> 01:03:53,440
mathematician or some of your strengths

1426
01:04:00,069 --> 01:03:56,559
who says i have strengthens

1427
01:04:04,309 --> 01:04:02,390
i'm a lazy bum

1428
01:04:06,069 --> 01:04:04,319
are you being modest when you say that

1429
01:04:07,829 --> 01:04:06,079
because i imagine someone who has an

1430
01:04:09,750 --> 01:04:07,839
accelerated degree two-year degree that

1431
01:04:11,510 --> 01:04:09,760
should ordinarily take four years it's

1432
01:04:14,069 --> 01:04:11,520
not as if you spend the majority of your

1433
01:04:16,710 --> 01:04:14,079
time playing video games and

1434
01:04:20,069 --> 01:04:16,720
and being on industrious oh you'll be

1435
01:04:23,430 --> 01:04:21,589
uh

1436
01:04:29,349 --> 01:04:23,440
i mean of course i didn't play video

1437
01:04:35,349 --> 01:04:33,109
you know video video games came later

1438
01:04:36,470 --> 01:04:35,359
uh

1439
01:04:39,349 --> 01:04:36,480
but

1440
01:04:40,950 --> 01:04:39,359
i definitely killed a lot of time

1441
01:04:43,430 --> 01:04:40,960
so who are you comparing yourself to

1442
01:04:45,910 --> 01:04:43,440
when you say that you're slothful

1443
01:04:51,829 --> 01:04:45,920
gee i compare i compare myself to who i

1444
01:05:04,069 --> 01:04:53,109
anyway

1445
01:05:10,630 --> 01:05:07,109
i think i'm decently good at explaining

1446
01:05:10,640 --> 01:05:13,670
um

1447
01:05:18,069 --> 01:05:17,029
often that involves thinking about them

1448
01:05:20,630 --> 01:05:18,079
i mean

1449
01:05:24,710 --> 01:05:20,640
explaining is not just

1450
01:05:30,309 --> 01:05:26,789
reproducing what you've heard somewhere

1451
01:05:33,910 --> 01:05:30,319
else i mean it's it's first of all

1452
01:05:35,430 --> 01:05:33,920
being creative about these things

1453
01:05:37,029 --> 01:05:35,440
um

1454
01:05:41,190 --> 01:05:37,039
but you know

1455
01:05:44,789 --> 01:05:42,870
ask the students

1456
01:05:46,549 --> 01:05:44,799
ask the people who listen to me in

1457
01:05:48,829 --> 01:05:46,559
lectures

1458
01:05:53,589 --> 01:05:48,839
when i give research

1459
01:05:58,789 --> 01:05:55,430
it's very hard to

1460
01:06:03,430 --> 01:06:00,630
you know

1461
01:06:05,589 --> 01:06:03,440
there's a famous uh story about einstein

1462
01:06:08,390 --> 01:06:05,599
that

1463
01:06:10,789 --> 01:06:08,400
somebody complained to einstein about

1464
01:06:12,950 --> 01:06:10,799
his problems with math

1465
01:06:15,349 --> 01:06:12,960
and their reference was to high school

1466
01:06:16,630 --> 01:06:15,359
math like i never got high school math

1467
01:06:19,349 --> 01:06:16,640
and

1468
01:06:23,109 --> 01:06:19,359
einstein said let me assure you that my

1469
01:06:24,789 --> 01:06:23,990
uh

1470
01:06:25,990 --> 01:06:24,799
so

1471
01:06:28,309 --> 01:06:26,000
uh

1472
01:06:29,589 --> 01:06:28,319
sort of meaning what what did he mean by

1473
01:06:31,589 --> 01:06:29,599
that

1474
01:06:36,390 --> 01:06:31,599
you know i

1475
01:06:42,789 --> 01:06:39,589
all his life struggling with mathematics

1476
01:06:47,349 --> 01:06:42,799
not just high school time

1477
01:06:49,190 --> 01:06:47,359
okay so in a similar way uh gee i'm

1478
01:06:51,430 --> 01:06:49,200
sorry i mean now it might sound like i

1479
01:06:52,470 --> 01:06:51,440
need some analogy which i do i'm not

1480
01:06:55,589 --> 01:06:52,480
making

1481
01:06:57,029 --> 01:06:55,599
i understand trust me uh but but still

1482
01:07:01,109 --> 01:06:57,039
um

1483
01:07:03,510 --> 01:07:01,119
you know i like to implement

1484
01:07:06,069 --> 01:07:03,520
i like to compute things

1485
01:07:08,470 --> 01:07:06,079
implement them on the computer

1486
01:07:12,230 --> 01:07:08,480
which means that i spend a lot of time

1487
01:07:15,109 --> 01:07:12,240
programming the concepts i work on

1488
01:07:18,309 --> 01:07:15,119
turning them into running programs

1489
01:07:20,069 --> 01:07:18,319
you could say it's my strength but when

1490
01:07:22,230 --> 01:07:20,079
i look at it

1491
01:07:24,470 --> 01:07:22,240
all i see is that i'm struggling and

1492
01:07:26,710 --> 01:07:24,480
struggling and struggling and failing

1493
01:07:28,470 --> 01:07:26,720
and here and then here and there there

1494
01:07:30,549 --> 01:07:28,480
is a minor success

1495
01:07:32,549 --> 01:07:30,559
which gets superseded a little bit later

1496
01:07:33,349 --> 01:07:32,559
by somebody else

1497
01:07:34,710 --> 01:07:33,359
so

1498
01:07:37,349 --> 01:07:34,720
um

1499
01:07:40,069 --> 01:07:37,359
yeah maybe one of my strengths is the

1500
01:07:44,789 --> 01:07:40,079
ability to implement things

1501
01:07:49,510 --> 01:07:47,109
you know turn mathematical concepts into

1502
01:07:50,630 --> 01:07:49,520
running programs

1503
01:07:52,789 --> 01:07:50,640
uh

1504
01:07:56,309 --> 01:07:52,799
but it's also one of the things that

1505
01:07:58,630 --> 01:07:56,319
that keeps me depressed uh was so much

1506
01:08:00,309 --> 01:07:58,640
of my time

1507
01:08:02,950 --> 01:08:00,319
some people who are watching this they

1508
01:08:04,630 --> 01:08:02,960
may be discouraged because they were

1509
01:08:07,670 --> 01:08:04,640
they weren't particularly great at high

1510
01:08:09,270 --> 01:08:07,680
school mathematics or some people may

1511
01:08:11,510 --> 01:08:09,280
have struggled during their undergrad

1512
01:08:12,789 --> 01:08:11,520
what advice do you have for those people

1513
01:08:15,589 --> 01:08:12,799
if they want to continue to learn

1514
01:08:17,110 --> 01:08:15,599
mathematics or physics at a

1515
01:08:19,430 --> 01:08:17,120
graduate perhaps even larger than

1516
01:08:21,189 --> 01:08:19,440
graduate phd level

1517
01:08:23,430 --> 01:08:21,199
do they just continue

1518
01:08:25,669 --> 01:08:23,440
plugging away and not feel discouraged

1519
01:08:28,709 --> 01:08:25,679
because they feel like in imbecile on a

1520
01:08:35,110 --> 01:08:31,829
what advice do you have for them

1521
01:08:37,030 --> 01:08:35,120
there is chug along

1522
01:08:39,269 --> 01:08:37,040
and there is realize when it's not

1523
01:08:41,269 --> 01:08:39,279
working

1524
01:08:43,430 --> 01:08:41,279
and i hate to tell you that i don't know

1525
01:08:45,189 --> 01:08:43,440
i mean i can't give you a

1526
01:08:58,470 --> 01:08:45,199
a

1527
01:09:02,550 --> 01:08:58,480
struggle until

1528
01:09:04,470 --> 01:09:02,560
they succeed sometimes some people don't

1529
01:09:08,630 --> 01:09:04,480
uh or they struggle and struggle and

1530
01:09:08,640 --> 01:09:13,669
you get

1531
01:09:13,679 --> 01:09:18,870
feedback

1532
01:09:22,070 --> 01:09:19,829
i mean

1533
01:09:24,070 --> 01:09:22,080
some people depend on daily feedback

1534
01:09:26,789 --> 01:09:24,080
some people can leave with a feedback

1535
01:09:32,470 --> 01:09:26,799
with a bit of feedback once a year

1536
01:09:32,480 --> 01:09:36,550
a clear answer

1537
01:09:41,030 --> 01:09:38,789
what did you learn from ed whitton with

1538
01:09:42,630 --> 01:09:41,040
respect to mathematical techniques or

1539
01:09:43,749 --> 01:09:42,640
meta mathematical so how you should

1540
01:09:46,630 --> 01:09:43,759
think about

1541
01:09:46,640 --> 01:09:53,749
or physics

1542
01:09:57,030 --> 01:09:56,149
well i learned specific mathematics from

1543
01:09:59,510 --> 01:09:57,040
him

1544
01:10:02,630 --> 01:09:59,520
right so you know i learned like many

1545
01:10:04,630 --> 01:10:02,640
other people i learned this formula

1546
01:10:06,870 --> 01:10:04,640
from him

1547
01:10:09,910 --> 01:10:06,880
right and how to read it and how to use

1548
01:10:11,910 --> 01:10:09,920
use it interpret it work with it right

1549
01:10:15,030 --> 01:10:11,920
do things with it

1550
01:10:16,390 --> 01:10:15,040
but i learned many other specific things

1551
01:10:18,950 --> 01:10:16,400
with him

1552
01:10:26,550 --> 01:10:22,550
um

1553
01:10:31,110 --> 01:10:26,560
mean like

1554
01:10:36,390 --> 01:10:32,470
researcher

1555
01:10:39,590 --> 01:10:36,400
but he's also a great expositor

1556
01:10:39,600 --> 01:10:45,030
when you come to his lectures

1557
01:10:47,830 --> 01:10:46,870
he is

1558
01:10:50,229 --> 01:10:47,840
uh

1559
01:10:52,709 --> 01:10:50,239
able to make

1560
01:10:54,870 --> 01:10:52,719
even very complicated things appear

1561
01:10:56,550 --> 01:10:54,880
simple

1562
01:10:59,110 --> 01:10:56,560
uh

1563
01:11:01,990 --> 01:10:59,120
the problem is that often you will not

1564
01:11:05,350 --> 01:11:02,000
see that because he's turning the hyper

1565
01:11:08,310 --> 01:11:05,360
complicated into merely complicated

1566
01:11:10,390 --> 01:11:08,320
uh so so so so so you don't

1567
01:11:14,550 --> 01:11:10,400
automatically realize

1568
01:11:18,790 --> 01:11:14,560
uh what a great uh exposition

1569
01:11:23,270 --> 01:11:21,189
and i i

1570
01:11:25,590 --> 01:11:23,280
think i learned well i don't know if i

1571
01:11:29,910 --> 01:11:25,600
learned that from him

1572
01:11:32,229 --> 01:11:29,920
but i strive to learn that from him

1573
01:11:34,950 --> 01:11:32,239
um

1574
01:11:37,270 --> 01:11:34,960
and then in other ways i

1575
01:11:39,030 --> 01:11:37,280
there are senses in which i didn't learn

1576
01:11:41,990 --> 01:11:39,040
anything from him

1577
01:11:44,709 --> 01:11:42,000
namely uh he is

1578
01:11:46,870 --> 01:11:44,719
so much more talented

1579
01:11:49,110 --> 01:11:46,880
there's just no way of no other way of

1580
01:11:52,830 --> 01:11:49,120
saying it the guy is smart

1581
01:11:58,550 --> 01:11:52,840
the guy is extremely productive

1582
01:11:59,990 --> 01:11:58,560
uh if you try to imitate his

1583
01:12:01,350 --> 01:12:00,000
brilliance

1584
01:12:03,189 --> 01:12:01,360
you'll fail

1585
01:12:05,910 --> 01:12:03,199
at least i failed

1586
01:12:09,590 --> 01:12:05,920
uh if you try to imitate his

1587
01:12:10,470 --> 01:12:09,600
productivity you'll just be disappointed

1588
01:12:11,990 --> 01:12:10,480
so

1589
01:12:14,790 --> 01:12:12,000
um

1590
01:12:16,310 --> 01:12:14,800
in some ways i haven't learned there are

1591
01:12:19,430 --> 01:12:16,320
certain things i haven't learned from

1592
01:12:21,350 --> 01:12:19,440
him and i just simply couldn't

1593
01:12:23,270 --> 01:12:21,360
do you mind describing your relationship

1594
01:12:25,270 --> 01:12:23,280
with eric weinstein when i was speaking

1595
01:12:28,310 --> 01:12:25,280
to eric he said that you acted as a de

1596
01:12:31,590 --> 01:12:28,320
facto supervisor to him

1597
01:12:33,510 --> 01:12:31,600
because raul bot wasn't particularly

1598
01:12:36,630 --> 01:12:33,520
although it was officially his

1599
01:12:38,470 --> 01:12:36,640
supervisor he didn't act as the

1600
01:12:40,390 --> 01:12:38,480
supervisor for whatever reason it was a

1601
01:12:41,110 --> 01:12:40,400
strange relationship i don't understand

1602
01:12:42,870 --> 01:12:41,120
it

1603
01:12:44,630 --> 01:12:42,880
i'm curious what do you think he means

1604
01:12:46,550 --> 01:12:44,640
when he says that you acted as the

1605
01:12:48,950 --> 01:12:46,560
supervisor you gave him advice or i

1606
01:12:59,990 --> 01:12:48,960
don't think it's correct it's more like

1607
01:13:00,000 --> 01:13:03,430
so eric

1608
01:13:08,630 --> 01:13:06,390
eric was very unbalanced

1609
01:13:11,669 --> 01:13:08,640
and he still is unbalanced and i don't

1610
01:13:13,669 --> 01:13:11,679
mean emotionally unbalanced i mean

1611
01:13:16,550 --> 01:13:13,679
uh he has

1612
01:13:19,990 --> 01:13:16,560
great talents

1613
01:13:21,430 --> 01:13:20,000
in certain directions

1614
01:13:23,030 --> 01:13:21,440
and

1615
01:13:24,630 --> 01:13:23,040
fear

1616
01:13:26,470 --> 01:13:24,640
of others

1617
01:13:29,350 --> 01:13:26,480
and there are certain

1618
01:13:33,910 --> 01:13:29,360
things that one has to do certain type

1619
01:13:38,790 --> 01:13:33,920
of computation a certain type of writing

1620
01:13:40,550 --> 01:13:38,800
basically he has fear of turning his um

1621
01:13:44,229 --> 01:13:40,560
his

1622
01:13:48,070 --> 01:13:46,370
uh so um

1623
01:13:49,669 --> 01:13:48,080
[Music]

