Transcription
people usually tended to write down
equations and try to solve the equations
and things like that I was not doing
that I was looking at General
features that space times can have I
think the point has got lost it's
missing something they've lost it in the
power of computing the thing is that
computers have got so powerful that
they've lost the thread of what they're
doing the complex numbers are absolutely
fundamental you see they're fundamental
to Quantum Mechanics the whole structure
of quantum mechanics depends on complex
numbers Twisted theory is very specific
to space-time geometry so your Nobel
price is for what it's for showing that
was wrong if you like the name is
wrong it's not artificial intelligence
it's not
intelligence intelligence would involve
Consciousness that these devices are not
conscious and they will not be be
conscious unless they bring in some
other ideas host of the interview is Dr
Matt keki a science popularizer and a
former digital ambassador of the
European Union if you remember from your
childhood the moment did you touch the
geometry for the first time you see I
tell this story as a joke now a joke
doesn't mean I really mean it as a as a
as a
realization the joke is as follows when
I was very young I was probably about
six or
seven I did I hated spinach I was given
this spinach to eat and I said oh I
don't like spinach I eating it and
so and the person who was dealing with
it said after a while look
okay you didn't use the word okay in
those days it would be all right all
right if you eat half of it that's
enough so when she wasn't looking I took
this circular patch reconstructed it
into a semicircle of the same volume but
now sh in a
semicircle and she came back and said
that's good thank you very much they can
go I guess it was the the volume is
different from
shape I think it was rather Elementary
Discovery uh is it true that when you
found out about your Nobel Prize you
organize a meeting on Zoom supposedly
you said that you didn't deserve the
Nobel Prize did you show The Singularity
exist but not that they are high and
behind a horizon of events yes well this
is well known it's all part of the story
see some people get confused by the
story and the Nobel what they say in the
is isn't completely correct what they
say you see it's the right idea but how
do they say it anyway it's difficult to
say and it depends what you mean by the
words you see what I showed was
what see when I collaborated later with
Steven Hawking he used a certain
terminology which was different from my
original terminology however it is the
terminology which I'm now going to
use what I'm now going to use which is
not actually quite my terminology it's
Steven Hawkings terminology okay what I
did prove then was that you got a
singularity now this was if you have a
certain Criterion for a collapse which
is beyond retrieve a collapse gone past
the point of no return which I phrased
in terms of what I called a trapped
surface that was really the key point
that if you have a what I call a trapped
surface which would happen in the
collapse you see there was a famous
paper by Oppenheimer and
Snider this was in something like 1939
just before the second world
war and in this paper they had a dust
cloud which
collapsed and it collapsed and it became
Singularity infinite density so the
collapse became infinitely dense in the
middle nobody really believed this
because oh well usual it wouldn't be so
spherical and you'd have pressure in the
opheim S picture there was no pressure
it was just what they call dust no
pressure but more importantly exactly
spherically symmetrical so exactly
everything falls towards one point
that's not
realistic and this was a time when these
quazar were being seen and something
really funny going on in these distant
galaxies huge activity it looks as
though there were bodies out there which
were
out um beyond the limit that you would
get in in the Oppenheimer Sider model in
fact beyond my well you see I didn't
have my theorem at that time my theorem
was developed as a response to the
arguments that people had they say well
the Oppenheimer snid picture is not
realistic because it could be very
irregular and it could swirl around and
come out
again and this was the common belief
because in addition to
the
observations there was a paper written
by two Russians liit and khalatnikov
and this kadnikov seemed to have proved
that in general you if it's complicated
you will not get
singularities that the things will not
become infinite density they will swish
around and come out again so this was
the view that people had formed largely
on the basis I suspect of this paper by
lit and col so your Nobel price is for
what it's for showing that was wrong if
you
like no yes yes you see my Nobel Prize
was to show I had to look at the paper I
didn't think that I didn't really
believe their methods I thought that's
not convincing enough there was a
mistake in the paper which balinsky
became collaborator with them later and
corrected the mistake and then they
found that singularities were generic do
you remember that moment that you found
that mistake no I didn't find the
mistake it was balinsky found the
mistake no no I found an inde dependant
show that it was there must have been a
mistake M but my argument was nothing to
do with the paper it was using
completely different methods and I was
looking at methods which I guess people
have never used before that's probably
why the that's what the priz was really
when you look at your life you are more
mathematicians or
physicist mathematical
physicist so I was using mathematical
Techni what's closer your heart
that's a difficult
question I think it's drifted more to
physics and it probably was more
mathematics
earlier you
see when I go to Cambridge me meeting on
on twister Theory and I learn all about
what many people are doing a lot of it
is very mathematical it's interesting
but it's not my where my heart is if you
like where my heart is is the physics
part that part of Twister Theory which
is is connected with physics there's a
twisted theory has grown outside that
area it's grown into a much bigger
mathematical area which is interesting
to me but not so near my heart if you
like it's not what I like to develop not
what not what I work on so what I work
on is where the mathematics ties in with
the physics it's hard to separate them
in this
sense so it's mathematical physics yes
the oppenheim and Snider model
that's right so I started thinking about
this independently of that I wondered
well suppose it is very
complicated and I imagined being inside
what you call a black hole I was I mean
and getting near these singularities and
what it would be like and I tried to
imagine that and
uh I'm not quite sure you see the
techniques which I had
developed came from a different area it
was I was looking at a different problem
altogether and I developed part some of
these
techniques of looking at the causal
structure you
see people usually tended to write down
equations and try to solve the equations
and things like that I was not doing
that I was looking at General
features that space times can have and
if you have a a region in space time and
you look at the future of that region so
what po look at all the places that can
be reached in the
future this point may not be reached
this point can be reached So Into the
Future IT sweeps out a
region now what does that region look
like what does its boundary look like
what does the edge of it look like it
looks like something which has light
rays on it so you I could prove that you
could prove a theorem which says any
point on the boundary must lie on a
light Ray
analg
adisc this way into the future but not
into the past if you go into the past it
may wind round and round and never end
it may wind round and round or it may go
back to the initial point of this thing
you start with so it's quite complicated
but I understood quite a lot about that
kind of structure and I was able to show
that once you have what I call a trapped
surface which is a General thing you see
it doesn't see in in the Oppenheimer
sniper picture he had to
assume exact situation I'm not assuming
any exact situation I'm assuming an
inequality so it has to a certain thing
has to how do I put it they difficult to
explain you see there's a thing called a
trapped surface which I introduced this
was a
notion which people hadn't thought of
before that can you around your body by
a surface so it's an ordinary
two-dimensional surface such that the
future of that surface you look at all
the things which can be reached into the
future from that surface what is the
edge of its surface what does it look
like just at the initial State and the
claim is that if the light rays at the
beginning are
converging that was my condition the
Trap surface as if the light rays are
converging both the in ones and the out
ones you see how do I put
this a surface element in space
time
is it's a space likee thing so it could
be an instantaneous
surface it could exist just for a moment
now suppose it's concave like that then
the ray
if you imagine a flash of light on that
surface the Rays on the inside will
converge and they will come closer and
closer and they will start meeting each
other the words on the outside will
diverge they never meet each
