Kind: captions
Language: en
there is a famous story about Einstein
that he used to you know go think think
and then go for a walk and like he would
whistle and sometimes so I remember the
first time I heard this story
I thought how interesting so the
coincidence that he came to him when he
was whistling but in fact it's not this
is how it works in some sense that
you have to prepare for it but then the
moment it happens when you stop thinking
actually it's okay the moment of
Discovery is the moment when thinking
stops and you know you kind of you kind
of almost become that truth that you're
seeking
the following is a conversation with
Edward Frankel one of the greatest
living mathematicians doing research on
the interface of mathematics and quantum
physics with an emphasis on the
langlands program which he describes as
a grand unified theory of mathematics he
also is the author of love and math the
heart of hidden reality
this is the Lex Friedman podcast to
support it please check out our sponsors
in the description and now dear friends
here's Edward Franco
you open your book love and math with a
question
how does one become a mathematician
there are many ways that this can happen
let me tell you how it happened to me so
how did it happen to you so first of all
I grew up in the Soviet Union
in a small town near Moscow
called columna
and I was a smart kid you know in school
but mathematics was probably my least
favorite subject
not because I couldn't do it I was you
know a straight A student and I could do
all the problems easily but I thought it
was incredibly boring
and
um since the only math I knew was what
was presented at school
I thought that was it and I was like
what kind of boring subject is this so
what I really liked was physics
and especially quantum physics so I was
buying
uh I would go to a bookstore and buy
popular books about elementary particles
and atoms and things like that and read
them you know devour them
and so I thought my dream was to become
a theoretical physicist
and to delve into this finer structure
of the universe you know so then
something happened when I was 15 years
old uh it turns out that a friend of my
parents
was a mathematician who was a professor
at the local College it was a small
College preparing Educators and teachers
it's a provincial Town imagine it's like
a 117 kilometers from Moscow which would
be something like 70 miles I guess you
do the math I like how you remember the
number exactly yeah it's not funny how
we remember numbers yeah so his name was
evgeny evgenievich Petrov yeah and if
this doesn't remind you of the great
works of Russian literature then you
haven't read them
like War and Peace you know like with
the patronym nickname yeah but this was
all real this was all happening so my
mom One Day by chance met is ganovic and
told him about me
but that was this bright kid and
interested in physics
and he said oh I want to meet him I'm
going to convert him into math
and my mom's like nah my ass he doesn't
like mathematics so they said okay let's
let's see what they can do
so I went to see him so I'm about 15.
and a bit a bit uh arrogant I would say
you know like average teenager
so he says to me
so I hear that you are
um interested in in physics Elementary
particles I said yeah sure
for example do you know what quirks
and I said yes of course I know what
quarks quarks are the you know
constituents
of particles like protons and neutrons
and it was one of the greatest
discoveries in theoretical physics in
the 60s that those particles were not
Elementary but in fact had the smaller
parts
and he said oh so then you probably know
representation theory of the group su3
this is like as you worked so
in fact
I wanted to know what was what were the
underpinnings of those theories I knew
the story I knew the narrative a new
kind of this basic story of what this
particles looked like but how did
physicists come up with these ideas
how were they able to theorize them
and so I remembered you know like it was
yesterday so he pulls out a book
and it's kind of like it's like a Bible
you know like a like a substantial book
and he opens um somewhere in the middle
and there I see the diagrams that I saw
in popular books but in popular books
there was no explanation and now I see
all these weird symbols and equations
it's clear that it is explained in there
oh my God
he said you think what they teach you at
school is mathematics
it's like no this is real mathematics
so I was instantly converted
that you understand the underpinnings of
physical reality
you have to understand what su3 is you
have to learn what are groups what this
group su3 what are representations of
sc3 there was a coherent
and beautiful I could appreciate the
beauty even though I could not
understand
heads and tails of it but you were drawn
to the the methodology the
the the Machinery of all such
understanding could be attained well in
retrospect I think what I was really
craving was a deeper understanding
and up to that point the deepest that I
could see was for those diagrams but for
that story that you know a proton
consists of three quarks and the neutron
consists of trick works and they're
called up and down and so on
but I didn't know
that there was actually underneath
beneath the surface there was this
mathematical theory if you can just link
around it what Drew you to quantum
mechanics
is there some romantic notion of
understanding the universe well what is
interesting to you is it the puzzle of
it or is it like the philosophical thing
now I am looking back yeah so um
whatever I say about Edward at 15 yeah
he's colored by
uh my you know all my experiences that
happen in in the meantime I should say
current views and so on for the people
who may not know you I think your book
and your presentations kind of revealed
that that 15 year old is still in there
somewhere
I think it is a conflict some of the joy
he's probably still here now yes yeah in
some way
yeah I think it was a joy of Discovery
and the joy of going deeper into the
kind of the
uh to the root uh to the so the deepest
structures of the universe the secrets
the the secrets and we may not discover
all of them we may not be able to
understand but we're going to try and go