1624
01:13:52,070 --> 01:13:49,679
uh

1625
01:13:55,350 --> 01:13:52,080
and and that's

1626
01:13:56,470 --> 01:13:55,360
part of the reason why he had difficulty

1627
01:13:59,590 --> 01:13:56,480
uh

1628
01:14:01,350 --> 01:13:59,600
with raul balt and with um

1629
01:14:02,709 --> 01:14:01,360
basically with the normal system in

1630
01:14:07,669 --> 01:14:02,719
harvard

1631
01:14:15,750 --> 01:14:11,030
my role was to help him pick something

1632
01:14:19,350 --> 01:14:17,830
big theories

1633
01:14:25,270 --> 01:14:19,360
and

1634
01:14:31,189 --> 01:14:25,280
thesis

1635
01:14:35,669 --> 01:14:32,709
yeah i also helped him with some

1636
01:14:37,750 --> 01:14:35,679
computations you know i you know

1637
01:14:41,510 --> 01:14:37,760
at the end of the day there are some

1638
01:14:43,669 --> 01:14:41,520
like so so he's come he's

1639
01:14:45,750 --> 01:14:43,679
you know big theories

1640
01:14:47,990 --> 01:14:45,760
lead to something very concrete and

1641
01:14:50,470 --> 01:14:48,000
specific which was a tiny part of the

1642
01:14:53,350 --> 01:14:50,480
big theories but we extracted that tiny

1643
01:14:55,750 --> 01:14:53,360
part and made it uh more concrete and at

1644
01:14:58,870 --> 01:14:55,760
the end it became a question you know

1645
01:15:00,310 --> 01:14:58,880
some big matrix 500 by 500 or whatever

1646
01:15:03,510 --> 01:15:00,320
it was

1647
01:15:06,870 --> 01:15:03,520
is it positive definite or not

1648
01:15:09,030 --> 01:15:06,880
and i helped him uh i helped him

1649
01:15:11,430 --> 01:15:09,040
decide that

1650
01:15:13,189 --> 01:15:11,440
and that was decided by compute by a

1651
01:15:15,350 --> 01:15:13,199
computer like you ended up programming

1652
01:15:16,310 --> 01:15:15,360
it that one that one was decided by

1653
01:15:17,910 --> 01:15:16,320
computer

1654
01:15:19,990 --> 01:15:17,920
so we just

1655
01:15:21,030 --> 01:15:20,000
uh but

1656
01:15:26,709 --> 01:15:21,040
but

1657
01:15:29,110 --> 01:15:26,719
have never done on on his own

1658
01:15:30,790 --> 01:15:29,120
because

1659
01:15:32,390 --> 01:15:30,800
he has this

1660
01:15:34,070 --> 01:15:32,400
fear of

1661
01:15:35,910 --> 01:15:34,080
uh

1662
01:15:37,189 --> 01:15:35,920
in a way it's a fear of testing your

1663
01:15:39,510 --> 01:15:37,199
theories

1664
01:15:42,790 --> 01:15:39,520
because they might fail but in another

1665
01:15:45,590 --> 01:15:42,800
way it's just inability he never

1666
01:15:47,669 --> 01:15:45,600
learned how to do it he never got good

1667
01:15:52,310 --> 01:15:47,679
at um

1668
01:15:54,870 --> 01:15:52,320
turning the very abstract into concrete

1669
01:15:54,880 --> 01:15:58,950
so yes so that was my role

1670
01:16:04,070 --> 01:16:01,669
have you read his recent geometric unity

1671
01:16:06,390 --> 01:16:04,080
papers or heard about geometric unity at

1672
01:16:08,470 --> 01:16:06,400
all i've heard a tiny bit about it i

1673
01:16:09,910 --> 01:16:08,480
have not read it i'm not in the position

1674
01:16:12,310 --> 01:16:09,920
to comment

1675
01:16:14,149 --> 01:16:12,320
you talked about it's difficult to make

1676
01:16:16,550 --> 01:16:14,159
a concrete or take something concrete

1677
01:16:18,310 --> 01:16:16,560
from a theory at least in his case

1678
01:16:20,070 --> 01:16:18,320
do you mind giving an example of his

1679
01:16:30,630 --> 01:16:20,080
strengths or some or an example of a

1680
01:16:44,709 --> 01:16:31,830
he

1681
01:16:44,719 --> 01:16:48,070
uh

1682
01:16:52,390 --> 01:16:49,350
how they

1683
01:16:54,390 --> 01:16:52,400
interact with each other

1684
01:16:55,750 --> 01:16:54,400
uh so

1685
01:16:57,750 --> 01:16:55,760
uh

1686
01:16:59,030 --> 01:16:57,760
the small groups like the classical

1687
01:17:00,390 --> 01:16:59,040
groups or what do you mean when you say

1688
01:17:04,149 --> 01:17:00,400
the smoke

1689
01:17:05,189 --> 01:17:04,159
okay what i mean by the small is um

1690
01:17:06,390 --> 01:17:05,199
so you know

1691
01:17:09,430 --> 01:17:06,400
uh

1692
01:17:11,350 --> 01:17:09,440
there are several families of so-called

1693
01:17:14,149 --> 01:17:11,360
symmetry groups

1694
01:17:16,550 --> 01:17:14,159
okay so there are uh

1695
01:17:19,430 --> 01:17:16,560
uh s-u-n

1696
01:17:21,430 --> 01:17:19,440
and s-uh

1697
01:17:23,830 --> 01:17:21,440
and s-o-n

1698
01:17:26,149 --> 01:17:23,840
and s-p-n

1699
01:17:28,149 --> 01:17:26,159
and then there are a few sporadic ones

1700
01:17:31,830 --> 01:17:28,159
there is uh

1701
01:17:35,350 --> 01:17:31,840
uh g2 and f4

1702
01:17:39,830 --> 01:17:35,360
and e6 and e7

1703
01:17:42,390 --> 01:17:39,840
and e8 and it doesn't go beyond eight

1704
01:17:46,550 --> 01:17:42,400
uh and all of these so these are

1705
01:17:50,470 --> 01:17:48,950
they they have so-called representation

1706
01:17:51,430 --> 01:17:50,480
theory

1707
01:17:52,310 --> 01:17:51,440
so

1708
01:17:55,030 --> 01:17:52,320
uh

1709
01:17:58,709 --> 01:17:55,040
each one of them can be represented can

1710
01:18:00,950 --> 01:17:58,719
be written as a group of matrices can be

1711
01:18:03,430 --> 01:18:00,960
realized within the world of matrices

1712
01:18:05,189 --> 01:18:03,440
but in many ways

1713
01:18:07,189 --> 01:18:05,199
so eric

1714
01:18:09,270 --> 01:18:07,199
uh

1715
01:18:14,870 --> 01:18:09,280
intimately knows

1716
01:18:18,709 --> 01:18:16,390
these groups

1717
01:18:20,870 --> 01:18:18,719
and their representations and how they

1718
01:18:23,430 --> 01:18:20,880
sit inside each other

1719
01:18:25,510 --> 01:18:23,440
for small values of n

1720
01:18:27,590 --> 01:18:25,520
and well for all of those sporadic ones

1721
01:18:29,990 --> 01:18:27,600
which are all small

1722
01:18:32,630 --> 01:18:30,000
and their symmetries and their so-called

1723
01:18:33,990 --> 01:18:32,640
outer symmetries i mean he knows all

1724
01:18:34,870 --> 01:18:34,000
about

1725
01:18:37,189 --> 01:18:34,880
uh

1726
01:18:38,630 --> 01:18:37,199
these things

1727
01:18:41,270 --> 01:18:38,640
now

1728
01:18:42,470 --> 01:18:41,280
this is relevant to physics

1729
01:18:45,590 --> 01:18:42,480
because

1730
01:18:48,630 --> 01:18:45,600
uh you know electro weak theory is

1731
01:18:50,950 --> 01:18:48,640
somehow about su 2

1732
01:18:58,070 --> 01:18:53,990
the grand unified theory so a strong and

1733
01:18:59,270 --> 01:18:58,080
electroweak is somehow about su 3

1734
01:19:00,390 --> 01:18:59,280
or

1735
01:19:03,350 --> 01:19:00,400
so

1736
01:19:05,669 --> 01:19:03,360
uh no no no no no i have it wrong

1737
01:19:08,070 --> 01:19:05,679
sorry electromagnetism is

1738
01:19:10,310 --> 01:19:08,080
well electromagnetism

1739
01:19:11,350 --> 01:19:10,320
is you one and then

1740
01:19:12,390 --> 01:19:11,360
you know i

1741
01:19:17,350 --> 01:19:12,400
i i

1742
01:19:19,910 --> 01:19:17,360
these things for many many years

1743
01:19:22,229 --> 01:19:19,920
so i could be saying things wrong

1744
01:19:24,630 --> 01:19:22,239
but yeah but his strength is that he

1745
01:19:26,950 --> 01:19:24,640
knows these things really really really

1746
01:19:26,960 --> 01:19:29,430
uh

1747
01:19:33,990 --> 01:19:31,750
or one of his strengths is that he knows

1748
01:19:35,270 --> 01:19:34,000
these things really really really well

1749
01:19:37,510 --> 01:19:35,280
earlier when we were talking about

1750
01:19:39,189 --> 01:19:37,520
particle physics well not theory you

1751
01:19:41,590 --> 01:19:39,199
mentioned that for every knot there's a

1752
01:19:44,870 --> 01:19:41,600
corresponding physics story of particles

1753
01:19:46,390 --> 01:19:44,880
dancing and so on is the opposite true

1754
01:19:47,990 --> 01:19:46,400
so does the arrow go in the other

1755
01:19:49,830 --> 01:19:48,000
direction as well

1756
01:19:53,750 --> 01:19:49,840
for every particle interaction is there

1757
01:19:57,669 --> 01:19:55,990
for every particle interaction of a

1758
01:20:00,709 --> 01:19:57,679
specific type

1759
01:20:02,790 --> 01:20:00,719
in three-dimensional space

1760
01:20:05,189 --> 01:20:02,800
yes

1761
01:20:07,669 --> 01:20:05,199
but uh but you have to

1762
01:20:10,470 --> 01:20:07,679
be very specific you have to be you have

1763
01:20:11,910 --> 01:20:10,480
to specialize a great deal

1764
01:20:14,229 --> 01:20:11,920
physics mostly happens in

1765
01:20:15,990 --> 01:20:14,239
four-dimensional space

1766
01:20:18,470 --> 01:20:16,000
if this can be easily explained why is

1767
01:20:20,709 --> 01:20:18,480
it not simple to just extend the three

1768
01:20:21,830 --> 01:20:20,719
dimensions to four dimensions

1769
01:20:25,990 --> 01:20:21,840
and

1770
01:20:28,629 --> 01:20:26,000
vector in we're talking about vector

1771
01:20:31,669 --> 01:20:28,639
spaces it's trivial to go from r3 to r4

1772
01:20:33,270 --> 01:20:31,679
the same theorems apply okay so so the

1773
01:20:34,310 --> 01:20:33,280
answer is

1774
01:20:35,910 --> 01:20:34,320
um

1775
01:20:40,390 --> 01:20:35,920
or there's

1776
01:20:41,590 --> 01:20:40,400
first of all certain things do extend

1777
01:20:43,669 --> 01:20:41,600
so

1778
01:20:45,430 --> 01:20:43,679
um

1779
01:20:46,950 --> 01:20:45,440
you know if not

1780
01:20:50,229 --> 01:20:46,960
theory is

1781
01:20:53,590 --> 01:20:50,239
to some extent about dance the dancing

1782
01:20:55,030 --> 01:20:53,600
of points in two-dimensional space

1783
01:20:57,030 --> 01:20:55,040
so

1784
01:20:58,629 --> 01:20:57,040
you know he he

1785
01:21:01,990 --> 01:20:58,639
here is a

1786
01:21:03,510 --> 01:21:02,000
a very rough uh

1787
01:21:07,510 --> 01:21:03,520
uh

1788
01:21:11,669 --> 01:21:07,520
so

1789
01:21:17,510 --> 01:21:12,550
or

1790
01:21:18,390 --> 01:21:17,520
is roughly about

1791
01:21:20,149 --> 01:21:18,400
one

1792
01:21:22,070 --> 01:21:20,159
dimensional

1793
01:21:24,390 --> 01:21:22,080
things

1794
01:21:25,390 --> 01:21:24,400
or curves or whatever

1795
01:21:27,990 --> 01:21:25,400
in

1796
01:21:31,110 --> 01:21:28,000
three-dimensional space

1797
01:21:32,950 --> 01:21:31,120
and as i mentioned before

1798
01:21:34,870 --> 01:21:32,960
it can be

1799
01:21:36,870 --> 01:21:34,880
um

1800
01:21:37,830 --> 01:21:36,880
interpreted

1801
01:21:39,830 --> 01:21:37,840
as

1802
01:21:42,709 --> 01:21:39,840
points dancing

1803
01:21:46,229 --> 01:21:42,719
in two-dimensional place space

1804
01:21:47,110 --> 01:21:46,239
so points are zero dimensional

1805
01:21:48,870 --> 01:21:47,120
so

1806
01:21:49,990 --> 01:21:48,880
uh you can

1807
01:21:52,470 --> 01:21:50,000
uh

1808
01:21:54,629 --> 01:21:52,480
so you can interpret no theory as zero

1809
01:21:56,310 --> 01:21:54,639
dimensional things

1810
01:21:57,910 --> 01:21:56,320
right a single point is a zero

1811
01:22:03,350 --> 01:21:57,920
dimensional thing

1812
01:22:04,790 --> 01:22:03,360
dancing

1813
01:22:06,149 --> 01:22:04,800
in

1814
01:22:16,310 --> 01:22:06,159
a

1815
01:22:18,470 --> 01:22:16,320
one dimension up

1816
01:22:21,510 --> 01:22:18,480
so you can say

1817
01:22:25,430 --> 01:22:21,520
uh let's uh

1818
01:22:32,550 --> 01:22:28,790
zero dimensional things dancing in r2

1819
01:22:34,790 --> 01:22:32,560
you can think of one-dimensional

1820
01:22:37,750 --> 01:22:34,800
things

1821
01:22:37,760 --> 01:22:40,149
in

1822
01:22:42,550 --> 01:22:41,189
uh

1823
01:22:57,590 --> 01:22:42,560
r

1824
01:22:59,830 --> 01:22:57,600
sections

1825
01:23:00,750 --> 01:22:59,840
they somehow corresponds

1826
01:23:04,830 --> 01:23:00,760
to

1827
01:23:09,990 --> 01:23:04,840
two-dimensional notes so two-dimensional

1828
01:23:13,350 --> 01:23:11,510
in

1829
01:23:14,629 --> 01:23:13,360
r4

1830
01:23:16,550 --> 01:23:14,639
now you can ask

1831
01:23:19,110 --> 01:23:16,560
now what exactly are what is that

1832
01:23:22,550 --> 01:23:19,120
supposed to be r3 dancing sorry not r4 i

1833
01:23:25,590 --> 01:23:22,560
i wanted to add one this is in r2 adding

1834
01:23:28,149 --> 01:23:25,600
one you get r3

1835
01:23:29,590 --> 01:23:28,159
sorry so one dimensional thing dancing

1836
01:23:31,270 --> 01:23:29,600
in r3

1837
01:23:34,470 --> 01:23:31,280
now you can ask yourself what are one

1838
01:23:36,790 --> 01:23:34,480
dimensional things dancing in r3 and

1839
01:23:39,030 --> 01:23:36,800
fortunately i'm ready for that

1840
01:23:41,189 --> 01:23:39,040
so here are here is a one dimensional

1841
01:23:44,790 --> 01:23:41,199
thing

1842
01:23:48,149 --> 01:23:45,910
and

1843
01:23:50,149 --> 01:23:48,159
uh right this is a loop it's a

1844
01:23:52,229 --> 01:23:50,159
one-dimensional thing that's another one

1845
01:23:54,470 --> 01:23:52,239
it's a loop it's a one-dimensional thing

1846
01:23:56,790 --> 01:23:54,480
and they can dance around they can fly

1847
01:24:00,229 --> 01:23:56,800
in r3 and they can fly in interesting

1848
01:24:03,189 --> 01:24:00,239
ways that don't exist one dimension less

1849
01:24:04,310 --> 01:24:03,199
namely they can fly through each other

1850
01:24:05,189 --> 01:24:04,320
okay

1851
01:24:08,390 --> 01:24:05,199
so

1852
01:24:11,830 --> 01:24:08,400
yes there is a theory of one-dimensional

1853
01:24:14,830 --> 01:24:11,840
things dancing in r3

1854
01:24:18,229 --> 01:24:14,840
and it corresponds to a theory of

1855
01:24:20,149 --> 01:24:18,239
two-dimensional spaces noted inside

1856
01:24:22,629 --> 01:24:20,159
four-dimensional space

1857
01:24:25,030 --> 01:24:22,639
so to some extent

1858
01:24:28,070 --> 01:24:25,040
the answer to your question is yes there

1859
01:24:31,350 --> 01:24:28,080
is higher there are higher dimensional

1860
01:24:33,189 --> 01:24:31,360
analogs of not theory

1861
01:24:33,990 --> 01:24:33,199
it turns out

1862
01:24:34,950 --> 01:24:34,000
that

1863
01:24:38,149 --> 01:24:34,960
uh

1864
01:24:42,229 --> 01:24:38,159
some features are different

1865
01:24:45,430 --> 01:24:42,239
it turns out that in some ways uh

1866
01:24:48,310 --> 01:24:45,440
and they're actually qualitatively

1867
01:24:52,470 --> 01:24:48,320
sort of the theory of not in one them so

1868
01:24:54,950 --> 01:24:52,480
so you know unlike um vector spaces

1869
01:24:57,110 --> 01:24:54,960
so vector spaces you kind of once you

1870
01:24:59,510 --> 01:24:57,120
learn

1871
01:25:03,990 --> 01:24:59,520
r3

1872
01:25:04,950 --> 01:25:04,000
r4 you've learned r to the 50.

1873
01:25:07,990 --> 01:25:04,960
okay

1874
01:25:10,310 --> 01:25:08,000
but but but here there are qualitative

1875
01:25:11,350 --> 01:25:10,320
differences

1876
01:25:12,870 --> 01:25:11,360
so

1877
01:25:13,830 --> 01:25:12,880
uh

1878
01:25:19,510 --> 01:25:13,840
so

1879
01:25:22,310 --> 01:25:19,520
translate to things here and vice versa

1880
01:25:23,750 --> 01:25:22,320
but not everything

1881
01:25:26,229 --> 01:25:23,760
so

1882
01:25:30,149 --> 01:25:26,239
myself i've spent most of my time

1883
01:25:33,510 --> 01:25:31,590
okay

1884
01:25:35,430 --> 01:25:33,520
but then there is higher there is even

1885
01:25:38,550 --> 01:25:35,440
higher stuff

1886
01:25:42,790 --> 01:25:41,189
by the way so you know

1887
01:25:46,470 --> 01:25:42,800
um

1888
01:25:49,590 --> 01:25:48,149
uh

1889
01:25:52,390 --> 01:25:49,600
when you take

1890
01:25:55,270 --> 01:25:52,400
a first class in linear algebra and

1891
01:25:57,990 --> 01:25:55,280
maybe also a second class in linear

1892
01:25:59,590 --> 01:25:58,000
algebra you get this impression

1893
01:26:01,910 --> 01:25:59,600
that

1894
01:26:03,430 --> 01:26:01,920
uh everything is the same in all

1895
01:26:04,310 --> 01:26:03,440
dimensions

1896
01:26:06,550 --> 01:26:04,320
yep

1897
01:26:08,709 --> 01:26:06,560
but that's not true

1898
01:26:09,910 --> 01:26:08,719
even in linear algebra even in linear

1899
01:26:10,709 --> 01:26:09,920
algebra

1900
01:26:13,030 --> 01:26:10,719
so

1901
01:26:15,270 --> 01:26:13,040
well not quite linear algebra but in

1902
01:26:18,070 --> 01:26:15,280
algebra

1903
01:26:21,830 --> 01:26:18,080
okay so you know there is something

1904
01:26:23,189 --> 01:26:21,840
called uh the real numbers

1905
01:26:25,669 --> 01:26:23,199
then you can

1906
01:26:30,709 --> 01:26:25,679
add i

1907
01:26:31,910 --> 01:26:30,719
and you get the complex numbers

1908
01:26:33,750 --> 01:26:31,920
and then

1909
01:26:37,910 --> 01:26:33,760
uh you can say

1910
01:26:39,110 --> 01:26:37,920
let's add uh j and k as well

1911
01:26:43,669 --> 01:26:39,120
and you get

1912
01:26:45,990 --> 01:26:43,679
uh the so-called uh quaternions

1913
01:26:48,229 --> 01:26:46,000
but the quaternions are different than

1914
01:26:49,590 --> 01:26:48,239
the complex numbers in that this is a

1915
01:26:50,470 --> 01:26:49,600
commutative

1916
01:26:55,430 --> 01:26:50,480
ring

1917
01:26:57,910 --> 01:26:55,440
and then you can add g i forgot what's

1918
01:26:59,830 --> 01:26:57,920
the standard name for what you add so i

1919
01:27:00,709 --> 01:26:59,840
don't know add

1920
01:27:05,430 --> 01:27:00,719
in

1921
01:27:08,229 --> 01:27:05,440
i forgot the name and and you get

1922
01:27:11,669 --> 01:27:08,239
octaniums and the octaniums are no

1923
01:27:14,709 --> 01:27:11,679
longer even associative

1924
01:27:17,510 --> 01:27:14,719
so it's still sort of a ring

1925
01:27:19,830 --> 01:27:17,520
namely it has a multiplication but it's

1926
01:27:22,070 --> 01:27:19,840
not even associative and then the

1927
01:27:26,070 --> 01:27:22,080
process ends there is just nothing

1928
01:27:27,510 --> 01:27:26,080
beyond that you can't continue

1929
01:27:28,629 --> 01:27:27,520
uh so

1930
01:27:31,510 --> 01:27:28,639
uh

1931
01:27:33,510 --> 01:27:31,520
so even in linear algebra so that's not

1932
01:27:36,310 --> 01:27:33,520
quite well

1933
01:27:38,950 --> 01:27:36,320
i don't know even in basic algebra not

1934
01:27:41,270 --> 01:27:38,960
all dimensions are the same 1 is not the

1935
01:27:44,149 --> 01:27:41,280
same as 2 is not the same as 4 is not

1936
01:27:47,270 --> 01:27:44,159
the same as 8 and not the same as 16

1937
01:27:48,470 --> 01:27:47,280
where things no longer exist

1938
01:27:53,240 --> 01:27:48,480
so

1939
01:27:57,430 --> 01:27:54,629
[Music]