other if it's the other way around then
they will converge in this way and the
other ones M there are certain surfaces
in space time which Converge on both
sides it's you think it's a rather
peculiar situation it's not so peculiar
as you might think I won't go into the
discussion you
can you have to bring in the the time as
well as the space when I look at all
your con
Concepts uh you very often you talk
about um your work with Hawking Stephen
Hawking I I think that that's my private
opinion of course
that almost all these
Concepts uh were more pen RS
than huling that hulking was much more
better getting
attention well you see this topic I
would say it was mainly me that's
true I would give some credit also to
Brandon Carter you see Steven Hawking
worked in his early work there were lots
of
mistakes and usually it was Brandon
Carter who corrected the
mistakes
um but he corrected them himself the
mistakes he was good enough to see when
there were mistakes and he corrected
them so the final results he had in his
thesis I was one of the examiners of his
thesis and I had listed the various
mistakes in this thing but he' corrected
them all by the time the exam so that
was okay but these techniques were he he
did develop some of them beyond what I'd
done but the main ideas came for me I
think that's
true um of course the the most important
work that he did was really quite
different it was the work on on black
hole I mean he he did a lot of hard work
on it so I wouldn't I wouldn't discredit
what he did he did a lot of hard work
it's not just me no no I would say the
initial ideas came from me but a lot of
the technicalities which came later he
did he worked at
himself and that's true uh there's a lot
of fatures um pen rose cube pen rers
NeverEnding numbers of uh you creation
um it's more science or more
your game with the reality your your
game with the humanity I don't draw a
clear line between games and serious
science how do you know when it's
serious science I mean the the
nonperiodic if you look at at uh T my
tiling out there and in the back of
because you know it's like a game with
our minds yeah but then a lot of a lot
of mathematical physics is games in a
sense you see you do it for
fun it's a combination you see partly
it's you have a drive to find an answer
to a problem but often it's the the you
do what looks looks looks
fun and I quite play like playing with
these causal spaces so you're looking at
at how SpaceTime structur
in your gen in general terms or what the
boundaries of Futures look like and that
was the kind of thing that was used for
the
theorem which eventually got the Nobel
Prize you see that was a a kind of
mathematics which I had developed not
particularly originally to prove this
theorem the the techniques were just
being developed for fun if you like to
see what things look like in space time
what the boundaries of Futures look
like and it's an interesting subject and
in mathematics that's what one does one
often is interested in a subject just
because it's entertaining to one so you
you do it because you like it a lot of
scientist people worldwide call you the
greatest mind of the world
genius well that's I don't ask you a
limited number of people hope I don't
ask you if you agree or not but I would
like to ask you
what are you doing
that having 93 years you
are in such good condition how you are
spending your day now I'm still I'm
rather slow I think I'm getting very
slow at things I always used to be
rather slow but I've got slower
um also I found that you know people say
when you get older you start to lose
your recent memories I find I lose my my
Distant
Memories I can't remember what I did and
somebody oh you did that what oh one
hours ago but you are still
remember any details of the
theories no the old things I lose you
see that's a I'm losing my just my
longterm memory no I don't know if it's
really this but what's your advice for
for for the people I'll tell you my
advice my advice is to be
lucky I think of so many things in my
life life which depended on pure
luck it's very hard to tell you see I
think I had to be in the right place at
the right time often that's certainly
true but I
also let me consider say work that was
developed see my early interest in
general relativity serious interest in
the sense of working effic efficiently
on the subject rather than
dabbling was
well Herman Bondi was doing things on
gravitational waves and how the mass
gets Carried Away by gravitational waves
and the most important work was done by
Ray sax Ray
sax he died quite
recently and um he had a v very
important result very beautiful result
which had to do with the way that the
radiation field behaved and he developed
this idea of what what he called the
peeling off theorem there these certain
directions which you get in the
curvature tensor and the most distant
they all Point outwards and then you
come in a little bit and then one
doesn't point and then they bit more and
they they he said they sort of peel off
as you come in very strange way you
behaving but then I remember some moment
when I was thinking about this and I
realized that this had to do with this
conformal it was the birth of conformal
infinity really the way of talking about
asymptotics was to look at the conformal
picture you see when you look at it
conformally all these things come
together and you can see why the peeling
theorem happens but that was very much
the fact that I knew RX and i' learned
about his result and I got the key point
out of what I was doing came from what
he
did Englebert shooking I happened to
share an office with him pure
coincidence I shared an office with him
and he explained the importance of the
conformal invariance of Max's equations
I had no idea about that before and the
importance of the splitting of positive
negative frequencies but that led me to
twist the theory if I hadn't shared that
office with Engelbert shooking would I
have had those ideas probably not I have
no idea so luck yes luck is
important Nobel committee and AI
takeover do you agree with thate Nobel
Prize committee uh uh when you look at
the Noble in physics for father sopi I I
haven't looked at the details of it what
I don't know what they say for
fundamental
uh work
under synthetic neutral networks for
Jeffrey Hinton is it
physic I'd be rather doubtful whether
it's really
physics I'm not sure you see Nobel
prizes you might question some of their
decisions
sometimes I would question a few of them
maybe I would question this one I'm not
sure you I haven't I haven't looked at
it carefully it depends exactly what
they
say you see it's a technological advance
I would say it's probably making use
of I is it a theoretical advance or
is I don't think so is it but I mean the
Nobel committee normally doesn't give
the prize for purely
theoretical I mean doesn't it does you
have to have a a physical application of
it yes now here I'm not quite
sure I I'd have to see what the wording
is in the Nobel Prize to say whether I'm
happy with it or not I don't know how do
you look at the AI development and
what's your prediction
about the future of AI see I don't
really know what AI does these days you
see so you're asking me a question
outside my area of expertise I would say
an area of expertise has to do with
whether these
devices actually do what we do I don't
think they do because they're not
conscious I don't think they will ever
become conscious by virtue of being
computers in our current sense of the
word
I don't know if that's an answer to your
question um it doesn't mean that they
won't be better than us the biggest risk
of AI development is yes so I have
nothing against that that's fine I think
there is a risk involved here part of
the risk is people thinking that they're
actually that there is a conscious
they're conscious yes there might be an
even more of a risk if they were
conscious you see it maybe one could
understand what's involved in
Consciousness and develop some kind of
device I'm not calling computer because
it in my view it would not be a computer
it would be something else some device
which is conscious and since I believe
Consciousness is a physical
process I don't think we understand it I
think it involves the collapse of the
wave
function that's partly a negative
conclusion from I don't see it anywhere
else um
but the collapse of the wave function is
very
mysterious and involves certain
retrocausal things which are a little
bit
puzzling I think the way that time works
is not so clear when you're talking
about but there are certain
things which are in contradiction you
almost say with ordinary causality it's
not so much that they are it's that you
have to have different concepts of what
you mean by
reality and there are two concepts which
I've tried to separate from each other
one is classical reality and the other
is quantum reality now classical reality
is the sort of thing we normally talk
about we can touch we understand using
our senses but the main difference I'm
saying is you can ask the system say if
I I take this glass and I can ask the
glass I can say hello glass what shape
are you and don't do it that way but I
say okay what shape is the glass and I
say oh it's got a round top it's more or
less cylindrical the classical it's
classical reality yeah now Quantum
reality is more
like well Einstein had a nice Criterion