as far and as deep as we can I think
that's what was the motivating factor in
this
yeah there's this mystery there's this
dark room and there's a few of these
mathematical physicists they're able to
shine
a flashlight briefly into there
uh we'll we'll talk about it but it also
kind of makes me sad that there's so few
of your kind that have the the
flashlight to look into the room
it's interesting
um I don't think there are so few to be
honest because I think I find a lot of
people are actually interested if you do
talk if you talk to people you know like
some people you wouldn't expect to uh to
be interested in this uh from all walks
of life from people of
all kinds of professions I tell them I'm
a mathematician and the mathematician
okay so that's a separate story a lot of
people I think have been traumatized by
their experience in their math classes
we can talk about it later but then they
ask me what kind of research I do and
I I mentioned that I I work on the
interface of math and quantum physics
and their eyes light up and say oh
quantum physics or like Einstein's
relativity I'm really curious about it I
watched this podcast or I watch that
podcast you know and I've learned this
it's like what do you think about that
so I actually find that that actually
physicists are doing great job at
educating
the public so to speak and uh in terms
of
um
popular books and videos and so on
mathematicians are behind that we're
starting to catch up a little bit have
been starting last 10 years but when
we're still behind but I think people
are people are curious
science is a is still a very much uh you
know something that people want to learn
because that's our kind of uh the best
way we know to establish some sort of
objective reality whatever that might be
yeah to figure out this whole puzzle to
figure out the secrets that the Universe
holds things that we can agree on kind
of you know like even though for me at
this point I always you know make an
argument that our physical theorists
always change they get updated so you
had Newton's theory of gravity
then um Einstein's theory you know
superseded it
but in mathematics
it seems that theories don't change
Pythagoras Theorem
has been the same for the last 2500
years x squared plus y squared equals z
squared we don't expect that next year
suddenly it will be z cubed you know so
and so that to me is actually even more
um hints even more at home how how much
we are connected to each other because
dagger's theory if you think about it or
any other mathematical theorem
means the same thing to anyone in the
world today regardless of their cultural
you know bringing uh religion you know
ideas ideal ideology gender whatever
nationality race whatever right and it
has meant the same to everyone
everywhere and most likely will mean the
same
so that's to me kind of an antidote
to the kind of
divisiveness that we sometimes observe
these days where it seems that we can't
agree on anything
to the political complexity of uh two
plus two equals five and George Orwell's
1984. I was in the Soviet Union in 1984
and so in many ways I see that it was
President the novel was present but we
still have not found the dictator who
would actually say two plus two equals
five and would demand their citizens to
repeat that the Knight is still young
has not happened yet
but it does feel like math and physics
are both sneaking up to a deep truth
from slightly different angles and you
stand at the crossroads or at the
intersection of the two it's interesting
to ask what do you think is the
difference between physics and
Mathematics in the way physics and
Mathematics look at the world
there is actually an essential
difference
which is that physicists are interested
in describing this universe
okay mathematicians are interested
describing all possible mathematical
universes of which uh you know and some
of our work I still consider myself more
of a mathematician than a physicist My
First Love for physics notwithstanding
um mathematicians are in a way
we have more diversity if you if you you
might say so we we are accepting for
instance uh our universe uh has three
special spatial dimensions and one time
Dimension right so what I mean is that
allegedly allegedly observed but that
way I can observe today right so of
course there are theories where there
are some hidden Dimensions as well well
let's just say absorb to observe
dimensions
um so this tabletop has two Dimensions
because you can have two axes two
coordinate axes now X and Y but then
there is also a third one to describe
the space of this room
and then there's a Time Time Dimension
so realistic theories of physics have to
be
about
spaces of of three three dimensions or
space time so four dimensions but
mathematically we are just as interested
in theories in 10 space time Dimensions
or 11 or 25 or whatever or or infinite
dimensional spaces you know
so that's the difference
on the other hand I have to give it to
the physicists we don't have the same
satisfaction that they have of having
their theories
um confirmed by an experiment we don't
get to play with big machines like LHC
in Geneva A Large Hadron Collider that
recently discovered you know the Higgs
boson and some other things
for us it's all like a mental exercise
in some sense we do we prove things by
using rules of logic and that's our way
of confirming experimental confirmation
if you will but I think we kind of I
kind of Envy a little bit my friends
visits that they they get to they get to
experience this sort of these big toys
you know and play with them but it does
seem that sometimes as you've spoken
about abstract mathematical Concepts map
to reality and it seems to happen quite
a bit that's right so the mathematics is
the underpins physics obviously it's a
language the the book of nature
famously said it's written in the
language of mathematics and the and the
you know the the letters in it are the
circles triangles and squares and those
who don't know the language I'm
paraphrasing
are left to wander in the dark Labyrinth
that's a famous quote from Galileo which
is very true and has become even more
true more recently in the in theoretical
physics in the more in the most
um actor of
far out