1940
01:27:59,110 --> 01:27:57,440
things are independent of the dimension

1941
01:28:01,270 --> 01:27:59,120
it's only they're only independent of

1942
01:28:01,990 --> 01:28:01,280
the dimension in the first two years of

1943
01:28:04,629 --> 01:28:02,000
uh

1944
01:28:07,189 --> 01:28:04,639
of of undergrad

1945
01:28:09,430 --> 01:28:07,199
now in this example we're going to

1946
01:28:11,750 --> 01:28:09,440
different spaces by adding one

1947
01:28:14,229 --> 01:28:11,760
or by adding whatever extra

1948
01:28:17,030 --> 01:28:14,239
variables there are there in the

1949
01:28:18,550 --> 01:28:17,040
previous example we're extending r 4 to

1950
01:28:22,310 --> 01:28:18,560
r 5 or

1951
01:28:25,189 --> 01:28:22,320
r n to n plus m

1952
01:28:27,350 --> 01:28:25,199
so we're in the same space in a sense

1953
01:28:30,149 --> 01:28:27,360
except adding an extra dimension so

1954
01:28:31,669 --> 01:28:30,159
what's an example that holds for r3

1955
01:28:33,189 --> 01:28:31,679
or actually sorry let's make this even

1956
01:28:36,870 --> 01:28:33,199
simpler what's an example that holds for

1957
01:28:39,510 --> 01:28:36,880
r2 but doesn't hold for r3

1958
01:28:41,590 --> 01:28:39,520
or you can say r3 to r4 like what's an

1959
01:28:43,830 --> 01:28:41,600
example of a quantity that drastically

1960
01:28:45,030 --> 01:28:43,840
changes as soon as you go to r4

1961
01:28:47,590 --> 01:28:45,040
and becomes

1962
01:28:49,750 --> 01:28:47,600
extremely complicated but in r3 it's

1963
01:28:52,790 --> 01:28:49,760
trivial

1964
01:28:56,229 --> 01:28:52,800
the motion of points

1965
01:28:56,950 --> 01:28:56,239
is fundamentally different

1966
01:29:01,110 --> 01:28:56,960
in

1967
01:29:03,030 --> 01:29:01,120
dimensions

1968
01:29:04,070 --> 01:29:03,040
so let me explain

1969
01:29:05,510 --> 01:29:04,080
so

1970
01:29:08,709 --> 01:29:05,520
uh

1971
01:29:09,669 --> 01:29:08,719
right suppose you have two points a and

1972
01:29:12,149 --> 01:29:09,679
b

1973
01:29:14,550 --> 01:29:12,159
in two dimensions

1974
01:29:17,110 --> 01:29:14,560
and you want them to trade places by

1975
01:29:22,070 --> 01:29:19,510
okay there are two basic ways they can

1976
01:29:23,110 --> 01:29:22,080
do it they can trade place

1977
01:29:27,669 --> 01:29:23,120
by

1978
01:29:28,550 --> 01:29:27,679
uh b going above a

1979
01:29:31,110 --> 01:29:28,560
or

1980
01:29:33,910 --> 01:29:31,120
they can trade places

1981
01:29:36,790 --> 01:29:33,920
uh in some sort sort of the opposite way

1982
01:29:39,430 --> 01:29:36,800
by a going above b so a will go to here

1983
01:29:40,310 --> 01:29:39,440
and b will go sorry a will go

1984
01:30:04,390 --> 01:29:40,320
a

1985
01:30:08,790 --> 01:30:04,400
continuously deform

1986
01:30:12,790 --> 01:30:08,800
this way of moving to that way of moving

1987
01:30:15,990 --> 01:30:12,800
but in r3 that's not

1988
01:30:19,270 --> 01:30:16,000
true anymore so in r3

1989
01:30:22,550 --> 01:30:19,280
points can trade places

1990
01:30:23,430 --> 01:30:22,560
in only one way

1991
01:30:27,669 --> 01:30:23,440
so

1992
01:30:28,470 --> 01:30:27,679
uh let me uh find two points for you

1993
01:30:31,910 --> 01:30:28,480
so

1994
01:30:32,870 --> 01:30:31,920
uh i suppose

1995
01:30:34,550 --> 01:30:32,880
uh

1996
01:30:39,669 --> 01:30:34,560
well they're not points but they're

1997
01:30:41,030 --> 01:30:39,679
close to points so here is uh red and

1998
01:30:44,790 --> 01:30:41,040
blue

1999
01:30:46,149 --> 01:30:44,800
so in r3 they can trade places going

2000
01:30:49,910 --> 01:30:46,159
this way

2001
01:30:52,790 --> 01:30:49,920
or they can trade places going that way

2002
01:30:54,950 --> 01:30:52,800
but there are many other ways they can

2003
01:30:57,350 --> 01:30:54,960
trade places they can trade places by

2004
01:30:59,590 --> 01:30:57,360
going that way or

2005
01:31:00,709 --> 01:30:59,600
that way

2006
01:31:02,870 --> 01:31:00,719
and

2007
01:31:05,270 --> 01:31:02,880
um

2008
01:31:08,070 --> 01:31:05,280
in a sense all of these

2009
01:31:10,629 --> 01:31:08,080
trading places ways

2010
01:31:12,070 --> 01:31:10,639
are equivalent to each other

2011
01:31:15,030 --> 01:31:12,080
because

2012
01:31:19,189 --> 01:31:15,040
if you trade places

2013
01:31:23,110 --> 01:31:19,199
wait if the two points trade places

2014
01:31:24,709 --> 01:31:23,120
they span a circle

2015
01:31:29,110 --> 01:31:24,719
right so

2016
01:31:31,189 --> 01:31:29,120
know they

2017
01:31:33,270 --> 01:31:31,199
spun a circle by

2018
01:31:36,310 --> 01:31:33,280
uh i wish i had a third hand maybe i

2019
01:31:39,830 --> 01:31:36,320
removed my sure sure sure okay they go

2020
01:31:43,430 --> 01:31:39,840
like that okay that spawns a circle and

2021
01:31:45,189 --> 01:31:43,440
the other way of spawning a circle is by

2022
01:31:47,830 --> 01:31:45,199
going the other way

2023
01:31:48,950 --> 01:31:47,840
around the same d around the same sorry

2024
01:31:56,550 --> 01:31:48,960
circle

2025
01:31:59,350 --> 01:31:56,560
and that homotops that deforms

2026
01:32:03,910 --> 01:31:59,360
one way of trading places to the other

2027
01:32:07,430 --> 01:32:03,920
way of trading places so in r3

2028
01:32:09,030 --> 01:32:07,440
so in r2 there are two

2029
01:32:10,709 --> 01:32:09,040
distinct

2030
01:32:14,149 --> 01:32:10,719
sorry this

2031
01:32:15,910 --> 01:32:14,159
can spell there are two

2032
01:32:18,709 --> 01:32:15,920
uh

2033
01:32:20,229 --> 01:32:18,719
distinct

2034
01:32:21,270 --> 01:32:20,239
ways

2035
01:32:22,310 --> 01:32:21,280
of

2036
01:32:24,149 --> 01:32:22,320
uh

2037
01:32:27,030 --> 01:32:24,159
trading

2038
01:32:29,189 --> 01:32:27,040
uh places

2039
01:32:31,270 --> 01:32:29,199
and in fact two are easy they're

2040
01:32:32,550 --> 01:32:31,280
actually a little bit more but anyway in

2041
01:32:33,950 --> 01:32:32,560
r3

2042
01:32:37,750 --> 01:32:33,960
so if you're talking about

2043
01:32:41,189 --> 01:32:39,350
and you have

2044
01:32:42,470 --> 01:32:41,199
two points in the three-dimensional

2045
01:32:43,830 --> 01:32:42,480
space there is

2046
01:32:45,030 --> 01:32:43,840
only

2047
01:32:46,229 --> 01:32:45,040
one

2048
01:32:51,430 --> 01:32:46,239
way

2049
01:32:55,270 --> 01:32:51,440
different let me say differently

2050
01:32:56,629 --> 01:32:55,280
uh all ways of trading places all

2051
01:32:57,910 --> 01:32:56,639
ways

2052
01:32:59,510 --> 01:32:57,920
of

2053
01:33:03,189 --> 01:32:59,520
trading

2054
01:33:07,430 --> 01:33:04,229
are

2055
01:33:09,830 --> 01:33:07,440
equivalent and again the basic the basic

2056
01:33:12,470 --> 01:33:09,840
point is that a way of trading places is

2057
01:33:14,790 --> 01:33:12,480
a circle right right one point goes

2058
01:33:18,310 --> 01:33:14,800
along one arc and the other point goes

2059
01:33:19,750 --> 01:33:18,320
about a guy over the other arc and you

2060
01:33:22,790 --> 01:33:19,760
can

2061
01:33:24,470 --> 01:33:22,800
switch from one place of trading place

2062
01:33:26,470 --> 01:33:24,480
one way of trading places to the other

2063
01:33:29,510 --> 01:33:26,480
by flipping the circle you can't do it

2064
01:33:31,030 --> 01:33:29,520
if you're only in the plane

2065
01:33:34,830 --> 01:33:31,040
um

2066
01:33:39,110 --> 01:33:34,840
since trading places is actually

2067
01:33:40,950 --> 01:33:39,120
fundamental it makes uh

2068
01:33:42,229 --> 01:33:40,960
but by the way it's also fundamental in

2069
01:33:44,470 --> 01:33:42,239
physics

2070
01:33:46,629 --> 01:33:44,480
so you know you you you know you you

2071
01:33:48,950 --> 01:33:46,639
might have heard of uh bosons and

2072
01:33:51,270 --> 01:33:48,960
fermions and how they behave

2073
01:33:53,830 --> 01:33:51,280
with respect to trading places and then

2074
01:33:56,390 --> 01:33:53,840
there are any ons that behave yet

2075
01:33:59,430 --> 01:33:56,400
differently uh with respect to trading

2076
01:34:01,669 --> 01:33:59,440
places so basically trading places or

2077
01:34:04,070 --> 01:34:01,679
how things behave under trading places

2078
01:34:05,110 --> 01:34:04,080
is a fundamental

2079
01:34:07,590 --> 01:34:05,120
thing

2080
01:34:10,070 --> 01:34:07,600
and it's different it's it's different

2081
01:34:11,990 --> 01:34:10,080
in two dimensions than in three

2082
01:34:13,830 --> 01:34:12,000
right likewise there are things that are

2083
01:34:14,870 --> 01:34:13,840
different between three dimensions and

2084
01:34:18,149 --> 01:34:14,880
four

2085
01:34:21,510 --> 01:34:18,159
and and so it's actually this kind of

2086
01:34:23,430 --> 01:34:21,520
myth or not myth but this um

2087
01:34:26,790 --> 01:34:23,440
the thing that you learn in first and

2088
01:34:30,070 --> 01:34:26,800
second year that uh rn is the same rn no

2089
01:34:31,669 --> 01:34:30,080
matter what n is is not actually true

2090
01:34:32,950 --> 01:34:31,679
have you heard of the hard problem of

2091
01:34:35,830 --> 01:34:32,960
consciousness

2092
01:34:38,070 --> 01:34:35,840
i have not heard it in this language

2093
01:34:39,990 --> 01:34:38,080
namely no no has nothing to do with

2094
01:34:41,590 --> 01:34:40,000
what was written on the board or maybe

2095
01:34:43,990 --> 01:34:41,600
it does but not as far as i see this is

2096
01:34:47,030 --> 01:34:44,000
sort of a clear philosophical problem

2097
01:34:49,830 --> 01:34:47,040
right but uh with the added prefix the

2098
01:34:52,709 --> 01:34:49,840
high and it's clearly hard

2099
01:34:54,229 --> 01:34:52,719
but but but as a phrase the hard problem

2100
01:34:57,350 --> 01:34:54,239
of consciousness i don't know what

2101
01:35:02,870 --> 01:34:59,270
there's only one consciousness that i

2102
01:35:05,430 --> 01:35:02,880
need to explain and it's my own

2103
01:35:07,990 --> 01:35:05,440
right from my perspective

2104
01:35:10,390 --> 01:35:08,000
you're not conscious

2105
01:35:13,590 --> 01:35:10,400
right you just react to

2106
01:35:15,430 --> 01:35:13,600
to to things that i do you know if i

2107
01:35:18,470 --> 01:35:15,440
you know if i tell you

2108
01:35:20,709 --> 01:35:18,480
uh you're stupid you get angry at me if

2109
01:35:22,149 --> 01:35:20,719
i give you a compliment you get happy

2110
01:35:24,790 --> 01:35:22,159
but these are all

2111
01:35:27,350 --> 01:35:24,800
i don't see consciousness here

2112
01:35:29,510 --> 01:35:27,360
okay i so there's only one consciousness

2113
01:35:31,109 --> 01:35:29,520
that i have to explain

2114
01:35:35,109 --> 01:35:31,119
and only one person that i have to

2115
01:35:46,950 --> 01:35:36,149
um

2116
01:35:46,960 --> 01:35:50,870
having said that

2117
01:35:50,880 --> 01:35:57,590
um

2118
01:35:57,600 --> 01:36:01,990
yeah i'll keep the rest private

2119
01:36:02,000 --> 01:36:10,790
what keeps you up at night

2120
01:36:10,800 --> 01:36:14,870
different things on different days

2121
01:36:19,030 --> 01:36:17,910
whether she loves me or not

2122
01:36:20,870 --> 01:36:19,040
uh

2123
01:36:22,950 --> 01:36:20,880
whether i can

2124
01:36:26,149 --> 01:36:22,960
complete the computer program or i'm

2125
01:36:29,030 --> 01:36:26,159
writing or not or why is it not written

2126
01:36:30,870 --> 01:36:29,040
my classes for tomorrow the theorem i

2127
01:36:33,590 --> 01:36:30,880
don't know how to

2128
01:36:34,950 --> 01:36:33,600
have no clue how to prove the state of

2129
01:36:37,270 --> 01:36:34,960
the world

2130
01:36:39,510 --> 01:36:37,280
covered i don't know different things at

2131
01:36:41,510 --> 01:36:39,520
different times

2132
01:36:44,070 --> 01:36:41,520
is there a through line so let's say one

2133
01:37:01,189 --> 01:36:44,080
that you've been thinking about for 15

2134
01:37:09,189 --> 01:37:04,470
you know i'm politically aware

2135
01:37:11,430 --> 01:37:09,199
and always been have always been so uh

2136
01:37:13,430 --> 01:37:11,440
uh

2137
01:37:15,109 --> 01:37:13,440
you know how to make the world a better

2138
01:37:18,470 --> 01:37:15,119
place

2139
01:37:21,030 --> 01:37:18,480
uh but but of course that's a subjective

2140
01:37:23,669 --> 01:37:21,040
thing what what is better

2141
01:37:25,590 --> 01:37:23,679
to me may or may not be the same as what

2142
01:37:27,590 --> 01:37:25,600
is better to you

2143
01:37:29,750 --> 01:37:27,600
so in a way when i'm saying

2144
01:37:31,669 --> 01:37:29,760
uh how to make a better pla the world a

2145
01:37:35,350 --> 01:37:31,679
better place it's more like how to make

2146
01:37:35,360 --> 01:37:44,709
i would how i would like it to be

2147
01:37:48,390 --> 01:37:46,629
yeah so i think about it a lot and

2148
01:37:50,709 --> 01:37:48,400
mostly my conclusion is that there's

2149
01:37:52,790 --> 01:37:50,719
nothing i can do or there is much i can

2150
01:37:57,109 --> 01:37:52,800
do

2151
01:38:05,510 --> 01:37:58,950
what direction would you like math

2152
01:38:12,310 --> 01:38:08,070
i think i mentioned

2153
01:38:12,320 --> 01:38:14,870
um

2154
01:38:14,880 --> 01:38:21,510
and i actually uh

2155
01:38:24,470 --> 01:38:23,350
so i mean it's not the only thing of

2156
01:38:26,709 --> 01:38:24,480