but he didn't call it quantum reality
I'm calling it quantum reality this was
how do you know that the wave function
is real is the wave function of a
particle real or not and a good example
of this is the spin of a spin half
particle now the spin of a spin half
particle is a Quantum thing now can you
ask the system hello hello system which
way are you
spinning it doesn't it looks at you
blankly and says I don't answer
questions like that ask me a different
kind of question please the right thing
to do is you say Okay particle is your
spin in that particular direction you
see the spin has an axis the way that
spin works for a spin half particle it
has a particular axis that's how you
describe the quantum state of a spin
half particle it has one particular
direction it spins about that direction
now Can you ascertain that direction no
you can't it's Quantum reality you
cannot ascertain Quantum reality you can
only confirm it so I like to use those
two words ascertain I can ascertain the
shape of this glass that's classical
reality I can only confirm
term quantum reality I can if I think I
know which direction it's spinning I
said yeah I've got my calculation done I
said you've done this blah blah yes it's
probably by now spinning that way I say
hello State I think you're spinning that
way have I got you have I got it right
and if I have got it right it says yes
with certainty so that was Einstein's
Criterion so if you can confirm with
certainty that it's then this gives you
an element of reality he calls an
element of reality I'm calling it an
element of quantum reality classical
reality is the other kind you can conf
you can astain classical reality you can
only confirm Quantum reality and you
need those two ideas and you need to
separate them and Quantum reality
behaves very
peculiarly it actually behaves retr
causally but you might think there are
these experiments with I think you talk
about the Nobel Prize the one before
that one to Zinger and people about
these I think epr type experiments I
can't quite remember what they got it
for but it's something like that you
have these effects which seem to affect
the instantaneous you see you share a a
spin between Alice and Bob and Alice and
Bob originally have a spin zero and
their spins are opposite so if Alice is
spin is this way Bobs is this
way now suppose measures her Spin and
she finds it to be that
way
retrocausal along the past light cone so
it's not just simultaneous worse than
that it's into the past but not faster
than the light could go from this one to
this one it's a strange way around but
retrocausal it becomes the opposite of
Alice's measurement Bob can't ascertain
it so he can't she can't send a signal
faster than light because because he can
only confirm it he doesn't know which
way it
is so you need that idea to make sense
of these epr Einstein pki Rosen type
experiments which I think would I'd have
to check exactly what the Nobel Prize
was the year before this one but I think
it was to do with that that's a very
important and fascinating Discovery but
to understand what's going on I think
the best way to do it is using Quantum
reality
and you you certainly can't send a
signal faster than light by these means
but you can
retrocausal backwards faster than light
or not as fast almost as fast as light
backwards if it's only Quantum reality
as long as we don't understand how
Quantum world work we cannot replace it
into I think it's not as bad as that you
see don't understand it's
saying rather trying to put it into a
classical
perspective we can understand the
mathematics of it and we can get used to
it okay and that is involving an
understanding somebody asks somebody ask
me a question I may not understand it
that well but I could do my best and I
might understand the quantum mechanics
well enough to give the answer that
quantum mechanics would say now that
means understanding sure it's an
understanding of what's going on you
there's this famous comment was it
nobody understands quantum mechanics was
that I I know I
was I think I think it was yes no you
see I think that's
misleading you
see
understanding doesn't require it to be a
classical understanding we are
determined by the nature to understand
the classical World Quantum world is
indeterministic and it's
ununderstandable for our our mind a
little bit you need to use the formulas
to try to understand the quantum world I
think it's it's unfortunate to use the
word understanding and limited you can
say I don't know what word to use but
if understanding in the in the sort of
classical sense and that sure that fails
yes that does fail but it's not lack of
understanding you get the picture and
you can see oh yes I know how to make
the predictions qu mechanics work and
they can be quite yes no predictions
some of these predictions don't have to
be just probabilities so I think the
view is it's get sort of mixed up with
the idea oh you only know the
probabilities or something I think
that's
misleading these things are puzzling not
just because they're probabilistic they
are sometimes just probabilistic but
that's what makes them consistent by
having them only probabilistic but the
things which I find Most Fascinating
about quantum mechanics are not
probabilistic things they're like these
epr
effects sure it's probabilistic if you
ask somebody to to make a measurement
and it's only a Quantum reality that I
mean he's trying to make a classical
reality measurement he's only going to
get a probability as
answer I just think one has to separate
the
quantum reality from the classical
reality and and realize that the quantum
reality behaves differently yeah for it
but it doesn't mean it's beyond
understanding I don't know if that's the
way people use the word understanding
often in that that way I think that's a
bit a bit
misleading AI
takeover few times you talk about the
Nobel Prize um we've back from Stockholm
uh this year we've been there
interviewing Nobel Prize winner don't
you think that this year Nobel PR prize
is the tribute to the Nobel comedy for
artificial intelligence Nobel Prize
Nobel Prize in physics father for
fathers of of AI Nobel Prize in
chemistry uh sir Demis hassabis
co-founder of deep mind that's AI system
David Baker computer vision
digitalization of proteins don't you
think there the tribute for AI I see
well you have to be careful
first of all the name is
wrong it's not artificial intelligence
it's not
intelligence intelligence would involve
Consciousness and I've always been the
strong promoter of the
idea that these devices are not
conscious and they will not be be
conscious unless they bring in some
other ideas the comput they're not
they're all computable Notions but
intelligence it's not
Consciousness it depends on
Consciousness you see well it depends on
how you use the word I think when people
use the word intelligence they mean
something which is
conscious I mean that you see I
developed my own ideas after going to a
course you see when I was a graduate
student in Cambridge I went to three
courses which were nothing to do what I
was supposed to be doing one was by
Bondi on General relativity one must be
dra on quantum mechanics distinguished
very distinguished Paul dra and the
third subject was on mathematical logic
and I learned about touring machines and
comput the notion of
computability and I no knew what
computability meant and I learned about
girdle theorem and girdle theorem I
found stunning because it told you that
there are
things that the
understanding transcends the use let me
put that more
clearly what girdle does it's very
clever what he does is to produce a
statement now suppose you you see you're
trying to develop your
mathematical methods of proof what do
you mean by proving a theorem in
mathematics how do you know it's really
true will you prove it what does proof
mean well you see does it mean okay
you've got a set of rules and if you
follow these rules that makes it a
proof now how do you know these rules
only give you truths well you've looked
at them carefully and you say oh but
maybe AI creates its own rules ah no no
you see have to be careful about this
this is the point but I I learned from
from Ste this is a man called Steen who
is the logician and I learned from him
this important thing about girdle's
theorem now girl's theorem is extremely
clever you make a statement which
asserts that it's it cannot be proved by
these
rules it's just you the clever thing is
to make it do it it says you give your
rules which you regard as the rules of
proof and you could put them on a
computer so that mean they're
computational
rules now I knew that there were things
that you cannot put on a computer I
learned from this course that there are
non-computable things there are things
in mathematics which are not computable
now what does a computable mean it means
that you can make a
computer well you have to Define what a
computer is and touring had one
definition of a computer there were
several other church and Curry other
people had their definitions of comput
they all turned out to be equivalent so
there is one universal notion of
computability which is what you mean by
what can be done by a computer maybe
this is only language problem that the
language development has not kept out
development of AI maybe we have just