parts of the theoretical physics that
have to do with Elementary particles and
and as well as the the structure of the
cosmos at the large scale what do you
think of uh Max tag Mark or wrote the
book mathematical universe
so do you think just lingering on that
point you think at the end of the day
the future Generations will all be
mathematicians
meaning meaning the ones that deeply
understand the way the universe works at
the core is it just
mathematics
at the core of you know
I would say mathematics is one half of
the core so the book is called love and
math yeah okay so these are the two
pillars
yeah in my view yes in other words you
can't cover everything by math so
mathematics gives you tools it gives you
way up uh
kind of a clear
vision
but mathematics by itself is not enough
for one to have a harmonious and uh and
balanced life you know so I I am
suspicious of any theory that
declares that everything is mathematics
so math can generate things that are
beautiful but it can't explain why it's
beautiful Matthew could say is a way to
discern patterns to find regularities in
the universe and both physical and
mental Universe the mathematics explores
the mind as much as it explores
um the physical world around us and it
helps us to find those patterns
um which kind of which makes our
perception more sophisticated our
ability to perceive things such as
Beauty
you know and
it sharpens our ability to see to see
beauty to understand Beauty so a world
becomes more complex
from thinking that our
that our that Earth is flat we go to
realizing that it is round that is shape
as a sphere
so that we can actually travel around
the Earth you know so there isn't a
place where we hit the end so to speak
and then
um
proceeding in the same vein then
Einstein's general relativity Theory
tells us that
our space-time is not flat either
this is much harder to to imagine the
band a band three-dimensional or
four-dimensional three-dimensional space
or four-dimensional space time because
this idea that the space around us is
flat is so deeply entrenched and yet we
know from this from this Theory
and from the experiments that have
confirmed it
that
a array of light bends around a star as
if being attracted by the by the force
of gravity but in fact the force of
gravity is the bending it's just that
it's not only depending on the space
it's also the bending of space-time
there is a curvature
not only between special spatial
dimensions
the way parallels and meridians come
together in a small scale they look like
perpendicular lines but if you zoom out
you see that the spacer at a curving the
space they are sort of the the tracks
along which the space gets curved that's
that's the that would be the curvature
of spatial Dimensions but in fact now
throw in time and one time imagine a
sphere which lives which has one of the
meridians correspond to time and the
perilous crisp into space I can't
imagine it but you can I can write
mathematical formula expressing that
curvature and that's in fact that
curvature is responsible for the force
of gravity attraction between the sort
of simplest instantiation of it
attraction between two planets all
between two human beings
at the time
bending time
it's not very nice that what that theory
did to time because
it feels like the marching of time
forward is fundamental to our Human
Experience
there of time
marching forward nicely
seems to be the only way we can
understand the universe and the fact
that you can start now up to now there
are people who claim that they can that
they have they possess other ways of of
experiencing it so truly can visualize
messing with time
well messing with time but not
necessarily messing with time because
one point of view is that you know
I think who who was it I think William
Blake
who wrote that eternity loves time
production
so
one point of view is that it is eternity
which is fundamental where time stands
still which our mind conceptualizes as
the time
so but in fact you know it's not
something mystical if you think about
when you about it
when you really absorbed in something
time does stand still and then you look
at the clock and it's like oh my God two
hours have passed and it felt like a
couple of seconds
when you are absorbed when you're in
love when you are passionate about
something when you're creating something
you're we lose ourselves and we lose the
sense of time and space for that matter
you see so there is only that which is
happening that creative process
um so I think that this this is familiar
to all of us and we may be actually the
closest to the truth at that moment
so yes so then there is a point of view
that this is where we are we are who we
are at our sort of fundamental at our
fundamental level and after that the
Mind comes in
and tries to conceptualize it it's like
oh because I was writing something
um
I was writing a book I was painting this
painting or maybe I was watching this
painting and got totally absorbed in it
or I fell in love with this person
that's what happened but in the moment
when it's happening you're not thinking
about it you're just there yeah we
construct narratives around the set of
memories that that seem to have happened
in sequence or at least that's the way
we tell ourselves that and we also have
a bunch of weird human things like
Consciousness and the experience of free
will that we chose a set of actions as
the time unrolled forward right
and we are intelligent conscious agents
making taste taking those actions
but what if all of that is just an
illusion an illusion and a nice
narrative would tell ourselves sure
that's a really difficult thing and
imagine imagine that to make it really
Catch-22 that I'll imagine that our
minds and are set up in such a way yeah
that they can't approach the world or
experience otherwise
so in other words to understand to see
that from a more
kind of all-encompassing point of view
we have to step out of the Mind
well I wonder what's the more honest way
to look at things
but I think we like to be to play with
time I think we like to play with these
experiences with all the drama of it
with all the memories with all the
tribulations I think we love it we love
it otherwise we wouldn't be doing it I
think this or Earth loves it The