value

2157
01:38:33,750 --> 01:38:26,719
in mathematics

2158
01:38:38,070 --> 01:38:35,109
regardless of whether they are

2159
01:38:41,750 --> 01:38:38,080
computable or not

2160
01:38:47,669 --> 01:38:44,950
but those parts of mathematics that can

2161
01:38:52,070 --> 01:38:47,679
be computed

2162
01:38:56,830 --> 01:38:54,629
and often

2163
01:38:58,629 --> 01:38:56,840
people

2164
01:39:00,950 --> 01:38:58,639
uh

2165
01:39:02,070 --> 01:39:00,960
just don't care about computations they

2166
01:39:03,750 --> 01:39:02,080
pretend

2167
01:39:05,270 --> 01:39:03,760
that

2168
01:39:07,270 --> 01:39:05,280
well

2169
01:39:09,590 --> 01:39:07,280
they think of computation as something

2170
01:39:13,270 --> 01:39:09,600
as a technical thing to to to live for

2171
01:39:16,870 --> 01:39:13,280
their graduate students

2172
01:39:19,669 --> 01:39:16,880
and i see it as a much more integral

2173
01:39:20,790 --> 01:39:19,679
part of the work

2174
01:39:28,149 --> 01:39:20,800
so

2175
01:39:31,990 --> 01:39:30,629
i i i would make computation a bigger

2176
01:39:33,510 --> 01:39:32,000
part

2177
01:39:35,910 --> 01:39:33,520
computation in the sense of

2178
01:39:38,870 --> 01:39:35,920
implementation on the computer not in

2179
01:39:41,030 --> 01:39:38,880
the sense of writing by hand

2180
01:39:46,149 --> 01:39:41,040
i would make it a much bigger part and i

2181
01:39:51,990 --> 01:39:48,310
and that happens at many levels so when

2182
01:39:54,629 --> 01:39:52,000
you teach a class in linear algebra

2183
01:39:59,350 --> 01:39:54,639
you teach about uh

2184
01:40:01,750 --> 01:40:00,709
well

2185
01:40:03,750 --> 01:40:01,760
uh

2186
01:40:05,750 --> 01:40:03,760
along with it there should be a computer

2187
01:40:07,109 --> 01:40:05,760
program to compute compute the

2188
01:40:08,709 --> 01:40:07,119
determinant

2189
01:40:11,430 --> 01:40:08,719
and should and there should be a

2190
01:40:13,510 --> 01:40:11,440
realization that there are maybe two

2191
01:40:16,470 --> 01:40:13,520
formulas for the determinant and one of

2192
01:40:18,070 --> 01:40:16,480
them is way better than the other

2193
01:40:21,510 --> 01:40:18,080
uh

2194
01:40:23,350 --> 01:40:21,520
if you try to implement it

2195
01:40:25,189 --> 01:40:23,360
uh so

2196
01:40:26,310 --> 01:40:25,199
um

2197
01:40:32,310 --> 01:40:26,320
i would

2198
01:40:35,830 --> 01:40:33,270
um

2199
01:40:38,229 --> 01:40:35,840
yeah maybe that would be the main change

2200
01:40:41,990 --> 01:40:38,239
do you have a philosophy of math so for

2201
01:40:43,750 --> 01:40:42,000
example there's platonism and formalism

2202
01:40:46,390 --> 01:40:43,760
if anything i would be an ultra

2203
01:40:47,350 --> 01:40:46,400
finalitist

2204
01:40:49,990 --> 01:40:47,360
so

2205
01:40:53,669 --> 01:40:50,000
uh

2206
01:40:56,790 --> 01:40:53,679
it's much more graded than that

2207
01:40:57,910 --> 01:40:56,800
so you know there is a hierarchy

2208
01:41:00,310 --> 01:40:57,920
of

2209
01:41:02,350 --> 01:41:00,320
um

2210
01:41:06,709 --> 01:41:02,360
of

2211
01:41:09,189 --> 01:41:06,719
or sizes

2212
01:41:09,990 --> 01:41:09,199
of things in mathematics

2213
01:41:12,550 --> 01:41:10,000
so

2214
01:41:14,629 --> 01:41:12,560
you know people in set theory and logic

2215
01:41:19,990 --> 01:41:14,639
and you know talk about

2216
01:41:20,000 --> 01:41:22,950
and

2217
01:41:26,470 --> 01:41:24,550
then there are

2218
01:41:29,189 --> 01:41:26,480
parts of mathematics that have to do

2219
01:41:31,270 --> 01:41:29,199
with uncountable or

2220
01:41:33,910 --> 01:41:31,280
bigger than uncountable

2221
01:41:36,310 --> 01:41:33,920
and then there are infinite parts

2222
01:41:38,070 --> 01:41:36,320
and then there are just infinite without

2223
01:41:40,310 --> 01:41:38,080
being uncountable right and just

2224
01:41:44,950 --> 01:41:40,320
countable say and then there are parts

2225
01:41:50,870 --> 01:41:47,830
finite but huge

2226
01:41:51,750 --> 01:41:50,880
uh so you know ramsey theory

2227
01:41:57,510 --> 01:41:51,760
uh

2228
01:42:00,229 --> 01:41:57,520
you know you prove that if a graph is

2229
01:42:01,910 --> 01:42:00,239
large enough then it has properties

2230
01:42:04,629 --> 01:42:01,920
certain properties

2231
01:42:06,870 --> 01:42:04,639
but large enough means really really

2232
01:42:09,030 --> 01:42:06,880
really really really really really

2233
01:42:12,830 --> 01:42:09,040
really huge bigger than the number of

2234
01:42:12,840 --> 01:42:17,430
uh and then there are

2235
01:42:21,189 --> 01:42:18,709
uh

2236
01:42:21,990 --> 01:42:21,199
you know parts of mathematics

2237
01:42:32,310 --> 01:42:22,000
uh

2238
01:42:34,070 --> 01:42:32,320
and 10 to the 12 i don't know what a

2239
01:42:36,070 --> 01:42:34,080
computer can do in a fraction of a

2240
01:42:37,990 --> 01:42:36,080
second to what a computer can do in an

2241
01:42:40,470 --> 01:42:38,000
hour

2242
01:42:43,270 --> 01:42:40,480
okay and you know maybe you can go a

2243
01:42:45,430 --> 01:42:43,280
little bit beyond to 10 to the 16 i

2244
01:42:48,470 --> 01:42:45,440
don't know 10 to the 15. i don't know

2245
01:42:53,510 --> 01:42:52,070
so there is this whole grading

2246
01:42:57,510 --> 01:42:53,520
and to me

2247
01:43:01,109 --> 01:42:57,520
the bigger things are

2248
01:43:04,470 --> 01:43:02,709
uh

2249
01:43:07,270 --> 01:43:04,480
and

2250
01:43:09,270 --> 01:43:07,280
because they're farther away from our

2251
01:43:12,870 --> 01:43:09,280
everyday experience

2252
01:43:14,470 --> 01:43:12,880
so they may have philosophical value and

2253
01:43:16,629 --> 01:43:14,480
some of them do

2254
01:43:17,910 --> 01:43:16,639
so i don't want to

2255
01:43:19,030 --> 01:43:17,920
completely

2256
01:43:21,430 --> 01:43:19,040
say

2257
01:43:22,709 --> 01:43:21,440
anything about large cardinals is not

2258
01:43:25,590 --> 01:43:22,719
interesting

2259
01:43:28,550 --> 01:43:25,600
or anything about infinity

2260
01:43:30,790 --> 01:43:28,560
is not interesting

2261
01:43:34,149 --> 01:43:30,800
but the bar is higher

2262
01:43:35,430 --> 01:43:34,159
for something that genuinely use uses

2263
01:43:37,189 --> 01:43:35,440
infinity

2264
01:43:39,030 --> 01:43:37,199
to be interesting

2265
01:43:41,350 --> 01:43:39,040
the bar is higher

2266
01:43:42,390 --> 01:43:41,360
than if the thing is

2267
01:43:45,270 --> 01:43:42,400
uh

2268
01:43:48,790 --> 01:43:45,280
in this in the range of sizes

2269
01:43:50,550 --> 01:43:48,800
that we can actually hold in our hands

2270
01:43:52,709 --> 01:43:50,560
so that's what i mean by an ultra

2271
01:43:54,070 --> 01:43:52,719
finitist i mean

2272
01:43:56,550 --> 01:43:54,080
sort of the

2273
01:43:58,629 --> 01:43:56,560
or or so this is a form so an ultra

2274
01:44:00,870 --> 01:43:58,639
finalities would say the only numbers

2275
01:44:02,629 --> 01:44:00,880
that exist are the numbers i could count

2276
01:44:04,709 --> 01:44:02,639
to

2277
01:44:07,430 --> 01:44:04,719
and maybe by uh

2278
01:44:10,550 --> 01:44:07,440
extension that my computer could count

2279
01:44:13,990 --> 01:44:10,560
to so maybe my computer can count up to

2280
01:44:16,149 --> 01:44:14,000
this number but 10 to the 100 does not

2281
01:44:19,350 --> 01:44:16,159
exist in some sense because my computer

2282
01:44:22,870 --> 01:44:19,360
will never be able to count there

2283
01:44:23,830 --> 01:44:22,880
okay we'll never be able to get there

2284
01:44:29,830 --> 01:44:23,840
so

2285
01:44:31,910 --> 01:44:29,840
there is value to this one too

2286
01:44:34,390 --> 01:44:31,920
and sometimes there is even value to

2287
01:44:36,709 --> 01:44:34,400
infinity and sometimes there is even

2288
01:44:38,950 --> 01:44:36,719
value to the bigger form of infinity but

2289
01:44:42,550 --> 01:44:38,960
the bar has to be higher

2290
01:44:44,870 --> 01:44:42,560
uh the the the the philosophical value

2291
01:44:47,990 --> 01:44:44,880
bar has to be higher

2292
01:44:49,830 --> 01:44:48,000
the bigger the the size is

2293
01:44:51,590 --> 01:44:49,840
these things are always interesting

2294
01:44:55,030 --> 01:44:51,600
these things are interesting only on

2295
01:44:58,790 --> 01:44:56,790
now i'm not sure do you classify

2296
01:45:00,470 --> 01:44:58,800
yourself as a pure mathematician

2297
01:45:02,709 --> 01:45:00,480
definitely

2298
01:45:05,109 --> 01:45:02,719
okay so for a pure mathematician who

2299
01:45:06,390 --> 01:45:05,119
seemingly doesn't care about reality

2300
01:45:09,590 --> 01:45:06,400
it's supposed to be discontinued again

2301
01:45:13,109 --> 01:45:09,600
the valuable math is the math that i can

2302
01:45:14,790 --> 01:45:13,119
or the more valuable math

2303
01:45:20,870 --> 01:45:14,800
is the math that i can turn into a

2304
01:45:25,669 --> 01:45:23,109
it's still pure math in the sense that

2305
01:45:29,189 --> 01:45:25,679
i'm not looking for an immediate or a

2306
01:45:29,199 --> 01:45:32,629
uh but

2307
01:45:38,070 --> 01:45:35,270
both from the application perspective

2308
01:45:39,830 --> 01:45:38,080
and from the pedagogical perspective

2309
01:45:42,950 --> 01:45:39,840
i still prefer

2310
01:45:44,950 --> 01:45:42,960
the map that the math that can be

2311
01:45:46,870 --> 01:45:44,960
implemented because the math that can be

2312
01:45:49,109 --> 01:45:46,880
implemented even if i'm not looking for

2313
01:45:51,030 --> 01:45:49,119
an immediate application

2314
01:45:52,709 --> 01:45:51,040
is there is the math that has a higher

2315
01:45:55,510 --> 01:45:52,719
chance

2316
01:45:57,750 --> 01:45:55,520
of being applied

2317
01:45:59,109 --> 01:45:57,760
because in the application you'll end up

2318
01:46:00,310 --> 01:45:59,119
computing

2319
01:46:02,310 --> 01:46:00,320
and also

2320
01:46:07,430 --> 01:46:02,320
from the teaching perspective from the

2321
01:46:07,440 --> 01:46:11,270
there is more value

2322
01:46:16,070 --> 01:46:13,830
to the education you give

2323
01:46:17,990 --> 01:46:16,080
if it comes with implementation because

2324
01:46:22,390 --> 01:46:18,000
you want your students to be able to

2325
01:46:26,950 --> 01:46:24,790
yes sorry what were you asking oh i was

2326
01:46:28,629 --> 01:46:26,960
saying you ultimately care about the

2327
01:46:32,709 --> 01:46:28,639
practical aspect of math even though

2328
01:46:38,709 --> 01:46:36,070
ultimately yes though possibly very

2329
01:46:43,109 --> 01:46:38,719
indirectly

2330
01:46:44,709 --> 01:46:43,119
so maybe the way the math i'm doing

2331
01:46:47,510 --> 01:46:44,719
or maybe the

2332
01:46:49,350 --> 01:46:47,520
maybe the way i care is in that the pure

2333
01:46:52,310 --> 01:46:49,360
math i'm doing

2334
01:46:55,430 --> 01:46:52,320
uh enables me to teach graduate students

2335
01:47:00,470 --> 01:46:55,440
who will then become college instructors

2336
01:47:00,480 --> 01:47:02,790
uh

2337
01:47:06,470 --> 01:47:04,629
actually

2338
01:47:07,669 --> 01:47:06,480
implement the mathematics they're

2339
01:47:09,910 --> 01:47:07,679
learning

2340
01:47:11,830 --> 01:47:09,920
so i mean it it doesn't have to be

2341
01:47:13,990 --> 01:47:11,840
immediate and direct

2342
01:47:16,470 --> 01:47:14,000
but yes i do care about

2343
01:47:19,189 --> 01:47:16,480
how at the end it gets applied

2344
01:47:21,669 --> 01:47:19,199
or how i get the end it it becomes

2345
01:47:23,350 --> 01:47:21,679
applicable

2346
01:47:26,310 --> 01:47:23,360
great now we just have some audience

2347
01:47:27,669 --> 01:47:26,320
questions i asked people beforehand

2348
01:47:29,430 --> 01:47:27,679
what are some questions you have for

2349
01:47:31,910 --> 01:47:29,440
professor jor barnetten so the

2350
01:47:34,149 --> 01:47:31,920
scientific mystical philosopher that's

2351
01:47:36,149 --> 01:47:34,159
the username he wants to know he or she

2352
01:47:42,790 --> 01:47:36,159
wants to know why the unreasonable

2353
01:47:46,550 --> 01:47:44,229
sorry

2354
01:47:49,990 --> 01:47:46,560
why is mathematics unreasonably

2355
01:47:55,510 --> 01:47:51,350
gee i don't know

2356
01:47:59,350 --> 01:47:57,430
uh

2357
01:48:01,750 --> 01:47:59,360
she may or may not be able to give you

2358
01:48:08,390 --> 01:48:01,760
an answer

2359
01:48:15,109 --> 01:48:11,510
yeah it's weird we live in a predictable

2360
01:48:18,629 --> 01:48:16,470
uh

2361
01:48:21,270 --> 01:48:18,639
right when we throw something up in the

2362
01:48:23,109 --> 01:48:21,280
air it always uh

2363
01:48:25,189 --> 01:48:23,119
shows this you know goes through the

2364
01:48:27,189 --> 01:48:25,199
same trajectory

2365
01:48:30,149 --> 01:48:27,199
uh

2366
01:48:33,990 --> 01:48:30,159
nearly i don't know i mean

2367
01:48:38,870 --> 01:48:36,550
roman gekwad wants to know have you ever

2368
01:48:44,550 --> 01:48:38,880
had your iq scored

2369
01:48:51,109 --> 01:48:47,189
no clue

2370
01:48:59,189 --> 01:48:54,629
you know iq scores are very limited in

2371
01:48:59,199 --> 01:49:02,149
you know are

2372
01:49:07,910 --> 01:49:05,430
you know there is a fun story

2373
01:49:12,550 --> 01:49:09,350
uh that i

2374