only language problem that we cannot you
know describe what we created no I don't
agree with that it's not a language
problem you see you make your new
language sure you can do that you make
your new language and that's what you
can do so let me describe the girdle
theorem how it works you see see the
girdle theorem says you construct a
statement which
says you see what it means the way
you've constructed the sentence you can
see what it means what it means is I am
not provable by those
rules and it does that it really says
that then you see okay well is it
perhaps it is provable by the rules if
it is provable by the rules then it must
must be true well I said it the wrong
way around doesn't matter the other way
suppose it's false then that means it's
provable by the rules and if it's
provable by the rules you've understood
the rules you said you looked at them
all and say yes that's okay that's okay
that sure if you follow those rules it
is true so that means you believe that
the rules only give you truths so
therefore it is true that it's not
provable by the rules if it's false you
see then it is provable by the rules and
therefore it's true so it has to be true
and not provable by the root I found
that amazing you see that's the whole
point about the girdle theorem the whole
point as far as I'm concerned about the
G theorem is how do you transcend the
rules and that's what you do by
understanding them you understand them
why they're true it's not that you use
the rules but you understand why use of
the rules only gives you truths and
that's how you can prove things which go
beyond the rules by knowing why they're
true now knowing why they're true well
what does it mean well it means you
understand them what does understand
mean you've got to be conscious of them
you see you can the wording is clear it
means that you have to know what you're
doing you have to know why they're true
not that they're true you can be told
that they're true you can have you can
learn at school that they're true that's
not the point you have to know know why
they're true why they're true needs
understanding them and understanding
them requires to being conscious of them
now that's require that you see the
point I was making is
that Consciousness enables you to
transcend the
rules you see why they're true and that
goes you beyond it you see what the
girdle theorem does it tells you how
to use your your understanding of why
the rules are true to transcend the
rules you think that AI is the simple
tool or simple thing that we can use in
the single case no I don't say single
it's obviously infinite no clearly
that's not the
point the point is it doesn't know what
it's
doing that's still true with AI you talk
to an AI thing it doesn't know what it's
doing it has it speaks from experiences
if you like you see people have confused
the story the story is they've lost it
in the power of
computing the thing is that computers
have got so
powerful that they've lost the thread of
what they're doing I think the point has
got lost I think touring wasn't too far
off you see he he was a a little bit
confused person in way because he it was
not clear what he
believed but he did call this thing the
touring test how do you de decide
whether an entity is conscious or not
will you have a conversation with it you
talk to it it's missing
something I think yeah that's the
trouble you see it's all I mean
obviously it has a role to play I'm not
going to say that clearly it has a role
to play it has a role but you must
mustn't be confused the fact that it has
a role to play it's to do with the power
of computation sure you computers have
got so powerful now that they can do
things Way Beyond what humans do in comp
Computing sure
and you can take a mass of data and you
can analyze that data and you can see
what the data says and does this thing
in in accordance with previous things in
the data or is it not and a that's all
it does it doesn't understand what it's
doing and understanding is different
from Computing no I I think people have
lost the plot yes no that's true you see
I wrote my book the emperor's new mind
but what does it mean that people lost
the plot yeah I think they've lost the
plot because the whole point of my train
of thought was we've got to find
something in
physics you see I believe I'm a
physicalist and that I believe whatever
is going on in our heads whatever
creates Consciousness is part of the
physical world I don't believe it's
magic comes in from who knows
what I claim is saying that the physics
that in is involved in conscious
thinking has to be non-computable
physics now the physics we
know there's a little bit of a glitch
here because it's not completely clear
but as far as we can see the physics we
know is
computable you see uh what about general
relativity where we have wonderful
machines which compete what black holes
do when they spiral around each other
and produce gravity ational wave signals
and you can say yeah yeah yeah that is a
black hole Collision because this has
this very clear feature and yeah you can
do all that that is fine but that's not
what I'm talking about what I'm talking
about is the physics has to be a physics
which is in principle
non-computable so AI can blast his go
ahead as much as it likes it's not going
to be able to get this you talk about a
black box but you don't know what's in
that box is it a
computer is it a computer of the kind we
understand now is it something which
involves a physics which involves a
non-computable process not so far I'm
not saying that won't happen I dread it
because I don't want it to happen I
can't help it because I suspect it will
happen someday but it's not AI as we now
know it AI we as we now know it is
computer
driven and that means it's not going
superhumans AI will never
exist what you trouble is that AI is a
bad term it means artificial
intelligence now intelligence in my view
is conscious that's what intelligence is
about okay so how I can call it
artificial um cleverness how about that
AC
you can see the difference to some
extent when you do mathematical you have
mathematics students some of them
understand what they're doing some are
just clever they can they can repeat
what they've learned they know how to do
it very cleverly they can calculate very
well but they don't necessarily
understand what they're doing that the
physics we don't
know involves non-computable
ility so that's my claim so I made this
claim in the emperor's new mind and I've
made it more a little bit more
forcefully in Shadows of the mind I mean
that maybe it's not the Consciousness
maybe it's something absolutely new
maybe it's not a wordness but that's
there may be completely unknowns which
we have no concept of at the moment that
could be true I'm talking about
things you see if you're talking about
AI that means unfortunately it's a bad
term because it says artificial
intelligence which to me what people use
that term they mean things that can be
done by
computers that's what they
mean they have computers and their
computers are very powerful and then
what they mean by AI is using computers
it may not be using in a straight
logical way usually as I haven't studied
these things so I'm probably out of date
but but as far as I can see what it is
is you look at masses of data and then
you s look for patterns or you you try
to analyze it in that kind of way but
it's all computational you're using
computers but its very nature it's
computational the word means
computational means by a computer now a
computer is a very specific kind of
mathematical structure it means
computational mathematics if you study
the mathematics as an ract subject you
rapidly learn that there are things Way
Way Beyond
computability it's a very limited part
of mathematics some of the mathematics
is involved is not computable you can't
get at it by an algorithm now you see
people often think well AI doesn't use
algorithms because it's using sort of
random methods or something I don't know
I haven't studied in detail what AI
really as so what is called AI really
involves when you put it on a computer
but it is being done by a computer so
it's still something computational no
question about that I'm claiming that
you want something non-computational now
you see people tend not to believe this
because they just think of computers and
they don't know there are non-computable
things if you study the mathematics
mathematical logic you see that there
are non-computable structures there are
could the Logic the physics of the world
could easily be
non-computable and my view is that yes
it is
non-computable and that somehow Nature
has been clever enough to produce beings
which can tap into the non-computable
aspect of the physics and they managed
to do this using natural
selection I have no idea how far down
the animal kingdom and goes humans are
certainly conscious I believe anybody
owns a dog who's absolutely convinced
that dogs are conscious I believe it
cats probably elephants certainly way
down way way down probably octopus is
I'm
sure I don't know is a bacterium
conscious I have no idea is a is a a
frog conscious probably yes is a uh an
amoeba conscious I have no
idea I'm just speculating I've no real
reason for the leaving these things but
I think
Consciousness is something
different it's not
computational and the thing is that it's