evolutionary process somehow loves it
whatever whatever this thing that's
being created here on Earth it seems to
like to create like to allow its
children to play with certain uh yeah
truths that they hold this subjective
truths that are useful for the
competition or whatever this dance that
we call Life broadly Define not just
humans and and you know I'm glad you
mentioned that because
what I find fascinating is that the
greatest scientists are on record
saying that when they were making their
discoveries they felt like children so
Isaac Newton said to myself I only
appeared as a child playing on the
seashore and every once in a while
finding a prettier Pebble or a prettier
shell whilst I think some he says
something like the infinite ocean of
knowledge lady was lying before me
who probably it was the greatest
mathematician of the second half of the
20th century the French mathematician
Alexander grotonic
wrote that discover is a privilege of a
child
the child who is not afraid to be wrong
once again to build to look like an
idiot you know to to try this and that
and paraphrasing and go through trial
and error that is for them in other
words for them
that innocence
of a child who is not afraid
who has not yet been told that it cannot
be done okay
that was essential to Scientific pursuit
to scientific discovery
and now and now also compared to Pablo
Picasso a great artist right so who said
every every child is an artist the
question is to how to preserve that as
we grow up
do you struggle with that you're one of
the most respected
mathematicians in the world
uh your Berkeley you're like this this
is the stature you're supposed to be
very like you know yeah sometimes I joke
I say I I think I take an elevator to
the top of the Eiffel Tower every day
yeah and you're supposed to speak like
royalty uh do you struggle to let those
uh strip all of that away to ReDiscover
the child when you're thinking about
problems when you're teaching when
you're thinking about the world
absolutely I mean that's part of being
human because when we grow up I mean all
of them all of these great scientists I
think they were so great in part because
they were able to maintain that
connection okay in that Fascination that
vulnerability
um that spontaneity you know and uh
um kind of looking at the World Through
The Eyes of a child but it's difficult
because you know you go through
education system and for many of us
uh it's not especially
helpful for maintaining that connection
that we kind of like we are being told
certain things that we accept
take for granted and so on and little by
little and also we get hit every time we
act different okay every time we act
that that's in a way that doesn't fit
sort of the pattern we get punished by
the teachers get punished by
parents and so on and don't get respect
when you act childlike in your thinking
when you are fearless and
uh looking like an idiot that's right
because there's a hierarchy nobody wants
to look like an idiot you know once you
start growing up or you think you're
growing up yeah in the beginning you
don't even think of you don't think in
these terms you just play you're just
playing and you are open to
possibilities to these infinite
possibilities that this world presents
to us so how do we I'm not saying that
education system should not be also uh
kind of taming that a little bit
obviously
the goal is balance
that acquiring knowledge
so that
we can be more mature and more
discerning more discriminating in terms
of our approach to the world in terms of
our connections to the world and people
and so on but how we do we do that while
also preserving that innocence of a
child
and my guess is that there is no formula
for this it is
alive is an answer every life every
human being is one particular answer to
how do we find balance
uh that's once imperfect approximation
approximate solution
but we could look we can look up to the
great ones yeah who have
credentials in the sense that they have
shown and they have proved that they
have done something that other humans
appreciate our civilization appreciates
say Isaac Newton or Alexander grotonic
or Pablo Picasso so they have
established their rights to speak about
this matters and we could not dismiss
them as mere Madman
they say okay well if the same thing was
said by somebody who never achieved
anything in in that in their in their
field of endeavor you will be it would
be easy for us to dismiss it but when it
comes from someone like Isaac Newton
we take notice so I think it's something
important that they teach us and
especially today in this age of AI
of course there's a big elephant in the
room always which is called AI yeah
right and so I know that you are an
expert in this subject
and we are going we're living now in
this very interesting times of new AI
systems coming online pretty much every
couple of weeks
so
I kind of um to me that whole debate
about
what is it what is artificial
intelligence where is it going what
should we do about it
needs an influx of this type of
considerations that we've just been
talking about
that for instance the idea that
inspiration creativity doesn't come from
accumulation of knowledge because
obviously child a child has not yet
accumulated knowledge and yet the great
ones are on record saying that a child
has a capacity
to to create
and at an adult
credits the inner child the inner child
yeah for this capacity to create as an
adult you see that's kind of weird if we
take the point of view
that everything is computation
everything is accumulation of knowledge
that just bigger and bigger data sets
finer and finer neural networks and then
we will be able to replicate human
consciousness if we take that point of
view then what I just said kind of
doesn't fit because obviously a child
has not been fed any training data as
far as we know yet they're perfectly
capable of of you know or distinguishing
between cats and dogs for instance and
stuff like that but much more than that
they're also capable of that
you know wide-eyed in the sort of
perspective
so does can it really be captured that
perspective that sense of or can it
really be captured by computation alone
I actually I don't know the answer so