01:49:13,669 --> 01:49:12,560
i've never verified it but i heard it

2375
01:49:14,390 --> 01:49:13,679
okay

2376
01:49:20,790 --> 01:49:14,400
that

2377
01:49:26,629 --> 01:49:24,390
when the people who introduced iq tests

2378
01:49:28,629 --> 01:49:26,639
first introduced them they run them on

2379
01:49:31,510 --> 01:49:28,639
test subjects

2380
01:49:39,350 --> 01:49:33,910
the women the females

2381
01:49:43,350 --> 01:49:41,589
that was back in the 50s or i don't know

2382
01:49:47,030 --> 01:49:43,360
exactly when but there was a long time

2383
01:49:49,750 --> 01:49:47,040
ago they figured hey that's impossible

2384
01:49:51,830 --> 01:49:49,760
uh and then they tweaked the tests again

2385
01:49:54,470 --> 01:49:51,840
a bit they changed the nature of the

2386
01:49:56,950 --> 01:49:54,480
questions they asked them differently

2387
01:50:02,709 --> 01:49:56,960
until they finally were able

2388
01:50:05,750 --> 01:50:02,719
to uh to make um uh men uh equal or

2389
01:50:08,229 --> 01:50:05,760
maybe better i don't know than women

2390
01:50:12,149 --> 01:50:08,239
and again this is true

2391
01:50:15,189 --> 01:50:12,159
to a certain system of education in a

2392
01:50:16,950 --> 01:50:15,199
certain time

2393
01:50:19,669 --> 01:50:16,960
right

2394
01:50:22,070 --> 01:50:19,679
men and women did not receive the same

2395
01:50:22,950 --> 01:50:22,080
education

2396
01:50:25,350 --> 01:50:22,960
uh

2397
01:50:27,589 --> 01:50:25,360
it would have been easy to do to

2398
01:50:28,550 --> 01:50:27,599
distinguish

2399
01:50:31,030 --> 01:50:28,560
because

2400
01:50:33,030 --> 01:50:31,040
they came as as their backgrounds were

2401
01:50:36,229 --> 01:50:33,040
different

2402
01:50:37,589 --> 01:50:36,239
uh so you could arrange

2403
01:50:39,510 --> 01:50:37,599
uh

2404
01:50:40,790 --> 01:50:39,520
such things

2405
01:50:42,550 --> 01:50:40,800
okay

2406
01:50:50,709 --> 01:50:42,560
uh

2407
01:50:54,709 --> 01:50:53,109
that's about the value of iq

2408
01:50:56,709 --> 01:50:54,719
of iq scores

2409
01:50:58,870 --> 01:50:56,719
okay they were

2410
01:51:02,070 --> 01:50:58,880
i mean

2411
01:51:03,910 --> 01:51:02,080
to some extent they measured something

2412
01:51:06,149 --> 01:51:03,920
to some extent they were cooked to

2413
01:51:10,550 --> 01:51:06,159
measure whatever people wanted them to

2414
01:51:13,990 --> 01:51:12,070
not much to learn from these

2415
01:51:15,669 --> 01:51:14,000
measurements

2416
01:51:18,550 --> 01:51:15,679
tori cole has

2417
01:51:21,589 --> 01:51:18,560
a question what do you think of biology

2418
01:51:23,510 --> 01:51:21,599
slash psychology slash philosophy

2419
01:51:25,669 --> 01:51:23,520
i think they're fun i think they're

2420
01:51:27,990 --> 01:51:25,679
foundational to understanding myself and

2421
01:51:29,990 --> 01:51:28,000
therefore my experience of the universe

2422
01:51:31,830 --> 01:51:30,000
do you think you would gain much of an

2423
01:51:34,310 --> 01:51:31,840
understanding

2424
01:51:37,750 --> 01:51:34,320
of an exploration from those fields to

2425
01:51:44,390 --> 01:51:39,830
again biology

2426
01:51:47,589 --> 01:51:45,189
i mean

2427
01:51:51,510 --> 01:51:47,599
they're all interesting fields i am not

2428
01:51:56,229 --> 01:51:54,709
what more to say you know

2429
01:51:57,910 --> 01:51:56,239
do you think there are insights there

2430
01:52:00,310 --> 01:51:57,920
that if you were to read a biology book

2431
01:52:01,430 --> 01:52:00,320
a psychology book perhaps a philosophy

2432
01:52:03,030 --> 01:52:01,440
book

2433
01:52:04,470 --> 01:52:03,040
do you think there are insights to be

2434
01:52:09,910 --> 01:52:04,480
gleaned from there that you can then

2435
01:52:09,920 --> 01:52:14,709
there are connections here and there

2436
01:52:14,719 --> 01:52:18,629
um

2437
01:52:23,830 --> 01:52:20,709
much of mathematics is independent of

2438
01:52:25,630 --> 01:52:25,270
uh

2439
01:52:28,870 --> 01:52:25,640
so

2440
01:52:33,430 --> 01:52:30,870
obviously

2441
01:52:36,149 --> 01:52:33,440
biology motivates parts of mathematics

2442
01:52:40,229 --> 01:52:36,159
so parts of mathematics

2443
01:52:46,070 --> 01:52:42,950
you know are about modeling biological

2444
01:52:49,510 --> 01:52:47,109
when we

2445
01:52:52,550 --> 01:52:49,520
compute the fibonacci numbers we give

2446
01:52:54,070 --> 01:52:52,560
examples of uh the reproduction rules of

2447
01:52:55,830 --> 01:52:54,080
rabbits

2448
01:52:57,589 --> 01:52:55,840
okay

2449
01:53:00,870 --> 01:52:57,599
and and then there is much more like

2450
01:53:04,629 --> 01:53:00,880
that and and then um

2451
01:53:07,669 --> 01:53:06,149
uh

2452
01:53:09,589 --> 01:53:07,679
but

2453
01:53:12,790 --> 01:53:09,599
and likewise and and and of course

2454
01:53:14,310 --> 01:53:12,800
philosophy so you know there are

2455
01:53:16,310 --> 01:53:14,320
bits of mathematics of great

2456
01:53:19,750 --> 01:53:16,320
philosophical values so

2457
01:53:20,629 --> 01:53:19,760
you know gideon's theorem says

2458
01:53:22,629 --> 01:53:20,639
uh

2459
01:53:25,510 --> 01:53:22,639
that there are all there will always be

2460
01:53:28,229 --> 01:53:25,520
things we do not we will not know

2461
01:53:31,510 --> 01:53:28,239
okay or said diff or or differently i

2462
01:53:34,070 --> 01:53:31,520
know there is no algorithm to decide

2463
01:53:41,270 --> 01:53:37,910
to find the proofs of theorems

2464
01:53:43,350 --> 01:53:41,280
uh these things have philosophical value

2465
01:53:44,790 --> 01:53:43,360
okay

2466
01:53:48,149 --> 01:53:44,800
uh

2467
01:53:49,030 --> 01:53:48,159
for most mathematicians it's not

2468
01:53:59,910 --> 01:53:49,040
a

2469
01:54:00,950 --> 01:53:59,920
benefits very little

2470
01:54:01,910 --> 01:54:00,960
if any

2471
01:54:04,229 --> 01:54:01,920
from the

2472
01:54:05,830 --> 01:54:04,239
from contact with biology

2473
01:54:11,750 --> 01:54:05,840
uh

2474
01:54:16,470 --> 01:54:13,910
okay phil thomas wants to know what led

2475
01:54:19,030 --> 01:54:16,480
him what led you professor to the field

2476
01:54:21,030 --> 01:54:19,040
of mathematics and is your field

2477
01:54:28,470 --> 01:54:21,040
something you think virtually anyone can

2478
01:54:28,480 --> 01:54:32,470
what led me there

2479
01:54:35,510 --> 01:54:33,430
you know

2480
01:54:37,830 --> 01:54:35,520
it's a question about my life story

2481
01:54:40,070 --> 01:54:37,840
right so what led me there is essentia

2482
01:54:48,310 --> 01:54:40,080
is is

2483
01:54:53,030 --> 01:54:50,750
a sequence of uh coincidences and

2484
01:54:54,870 --> 01:54:53,040
misunderstandings i don't know

2485
01:54:55,830 --> 01:54:54,880
a number of things but

2486
01:54:56,790 --> 01:54:55,840
so

2487
01:54:59,669 --> 01:54:56,800
um

2488
01:55:01,430 --> 01:54:59,679
to some extent to some extent i was good

2489
01:55:03,350 --> 01:55:01,440
at that

2490
01:55:11,990 --> 01:55:03,360
and that

2491
01:55:14,030 --> 01:55:12,000
many things right people tend to do what

2492
01:55:15,589 --> 01:55:14,040
they're good at

2493
01:55:18,149 --> 01:55:15,599
misunderstandings you said

2494
01:55:21,109 --> 01:55:18,159
misunderstandings as well yes to some

2495
01:55:23,270 --> 01:55:21,119
extent uh

2496
01:55:25,030 --> 01:55:23,280
i misunderstood math

2497
01:55:27,350 --> 01:55:25,040
so

2498
01:55:31,830 --> 01:55:27,360
you know there was a time that i really

2499
01:55:34,950 --> 01:55:31,840
liked uh computers and electronics

2500
01:55:36,790 --> 01:55:34,960
i uh at some point

2501
01:55:39,109 --> 01:55:36,800
realized that there is a lot of kind of

2502
01:55:40,390 --> 01:55:39,119
hard work in it

2503
01:55:43,189 --> 01:55:40,400
so

2504
01:55:47,910 --> 01:55:45,589
writing a computer program is very hard

2505
01:55:49,510 --> 01:55:47,920
you have to write hundreds of lines of

2506
01:55:51,669 --> 01:55:49,520
code and then

2507
01:55:54,310 --> 01:55:51,679
debug them and they whatever and

2508
01:55:56,550 --> 01:55:54,320
similarly for electronics right you have

2509
01:55:59,350 --> 01:55:56,560
to place those transistors on the board

2510
01:56:01,350 --> 01:55:59,360
and solder them together and

2511
01:56:03,109 --> 01:56:01,360
solder them together and

2512
01:56:05,270 --> 01:56:03,119
and you always get it wrong and you know

2513
01:56:07,510 --> 01:56:05,280
there is a lot of hard work where

2514
01:56:10,709 --> 01:56:07,520
mathematics is so much easier all you

2515
01:56:12,470 --> 01:56:10,719
have to do is to prove theorems

2516
01:56:16,070 --> 01:56:12,480
that was a complete misunderstanding i

2517
01:56:17,589 --> 01:56:16,080
mean i thought it was like much purer

2518
01:56:19,910 --> 01:56:17,599
uh i didn't

2519
01:56:23,189 --> 01:56:19,920
at the time i didn't realize how much

2520
01:56:24,950 --> 01:56:23,199
hard work is involved

2521
01:56:27,109 --> 01:56:24,960
so in some sense i got there i go to

2522
01:56:29,750 --> 01:56:27,119
mathematics by misunderstanding by being

2523
01:56:31,270 --> 01:56:29,760
lazy and not realizing that

2524
01:56:33,750 --> 01:56:31,280
i'm i'm

2525
01:56:35,750 --> 01:56:33,760
getting trapped into into a place where

2526
01:56:38,790 --> 01:56:35,760
laziness is is not

2527
01:56:41,270 --> 01:56:38,800
it is is not always enough

2528
01:56:44,470 --> 01:56:41,280
and also at the end i ended up liking

2529
01:56:48,149 --> 01:56:44,480
those parts that i first thought i was

2530
01:56:50,550 --> 01:56:48,159
going away from namely computation

2531
01:56:52,870 --> 01:56:50,560
so i ended up i mean computation to me

2532
01:56:54,870 --> 01:56:52,880
was like a childhood thing and a later

2533
01:56:56,709 --> 01:56:54,880
acquired taste

2534
01:56:58,550 --> 01:56:56,719
there was a period in between when in

2535
01:57:02,070 --> 01:56:58,560
between when i thought i was pure i

2536
01:57:02,080 --> 01:57:05,350
um

2537
01:57:09,109 --> 01:57:07,750
right what else did i answer or did i

2538
01:57:11,830 --> 01:57:09,119
mean there was a second part to the

2539
01:57:13,750 --> 01:57:11,840
question do you believe that your field

2540
01:57:15,189 --> 01:57:13,760
either the field of mathematics or your

2541
01:57:17,189 --> 01:57:15,199
subfield the one that you're working in

2542
01:57:19,270 --> 01:57:17,199
currently do you feel that your field is

2543
01:57:22,229 --> 01:57:19,280
something that virtually anyone can

2544
01:57:22,239 --> 01:57:25,589
no

2545
01:57:33,589 --> 01:57:26,390
uh

2546
01:57:42,950 --> 01:57:36,830
some

2547
01:57:47,510 --> 01:57:44,709
everybody can learn

2548
01:57:49,669 --> 01:57:47,520
and everybody should learn

2549
01:57:54,470 --> 01:57:49,679
and maybe it's more

2550
01:57:57,189 --> 01:57:54,480
than what is taught in uh

2551
01:58:00,390 --> 01:57:57,199
in our current educational system

2552
01:58:01,669 --> 01:58:00,400
education system okay

2553
01:58:03,350 --> 01:58:01,679
uh

2554
01:58:12,070 --> 01:58:03,360
but

2555
01:58:17,589 --> 01:58:13,189
you know i

2556
01:58:17,599 --> 01:58:21,189
okay

2557
01:58:29,510 --> 01:58:21,990
the

2558
01:58:32,310 --> 01:58:29,520
which he knows things

2559
01:58:35,910 --> 01:58:32,320
i'll never get there

2560
01:58:36,870 --> 01:58:35,920
it's not i'm not talented enough to get

2561
01:58:40,470 --> 01:58:36,880
there

2562
01:58:43,270 --> 01:58:40,480
it might be that in my 30 years in the

2563
01:58:45,750 --> 01:58:43,280
subject i've learned things that uh

2564
01:58:49,350 --> 01:58:45,760
most people

2565
01:58:56,149 --> 01:58:49,360
also wouldn't be able to catch up with

2566
01:58:59,990 --> 01:58:57,430
you know

2567
01:59:01,589 --> 01:59:00,000
there is the mushizuki proof of the abc

2568
01:59:03,750 --> 01:59:01,599
conjecture

2569
01:59:06,470 --> 01:59:03,760
disputed

2570
01:59:08,950 --> 01:59:06,480
okay moshizuki claims it's a proof other

2571
01:59:10,950 --> 01:59:08,960
people think it isn't

2572
01:59:13,669 --> 01:59:10,960
i will never be in the position to

2573
01:59:17,589 --> 01:59:13,679
understand that

2574
01:59:21,830 --> 01:59:20,149
possibly if i started early enough i'm

2575
01:59:24,070 --> 01:59:21,840
not even sure

2576
01:59:26,950 --> 01:59:24,080
i happen to know moshizuki i remember

2577
01:59:29,750 --> 01:59:26,960
him when he was young we we were friends

2578
01:59:31,109 --> 01:59:29,760
when like we went we're went to graduate

2579
01:59:32,550 --> 01:59:31,119
school together

2580
01:59:35,669 --> 01:59:32,560
so i uh

2581
01:59:38,470 --> 01:59:35,679
so i remember him when he was young

2582
01:59:40,550 --> 01:59:38,480
he was smarter and faster than me

2583
01:59:42,470 --> 01:59:40,560
it's conceivable that after 20 years

2584
01:59:45,030 --> 01:59:42,480
he's gone so far

2585
01:59:47,910 --> 01:59:45,040
that i will never be able to catch up

2586
01:59:49,430 --> 01:59:47,920
it's equally possible that

2587
01:59:52,229 --> 01:59:49,440
there are people who would never be able

2588
01:59:52,930 --> 01:59:52,239
to catch up with me

2589
01:59:55,109 --> 01:59:52,940
um

2590
01:59:57,990 --> 01:59:55,119
[Music]