just people are so hypnotized I don't
should use a rude word like that really
by the fact that computers have got so
powerful that yeah there's the answer
the computers are so powerful we found
the answer it's just computers I'm
saying no it's not the answer is
something much more deeper than that
it's not it's not more complicated than
that it's deeper than that it involves a
kind of physics which we don't probably
know yet it's deeper because it's based
on the quantum
world it's be it's beyond the quantum
world you see the quantum World Is Still
computable what's not computable in far
as we know what we don't there's a basic
unknown in Quantum world the quantum
theory is fundamentally in complete is I
call it even wrong in a certain sense
because it believes that Quantum
superpositions persists at all
levels the Twister
Theory what is a twister Theory which
describes the structure of
SpaceTime in an unusual way so you're
rather than thinking of space time which
is a four-dimensional space three of
space and one of time and a point
represents a moment which which has a
momentary existance so that so it's the
basic element of space time is a point
and then you built it out out of the
points now in TST the you take a
different point of view the basic
element is not so much a point but as a
light Ray so you think of the history of
a photon if you like which is a a line
in space time it's a it's
what's called a null line it it uh
travels with the speed of light well
light Ray would and
uh if you like your analog of a point is
a light Ray it's actually not quite that
it's more than that because the light
Ray is only the tra trajectory of a
photon the Twister idea
incorporates other things like the the
momentum and the angular momentum of the
photon
however when the and the spin of the
photon you see photons have a have a
lity and the spin the Hally depends on
which we spinning right-handed or
left-handed
and when you incorporate the handedness
of the SP of the of the photon you find
it's not completely localized and there
is a structure which is not localized
along a light R it's spread out in a
certain way and it twists around itself
self and this twisting configuration is
the origin of the name Twister so the
element has this twist twisting
characteristic but the the the original
idea of the subject is has it has a sort
of complicated history let me try and
explain it it came from basically two
ideas you see when I was um I think it
was in
1961 62 I think 62 I think I was in
Syracuse
University um I had done my PhD in
Cambridge and I then went and did some
research mainly at
Princeton and then I was at Princeton on
a fellowship for a year and a half and
it was a two-year fellowship and the
other half of the year I spent at
Syracuse in New York state and I shared
an office with uh angelbert shooking
who is a German who' left Germany just
before the war and he was a very
original man who knew everything also he
knew everything and everybody and
original which is unusual but he I had
discussions with him and he explained
that two most important things one most
important thing of quantum field Theory
which had to do with um the splitting of
fields amplitudes into positive and
negative frequencies hard to explain
what that means but it depends on
normally where you do it you do a
complicated kind of thing called Furia
compos decomposition you spread things
into different frequencies and then you
take the positive frequency and not the
negative frequency that's a comp
complicated thing to explain to an to
somebody who's not not a scientist but
then the other thing he told me about
was the um the conformal invariance of
the maxal equations the maxal equations
describe a electricity magnetism and
light an amazing set of equations and
they theoretically explained light which
is an amazing thing light was a quite
complete mystery before this and the
different frequencies that you have and
and the ones that we don't see and all
that sort of part of Max was equations
but it described electricity and it was
a sort of unification of these ideas
electricity magnetism and
light and the maxal equations another
thing angelbert shooking mentioned to me
was the Maxwell equations are
conformally invariant now what does
conformally invariant mean that means
that it's independent of scale so big
and small are
equivalent um people might be familiar
with the pictures of the Dutch artist MC
eer and there are pictures which depict
um a sort of universe with angels and
devils in them and it's it War within a
circle and then this the angels and
Devils you get towards the edge they
look smaller and smaller and smaller but
they're conformal but the shapes
especially small shapes if you look at
the eyes of the Devils you see exactly
the same shape even though they get
smaller as you go to the edge but this
is what's called conformal and
conformal way of looking at physics was
very important to me because it led to
various things for example how you talk
about about radiation and Fields
infinity and you use the eer trick by
bringing Infinity to a finite place and
then you can study it just as though it
was like anywhere else so conformal is
useful when you're thinking about things
which have no Mass you see photons have
no Mass so they're a good thing to think
about
conformally Mass adds another
ingredient
and
um you know it's a little bit difficult
to get round to interested here you see
because the idea was to think of
conformal
invariance because as I understand
correctly in the Twister story SpaceTime
points stop to play the main role the
basic role uh for accurancy of physical
phenomenons uh SpaceTime points are
secondary construction and the primary
is Twist
yes well think of them as light rays but
the Twister is more complicated because
that's where you consider the spin mhm
of the photon see see when it has spin
it's not localized yeah and it becomes
spread out to some degree and the way
you can describe this in terms of this
twisting
configuration and that and I had a nice
way of describing this and this the
Advan AG of this let me I go back to the
other story was to describe positive and
negative frequencies in a conformally
invariant way because the normal way
people do it it's not conformally
invariant it depends on on the metric
but for
electromagnetism I wanted to have it
conformal invariant so how do you
describe that in a nice geometrical way
and this was the origin of Twister
Theory
because the the original
thought it's it's quite hard to explain
these things but with the being a little
bit technical but let me just
explain
um there is a a a structure called a
reman sphere you see the you have to
think first of all of complex numbers
now a complex number involves the square
root of minus one see in ordinary
mathematics you think of real numbers
and the square root of a real real
number a positive real number is a is
another number but if it's a negative
here the idea is to use complex number
instead of real numbers yes the complex
numbers are absolutely fundamental you
see they're fundamental to Quantum
Mechanics the whole structure of quantum
mechanics depends on complex numbers the
wave function of a photon wave function
of any system is a complex number system
so when you think of the shrodinger
equation which talks about the evolution
of a wave function this really is a
complex equation so in order to
understand the physics of comp of
quantum mechanics you need to understand
about complex numbers now complex number
is called complex because it's not
simple as to say involves not only a
renal number but but an imagin what
people call an imaginary number we don't
like to think of it as imaginary in
mathematics because it's just as real as
a real number in a certain sense but you
can't see it so directly you see that
the way that a a ruler measures in One
Direction and it it measure in terms of
real numbers but a complex number
involves a real number and an imaginary
number together and it forms a very
beautiful um algebra and
calculus which sort of extends from the
ordinary um algebra and calculus of real
numbers to the complex numbers which are
essential for quantum mechanics now now
you can understand this problem of the
comp of the positive and negative
frequencies very nicely in terms of
complex numbers see basically it
says you have to think of the complex
plane the complex plane or the vessel
plane I guess it was vessel who first
thought of it people call it the gaus
plane sometimes gaus was probably a
little bit later than vessel usually he
was before everybody else but in this
case I think he was a bit later um then
you sort of have a picture where you
have the real numbers going off along
one axis and then the imaginary numbers
involving the square roots of negative
numbers I is the square root of minus
one and then the multiples of I go up in
one day and the multiples of minus I go
that way and you have a plane so all the
complex numbers are represented on this
plane the point on that plane represents
a complex number Twisters arise from
mathematics of complex number yes very
much so it's it's absolutely crucial to
subject and the idea was to make the
fundamental principle of quantum field
Theory which is to split your fun your
Fields into positive and negative