I'm not sort of trying to
uh to present a particular point of view
interesting to question
um any theory that starts out by saying
life is this or Consciousness is this
because when you look more closely you
recognize that there are some other
things at play
which do not quite fit the narrative
and it's hard to know where they come
from it's it's also possible that the
evolutionary process has created
is the very it is computation and the
and the child is actually not a blank
slate but the result of one of the most
incredible
several billion year old computations uh
that
that had explored all kinds of aspects
of of life on Earth
of of war and love and Terror and
ambition and violence and invention all
of that from the bacteria to today so
like that young child is not is not a
blank slate they call me they're they're
actually they hold within them the
knowledge of several billions of years
right the question is whether as a child
you carry that in the form of the kind
of computational algorithms that we are
aware today you see what what strikes me
as unlikely
is that
how should I put it how interesting that
you know we you you are a computer
scientist and there are other people
come I have studied computer science so
I know a little bit
and so it's tempting to say
oh
the whole world
is computer science or is based can be
explained by computer science yes why
because it makes me feel good because I
have mastered it I have learned it my
ego is very happy and people come to me
and and they look up to me and they
Revere me kind of like priests in the
old in old days when the religion was
Paramount wonder when you would be would
tend to explain things in theological
religious terms today science has
progressed there are fewer people who
kind of buy into religion official
religion you know so
we have this urge I suppose to to
explain and to know and to dissect and
to analyze and to conceptualize which is
a wonderful quality that we have and we
should definitely pursue that but I find
it a little bit
unlikely
that the universe is just exactly what I
have learned
and not something that I don't know you
see
well there's a lot of interesting
aspects of the current large language
models
that one perspective of it I think
speaks to the love and math that you
talk to which is
they're trained on
the human data from the internet
so at its best a large language model
like gpt4
captures the magic of The Human
Condition on its full display it's full
complexity
it's just mimicking it's trying to
compress all the weirdness of humans
of all the debates and discussions the
perspectives all the different ways that
people approach solving different
problems all of that compressed so we
live we're each individual ants we only
have like we have a family we interact
with a few little ants and here comes AI
That's able to summarize like a tldr
report of humanity and that's the beauty
of it so I embrace it but I wonder I'm
very impressed by it I wonder if
they can be very impressive meaning
way more impressive in being able to
fake or simulate or emulate a human
right I'm glad you mentioned that
because that's just it seems to be the
Mantra it's just fake fake it till you
make it yeah isn't it isn't that what we
all do though no well yes we do that but
we also do other things we can be truly
in love we can be truly inspired when it
is not fake I do believe call me a
romantic okay but I do believe
and this is a very good I'm glad you're
putting it in these terms because I've
had conversations like that that yeah
fake it till you make it but that's like
that's what humans do yes we do that but
not all the time so and that is
debatable because also I speak from my
own experience and that's where the
first person perspective comes in the
subjective view I cannot prove to you
for instance or anyone else that there
are certain moments in my life where I
am genuine I am pure so to speak when
it's not faking it but I do I do have a
tremendous
a certainty of it and that's a
subjective certainty now I am as a
scientist I'm also trained to give more
um credibility to objective arguments
that another things that can be
reproduced things that I can demonstrate
that I can show
but as I get older there we go as I get
more mature hopefully you know
I'm starting to question why I am not
giving as much
credibility to my subjective
understanding of the world the kind of
the first person perspective when I
actually modern science has already sold
on that you know quantum mechanics
has shown unambiguously that the
Observer is always involved in the
observation
likewise yodel's incompleteness
ethereums to me
a show that how essential
is the Observer of the mathematical
theory for one thing that's the one who
chooses the axioms and we can talk about
this in more detail likewise Einstein's
relativity where
time is relative to The Observer for
instance that's brilliant you're just
describing all of these different scales
The Observer what they Observer science
so we signs of 19th century had the
from Modern perspective and I don't want
to offend anybody I had the delusion
that somehow you could analyze the world
being completely detached from it we now
know after the The Landmark achievements
of the first half of the 20th century
that this is nonsense that is simply not
true and this has been experimentally
proved time and time again so to me
I'm thinking maybe it's a hint that I
should take my first person perspective
seriously as well and not just rely on
kind of objective phenomena things that
can be proved in a in a in a traditional
sort of objective Way by setting up an
experiment that can be repeated many
times maybe I fall in love in a party
you know the deepest love my of my life
Perhaps Perhaps hasn't happened yet
Perhaps I will fall in love and this but
it's Unique it's a unique event you
can't reproduce it necessarily you see
so so in that sense you see how these
things are closely connected I think
that if you if we are declaring from the
outset that all there is to life is
you know computation in the form of
neural networks or something like this
however sophisticated they might be
I think we are from the outside denying
to ourselves the possibility that yes
there is the side of me which is not