2591
02:00:01,910 --> 01:59:58,000
they said

2592
02:00:01,920 --> 02:00:05,669
is useful to everybody

2593
02:00:10,629 --> 02:00:07,750
you know

2594
02:00:12,310 --> 02:00:10,639
we're we're now in the in the midst of a

2595
02:00:14,790 --> 02:00:12,320
pandemic

2596
02:00:16,790 --> 02:00:14,800
understanding what's the exponential

2597
02:00:21,750 --> 02:00:16,800
function

2598
02:00:25,350 --> 02:00:23,669
is basic knowledge is something that

2599
02:00:26,709 --> 02:00:25,360
every human should

2600
02:00:29,350 --> 02:00:26,719
should have

2601
02:00:31,189 --> 02:00:29,360
because it actually dictates if it tells

2602
02:00:33,189 --> 02:00:31,199
us something

2603
02:00:35,750 --> 02:00:33,199
about how to behave

2604
02:00:37,910 --> 02:00:35,760
uh at this time

2605
02:00:41,350 --> 02:00:37,920
uh

2606
02:00:43,030 --> 02:00:41,360
likewise making various probabilistic

2607
02:00:46,550 --> 02:00:43,040
estimates

2608
02:00:52,870 --> 02:00:49,510
if the chance of such and such type of

2609
02:00:55,750 --> 02:00:52,880
side effects is is one in a million what

2610
02:00:57,750 --> 02:00:55,760
does it mean

2611
02:01:00,149 --> 02:00:57,760
what does one in a million means in

2612
02:01:01,830 --> 02:01:00,159
practical term for me terms for me

2613
02:01:04,149 --> 02:01:01,840
should i fear it

2614
02:01:07,189 --> 02:01:04,159
or is it so remote that i have that i

2615
02:01:14,070 --> 02:01:11,109
so basic numeracy is is is is an

2616
02:01:15,189 --> 02:01:14,080
absolute necessary ingredient and for

2617
02:01:19,589 --> 02:01:15,199
everyone

2618
02:01:21,430 --> 02:01:19,599
when you mentioned that you'll never be

2619
02:01:22,629 --> 02:01:21,440
able to catch up to whitten and may

2620
02:01:25,030 --> 02:01:22,639
perhaps some people won't be able to

2621
02:01:27,189 --> 02:01:25,040
catch up to you and so on

2622
02:01:29,189 --> 02:01:27,199
what is that a function of biology you

2623
02:01:31,430 --> 02:01:29,199
mentioned the word talent so is it is

2624
02:01:33,589 --> 02:01:31,440
that just innate is

2625
02:01:36,390 --> 02:01:33,599
is what's innate called intelligence is

2626
02:01:37,910 --> 02:01:36,400
that associated with iq like what are

2627
02:01:40,070 --> 02:01:37,920
you referring to when you say you won't

2628
02:01:43,350 --> 02:01:40,080
be able to catch up

2629
02:01:45,589 --> 02:01:43,360
it's a number of things

2630
02:01:47,990 --> 02:01:45,599
you can call it talent

2631
02:01:50,870 --> 02:01:48,000
you can call it iq if you wish but of

2632
02:01:53,109 --> 02:01:50,880
course there is no numerical measurement

2633
02:02:01,350 --> 02:01:53,119
and it's a much much more complicated

2634
02:02:08,870 --> 02:02:03,750
you know so much of

2635
02:02:12,790 --> 02:02:10,790
depends on how much you concentrate on

2636
02:02:15,750 --> 02:02:12,800
mathematics

2637
02:02:20,149 --> 02:02:15,760
so you know uh

2638
02:02:25,109 --> 02:02:22,629
if at a certain part of your life you're

2639
02:02:28,870 --> 02:02:25,119
able to completely isolate yourself and

2640
02:02:31,510 --> 02:02:28,880
think on nothing but mathematics

2641
02:02:33,910 --> 02:02:31,520
you'll end up knowing more mathematics

2642
02:02:35,030 --> 02:02:33,920
than if you are also a human a human

2643
02:02:39,350 --> 02:02:35,040
along

2644
02:02:40,550 --> 02:02:39,360
okay uh

2645
02:02:53,470 --> 02:02:40,560
so

2646
02:02:57,910 --> 02:02:55,669
circumstance and

2647
02:02:59,669 --> 02:02:57,920
uh

2648
02:03:03,189 --> 02:02:59,679
and luck

2649
02:03:09,589 --> 02:03:06,870
in some sense being narrow-minded

2650
02:03:12,149 --> 02:03:09,599
so now being narrow-minded helps in

2651
02:03:15,430 --> 02:03:12,159
certain ways

2652
02:03:18,709 --> 02:03:17,669
speaking of eric weinstein you mentioned

2653
02:03:19,910 --> 02:03:18,719
him

2654
02:03:20,709 --> 02:03:19,920
okay so

2655
02:03:25,510 --> 02:03:20,719
so

2656
02:03:28,629 --> 02:03:25,520
talent for certain kind of things and

2657
02:03:30,149 --> 02:03:28,639
great fear of others

2658
02:03:32,310 --> 02:03:30,159
and

2659
02:03:35,270 --> 02:03:32,320
maybe he would have been a much more

2660
02:03:38,229 --> 02:03:35,280
famous mathematician physicist now

2661
02:03:40,830 --> 02:03:38,239
if if it wasn't for these

2662
02:03:44,550 --> 02:03:40,840
coincidences

2663
02:03:48,390 --> 02:03:45,669
i don't know

2664
02:03:54,950 --> 02:03:50,069
you could call it

2665
02:03:57,350 --> 02:03:54,960
uh learn you can call it many things but

2666
02:03:59,589 --> 02:03:57,360
it's a very complicated combination of

2667
02:04:01,830 --> 02:03:59,599
things

2668
02:04:03,830 --> 02:04:01,840
tyler goldstein has a question

2669
02:04:05,910 --> 02:04:03,840
do you think we need to make new

2670
02:04:07,990 --> 02:04:05,920
research institutions that aren't linked

2671
02:04:11,109 --> 02:04:08,000
to academia

2672
02:04:12,709 --> 02:04:11,119
and i imagine what he's referring to

2673
02:04:14,390 --> 02:04:12,719
is something that weinstein has brought

2674
02:04:16,709 --> 02:04:14,400
up in wolfram as well

2675
02:04:18,550 --> 02:04:16,719
they're not huge fans of the peer review

2676
02:04:20,390 --> 02:04:18,560
process or at least they're not huge

2677
02:04:21,830 --> 02:04:20,400
fans of only

2678
02:04:23,270 --> 02:04:21,840
thinking that work

2679
02:04:25,589 --> 02:04:23,280
is worth it if it's gone through the

2680
02:04:27,510 --> 02:04:25,599
peer review process

2681
02:04:29,589 --> 02:04:27,520
and

2682
02:04:31,669 --> 02:04:29,599
while that's associated with academia

2683
02:04:40,550 --> 02:04:31,679
i'm curious if you have any thoughts as

2684
02:04:44,149 --> 02:04:42,470
well there are things outside of

2685
02:04:46,709 --> 02:04:44,159
academia

2686
02:04:50,470 --> 02:04:48,950
arguably most research is done outside

2687
02:04:52,310 --> 02:04:50,480
of academia

2688
02:04:55,350 --> 02:04:52,320
i mean you know there are a lot of a lot

2689
02:04:56,950 --> 02:04:55,360
of research is done inside companies

2690
02:04:59,430 --> 02:04:56,960
inside

2691
02:05:03,189 --> 02:04:59,440
well a lot of research is done outside

2692
02:05:03,199 --> 02:05:08,149
um

2693
02:05:12,310 --> 02:05:10,470
but overall i think the system is

2694
02:05:14,390 --> 02:05:12,320
reasonable

2695
02:05:17,910 --> 02:05:14,400
sorry overall you think the system is i

2696
02:05:19,270 --> 02:05:17,920
think the system is reasonable

2697
02:05:23,589 --> 02:05:19,280
so

2698
02:05:26,069 --> 02:05:23,599
uh you know you can um

2699
02:05:27,669 --> 02:05:26,079
say bad things as much as you want about

2700
02:05:32,390 --> 02:05:27,679
peer review

2701
02:05:32,400 --> 02:05:36,870
it's better than having no review

2702
02:05:36,880 --> 02:05:41,030
um

2703
02:05:44,069 --> 02:05:42,870
you can say

2704
02:05:46,229 --> 02:05:44,079
uh

2705
02:05:47,990 --> 02:05:46,239
maybe mathematical should be more

2706
02:05:50,790 --> 02:05:48,000
hierarchical

2707
02:05:51,830 --> 02:05:50,800
okay there should be big bosses

2708
02:05:54,310 --> 02:05:51,840
who

2709
02:05:56,069 --> 02:05:54,320
determine which theorems we should be

2710
02:06:00,550 --> 02:05:56,079
proving

2711
02:06:04,069 --> 02:06:01,669
have their

2712
02:06:06,870 --> 02:06:04,079
smaller bosses who would be responsible

2713
02:06:09,109 --> 02:06:06,880
to specific theorems and they would be

2714
02:06:11,109 --> 02:06:09,119
the big bosses of other people who would

2715
02:06:12,870 --> 02:06:11,119
be proving dilemmas

2716
02:06:15,350 --> 02:06:12,880
you could say something like that it

2717
02:06:17,510 --> 02:06:15,360
sounds like it sounds ridiculous it

2718
02:06:18,950 --> 02:06:17,520
would work just as ridiculously as it

2719
02:06:21,750 --> 02:06:18,960
sounds

2720
02:06:23,350 --> 02:06:21,760
current system is

2721
02:06:25,030 --> 02:06:23,360
you know

2722
02:06:29,910 --> 02:06:25,040
given

2723
02:06:31,669 --> 02:06:29,920
reasonably good i believe there are some

2724
02:06:33,830 --> 02:06:31,679
arguments to say that

2725
02:06:36,229 --> 02:06:33,840
the what you just outlined is

2726
02:06:39,510 --> 02:06:36,239
somewhat like it happens given grant

2727
02:06:41,669 --> 02:06:39,520
agencies they have some field that they

2728
02:06:43,589 --> 02:06:41,679
fund and so then the research tends to

2729
02:06:46,390 --> 02:06:43,599
go toward there so you can view them as

2730
02:06:48,470 --> 02:06:46,400
the large boss and i believe lee smallin

2731
02:06:50,629 --> 02:06:48,480
makes some arguments saying that that's

2732
02:06:52,790 --> 02:06:50,639
why string theory is as large as as it

2733
02:06:54,390 --> 02:06:52,800
is even though it shouldn't be because

2734
02:06:56,629 --> 02:06:54,400
we haven't seen much success from it and

2735
02:06:58,709 --> 02:06:56,639
so on so do you see what you just

2736
02:07:00,790 --> 02:06:58,719
outlined as the ridiculous scenario do

2737
02:07:06,790 --> 02:07:00,800
you see that as having any bearing to

2738
02:07:06,800 --> 02:07:09,109
so

2739
02:07:09,119 --> 02:07:18,149
yes of course there is bias

2740
02:07:23,430 --> 02:07:21,189
generated by the granting agencies by

2741
02:07:25,990 --> 02:07:23,440
the powerful people

2742
02:07:29,030 --> 02:07:26,000
be them be them the writing granting

2743
02:07:31,189 --> 02:07:29,040
agencies or the editorial boards of

2744
02:07:33,750 --> 02:07:31,199
journals

2745
02:07:37,030 --> 02:07:33,760
so you know

2746
02:07:40,069 --> 02:07:37,040
if you publish if you have a result

2747
02:07:43,030 --> 02:07:40,079
uh that somebody on the editorial board

2748
02:07:44,310 --> 02:07:43,040
of an excellent journal uh

2749
02:07:46,310 --> 02:07:44,320
likes

2750
02:07:48,390 --> 02:07:46,320
you know that's close to the field of

2751
02:07:50,550 --> 02:07:48,400
somebody in the editorial board of an

2752
02:07:52,470 --> 02:07:50,560
excellent excellent journal then your

2753
02:07:56,550 --> 02:07:52,480
result is much more likely to get

2754
02:07:58,470 --> 02:07:56,560
published in this uh excellent journal

2755
02:08:01,830 --> 02:07:58,480
and then you're much more likely to get

2756
02:08:04,550 --> 02:08:01,840
tenure and then

2757
02:08:06,629 --> 02:08:04,560
more work will be produced in that field

2758
02:08:09,030 --> 02:08:06,639
and you'll advise students who will

2759
02:08:11,189 --> 02:08:09,040
produce even more more work on that

2760
02:08:16,470 --> 02:08:11,199
field

2761
02:08:16,480 --> 02:08:20,229
but

2762
02:08:25,270 --> 02:08:22,310
it's not clear that you can think of a

2763
02:08:27,589 --> 02:08:25,280
better alternative

2764
02:08:30,149 --> 02:08:27,599
and also

2765
02:08:33,750 --> 02:08:30,159
there is still some amount of academic

2766
02:08:37,510 --> 02:08:33,760
freedom so the granting agency

2767
02:08:41,270 --> 02:08:37,520
decides once every five years

2768
02:08:49,109 --> 02:08:46,069
in those five years some of my time i do

2769
02:08:51,430 --> 02:08:49,119
what is necessary to get my next grant

2770
02:08:54,470 --> 02:08:51,440
but some of the time i also do things

2771
02:08:55,990 --> 02:08:54,480
that i think are useful that i think are

2772
02:08:58,390 --> 02:08:56,000
useful

2773
02:08:59,350 --> 02:08:58,400
uh likewise

2774
02:09:02,709 --> 02:08:59,360
uh

2775
02:09:05,350 --> 02:09:02,719
you know some of my career

2776
02:09:09,589 --> 02:09:05,360
is is determined by which journal i

2777
02:09:12,470 --> 02:09:09,599
publish in but some is determined by

2778
02:09:14,069 --> 02:09:12,480
uh other factors

2779
02:09:16,390 --> 02:09:14,079
okay by the results that aren't

2780
02:09:19,750 --> 02:09:16,400
published by the lectures that i give in

2781
02:09:23,109 --> 02:09:19,760
conferences in china you know

2782
02:09:24,870 --> 02:09:23,119
it's much more multi-dimensional

2783
02:09:27,189 --> 02:09:24,880
than uh

2784
02:09:31,830 --> 02:09:27,199
than just having a boss and the boss is

2785
02:09:35,830 --> 02:09:33,910
even the fact that the editorial boards

2786
02:09:39,030 --> 02:09:35,840
are different than the review boards of

2787
02:09:40,950 --> 02:09:39,040
the granting agencies allows make some

2788
02:09:43,910 --> 02:09:40,960
variety

2789
02:09:47,350 --> 02:09:43,920
and again what is the alternative

2790
02:09:52,149 --> 02:09:50,069
one stupid alternative would be to say

2791
02:09:54,709 --> 02:09:52,159
to allow anyone to say

2792
02:09:57,910 --> 02:09:54,719
i am a mathematician

2793
02:10:01,350 --> 02:09:57,920
uh here is my proof that

2794
02:10:03,750 --> 02:10:01,360
pi is rational

2795
02:10:05,910 --> 02:10:03,760
or that you can

2796
02:10:08,709 --> 02:10:05,920
divide you know

2797
02:10:10,310 --> 02:10:08,719
here is my proof of the uh goldbach

2798
02:10:13,189 --> 02:10:10,320
conjecture

2799
02:10:15,350 --> 02:10:13,199
who's arguing with me i'm saying it's a

2800
02:10:20,390 --> 02:10:15,360
proof

2801
02:10:25,750 --> 02:10:23,189
it's much better not to lose control

2802
02:10:27,510 --> 02:10:25,760
completely

2803
02:10:29,669 --> 02:10:27,520
you just use the word mathematician and

2804
02:10:31,350 --> 02:10:29,679
i'm curious what do you see as a

2805
02:10:33,109 --> 02:10:31,360
mathematician is it someone who's a

2806
02:10:35,669 --> 02:10:33,119
professor of math is this someone who

2807
02:10:37,750 --> 02:10:35,679
gets their masters or phd do you have to

2808
02:10:39,510 --> 02:10:37,760
frequently publish research in order for

2809
02:10:40,790 --> 02:10:39,520
you to call yourself a mathematician

2810
02:10:43,830 --> 02:10:40,800
like what gives

2811
02:10:47,350 --> 02:10:43,840
obviously it's a nebulous term but it's

2812
02:10:49,589 --> 02:10:47,360
not extremely amorphous it's defined

2813
02:10:53,990 --> 02:10:49,599
so what do you define it as

2814
02:11:02,950 --> 02:10:55,030
you know

2815
02:11:09,430 --> 02:11:05,270
many definitions don't have sharp

2816
02:11:12,390 --> 02:11:09,440
boundaries in fact only in mathematics

2817
02:11:14,709 --> 02:11:12,400
uh there are sharp boundaries between

2818
02:11:17,270 --> 02:11:14,719
things like either

2819
02:11:20,229 --> 02:11:17,280
the series is convergent or it is not

2820
02:11:21,750 --> 02:11:20,239
convergent but only and there is a very

2821
02:11:24,310 --> 02:11:21,760
very specific

2822
02:11:26,790 --> 02:11:24,320
uh criteria to decide only in

2823
02:11:28,950 --> 02:11:26,800
mathematics there are

2824
02:11:30,709 --> 02:11:28,960
uh sharp boundaries and now you're

2825
02:11:32,310 --> 02:11:30,719
asking a meta-mathematical question

2826
02:11:33,830 --> 02:11:32,320
you're asking a question about

2827
02:11:36,390 --> 02:11:33,840
mathematics not a question in

2828
02:11:38,550 --> 02:11:36,400
mathematics so there aren't

2829
02:11:39,990 --> 02:11:38,560
sharp boundaries so basically all of the

2830
02:11:41,990 --> 02:11:40,000
above you know

2831
02:11:44,709 --> 02:11:42,000
if you teach mathematics if you think a

2832
02:11:47,510 --> 02:11:44,719
lot about mathematics if your way of

2833
02:11:50,830 --> 02:11:47,520
thought is abstraction

2834
02:11:50,840 --> 02:11:54,950
proof um

2835
02:12:00,709 --> 02:11:57,589
you know then that's mathematics but

2836
02:12:03,350 --> 02:12:00,719
but but you can always

2837
02:12:05,589 --> 02:12:03,360
you can always find the borderline

2838
02:12:07,830 --> 02:12:05,599
things that will be hard to decide

2839
02:12:09,270 --> 02:12:07,840
here's a reason why i'm asking because

2840
02:12:11,350 --> 02:12:09,280
not everyone can call themselves a

2841
02:12:13,589 --> 02:12:11,360
doctor i know that some people they get

2842
02:12:15,350 --> 02:12:13,599
their md and then they're no longer

2843
02:12:16,950 --> 02:12:15,360
practicing researchers they no longer

2844
02:12:18,870 --> 02:12:16,960
are connected with the field but then

2845
02:12:20,470 --> 02:12:18,880
they'll give health advice resting on

2846
02:12:21,910 --> 02:12:20,480
the laurel that they have an md and

2847
02:12:22,950 --> 02:12:21,920
they'll say well this comes from a

2848
02:12:25,350 --> 02:12:22,960
doctor

2849
02:12:27,270 --> 02:12:25,360
and i'm sure the same occurs in

2850
02:12:29,189 --> 02:12:27,280
mathematics though

2851
02:12:31,030 --> 02:12:29,199
to a much lesser degree same with

2852
02:12:33,109 --> 02:12:31,040
physics someone may say well i'm a

2853
02:12:36,149 --> 02:12:33,119
physicist because i

2854
02:12:37,990 --> 02:12:36,159
i have a degree from a university but

2855
02:12:40,229 --> 02:12:38,000
that in physics but that doesn't

2856
02:12:41,669 --> 02:12:40,239
necessarily make you a physicist doesn't

2857
02:12:43,669 --> 02:12:41,679