frequencies so you you do this in a nice
geometrical way rather than talking
about the fuad decomposition which is a
bit complicated and it does it in a
conformally invariant way so you could
talk about
the um pH physics being conformally
invariant which I should say really
applies to things without
mass when they have mass then it's more
complicated but originally Twisted
theory is concerned with things without
mass so then you can talk about the
positive and negative frequency very
nicely because you see what I was trying
to
do it's hard to explain these ideas
because they're they're very
mathematical see you have to think of
the how you
describe um this notion of positive and
negative
frequency in one dimension it's quite
easy because you think of the complex
plane and the functions which extend
into one half are positive frequency and
the ones which extend into the other
half when I say one half I mean we have
the real axis and then you've got one
half of the complex plane goes up the
other part goes down and those function
which go up are the positive frequency
ones and the ones which go down are the
negative frequency ones so you have a
very nice picture of comp of positive
and negative frequency splitting in this
geometrical way now how do you do that
for the full four-dimensional space time
see that's just one dimension if you're
talking about one time Dimension that's
fine that's a good picture but if you
want to talk it all together for space
time how do you do this for space time
well you can make space time
complex but that doesn't help too much
because in this complex you have a an
eight dimensional space you see each
each space Dimension is becomes two each
time Dimension becomes two again so
three space dimensions come six the two
time Dimensions become two more and that
gives you an eight dimensional space and
how do you see in this eight dimensional
space how to split functions into their
positive and negative frequency it
doesn't work
anymore because your real space doesn't
divide it in two halves because it's
only four dimensions sitting inside an
eight dimensional space that doesn't cut
us in two hours it's just a little four
dimensions is a tiny little sliver in
this huge eight dimensional space so to
try and do this splitting in a conform
in a a nice geometrical way
I the the idea I had was to say ah you
don't think of points you think of the
light rays and the light rays in space
time form a five-dimensional
space now the the Twisters involve the
light rays which spin round so you think
of the photon having angular momentum as
well or spin you see it has a spin then
they incorporate the other dimension and
so you get six dimensions
so you have the space which is the twist
of space which is six
dimensional and this does split in two
halves because the real light Ray space
is
five-dimensional and the space of the
Twisters these are what I call
projective Twisters actually but never
mind about that this twister space is
six dimensional so five does split it
into two halves and can so the ones
which go one way are the positive
frequency and the ones go the other way
or the negative frequency and so this
gives you a very nice geometrical way of
thinking of this key property needed for
Quantum field Theory and that was the
original motivation of Twister Theory
now the subject has got developed in
much much more complicated
ways
and you have to describe Fields you can
describe Max Maxwell's equations very
nicely in the subject and you can see
where the positive and negative
frequencies work and make it quantum
mechanical and uh all these things
become nice it becomes a nice geometry
it was nice for me because I think
visually and I like to think of things
in geometrical way because you are
geometry yes I think very geometrically
uh uh on the website of the Columbia
University there is this sentence about
you and
twistory his work on Twisters is the
most important new idea about the STA
SpaceTime geometry post Einstein and we
believe it will be study long after
String
Theory well I think that's I hope that's
true you see String Theory the main
trouble with string theory in my view is
it's not very carefully focused on the
dimensionality of
SpaceTime originally the idea of strings
quite a appealed to me when I heard
about it but then when they said oh it
only works in 26 Dimensions so okay well
that's the end as far as I'm concerned
that's the wrong number of dimensions
then they got it down to 10 Dimensions
which seemed to be an improvement but
it's a long way WR from the four
dimensions we need for space time so I
didn't get very excited about twist
Theory when I when I learned it only you
had to do it in in 10 Dimensions or 26
Dimensions or 10 and 26 at the same time
time which was even conf more confusing
to me it didn't really make geometrical
sense now there have ways of dealing
with this in string theory but it's not
very natural and it doesn't really fit
in with the geometry of space time in a
nice way so I I never after I the
dimensionality became too big I gave up
on the subject although I was quite
attractive to the original ideas of it
but not after it became 10 in 26
Dimensions at the same time in now 11 it
all seems to be not focused directly on
the space we live in the space we live
in has four space and one time three
space and one time Dimension and it's
four dimensional without particular
signature see one and three that's
important too because the Twisted Theory
relates very specifically to SpaceTime
with one time and three space and the um
where it works I should say there are
variant of Twisted Theory because after
developing some of these ideas the
mathematicians picked
up actually interestingly because they
supplied some useful ideas in in the
twist particularly Michael AA who is a a
friend of mine and we were in the same
Institute in Oxford for a while and uh I
learned a lot of the mathematics that is
needed for Twisted Theory some of these
ideas which involve um what a an qu a
quality known as cohomology and
cohomology is very necessary as part of
Twister theory if you want to describe
Fields like an electromagnetism if you
want to describe the Maxwell field in
Twisted Theory you have to bring in this
mathematical notion of cohomology which
fits in very beautifully with twist
Theory so I needed this input from the
mathematicians particularly
michaeler and then the mathem Ians
picked up on some of these ideas in
twister Theory how you describe
nonlinear fields and things like this uh
and this became a a sizable subject
within mathematics and so it's developed
in certain directions which are not
exactly the same I should say there are
certain
differences
um I'm not quite sure how to say this
you see it depends on the geometry of
space
time it has what's called a minkovski in
signature so you have one time and three
space so it's not just like a
four-dimensional space time it's very
specific to one time and three space and
the Twisters work very naturally in that
framework now if you're just doing pure
mathematics as the mathematicians are
then they like to have it four space
dimensions all four see they don't like
one and three they like them to be I can
give you uh example um maybe that's the
answer for the question um Professor Mai
duni polish scientist from University of
Cambridge yes um he W who works on the
teritory of of Twisters wrote to me a
few days ago this email in the last few
months I have been most scientifically
involved in the so-called Twist of Tory
in which a breakthrough has occurred we
had a program on this topic in the
Cambridge in September and Roger Penrose
came in person it seems that the almost
60 years old idea of unifying the theory
of gravity and quantum theory may have a
positive solution in this
theory yes well I've worked with match
dunki for quite a long time and
um he's he's a very skillful
mathematician who understands about
Twisted Theory very much
um I think the thing specific you see
Twisted theory is very specific to
space-time
geometry it's um you see if you take the
formalism of general relativity it
depends on remanion or what you call
pseudo remanion geometry the pseudo
means that you've got only one time in
three space so it's not really ranian
geometry ranian geometry is when you
have four four space
dimensions but it's curved and Einstein
needed this Theory to develop general
relativity it was absolutely he couldn't
have done it otherwise and he had to
have um a mathematician to help him to
learn the needed
geometry differential geometry well
ranian
geometry um which is the geometry of
curved spaces of any Dimension and it's
very specific it's not any Dimension
because the general relativity Theory
requires four dimensions and it's not
ordinary reman geometry because it has
one time and three space so that's what
people call pseudo ranian geometry now
Twisted theory is very geared
when I say twisted Theory I mean the ma
what I mean by the kind of Twisted
theory that I work on and which is
geared to looking at
physics the mathematicians have picked
up on twister Theory very much and they
have a different version of Twisted
Theory where instead of having one time
in three space it's though you have four
space dimensions and that's a different
kind of Twisted Theory it's what I'm
calling pseudo twister theory if you