faking it yes there is a side of me
which cannot be captured by Logic and
reason and you know what another great
scientist said bless Pascal
he said the heart has its reasons of
which the reason knows nothing
and then he also said the last step of
reason is to grasp that there are
infinitely many things Beyond Reason
how interesting this was not a
theologian this was not a priest this
was not a spiritual Guru
um it was a hardcore scientist who
actually developed I think one of the
very first calculators
how interesting that this guy also was
able to
uh impart on us that wisdom now you can
always say that's not the case
but why should we
from the outset
exclude this possibility that there is
something to what
he was saying that is my question I'm
not taking sides
um what I'm trying to do is to shake a
little bit the debate because most
mathematicians that I know and computer
scientists even more so they're kind of
already sold on this
um we are just you know reminds me of
this famous Lord kelvin's quote from the
end of 19th century
there's some debate whether he actually
said that but
never let a good story you know
he said physics is basically finished
yeah All That Remains is more more
precise measurement so I find a lot of
my colleagues are happy to say
yeah everything's finished we already
got we got it we got it uh maybe little
tweaks
in uh in the in our large language
models you know so now here's my
question
I'm kind of Playing devil's advocate a
little bit because I don't see the other
side
represented that much
and I'm saying okay could it be also
that if you believe in that that becomes
your reality
that you can kind of put yourself in a
box
where everything is competition and then
you start seeing things as as being such
it's confirmation bias if you will you
know this also reminds me you know I
think a good analogy is it's a friend of
mine uh Philip caution told me that in
France there is this literary movement
which is called ulipo
o u l uh IPO
and it's a bunch of writers and
mathematicians who create works of
literature
where in which they basically impose
certain constraints
a good example of this
is a novel which is called the void or
disappearance by a writer named George
pereck
which is a 300 page novel in French
with no no which never uses the letter e
which is the most used widely used
letter of the French language so in
other words he said these parameters for
himself I'm going to write a book where
I don't use this letter which is a great
you know it's a great experiment and I
upload it
but that's what it's one thing to do
that and to kind of show his
gamesmanship if you will and and his
proclivity and his ability as a writer
but it's another thing if at the end of
writing this book when you finish the
book he would say letter e actually
doesn't exist
and try to convince us that in fact
French French language does not have
that letter simply because he was able
to go so far without using it you see so
self-imposed limitation that's how I see
it and I wonder why
we should do that do we really need do
we really feel the urge to say the world
is like that the world can be explained
this way or that way and I'm saying it
you know it's a personal question for me
because I am addicted to knowledge
myself
I you know hi my name is Edward
and I'm an English addict okay I'm being
serious I'm not being facetious up until
very recently maybe a couple years ago
I simply did not feel comfortable if I
could not say the given answer
explanation it's like oh there has to be
some explanation and I try to
frantically search for it
just for somebody like me
I know heard you know a left Brainiac
and uh
you know
that's kind of typical typical for a
scientists for mathematician it is
incredibly hard
just to allow the possibility that it's
a mystery
and not to feel the urge
to get the answer it is incredibly hard
but it's possible and it is liberating
it's recovering is recovering addict to
knowledge
let me say
what you gain from it for instance I
understand the value of paradoxes I I
appreciate paradoxes more and you know
to to use another philosopher uh Soren
kirkegar the Danish philosopher said uh
I think or without Paradox is like a
lover without passion
a paltry mediocrity what's a good line
all right
so and you know
Niels Bohr Niels Bohr said
um in similar Vein The Great uh Danish
also something about that something
about Danes I think it all started with
scramble it you know
he said the opposite of a simple truth
is a falsity
but the opposite of a great truth
is another great truth
in other words
things are not black and white you know
they are not
and I would even venture to say the most
interesting the interesting things in
life
are like that the ones which are
ambiguous
it's an electron a particle or a wave
it depends how you set up an experiment
it will reveal itself as this or that
depending on how you set up an
experiment
this bottle if you project it down onto
the table
you will see more or less a square it
will project it onto wall you will see a
different shape a naive question would
be is it this or that
because we understand that it's neither
but both projections reveal something
the real different sides of it a paradox
is like that it's only paradoxical
um if we if we are confined in a
particular
Vision if we are wedded to a particular
point of view
it's a Harbinger if you will of a
possibility of seeing things uh in a
more in in a as they are as a more
sophisticated than we thought before you
see this is such a difficult idea for
science to Grapple with that you know I
don't know how there's so many ways to
describe this but you could say maybe
that the subjective experience of the
world
from an observer is actually fundamental
but we know that our best physical
theories tell us that unambiguously in
quantum mechanics actually you know
Heisenberg I think captured it the best
when he said what we observe is not
reality itself
but reality
subjected to our method of questioning
um when I talk about uh electrons for
instance so that there is a very
specific way in which you in which this
is realized there is a so-called double
slit experiment right so
um for those who don't know it's you you
have a you have a screen and and you