mean your physics works should be taken

2858
02:12:47,350 --> 02:12:43,679
more seriously because you have that

2859
02:12:52,470 --> 02:12:49,990
if you're so if you're looking for a

2860
02:12:54,550 --> 02:12:52,480
set of thumb rules

2861
02:12:57,510 --> 02:12:54,560
to decide uh

2862
02:12:59,510 --> 02:12:57,520
uh which experts are to be trusted and

2863
02:13:02,310 --> 02:12:59,520
which should not

2864
02:13:07,430 --> 02:13:02,320
be them experts in mathematics or

2865
02:13:13,910 --> 02:13:09,669
well the answer is these questions are

2866
02:13:13,920 --> 02:13:23,510
so you know in medicine uh

2867
02:13:28,470 --> 02:13:25,990
you probably have to look for the bigger

2868
02:13:30,870 --> 02:13:28,480
name doctors the more you know the more

2869
02:13:33,030 --> 02:13:30,880
established doctors because

2870
02:13:37,270 --> 02:13:33,040
the system actually does

2871
02:13:40,470 --> 02:13:37,280
on average promote the better people

2872
02:13:43,350 --> 02:13:40,480
even if not always

2873
02:13:46,149 --> 02:13:43,360
okay and you should look for

2874
02:13:47,910 --> 02:13:46,159
was it said by

2875
02:13:50,390 --> 02:13:47,920
most doctors

2876
02:13:52,709 --> 02:13:50,400
or by

2877
02:13:54,390 --> 02:13:52,719
one doctor who hasn't practiced for a

2878
02:13:57,830 --> 02:13:54,400
long time

2879
02:14:03,109 --> 02:13:59,589
and the same is in

2880
02:14:08,310 --> 02:14:05,270
uh

2881
02:14:11,270 --> 02:14:08,320
yes there are phd in mathematic people

2882
02:14:13,910 --> 02:14:11,280
with a phd in mathematics who who who

2883
02:14:16,229 --> 02:14:13,920
shouldn't have gotten their phd

2884
02:14:19,750 --> 02:14:16,239
yes there are people brilliant people

2885
02:14:22,229 --> 02:14:19,760
with bro who did real brilliant phd phds

2886
02:14:25,189 --> 02:14:22,239
in mathematics and 10 years later

2887
02:14:27,430 --> 02:14:25,199
uh lost their mind and are

2888
02:14:29,669 --> 02:14:27,440
speaking nonsense

2889
02:14:31,270 --> 02:14:29,679
i mean

2890
02:14:33,589 --> 02:14:31,280
it's

2891
02:14:37,030 --> 02:14:33,599
there is no look at this certificate and

2892
02:14:38,830 --> 02:14:37,040
if somebody has the certificate then

2893
02:14:41,750 --> 02:14:38,840
then they're

2894
02:14:43,510 --> 02:14:41,760
trustworthy ashley ship wants to know is

2895
02:14:45,589 --> 02:14:43,520
there a connection between not theory

2896
02:14:47,830 --> 02:14:45,599
and protein folding

2897
02:14:49,510 --> 02:14:47,840
and is it possible to use

2898
02:14:51,589 --> 02:14:49,520
well if so is it possible to use the

2899
02:14:53,830 --> 02:14:51,599
artificial intelligence research that

2900
02:14:57,990 --> 02:14:53,840
has been done on protein folding to

2901
02:15:03,510 --> 02:15:00,229
there is a connection between protein

2902
02:15:06,950 --> 02:15:03,520
folding and between dna and stuff like

2903
02:15:11,589 --> 02:15:09,589
in in not theory

2904
02:15:14,390 --> 02:15:11,599
uh people

2905
02:15:16,950 --> 02:15:14,400
it's not very strong

2906
02:15:20,629 --> 02:15:16,960
like in general

2907
02:15:20,639 --> 02:15:24,390
he

2908
02:15:29,510 --> 02:15:26,870
people like to say things about it but

2909
02:15:32,310 --> 02:15:29,520
the actual research at least my own

2910
02:15:35,990 --> 02:15:32,320
research is very different

2911
02:15:38,790 --> 02:15:36,000
from um

2912
02:15:43,510 --> 02:15:38,800
what you would end up doing with

2913
02:15:48,069 --> 02:15:46,790
of dnas or or proteins

2914
02:15:49,510 --> 02:15:48,079
by the way

2915
02:15:54,310 --> 02:15:49,520
uh

2916
02:15:57,109 --> 02:15:54,320
dna

2917
02:15:58,229 --> 02:15:57,119
the the study or

2918
02:16:00,229 --> 02:15:58,239
okay

2919
02:16:03,350 --> 02:16:00,239
so

2920
02:16:05,510 --> 02:16:03,360
dna molecules are really really really

2921
02:16:07,030 --> 02:16:05,520
really long strings

2922
02:16:09,189 --> 02:16:07,040
chromosomes

2923
02:16:11,350 --> 02:16:09,199
are really really really really really

2924
02:16:15,109 --> 02:16:11,360
long strings

2925
02:16:17,830 --> 02:16:15,119
namely they are of length billions

2926
02:16:21,189 --> 02:16:17,840
or the ratio of their length to their

2927
02:16:26,069 --> 02:16:21,199
width is billions

2928
02:16:33,509 --> 02:16:30,390
uh amino acids along them all right

2929
02:16:35,830 --> 02:16:33,519
and um

2930
02:16:37,270 --> 02:16:35,840
so so you know if you were to make it

2931
02:16:39,030 --> 02:16:37,280
out of probe

2932
02:16:41,830 --> 02:16:39,040
it would be

2933
02:16:43,349 --> 02:16:41,840
very very very thin rope which is very

2934
02:16:47,190 --> 02:16:43,359
very long

2935
02:16:53,349 --> 02:16:47,200
but yet this rope is compressed into a

2936
02:16:53,359 --> 02:16:57,110
so they get knotted

2937
02:17:01,429 --> 02:16:58,150
and

2938
02:17:04,389 --> 02:17:01,439
even your experience from a much smaller

2939
02:17:06,629 --> 02:17:04,399
knot so here's an electric cable if you

2940
02:17:09,190 --> 02:17:06,639
have a little bit of an experience with

2941
02:17:11,190 --> 02:17:09,200
letting loose of cables not tying them

2942
02:17:14,709 --> 02:17:11,200
nightly

2943
02:17:17,190 --> 02:17:14,719
nicely as i tied this yeah if you let it

2944
02:17:19,750 --> 02:17:17,200
loose it gets melted

2945
02:17:23,110 --> 02:17:19,760
and it it's it's very it's nearly

2946
02:17:25,830 --> 02:17:23,120
impossible to untie

2947
02:17:31,190 --> 02:17:28,389
chromosomes are much worse they're much

2948
02:17:34,469 --> 02:17:31,200
much much longer

2949
02:17:38,070 --> 02:17:34,479
in in relative terms and they get

2950
02:17:40,870 --> 02:17:38,080
cramped into tiny tiny tiny spaces so

2951
02:17:43,429 --> 02:17:40,880
how come they don't get knotted

2952
02:17:45,270 --> 02:17:43,439
and if they do get knotted

2953
02:17:46,230 --> 02:17:45,280
how come

2954
02:17:52,309 --> 02:17:46,240
uh

2955
02:17:55,270 --> 02:17:52,319
parts of the life of a cell so when when

2956
02:17:56,870 --> 02:17:55,280
when cells um

2957
02:17:59,509 --> 02:17:56,880
uh split

2958
02:18:02,389 --> 02:17:59,519
uh they split they somehow managed to

2959
02:18:04,629 --> 02:18:02,399
untie themselves and disconnect

2960
02:18:05,990 --> 02:18:04,639
so how how is it happening so there must

2961
02:18:09,030 --> 02:18:06,000
be some

2962
02:18:12,790 --> 02:18:09,040
huge brain inside every cell

2963
02:18:14,709 --> 02:18:12,800
uh that can untangle knots which are

2964
02:18:16,309 --> 02:18:14,719
much much much much much more

2965
02:18:20,230 --> 02:18:16,319
complicated

2966
02:18:23,110 --> 02:18:20,240
uh than the knots that uh

2967
02:18:24,709 --> 02:18:23,120
that you can untie

2968
02:18:27,429 --> 02:18:24,719
or you know the notes that you take

2969
02:18:28,469 --> 02:18:27,439
hours to untie with sometimes

2970
02:18:31,750 --> 02:18:28,479
okay

2971
02:18:34,309 --> 02:18:31,760
so there must be something there

2972
02:18:36,309 --> 02:18:34,319
and this and there is something there

2973
02:18:39,270 --> 02:18:36,319
and there are enzymes

2974
02:18:41,429 --> 02:18:39,280
that actually uh you know so

2975
02:18:42,790 --> 02:18:41,439
when when uh

2976
02:18:44,549 --> 02:18:42,800
uh

2977
02:18:49,270 --> 02:18:44,559
dna molecules

2978
02:18:52,389 --> 02:18:49,280
need to are not to untangle

2979
02:18:55,910 --> 02:18:52,399
there are enzymes that allow one

2980
02:18:59,190 --> 02:18:55,920
molecule to pass through the other so

2981
02:19:01,589 --> 02:18:59,200
basically you want to pass one string

2982
02:19:04,230 --> 02:19:01,599
through another so that they will come

2983
02:19:07,349 --> 02:19:04,240
to position there are enzymes that cut

2984
02:19:09,110 --> 02:19:07,359
this one temporarily it gets cut it

2985
02:19:11,429 --> 02:19:09,120
passes to the other side and it gets

2986
02:19:14,150 --> 02:19:11,439
reconnected

2987
02:19:16,709 --> 02:19:14,160
so in a sense

2988
02:19:20,709 --> 02:19:18,150
biology

2989
02:19:22,709 --> 02:19:20,719
invented anti-nautiorianza

2990
02:19:24,549 --> 02:19:22,719
enzymes

2991
02:19:27,589 --> 02:19:24,559
and and they are

2992
02:19:30,150 --> 02:19:27,599
necessary because of not theory

2993
02:19:33,270 --> 02:19:30,160
because if there were nots you wouldn't

2994
02:19:34,389 --> 02:19:33,280
be able to divide cells

2995
02:19:37,750 --> 02:19:34,399
uh

2996
02:19:40,870 --> 02:19:37,760
so so so so so biology invented some

2997
02:19:42,950 --> 02:19:40,880
some anti-node theory enzymes that allow

2998
02:19:45,509 --> 02:19:42,960
things to pass through each other that

2999
02:19:47,589 --> 02:19:45,519
nullify not theory so in some sense the

3000
02:19:52,630 --> 02:19:47,599
most interesting not theory that happens

3001
02:19:58,389 --> 02:19:56,309
that's a lovely story but in practice

3002
02:20:00,150 --> 02:19:58,399
there isn't much

3003
02:20:02,309 --> 02:20:00,160
jack desart wants to know is math a

3004
02:20:04,630 --> 02:20:02,319
human construct that we've devised to

3005
02:20:06,870 --> 02:20:04,640
better understand the universe or is

3006
02:20:09,429 --> 02:20:06,880
math a set of universal unchanging

3007
02:20:13,590 --> 02:20:09,439
principles i'm a human how would i know

3008
02:20:19,030 --> 02:20:16,469
you know how non-humans would say math

3009
02:20:21,190 --> 02:20:19,040
or how you know i

3010
02:20:22,469 --> 02:20:21,200
i don't know

3011
02:20:24,630 --> 02:20:22,479
but

3012
02:20:25,910 --> 02:20:24,640
this said

3013
02:20:27,750 --> 02:20:25,920
i mean i don't want to answer the

3014
02:20:30,550 --> 02:20:27,760
philosophical question but i want to

3015
02:20:32,550 --> 02:20:30,560
answer some there is some practical

3016
02:20:34,710 --> 02:20:32,560
things that comes out of it

3017
02:20:38,309 --> 02:20:34,720
every bit of math

3018
02:20:39,990 --> 02:20:38,319
so you know pick up a math book

3019
02:20:43,110 --> 02:20:40,000
here

3020
02:20:45,910 --> 02:20:43,120
every bit of math in this book

3021
02:20:48,710 --> 02:20:45,920
and not just this i mean every bit of

3022
02:20:52,630 --> 02:20:48,720
math in every book

3023
02:20:56,550 --> 02:20:54,070
ah

3024
02:20:59,429 --> 02:20:56,560
that's a good thing to remember it means

3025
02:21:01,990 --> 02:20:59,439
that there are no miracles

3026
02:21:05,270 --> 02:21:02,000
it means that

3027
02:21:05,280 --> 02:21:09,590
you know when you see a proof

3028
02:21:15,190 --> 02:21:10,830
and you have no

3029
02:21:17,510 --> 02:21:15,200
idea where could it come from

3030
02:21:23,110 --> 02:21:17,520
well you have no idea but somebody had

3031
02:21:23,120 --> 02:21:25,750
so

3032
02:21:32,870 --> 02:21:29,750
it's often extremely instructive

3033
02:21:34,870 --> 02:21:32,880
to try to reverse engineer somehow

3034
02:21:37,590 --> 02:21:34,880
not just understand the proof but

3035
02:21:40,070 --> 02:21:37,600
understand how

3036
02:21:44,230 --> 02:21:40,080
humans with all their failures could

3037
02:21:51,190 --> 02:21:45,830
so

3038
02:21:53,190 --> 02:21:51,200
math was entirely created by humans at

3039
02:21:55,190 --> 02:21:53,200
the end

3040
02:21:58,550 --> 02:21:55,200
do you think we don't spend enough time

3041
02:22:00,389 --> 02:21:58,560
in books talking about the missteps so

3042
02:22:02,389 --> 02:22:00,399
for example here's how the person

3043
02:22:05,750 --> 02:22:02,399
arrived at this proof they originally

3044
02:22:07,429 --> 02:22:05,760
thought of it like so this didn't work

3045
02:22:08,950 --> 02:22:07,439
or would that just bloat the book

3046
02:22:11,910 --> 02:22:08,960
unnecessarily

3047
02:22:13,030 --> 02:22:11,920
it would probably bloat the book

3048
02:22:19,030 --> 02:22:13,040
but

3049
02:22:23,670 --> 02:22:19,040
[Music]

3050
02:22:25,830 --> 02:22:23,680
and when i say motivate okay so

3051
02:22:27,429 --> 02:22:25,840
so some story is

3052
02:22:29,349 --> 02:22:27,439
should be told

3053
02:22:31,110 --> 02:22:29,359
like when you present

3054
02:22:32,950 --> 02:22:31,120
a proof

3055
02:22:36,389 --> 02:22:32,960
there should always be some plausible

3056
02:22:38,950 --> 02:22:36,399
discovery story how could this proof

3057
02:22:41,670 --> 02:22:38,960
have been found

3058
02:22:43,510 --> 02:22:41,680
it doesn't have to be a a historically

3059
02:22:45,990 --> 02:22:43,520
accurate

3060
02:22:48,389 --> 02:22:46,000
uh story

3061
02:22:51,270 --> 02:22:48,399
but but but but there has to be some

3062
02:22:54,230 --> 02:22:51,280
story explaining that this proof could

3063
02:22:56,150 --> 02:22:54,240
have been found by humans it wasn't

3064
02:22:59,270 --> 02:22:56,160
created by some

3065
02:23:00,349 --> 02:22:59,280
supernatural entity

3066
02:23:02,870 --> 02:23:00,359
this question

3067
02:23:05,110 --> 02:23:02,880
cx770 asks does he believe in the

3068
02:23:08,309 --> 02:23:05,120
concept of god

3069
02:23:13,990 --> 02:23:11,030
okay this one's a tangential question

3070
02:23:15,990 --> 02:23:14,000
bill mcgonicle asks ramanujan said that

3071
02:23:19,429 --> 02:23:16,000
he learned from his goddess

3072
02:23:20,630 --> 02:23:19,439
others suggest well ramona john said

3073
02:23:22,790 --> 02:23:20,640
that he learned from his goddess by

3074
02:23:24,950 --> 02:23:22,800
meditating and praying or came to him in

3075
02:23:28,309 --> 02:23:24,960
dreams some of his

3076
02:23:33,190 --> 02:23:28,319
formulas esoteric formulas what does

3077
02:23:38,469 --> 02:23:36,230
can speak from ramanu for ramanujan

3078
02:23:39,990 --> 02:23:38,479
i tend to be a

3079
02:23:40,950 --> 02:23:40,000
rationalist

3080
02:23:42,389 --> 02:23:40,960
uh

3081
02:23:43,349 --> 02:23:42,399
atheist

3082
02:23:46,870 --> 02:23:43,359
uh

3083
02:23:52,230 --> 02:23:49,270
if i think hard about something i either

3084
02:23:55,670 --> 02:23:52,240
solve it or don't but there's there's no

3085
02:23:57,670 --> 02:23:55,680
there are no miracles in business

3086
02:23:59,750 --> 02:23:57,680
another question this one this is my

3087
02:24:03,030 --> 02:23:59,760
question are there some relatively

3088
02:24:05,990 --> 02:24:03,040
elementary concepts that you've recently

3089
02:24:07,030 --> 02:24:06,000
had a new insight on so for example my i

3090
02:24:09,990 --> 02:24:07,040
don't know if you know my brother

3091
02:24:13,750 --> 02:24:10,000
sebastian he's a professor at u of t as

3092
02:24:15,750 --> 02:24:13,760
well in math finance he was telling me

3093
02:24:17,990 --> 02:24:15,760
kurt you know only recently maybe last

3094
02:24:20,469 --> 02:24:18,000
year i thought i realized oh the

3095
02:24:22,230 --> 02:24:20,479
triangle inequality is actually about a

3096
02:24:24,230 --> 02:24:22,240
triangle he would only just use the

3097
02:24:26,389 --> 02:24:24,240
formula

3098
02:24:28,309 --> 02:24:26,399
also recently okay the jacobian

3099
02:24:29,670 --> 02:24:28,319
determinant the jaycobian is actually

3100
02:24:33,910 --> 02:24:29,680
like

3101
02:24:34,950 --> 02:24:33,920
that point

3102
02:24:37,030 --> 02:24:34,960
doing

3103
02:24:38,710 --> 02:24:37,040
close instead of just okay think of it

3104
02:24:40,550 --> 02:24:38,720
as an abstraction of slopes and stuff

3105
02:24:42,469 --> 02:24:40,560
yeah so do you have an example

3106
02:24:44,630 --> 02:24:42,479
sorry of what of things that i've only

3107
02:24:46,230 --> 02:24:44,640
recently understood no no no of

3108
02:24:48,070 --> 02:24:46,240
something you have understood you've

3109
02:24:49,510 --> 02:24:48,080
used before but then maybe you've come

3110
02:24:51,510 --> 02:24:49,520
to a different understanding of you and

3111
02:24:52,790 --> 02:24:51,520
you say oh that's an interesting way of

3112
02:24:54,790 --> 02:24:52,800
thinking about it i didn't see that

3113
02:24:57,510 --> 02:24:54,800
before

3114
02:24:58,950 --> 02:24:57,520
it happens all the time well i wish it

3115
02:25:01,429 --> 02:24:58,960
would have happened all the times when

3116
02:25:03,030 --> 02:25:01,439
it happens it's a great day not all day

3117
02:25:04,790 --> 02:25:03,040
is a great day but there is the

3118
02:25:05,910 --> 02:25:04,800
occasional great day

3119
02:25:07,990 --> 02:25:05,920
uh

3120
02:25:14,710 --> 02:25:08,000
you know every time you learn some

3121
02:25:20,469 --> 02:25:17,750
a higher meaning it's it's or more

3122
02:25:22,389 --> 02:25:20,479
meaning than you thought it's great news

3123
02:25:25,190 --> 02:25:22,399
it happens all the time in the life in

3124
02:25:27,110 --> 02:25:25,200
the professional life of a

3125
02:25:28,630 --> 02:25:27,120
scientist

3126
02:25:32,010 --> 02:25:28,640
though not every day

3127
02:25:32,020 --> 02:25:35,830
[Music]