like because if you like the um kind of
geometry which is useful for general
relativity is pseudo remanion geometry
it's not the signature is different you
you the number of pluses and and minuses
you have see an ordinary distance reman
and distance or ukian distance if you
have a you have a a tri well if you want
an
ordinary coordinates you want the
distance between two points it's the sum
of squares you take the square root of
the summer squares but in minkovski
Geometry this was the idea that was
introduced by by
minkovski in order to understand special
relativity when Einstein first heard
about it he didn't like it at all quite
ironic but later on it was crucial to
his development of general relativity
because you see minkovski geometry as
one time and three space it's very
specific to that kind of geometry and
that's what special relativity depends
upon and when Einstein got finally
converted to minkowski's ideas he
realized that that's what you need to
make that kind of geometry curved and
then you talk about gravity so the
gravity is incorporated into the theory
once your minkovski space is not so much
minkovski anymore but it's curved in
this way which describes the grav this
is right that the Twister Theory can
unify the gravity Theory and uh uh
quantum theory well you see it may be
I'm not sure what mat matek was saying
in the comment he was making there but
you see there is a development of
Twisted Theory which I call by
Twisters there's a certain irony about
about all this let me explain the
irony when I was originally starting on
this I I 60 years ago this was in
1962 almost 60 years more than 60 years
ago yes more than yes
1962 um when I was thinking about the
positive and negative frequency
problem and that was the initial
motivation but then a little later when
I started to work out Maxwell equations
and Fields and all that it became we
were talking about positive and negative
frequency sorry positive negative
helicity so that your Photon spins
right-handed or left-handed see and that
are the two kinds of spin you have and
the two halves of Twisted space became
more connected with helicity
right-handed or left-handed than
frequency which is positive or
negative and this led to what I call the
fundamental confusion of Twister Theory
because when I started to develop curved
twister Theory to try and fit in with
general
relativity I produced a thing which I
called the nonlinear graviton mhm this
was the first time that curv twister
Theory came
in and it did make a curved twister
space and you when you make the curve
Twisted space you can
incorporate the the spin of a graviton
so graviton would be the gravitational
particle like the photon describes the
particle for electromagnetic field when
you quantize it the light
becomes partic if you like particle like
as we know photons have this particle
characteristic and they have the wave
characteristic and quantum theory is
needed to bring these things together
and the idea is that general relativity
which talks about gravity should have
the same sort of character you have the
particle form of gravity which would be
gravitons and the waveform which would
be gravitational fields as we understand
them well nobody has observed a graviton
we because the energies would be all
difficult to observe directly so um
that's part of what one may call
quantizing gravity so the quantum theory
of gravity would involve making the
gravitational field consistent with a
kind of graviton picture of gravity now
this
particular solution I found but it
wasn't a particular solution it's a
class of solutions which describe
gravitons in accordance with general
relativity so they are curved they're
not flat they're actually curved
spaces but they involve this fundamental
confusion of Twisted Theory
because the helicity and the spin sorry
the helicity and the frequency become
mixed together so to describe that the
graviton should have positive frequency
the graviton a proper graviton should
have positive
frequency but when you try to do it with
trist Theory it has positive Felicity at
the same time so these two ideas get
joined up together and they only sort of
half
describe the gravitational quantized
gravitational structure so they only
half
describe the U when I say only half
describe they only describe half of the
gravitons those are the ones which spin
I think it's left-handed yes not right
it depends on your conventions you see
and this was a very puzzling situation
it came about because of this confusion
which is inherent in twister Theory as
it started the confusion was the the
positive frequency and the positive
elicity and they are both together in
Twisted Theory now you can separate
them if you take what you call dual
Twisters you can take the Twister space
or the Dual Twisted space now the Dual
Twisted space is very similar to Twisted
space but it's the other way around so
the instead of the positive frequency
being the positive helicity I forget
with it's positive or negative now
negative elicity it's the other way
around for the Dual ones so the idea I
had and described in the Cambridge
conference is how you fit these two
ideas together and you make a structure
which I refer to as by Twisters you have
to have them instead of being a a four
complex dimensional space as Twisted
theory is ordinary Twisted Theory
involves four complex Dimensions but you
might want to make it through three
complex Dimensions when you talk about
projective space rather than the vector
space the projective
space that's a a mathematical concept
which is like projective geometry you
see but the projective geometry when
it's complex projective geometry this is
the six-dimensional space where you you
each um real Dimension becomes complex
the Theory versus other Penrose theories
from all your theories you
from uh human consciousness try to
answer the question how human
consciousness was born through the
questions about black hole Twist of
story is the most important for you it's
the most developed yes you
see um the Consciousness thing is an
idea I thought it the most developed yes
are that connected with black
hole no TR the is much more developed as
as a as a subject mhm I mean the black
holes are more direct because we we have
evidence for them they're there and I
guess that's what the Nobel Prize was
for yeah so the black holes cuz we have
a pictures pictures and they are an
important part of physics quite clearly
but
they they sort of fit in with TR you see
you you the missing thing in twister
Theory had been and I think it needs
more development the missing theory is
how you combine twister Theory with
general relativity with proper curved
space times and you could do it
partially by confusing the spin with the
helicity and so these describe
left-handed
gravitons now you want to have both
left-handed and right-handed Ed to make
a proper theory of the quantum
gravitational field if you like so you
need bothh handedness and the idea which
had developed only rather recently over
the last few
years and I wrote a paper in honor of
Cen Yang who was becoming the 100 years
old he is 100 he's 102 or something like
that I think and he was very famous for
developing the theory of weak
interactions with with Lee so Yang and
Lee and it's important part of that
theory is it's handed you see
left-handed and right-handed are not the
same and weak
interactions apparently unique amongst
physical theories are not left right
symmetrical see most of physics is Left
Right symmetrical if you have the theory
describes left-handed it's right-handed
describes left-handed at the same time
so this applies to almost all physics
however the weak interactions that's not
true and they have a handedness and yang
and Lee got the Nobel Prize for
developing this theory of weak
interactions which involves a handedness
now the article I wrote for for Yang's
100th birthday was developing if you
like the theory is going the other way
you see it's it's quite ironic in a way
because it's it's making twist Theory
not handed you see twist theory was very
much a sort of left-handed theory if you
like and the the graviton comes out as
being necessarily left-handed but you
don't want that to describe gravity
because it's not a left-handed Theory
it's it's a theory which involves both
left and right so what you do in my
later what I was was describing in
Cambridge was is this idea how you take
the normal Twist of theory which if you
like is Left-Handed and you take dual
Twist of theory which is right-handed
but that's just changing a sign it's not
doing anything clever you can have these
two theories but what you do is you
bring them together and the important
thing when you bring them together is
that it brings quantum mechanics in you
see the if you stick with one side or
the other then the crystal theory is not
quantum mechanical it's classical really
but when you put the two sides together
it's like how would I put it it's like
position and momentum so in quantum
mechanics position and momentum are what
I call canonical conjugates so
position
um you if you have a a state of a
particle which is well defined in its
position then it's completely undefined
on its momentum and the other way around
if it's well defined in its momentum
then it's completely undefined in its
position and most things are sort of in
between so they're fairly well defined