have an emitter from which you send you
kind of shoot electrons and in between
you put another screen which has two
vertical slits parallel to each other if
we were shooting you know tennis balls
each ball would go through one slit or
another and then hit the screen behind
this or that slit so you would have
let's say they colored they painted so
they'll be sort of bumps or or or spots
of paint behind this or that
but that's not what happens when we
shoot electrons we see an interference
pattern as if we were actually sending a
wave so that each electron
it seems like the each electron goes
through both slits at once and then and
then has the audacity to interfere with
it with itself where at some points you
know two crests would amplify and at
some points aggress in the draft would
cancel each other
yet so that suggests okay so no electron
is a wave not so fast because if you put
a detector behind one of the slits and
you say I'm going to I'm going to
capture you
I am going to find out which lid you
went through the pattern will change and
it will look like the particles so
that's a very concrete realization of
the idea that depending on how we set up
an experiment we will see different
results
and the problem the problem is that our
psyche I feel kind of lagging is lagging
behind in part because maybe our
scientists are not doing such a great
job so I take responsibility for this
that why haven't I explained this
properly you know
I I tried you know in a bunch of talks
and so on so now I'm talking about this
again
our psychic kind of lagging behind we're
still even though our science has
progressed so much from the certainty
and the determinism and and all of that
of the 19th century
our psyche is somehow still attached to
those ideas the ideas of causality of
this naive determinism that that the war
the world has a bunch of billiard balls
hitching each other driven by some blind
forces you know that's not at all like
this and we've known this for over for
well for about 100 years at least you
know and you call this self-imposed
limitation it is a self-imposed
limitation when we when we pretend that
uh that for instance that this naive
ideas of 19th century
um physics are still valid and and then
start applying them to our lives and
then also derive conclusions from it and
for instance people say there is no free
will why or because the world is just a
bunch of uh billiard balls where is the
free will but excuse me didn't you get
the memo that this has been debunked
thoroughly by the so-called quantum
mechanics which is our best scientific
theory this is not some some kind of
bullshit or some kind of you know
concoction of of a of a Madman this is
our scientific theory which has been
confirmed by experiment so we should pay
attention to that so but of course it's
not just
um self-imposed limitation unfortunately
in this case there is a big issue of
Education
so a lot of people are not aware of it
through no fault of their own because
they were never properly taught that
because our system is broken education
system is broken especially in math
and then our so where do we get them do
you get information you get information
from
our scientists who actually write
popular books and so on which is a great
you know
um great thing that they do but a lot of
scientists somehow
um when it comes to explaining the laws
of physics they are doing a fantastic
job
um talking about this phenomenon for
instance double slit experiments and
things like that but then you know
interviewed by science managers in about
three wheel and so on they revert back
to 19 19th century physics as if those
developments actually never happened so
to me this is single most
important sort of issue in our
Popular Science
the idea that somehow there is this
world out there but it's complete has
nothing to do with me so I can I can
reveal in the
intricacies of this particles and their
interactions
but but completely ignore what
implications this has
for my own relationship to the physical
reality to my own life you know because
it's kind of scary I guess you know but
also what are the tools
with which we can talk about the
Observer
the subjective view in reality what are
the tools of which we could talk about
rigorously talk about Free Will and
Consciousness what are the tools of
mathematics that allow that I don't
think we have those tools because we
haven't been taught properly so actually
tools are there for instance
um
I think well
here we have to
I have to say my conviction is that
everybody knows
in the heart of hearts everybody knows
that there is that there is something
in our football there is something
mysterious and in fact you know
somehow immediately I feel that
um you know the impulse to quote
somebody on this because as if as if my
own opinion doesn't occur
there's a long dead expert that has when
Einstein said that he doesn't like how
see look at me I am supposed to do like
this smart intelligent person
I am afraid to say it and own it myself
I have to find a confirmation I have to
find an authority who agrees with me and
in fact it's not so difficult to find
because Albert Einstein literally said
the most important thing in life is the
mysterious okay he actually said that
there are some quotes which are
attributed to him which he never said
but this he did I investigated okay so
but more importantly you know
how do you feel about it
um I think that everybody knows
but
in other words he also said Einstein
imagination is more important than
knowledge okay and explain for knowledge
is always limited
whereas the imagination Embraces the
entire world giving birth to Evolution
it is uh strictly speaking a real factor
in scientific research he says and he
says I am enough of an artist to follow
my intuition and Imagination that's
Albert Einstein again so and I feel the
same way to be honest if I think about
my own mathematical research
it's never linear
it's never like give me more data give
me more data give me more data Boom the
glass is full and then I come up with a
discovery no it's always it always is
always felt as a jump
as a leap
and I I have actually been studying
various
examples in a history of mathematics of
some fundamental discoveries like