3128
02:25:39,349 --> 02:25:37,110
well

3129
02:25:41,590 --> 02:25:39,359
uh

3130
02:25:43,990 --> 02:25:41,600
i'll give you an example which somehow

3131
02:25:47,110 --> 02:25:44,000
which i think also partially involves

3132
02:25:50,469 --> 02:25:47,120
you so um

3133
02:25:53,270 --> 02:25:50,479
a few years ago i was asked to give a

3134
02:25:56,070 --> 02:25:53,280
10 minutes talk or something

3135
02:25:57,830 --> 02:25:56,080
uh to a i'm

3136
02:25:59,349 --> 02:25:57,840
i don't even remember what was the event

3137
02:26:00,950 --> 02:25:59,359
but you were there

3138
02:26:03,670 --> 02:26:00,960
oh you remember that

3139
02:26:05,349 --> 02:26:03,680
mentorship event or something like that

3140
02:26:07,590 --> 02:26:05,359
i don't remember that's what that was

3141
02:26:09,750 --> 02:26:07,600
that's right and i thought what would i

3142
02:26:11,750 --> 02:26:09,760
talk about and i

3143
02:26:14,150 --> 02:26:11,760
well okay the truth is that i have some

3144
02:26:16,870 --> 02:26:14,160
list of uh

3145
02:26:17,910 --> 02:26:16,880
ready-made topics that i can talk about

3146
02:26:19,990 --> 02:26:17,920
you know

3147
02:26:22,550 --> 02:26:20,000
if you ask me to talk in front of high

3148
02:26:25,590 --> 02:26:22,560
school students i sort of have a number

3149
02:26:28,550 --> 02:26:25,600
of topics that are ready okay

3150
02:26:31,030 --> 02:26:28,560
uh but nothing really fit

3151
02:26:33,030 --> 02:26:31,040
and also sometimes i i get bored of

3152
02:26:35,670 --> 02:26:33,040
myself

3153
02:26:37,670 --> 02:26:35,680
so i have to occasionally add something

3154
02:26:40,710 --> 02:26:37,680
so i said okay why don't i talk about a

3155
02:26:43,110 --> 02:26:40,720
prisoner's dilemma

3156
02:26:45,910 --> 02:26:43,120
and um

3157
02:26:48,550 --> 02:26:45,920
so i i mentioned the prisoner's dilemma

3158
02:26:51,110 --> 02:26:48,560
in five minutes or so

3159
02:26:53,830 --> 02:26:51,120
and it's a very light map right it's

3160
02:26:56,230 --> 02:26:53,840
hardly math it's so light that it's

3161
02:26:58,950 --> 02:26:56,240
hardly math

3162
02:27:00,309 --> 02:26:58,960
but then i realized that it's that it

3163
02:27:03,190 --> 02:27:00,319
has a

3164
02:27:04,950 --> 02:27:03,200
profound i i guess the economists have

3165
02:27:07,270 --> 02:27:04,960
always understood that

3166
02:27:09,910 --> 02:27:07,280
they always thought it was important but

3167
02:27:12,309 --> 02:27:09,920
i realized it only relatively recently

3168
02:27:13,590 --> 02:27:12,319
so that was what is it three four years

3169
02:27:16,550 --> 02:27:13,600
ago

3170
02:27:18,790 --> 02:27:16,560
uh i only then understood how

3171
02:27:21,670 --> 02:27:18,800
profoundly

3172
02:27:23,990 --> 02:27:21,680
important it is

3173
02:27:28,070 --> 02:27:25,030
you know

3174
02:27:30,469 --> 02:27:28,080
the prisoner's dilemma is some numerical

3175
02:27:34,790 --> 02:27:30,479
example

3176
02:27:40,070 --> 02:27:36,150
you have

3177
02:27:42,469 --> 02:27:40,080
two sides two people a and b

3178
02:27:44,389 --> 02:27:42,479
and they can choose whether to

3179
02:27:48,150 --> 02:27:44,399
cooperate or

3180
02:27:51,190 --> 02:27:48,160
betray each one chooses independently

3181
02:27:53,990 --> 02:27:51,200
whether to cooperate with the other or

3182
02:27:57,830 --> 02:27:54,000
betray the other

3183
02:28:01,830 --> 02:27:57,840
and if you look at the numbers

3184
02:28:05,110 --> 02:28:01,840
each one no matter what the other does

3185
02:28:07,670 --> 02:28:05,120
would prefer to betray

3186
02:28:11,270 --> 02:28:07,680
and as a result both of them would

3187
02:28:17,510 --> 02:28:14,950
and the overall outcome is worse to both

3188
02:28:19,349 --> 02:28:17,520
of them again i'm not describing the

3189
02:28:20,710 --> 02:28:19,359
whole thing i'm not telling the numbers

3190
02:28:23,510 --> 02:28:20,720
i'm just saying

3191
02:28:26,950 --> 02:28:23,520
there is this situation where if each

3192
02:28:32,469 --> 02:28:26,960
one acts selfishly

3193
02:28:32,479 --> 02:28:35,190
and

3194
02:28:38,790 --> 02:28:36,389
well

3195
02:28:42,630 --> 02:28:38,800
it has huge philosophical implications

3196
02:28:43,590 --> 02:28:42,640
you know there is a whole a whole um

3197
02:28:46,070 --> 02:28:43,600
uh

3198
02:28:47,590 --> 02:28:46,080
political class

3199
02:28:49,910 --> 02:28:47,600
that believes

3200
02:28:52,630 --> 02:28:49,920
that people should be acting selfishly

3201
02:28:55,750 --> 02:28:52,640
because if each one acts selfishly it's

3202
02:28:56,710 --> 02:28:55,760
actually for the best of the

3203
02:28:57,590 --> 02:28:56,720
uh

3204
02:29:01,670 --> 02:28:57,600
for

3205
02:29:05,190 --> 02:29:01,680
that's somehow the foundation of the

3206
02:29:06,870 --> 02:29:05,200
belief in free markets

3207
02:29:09,349 --> 02:29:06,880
uh so

3208
02:29:12,710 --> 02:29:09,359
uh uh

3209
02:29:15,110 --> 02:29:12,720
so so yes i am actually still a great

3210
02:29:17,510 --> 02:29:15,120
believer in free markets

3211
02:29:19,910 --> 02:29:17,520
i actually still greatly believe that

3212
02:29:22,950 --> 02:29:19,920
free markets are a good thing

3213
02:29:24,790 --> 02:29:22,960
but there is a little asterisk

3214
02:29:28,389 --> 02:29:24,800
sorry that's not duality that's an

3215
02:29:31,590 --> 02:29:28,399
asterisk so there is a little asterisk

3216
02:29:34,950 --> 02:29:31,600
asterisk and the asterisk says

3217
02:29:38,870 --> 02:29:34,960
provided somebody arranges so that free

3218
02:29:41,429 --> 02:29:38,880
markets when each one acts selfishly

3219
02:29:42,550 --> 02:29:41,439
you will not be led into prisoners

3220
02:29:47,349 --> 02:29:42,560
dilemma

3221
02:29:48,830 --> 02:29:47,359
you will be you'll be you'll stay out

3222
02:29:54,550 --> 02:29:48,840
and

3223
02:29:57,670 --> 02:29:54,560
benefit

3224
02:30:02,790 --> 02:29:57,680
the overall good so i mean this asterisk

3225
02:30:07,670 --> 02:30:05,270
ah sorry i well okay yes yes yes i get

3226
02:30:10,230 --> 02:30:07,680
it anyway uh

3227
02:30:11,990 --> 02:30:10,240
and you think it's a small asterisk but

3228
02:30:14,550 --> 02:30:12,000
the more you think about it you realize

3229
02:30:18,309 --> 02:30:14,560
it's actually a huge asterisk

3230
02:30:20,950 --> 02:30:18,319
it completely changes the picture

3231
02:30:23,910 --> 02:30:20,960
and it's much much much more common

3232
02:30:25,349 --> 02:30:23,920
you think of it as an esoteric example

3233
02:30:26,790 --> 02:30:25,359
but then you realize that it's

3234
02:30:28,790 --> 02:30:26,800
everywhere

3235
02:30:30,469 --> 02:30:28,800
so it's actually a very very big

3236
02:30:31,349 --> 02:30:30,479
asterisk

3237
02:30:32,550 --> 02:30:31,359
and

3238
02:30:35,349 --> 02:30:32,560
um

3239
02:30:36,710 --> 02:30:35,359
i think i realized it relatively

3240
02:30:38,469 --> 02:30:36,720
recently

3241
02:30:40,230 --> 02:30:38,479
i'm honored that you remember that i

3242
02:30:42,150 --> 02:30:40,240
didn't think that uh i'm honored to even

3243
02:30:44,710 --> 02:30:42,160
be a footnote in your memory

3244
02:30:45,750 --> 02:30:44,720
oh don't be silly

3245
02:30:48,150 --> 02:30:45,760
okay

3246
02:30:51,910 --> 02:30:48,160
what have you applied also this question

3247
02:30:55,590 --> 02:30:51,920
comes from harinav harinavis harinivis

3248
02:30:58,389 --> 02:30:55,600
sorry harinivis p asks has drawer

3249
02:31:02,150 --> 02:30:58,399
applied the principles of mathematics to

3250
02:31:08,710 --> 02:31:03,670
like let's give an example of a

3251
02:31:12,950 --> 02:31:10,630
well okay i mean

3252
02:31:15,830 --> 02:31:12,960
i can give two answers okay

3253
02:31:17,830 --> 02:31:15,840
one answer is uh well i don't know if

3254
02:31:19,110 --> 02:31:17,840
it's the principles of mathematics but

3255
02:31:20,870 --> 02:31:19,120
you know

3256
02:31:27,670 --> 02:31:20,880
uh

3257
02:31:29,270 --> 02:31:27,680
there was a claim going on and it's been

3258
02:31:31,190 --> 02:31:29,280
going around and in fact it's still

3259
02:31:33,429 --> 02:31:31,200
going around

3260
02:31:36,950 --> 02:31:33,439
uh that uh

3261
02:31:38,550 --> 02:31:36,960
you that the bible contains predictions

3262
02:31:41,030 --> 02:31:38,560
in code

3263
02:31:45,190 --> 02:31:41,040
so if you read the bible with letter

3264
02:31:49,429 --> 02:31:45,200
skips if you read every tenth letter

3265
02:31:51,510 --> 02:31:49,439
you will occasionally find a word

3266
02:31:55,349 --> 02:31:51,520
that's not surprising

3267
02:31:57,349 --> 02:31:55,359
but the claim was that these words

3268
02:32:00,389 --> 02:31:57,359
where

3269
02:32:01,990 --> 02:32:00,399
that that it actually happens more than

3270
02:32:04,950 --> 02:32:02,000
statistics would

3271
02:32:07,830 --> 02:32:04,960
uh predict and that these words have

3272
02:32:09,429 --> 02:32:07,840
messages in them

3273
02:32:13,590 --> 02:32:09,439
and uh

3274
02:32:15,270 --> 02:32:13,600
and there was a group of people in

3275
02:32:16,150 --> 02:32:15,280
jerusalem

3276
02:32:18,230 --> 02:32:16,160
that

3277
02:32:19,830 --> 02:32:18,240
published a paper and in fact it passed

3278
02:32:24,150 --> 02:32:19,840
peer review

3279
02:32:26,230 --> 02:32:24,160
uh but so so they published a paper

3280
02:32:27,190 --> 02:32:26,240
in which they

3281
02:32:29,670 --> 02:32:27,200
uh

3282
02:32:32,630 --> 02:32:29,680
supposedly proved this fact

3283
02:32:34,790 --> 02:32:32,640
they did careful statistical analysis

3284
02:32:36,150 --> 02:32:34,800
again carefully in quotes

3285
02:32:39,030 --> 02:32:36,160
uh

3286
02:32:40,870 --> 02:32:39,040
and and and and and showed that the

3287
02:32:42,550 --> 02:32:40,880
effect was real

3288
02:32:45,349 --> 02:32:42,560
and therefore

3289
02:32:46,469 --> 02:32:45,359
the bible uh must have been written by

3290
02:32:48,950 --> 02:32:46,479
god

3291
02:32:51,349 --> 02:32:48,960
because no human could have put this

3292
02:32:53,510 --> 02:32:51,359
information into the bible

3293
02:32:55,590 --> 02:32:53,520
it's information information that was

3294
02:32:57,910 --> 02:32:55,600
not did not even exist at the time that

3295
02:33:00,710 --> 02:32:57,920
the bible was written

3296
02:33:02,230 --> 02:33:00,720
and therefore in prayer and so so god

3297
02:33:03,429 --> 02:33:02,240
wrote the bible

3298
02:33:10,070 --> 02:33:03,439
uh

3299
02:33:12,710 --> 02:33:10,080
there is a god and that god loves hebrew

3300
02:33:14,710 --> 02:33:12,720
more than she loves japanese i

3301
02:33:17,990 --> 02:33:14,720
understand yeah uh you know this would

3302
02:33:19,590 --> 02:33:18,000
be the greatest discovery in if it was

3303
02:33:21,590 --> 02:33:19,600
true it would have been the greatest

3304
02:33:23,349 --> 02:33:21,600
discovery in the history of science and

3305
02:33:25,190 --> 02:33:23,359
i'm not kidding

3306
02:33:28,389 --> 02:33:25,200
right i mean there's no longer an

3307
02:33:30,230 --> 02:33:28,399
argument between atheism and tazin

3308
02:33:33,030 --> 02:33:30,240
pays and wins

3309
02:33:35,429 --> 02:33:33,040
my role was to debunk this

3310
02:33:38,950 --> 02:33:35,439
is this real life or not

3311
02:33:42,630 --> 02:33:38,960
i don't know i me and a group of people

3312
02:33:44,469 --> 02:33:42,640
read critically these assertions that go

3313
02:33:45,670 --> 02:33:44,479
that were good enough that they passed

3314
02:33:48,630 --> 02:33:45,680
peer review

3315
02:33:50,309 --> 02:33:48,640
in a respectable journal and we found

3316
02:33:55,030 --> 02:33:50,319
gaps

3317
02:33:57,750 --> 02:33:55,040
that the same peer-reviewed journal

3318
02:34:00,630 --> 02:33:57,760
accepted our paper too

3319
02:34:02,950 --> 02:34:00,640
okay so you know in some sense my role

3320
02:34:04,950 --> 02:34:02,960
was negative right what could have been

3321
02:34:07,670 --> 02:34:04,960
the greatest discovery in the history of

3322
02:34:09,910 --> 02:34:07,680
science a proof that there is god and

3323
02:34:10,790 --> 02:34:09,920
it's the hebrew god

3324
02:34:13,030 --> 02:34:10,800
uh

3325
02:34:14,870 --> 02:34:13,040
was debunked maybe it's a negative

3326
02:34:17,590 --> 02:34:14,880
discovery but

3327
02:34:19,590 --> 02:34:17,600
well i mean even maybe my effect well my

3328
02:34:22,469 --> 02:34:19,600
part was negative i've killed a great

3329
02:34:26,870 --> 02:34:22,479
discovery but that's also a

3330
02:34:30,870 --> 02:34:26,880
a valuable thing to do i mean to kill a

3331
02:34:32,790 --> 02:34:30,880
uh the other thing is uh

3332
02:34:36,710 --> 02:34:32,800
otherwise

3333
02:34:39,349 --> 02:34:36,720
mathematics plays an extremely limited

3334
02:34:41,910 --> 02:34:39,359
role in my life

3335
02:34:44,389 --> 02:34:41,920
other than my professional life if you

3336
02:34:46,950 --> 02:34:44,399
ex if you cut out

3337
02:34:48,950 --> 02:34:46,960
uh the eight hours a day that i work on

3338
02:34:51,510 --> 02:34:48,960
mathematics mathematics has no role in

3339
02:34:54,309 --> 02:34:51,520
my life or hardly any role so i mean you

3340
02:34:56,710 --> 02:34:54,319
do and in fact also almost no role in

3341
02:35:00,389 --> 02:34:56,720
your life so basically

3342
02:35:03,830 --> 02:35:00,399
you know if you um

3343
02:35:07,030 --> 02:35:03,840
you give change in restaurants you uh so

3344
02:35:08,309 --> 02:35:07,040
so or in when shops sorry you add 15

3345
02:35:09,830 --> 02:35:08,319
percent

3346
02:35:11,670 --> 02:35:09,840
tip

3347
02:35:12,750 --> 02:35:11,680
that's about the math you need in real

3348
02:35:16,389 --> 02:35:12,760
life

3349
02:35:18,950 --> 02:35:16,399
multiplication you don't need

3350
02:35:22,950 --> 02:35:21,910
but if you're a carpenter you probably

3351
02:35:25,270 --> 02:35:22,960
need it

3352
02:35:27,750 --> 02:35:25,280
right you need to

3353
02:35:30,710 --> 02:35:27,760
tiles or you know if you're a trade

3354
02:35:33,429 --> 02:35:30,720
person you need to tile a certain room

3355
02:35:36,070 --> 02:35:33,439
this the room is five by six right how

3356
02:35:38,469 --> 02:35:36,080
many tiles do you need so multiplication

3357
02:35:41,030 --> 02:35:38,479
trade people need but but but but people

3358
02:35:41,870 --> 02:35:41,040
like me don't need

3359
02:35:45,190 --> 02:35:41,880
um

3360
02:35:48,550 --> 02:35:45,200
trigonometry well maybe architect nitric

3361
02:35:51,190 --> 02:35:48,560
architecture trigonometry some parts of

3362
02:35:52,630 --> 02:35:51,200
engineering and we get more and more

3363
02:35:54,710 --> 02:35:52,640
esoteric

3364
02:35:56,790 --> 02:35:54,720
need higher and higher mathematics

3365
02:35:59,750 --> 02:35:56,800
without the very high mathematics

3366
02:36:02,469 --> 02:35:59,760
without general relativity

3367
02:36:05,030 --> 02:36:02,479
gps satellites wouldn't work so in some

3368
02:36:07,270 --> 02:36:05,040
sense we use mathematics every day

3369
02:36:09,670 --> 02:36:07,280
but we're not the engineers who design

3370
02:36:12,870 --> 02:36:09,680
gps city live seat satellites gps

3371
02:36:14,950 --> 02:36:12,880
satellites were designed by a group of

3372
02:36:16,710 --> 02:36:14,960
a very small group of people somewhere

3373
02:36:17,750 --> 02:36:16,720
in some

3374
02:36:19,750 --> 02:36:17,760
you know

3375
02:36:22,070 --> 02:36:19,760
design bureau

3376
02:36:25,190 --> 02:36:22,080
and they use high-level mathematics so

3377
02:36:27,670 --> 02:36:25,200
so so but my real life

3378
02:36:29,349 --> 02:36:27,680
high level mathematics

3379
02:36:32,070 --> 02:36:29,359
is almost nothing

3380
02:36:34,309 --> 02:36:32,080
except once sorry the bible codes and

3381
02:36:37,670 --> 02:36:34,319
another time

3382
02:36:42,150 --> 02:36:37,680
and i've given talks with this title

3383
02:36:44,309 --> 02:36:42,160
so uh the title was uh the

3384
02:36:45,429 --> 02:36:44,319
hardest

3385
02:36:54,230 --> 02:36:45,439
uh

3386
02:36:56,309 --> 02:36:54,240
ever

3387
02:36:57,190 --> 02:36:56,319
really

3388
02:36:59,670 --> 02:36:57,200
yeah

3389
02:37:02,150 --> 02:36:59,680
and if you google this title probably

3390
02:37:02,950 --> 02:37:02,160
you'll be able to find a video of that

3391
02:37:05,670 --> 02:37:02,960
talk

3392
02:37:07,990 --> 02:37:05,680
and you'll find that one time

3393
02:37:10,469 --> 02:37:08,000
where

3394
02:37:13,110 --> 02:37:10,479
it was actually in my professional life

3395
02:37:15,910 --> 02:37:13,120
but in a meta way

3396
02:37:18,389 --> 02:37:15,920
so not my research but something about

3397
02:37:21,110 --> 02:37:18,399
how to present my research i ended up

3398
02:37:23,990 --> 02:37:21,120
using a very high level mathematics

3399
02:37:26,550 --> 02:37:24,000
hyperbolic geometry in fact

3400
02:37:29,190 --> 02:37:26,560
so one time it happened anyway what was

3401
02:37:33,030 --> 02:37:29,200
your next question

3402
02:37:35,110 --> 02:37:33,040
why does it take 360 pages of abstruse

3403
02:37:36,469 --> 02:37:35,120
symbols to prove that one plus one

3404
02:37:38,550 --> 02:37:36,479
equals two

3405
02:37:40,790 --> 02:37:38,560
occam's razor says we can cut this we

3406
02:37:42,550 --> 02:37:40,800
can just say one plus one equals two

3407
02:37:44,070 --> 02:37:42,560
because every single last one of us

3408
02:37:46,150 --> 02:37:44,080
believes it does

3409
02:37:47,750 --> 02:37:46,160
so what do you make of that why is it so

3410
02:37:50,070 --> 02:37:47,760
complex to prove something simple like

3411
02:37:51,110 --> 02:37:50,080
one plus one equals two do we even need

3412
02:38:02,630 --> 02:37:51,120
that

3413
02:38:07,429 --> 02:38:03,990
so

3414
02:38:12,830 --> 02:38:09,030
let me answer the

3415
02:38:16,469 --> 02:38:12,840
let me answer a different question

3416
02:38:19,510 --> 02:38:16,479
uh you know so one plus one equals two

3417
02:38:21,910 --> 02:38:19,520
so the the reference is probably to uh

3418
02:38:24,790 --> 02:38:21,920
work of uh russell

3419
02:38:24,800 --> 02:38:29,990
basically

3420
02:38:36,550 --> 02:38:32,950
if your axiom system is

3421
02:38:37,990 --> 02:38:36,560
very very very basic

3422
02:38:40,469 --> 02:38:38,000
and

3423
02:38:45,349 --> 02:38:40,479
um

3424
02:38:49,590 --> 02:38:47,030
primitive in a way very very

3425
02:38:52,150 --> 02:38:49,600
simple-minded and you want your axiom

3426
02:38:55,190 --> 02:38:52,160
system to be very very very basic

3427
02:38:58,469 --> 02:38:55,200
then it might be that even proving one

3428
02:39:01,349 --> 02:38:58,479
plus one equal to would be difficult

3429
02:39:03,670 --> 02:39:01,359
but it will be a part of the build up

3430
02:39:07,830 --> 02:39:03,680
and later you will be uh

3431
02:39:13,510 --> 02:39:10,870
but the truth is it's silly okay but let

3432
02:39:15,349 --> 02:39:13,520
me give you an another example okay so

3433
02:39:17,190 --> 02:39:15,359
uh you know there is the intermediate

3434
02:39:22,150 --> 02:39:17,200
value theorem

3435
02:39:25,349 --> 02:39:22,160
that if you have a function

3436
02:39:26,550 --> 02:39:25,359
continuous function so if f is

3437
02:39:30,389 --> 02:39:26,560
continuous

3438
02:39:35,270 --> 02:39:30,399
and it's negative here and positive here

3439
02:39:41,190 --> 02:39:38,550
uh we teach it in week seven

3440
02:39:43,270 --> 02:39:41,200
maybe i don't know of undergraduate

3441
02:39:45,270 --> 02:39:43,280
calculus maybe it's just week five or

3442
02:39:46,469 --> 02:39:45,280
maybe it's week nine i don't remember

3443
02:39:47,750 --> 02:39:46,479
okay

3444
02:39:50,150 --> 02:39:47,760
you can ask

3445
02:39:50,950 --> 02:39:50,160
this is so idiotic

3446
02:39:52,469 --> 02:39:50,960
right

3447
02:39:58,230 --> 02:39:52,479
why

3448
02:40:00,950 --> 02:39:58,240
prove the obvious that if you go

3449
02:40:04,070 --> 02:40:00,960
continuously from here to here you'll be

3450
02:40:09,990 --> 02:40:07,030
and the answer

3451
02:40:12,150 --> 02:40:10,000
is that when you prove the intermediate

3452
02:40:14,790 --> 02:40:12,160
value theorem

3453
02:40:16,950 --> 02:40:14,800
you are not actually proving the

3454
02:40:20,230 --> 02:40:16,960
intermediate value theorem

3455
02:40:23,429 --> 02:40:20,240
you are actually testing

3456
02:40:25,030 --> 02:40:23,439
your definition of continuity

3457
02:40:27,750 --> 02:40:25,040
you're testing

3458
02:40:33,110 --> 02:40:27,760
your abstract setup

3459
02:40:35,110 --> 02:40:33,120
your language you're testing

3460
02:40:38,230 --> 02:40:35,120
uh

3461
02:40:40,790 --> 02:40:38,240
you know the the machinery of for every

3462
02:40:43,750 --> 02:40:40,800
epsilon there exists a delta such that

3463
02:40:46,790 --> 02:40:43,760
blah blah blah if you could not prove

3464
02:40:50,469 --> 02:40:46,800
the intermediate value theorem

3465
02:40:53,110 --> 02:40:50,479
you'd be rejecting the abstract system

3466
02:40:56,710 --> 02:40:53,120
not the intermediate value theorem you'd

3467
02:40:57,590 --> 02:40:56,720
be rejecting this not that

3468
02:40:59,590 --> 02:40:57,600
so

3469
02:41:01,910 --> 02:40:59,600
the seven weeks were not about the

3470
02:41:03,030 --> 02:41:01,920
intermediate value theorem they were

3471
02:41:05,750 --> 02:41:03,040
about

3472
02:41:08,469 --> 02:41:05,760
this for every epsilon there exists

3473
02:41:10,870 --> 02:41:08,479
delta and then you can ask

3474
02:41:13,510 --> 02:41:10,880
what's for every epsilon there exists

3475
02:41:15,110 --> 02:41:13,520
delta for why do we need this well we

3476
02:41:17,110 --> 02:41:15,120
don't need it to prove the intermediate

3477
02:41:19,030 --> 02:41:17,120
value theorem the intermediate value

3478
02:41:21,030 --> 02:41:19,040
theorem was testing this

3479
02:41:23,670 --> 02:41:21,040
what do we need it for

3480
02:41:24,710 --> 02:41:23,680
and the answer is well there are later

3481
02:41:25,670 --> 02:41:24,720
things

3482
02:41:29,349 --> 02:41:25,680
like

3483
02:41:33,510 --> 02:41:29,359
uh e to the x is equal to sum of x to

3484
02:41:35,750 --> 02:41:33,520
the n divided by n factorial

3485
02:41:37,429 --> 02:41:35,760
which is this by the way looks innocent

3486
02:41:39,670 --> 02:41:37,439
and people think they understand it but

3487
02:41:42,230 --> 02:41:39,680
it's actually a miracle

3488
02:41:43,910 --> 02:41:42,240
and this miracle depends on well it

3489
02:41:46,389 --> 02:41:43,920
doesn't depend but i mean there are

3490
02:41:48,469 --> 02:41:46,399
maybe other ways to reach there but but

3491
02:41:50,550 --> 02:41:48,479
but you you will believe this miracle

3492
02:41:52,710 --> 02:41:50,560
miracle after you've understood this

3493
02:41:53,510 --> 02:41:52,720
system

3494
02:41:58,389 --> 02:41:53,520
so

3495
02:41:59,429 --> 02:41:58,399
didn't go from

3496
02:42:03,190 --> 02:41:59,439
uh

3497
02:42:04,870 --> 02:42:03,200
here to here

3498
02:42:07,590 --> 02:42:04,880
to here

3499
02:42:10,790 --> 02:42:07,600
but more like this was known it

3500
02:42:14,150 --> 02:42:10,800
validated this and then uh we could use

3501
02:42:17,830 --> 02:42:16,150
the podcast is now finished if you'd

3502
02:42:21,030 --> 02:42:17,840
like to support conversations like this

3503
02:42:25,110 --> 02:42:21,040
then do consider going to patreon.com

3504
02:42:27,750 --> 02:42:25,120
c-u-r-t j-a-i-m-u-n-g-a-l

3505
02:42:29,510 --> 02:42:27,760
that is kurt jaimungle it's support from

3506
02:42:31,349 --> 02:42:29,520
the patrons and from the sponsors that