position and fairly well def momentum
but these Notions are called um
conjugate yeah the canonical
conjugates and you have in quantum
theory this is the Heisenberg mhm idea
which really started off quantum
mechanics you have these things which do
not commute AB is not equal to ba a so
if you have a if you if you work just
with position then AB is equal to ba if
you work just with momentum then AB is
equal to ba but if you want to have
position and momentum together then
AB minus ba is the other one so you have
to bring them together so that the way
the mathematics work
is that the What's called the commutator
that is to say why isn't AB equal ba
well you look at the difference between
a and ba and it volves the other thing
so if you do this for position then you
get momentum and you do it for momentum
you get position and this is the sort of
fundamental thing in quantum mechanics
now that
idea comes into twister Theory and it
comes in that the
Twisters what's the iCal conjugate of
tses it's the D dual Twisters so you
have the Twisters and the Dual tses and
one of them is the canonical conjugate
of the other and the other is the
canonical conjugate of the one so that
when you do it with with quantum theory
and ab is not equal to ba but AB minus
ba involves the other thing and a B
minus ba the other thing involves the
one thing these are the conjugate
variables now in Chrystal Theory the
conjugate variables are twisters and the
Dual Twisters so those are conjugate to
each other now you make an algebra which
involves both twisters and the Dual
twisters and when you make that algebra
it has quite curious
implications which might seem to involve
things like particle
physics uh I I think that hasn't been
developed I should say that's only an
idea but I think there's a reasonable
chance that the ideas
that well when it talks about strong
interactions that's the interactions
which hold particles
together how can the Twister theory help
us which the most fundamental questions
we can find when we have a
confirm Twisters theory in all details
well see it's as a math say as a
mathematical Theory it doesn't need
confirmation it's just a theory it's
just a mathematical structure this I'm
talking now about things which haven't
been developed so I'm speculating now
this is speculation okay now I think
it's quite possible that these by
Twisters which do involve both the
Twisters and the Dual Twisters so you
are enabled to talk about left-handed
and right-handed together and I think
they would enable you to talk about
general relativity together this is
still not achieved yet but I think there
are good indications that this could be
done
um
now could it go beyond that and talk
about how the quantum aspects of general
relativity are brought
out this is speculation I don't know um
does it fit in with particle physics up
to this
point it doesn't I remember I had an
idea about how to make particle physics
fit in with twist Theory and I remember
I was
visiting Caltech at one point and uh I
think Steven Hawking was there and he
arranged a meeting between me and and
Richard Fineman and I talked about
Twisters to Richard
Fineman and I asked him about some ideas
I had about particle physics and he was
very good he said don't follow that
that's not going to be useful but do
follow what you're doing on twister
theory he thought that was a good idea
so I I give him credit because the
particular idea was looking at for
particle physics was probably completely
wrong and he was noticing that it was
not a fruitful idea so so far particle
physics has not really fitted in with
Twist of theory now I think there is a
reasonable chance that it would fit in
with by twister Theory
the reason I'm saying this
initially this is speculation I don't
know to what extent this is
correct but the theory of strong
interactions you see
in see in particle physics you have weak
interactions that's the Yang and Lee
business which I mentioned before which
have a handedness to them yes and there
are gravitational interactions which
don't really form part of normal
particle physics and you got these
strong interactions now the strong
interactions are are strong because they
dwarf everything else Y and uh they hold
the particles together if you like they
they they're the main thing which which
dominates the particle physics now how
do they fit in with Trista Theory well
they might do because of when you do the
bi
twisters and you look at the way that
the um twisters and B Twisters fit
together you find there is a very nice
kind of triple
product um how to explain this it's a
bit like see when you go back to to
Hamilton Hamilton was a very
distinguished mathematical
physicist and many of the ideas become
important in physics hamiltonians and
things like this
but what excited him the most was his
discovery of
quarians this was a kind of algebra
which you could you see rather than the
complex numbers which
describe um well one space of
time it's only a two-dimensional space
the quorans talk about a
three-dimensional space and you but the
key thing about it is that AB is not
equal to ba a
and he formed this algebra which is
called querian and this quaternionic
algebra Hamilton got very sold on this
and he spent the rest of his life many
people say he wasted the rest of his
life on developing a theory of H of
cians now it's a bit mixed story this
you see but very shortly after Hamilton
discovered his
cians people other PE I think there are
about three mathemati
independently saw saw how to develop
this idea into what are called octonian
MH and these are not just
four-dimensional structures they're
eight dimensional and they you see
hamiltonians Hamilton's quorans have a
is not equal to ba a the
octonian have a more complicated thing
that a * B * C is not the same as a * B
* C so it depends where you put the
bracket ET AB * C is not the same as a *
BC so it's a little more complicated
piece of but today we know that it's not
true you see it's only it's not true in
in in the octonian algebra you see the
cians it is true mhm so the octonian
it's not true now I had a phase of
thinking I wonder whether octonian in
the split form you see there again it's
the signature qu question do you have
three pluses and one minus in space time
now there is another version of octonian
which is called split octonian and those
instead of having all pluses normal
octonian have eight pluses or well
there's seven pluses because eight
things which are added together and
that's the structure which is developed
on but there's a special kind of
octonian called split octonian where you
have four pluses and four
minuses and I often wondered with this
had anything to do with twister Theory
and what I finally realize is it does
have something to do with
the um bi twister theory that the bi
twister Theory you can construct the
octonian or the split octonian so it
really is connected with the split
octonian and the question is do these
spit octonian have anything to do with
particle physics
um I think they may well
do um mainly because in this
construction of the split
octonian you have
a you see yes you have a triple you see
the you say this see the
quarians involved a thing which is
called a vector product you have the
Scala part and the vector part and when
you multiply the vectors together you do
this with this uh construction of What's
called the um cross product so you have
two vectors and you produce another
Vector at right angles to the two so you
have two in space in ordinary three
space two that one there that and then
the product points perpendicular to the
plane of the two but AB is not the same
as ba so you have this hamiltonian
structure for the querian that AB is not
ba but ABC is still the same as a BC AB
BC you see what I mean but the octonian
go One Step Beyond that and you have an
eight dimensional structure where this
this algebra for ABC well AB * C is not
the same as a * BC when I'm hearing you
now I think that that obstructional
thinking is The Neverending
Story well it's it's I hope never ending
see it does end in a certain sense
because there are certain theorems
if you have the associative rule which
is AB b c well then you you stick at
four dimensions and if you have the for
the octonian rule with with the with the
uh
um what it's what they call the
alternative rule which mean is another
algebraic structure but AB * C is not
the same as a * BC you you have these
octonian but they use stuck there that's
the end you see you might say it's an
unending story in a certain sense it is
because you can talk about groups and
they get bigger and bigger and it gets
huge you see but if you want about these
algebras they do stop and they stop at
the
octonian and and this may well be you
see particle physics really stops at a
certain point it doesn't keep on going
the space-time structure only stopped at
a certain point you've only got three
space in one time so it's not as so you
you
physics is more I mean it
doesn't it doesn't how do I put this see
mathematically you sure you can go
endlessly
complicated but physics is only
interested in certain aspects of
mathematics if something exists in the
nature yes that's right thank you very
much for your time right okay my
pleasure no it's been good fun thank you
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