Discovery complex numbers like square
root of negative one
I wonder if a large language model could
actually ever come up with the idea that
square root square root of negative one
is something that is essential or
meaningful because if all the
information that you get
the all the knowledge that had been
accumulated up to that point tells you
that you cannot have a square root of a
negative number why because if you had
such a square root
we know that if then we would have to if
you square it you get a negative number
but we know that if you square any real
number positive or negative you will
always get a positive number so
Checkmate you know it's over square root
of negative one doesn't exist yet we
know that these numbers make sense
they're called complex numbers and in
fact quantum mechanics is based on
complex numbers they are in essential
and indispensable for quantum mechanics
could one discover that so to me that
sounds like
I discontinue it in the process of
discovery it's a jump It's a departure
it is like a child who is experimenting
it's like a child who says I'm not
afraid to be an idiot everybody says the
adults are saying square root of
negative number doesn't exist but guess
what I'm going to accept it and I'm
going to play with it and I'm going to
see what happens this is literally how
they were discovered there was an
Italian
mathematician
astronomer astrologer he was he he made
money apparently by compiling
astrological sort of readings for for
the elite you know of his ears this is
16th century everyone does example
all around interesting guy I'm sure we
would have an interesting conversation
with him gerolamo cardano he's all he
also invented the what's called cardan
shaft so which is an essential component
of of a car
we say in Russian so so he wrote a book
which is called uh our ass Magna which
is a great art of algebra and he was
writing solutions for the
cubic and quartic equations
this is something that is familiar
because
it's cool we study Solutions of
quadratic equations equations of degree
two so you have x a x squared plus BX
plus C equals zero and there is a
Formula which solves it using radicals
using square roots
and cardano was trying to find a similar
formula for the cubic and quadratic
equations for which which would start
with x cubed or x to the power 4 as
opposed to x squared and in the process
of solving these equations it came up
with square root of a negative number
specifically square root of -17
and he wrote that I have to forego some
mental tortures
to deal with it but I am going to accept
it and see what happens and in fact at
the end of the four at the end of the
calculation
this this this weird numbers got
canceled it kind of canceled out in the
formula appeared square root of negative
17 and its negation so they kind of
conveniently gave the right answer which
is not involve those numbers so he was
like okay
what does it mean mental tortures so you
see from the point of view
over of the of the thinking mind
it is something almost unbearable it's
almost I feel that a large language more
the computer running a large language
model trying to do that would just
explode
and yeah the human mathematician was
able to find the courage and inspiration
to say you know what what is wrong why
why are we so adamant that these things
don't exist that's just our past
knowledge based on what our past
knowledges and knowledge is limited what
if we make the next step
today for us mathematicians context
numbers that we call them are not at all
mysterious the idea is simply that
you plot real numbers that is to say all
the whole numbers like 0 1 and so on to
and so on right all fractions like one
half or three halves or four over three
but then also numbers like square root
of two or Pi we plot them as points on
the real line so we draw this is a this
is one of the kind of perennial Concepts
even in a in our very poor math
curriculum at school but now imagine
that instead of one line you have a pla
you have a one axis you have a second
access
and so you numbers now have two
coordinates X and Y and you associate to
this point with coordinates X and Y
and the number X which is a real number
plus y times square root of negative one
this is a graphical geometrical
representation of complex numbers which
is not mysterious at all now it took
another two or three hundred years for
mathematicians to figure that out but
initially it looked like a completely
crazy idea you know
so all it is all a complex number is
it's just an experience
the real part and the imaginary part
it's just an expansion of your view of
the mathematical world the fact that you
can actually multi you can add them up
by adding um together the real parts and
imagining parts that's easy but there is
also formula for the product for the
multiplication which uses the fact that
square root of minus 1 squared is minus
one
and the amazing thing is that that that
product that multiplication satisfies
the same rules the same properties that
are usual operation of multiplication
for real numbers for instance there is
an inverse for every non-zero number
that you can find like number five has
an inverse one over five but uh OnePlus
I also has an inverse for instance you
know that was always there in the
mathematical universe but we humans
didn't know it and here comes along this
guy who engages in the mental torture
who takes a leap off the cliff of
comfort of like mathematical established
knowledge established knowledge right
and now obviously for each each um sort
of
fruitful leap like that there probably
were thousands of like things which went
nowhere I'm not saying that every Leap
you know it's like it's a it's a it's a
open shooting game yeah because for
example you can try to do the same with
three-dimensional space so you have
coordinates x y and z
and you can say oh uh if there's one
dimensional we have an abonified
numerical system called real numbers
if it's two-dimensional which is like
you know geometrically it's just like
the stable top extended to Infinity in
all directions
these are complex numbers and we can
Define addition and multiplication and
they will satisfy the same properties as
real numbers that we're used to wha