Do you believe twisters are a more
fundamental description of the world?
Well, I do, yes. I mean, I don't
normally say that out loud,
but now you've put me in a position. Yes.
I think that's fucking great. I mean,
in other words it's like
you have to say this,
I believe and in general
people won't say it.
We've been discussing the fact
that this intuition is very,
very strange and involving
how to think about
spaces of the type that Einstein and
Minkovski and Ponka Ray were considering.
How does that begin to
lead us towards these more
speculative ideas of yours surrounding
complex numbers and the twister
program? I don't think many people
many, many of them may have heard of it,
but even in a, even in mathematics,
you have to know that you got,
you were sort of seen as leading
a cult. It had its own newsletter,
its own bizarre drawings.
It was very difficult to communicate to
members of the twister cult because they
didn't speak like other people.
Well, we had this twist of
newsletter, which was a,
it started off by, it's
just in handwriting.
And it was duplicated. And then let's
not go into that for the moment.
Talk about the base, the origin of
twisted theory if you like. How,
where did it come from?
It was really in fact your big
bet in physics do you think? Yeah,
I think so.
Well you see it's between that and the
cosmology but the cosmology is a bit
different cause it's not such a,
okay it's a wild idea but
it's not a whole body of wild
ideas which twists the
theory more is alright.
But it has lots of connections with
mathematics as pure mathematics and
connections with physics. Let,
let me describe the basis of it because
I think we've got most of the things we
need.
You see the light cone describes
how from a one point or one
event in space time,
all the different points of zero
distance from it or another.
It was all the light
rays from that point. Now
let me think about the other way
around. That is my past light cone.
So I'm sitting at a certain point in
space time and I look out at the universe
and all the light rays that get
to me as a particular instant
moment of my time come
along this past like her.
So that's,
you imagine this kind of stretching out
into the past and getting bigger and
bigger as it goes back in time.
And that's all the events,
which are one moment of my time.
I see those events. So I see
a lot of stars in the sky.
Now let's suppose that,
I mean the stars and it's
gotta look like points you see,
so that you have the sphere,
the celestial sphere,
which is my field of vision.
If I'm managing myself out in,
so imagine that the earth was transparent
so you weren't, that's why my, Oh,
let's go out into space then I can,
I can be looking at the
world all around me. Now,
let's imagine that another astronauts
comes whizzing past me at nearly the
speed of light and just as
we pass each other, he looks,
he or she looks out at the sky
the same moment as I do now
because of a phenomenon
known as aberration.
The stars will be slightly not in the same
place with regard to that astronaut as me.
This guy is somewhat distorted, but
it's distorted in a very particular way,
which is what's called conformal way.
Say this in a simple way.
I suppose I happen to see a configuration
of stars that happened to be on a
circle. Suppose they
were concise, click this,
then this astronaut passing by me.
We'd also see these in a circle even
though the transformation would not be a
rotation of the stairs,
sky would be squashed up more on one
end and stretched out at the other end.
But the thing about that transformation,
it's something which I knew about
from my complex analysis days.
Do you think of the what's
called the remand sphere?
This is the plane of points.
Is it the complex plane
or the vessel plane?
Other point play the points
represent the complex numbers.
So zero is in the middle of your life
and then you've got one and then you've
got minus one and I and minus
either all on the circle and you
go out and infinity is way out to
infinity. But the remains fair foals,
all this up into a sphere.
So infinity is not point just
a little bit like if you have a
caramel coating around an Apple, you're
folding that, you feel it around.
That's right at the point where
the stick would go into the Apple,
all of the boundary of that
candy would come together.
Yes. And it's what's called a
steer, a graphic projection.
You can project from the North pole and
all the other points flattened out into
the plane.
So you can see all the points on the
sphere except for the point from which
you're projected. Exactly. And that's
called a steer, a graphic projection.
And it has this remarkable property
that it sends circles to circles or you
could say it's conformal that his angles
are preserved and it's a very beautiful
transmitter. I used to play around
with these things just for fun of them.
Now the thing is that
the transformations of
this sphere to itself,
which preserve the angles,
it's also transformation, which is what's
called analytic or column holographic.
It's, it's the most smooth transformation.
You can have just the analog
of smooth but for complex
objects rather than real objects. Real
and complex means the types of numbers.
Yes, that's right. So it's,
so it's what smooth smoothies
and complex analysis and those
transformations which send the
sphere to sphere are exactly those in
relativity.
So the different observers passing
me at different speeds looking at the
same sky, the map from my sky.
So their skies is exactly this
complex transformations of the sphere.
And this actually is what you exactly get
when you use two components, spinners,
and you see the description when you
move from one observer to another is
exactly those ones which transform
the sky in this conformal way to
itself. And often people
find this puzzling.
I find it puzzling originally because
the most you had to a sphere which is
whizzing, you know, an alien spaceship,
which is a sphere shooting past
you at nearly the speed of light.
Well you see the direction of motion,
it will be contracted by the Lorentz
contractions. So when you look at it,
you should see it sort of
flattened out. You don't,
because the sphere goes a
circle, it goes to a circle.
If you see it as a circle,
when it's not moving,
you will still see it as a circle and the
boundary of the thing will look like a
circle where it is moving and
you work away and think about it.
Well you see where the lightweight is
go in the front of it and the back of it
and all that. And you see really you
don't see the flattening. It really is,
doesn't look like a, like a circle.
It's boundary looks like a circle.
So I wrote a paper on this
almost simultaneously.
There was somebody else
wrote a paper on mainly
thinking of the small circles and spheres.
But this transformation, that's
really what started me off.
If I understand correctly,
maybe I don't. Yeah.
we have another mutual
acquaintance or friend, Raul bot,
and he showed us that the world
seems to repeat every eight
dimensions in a certain way.
But during the first cycle of what you
might call bot periodicity from zero to
seven or one to eight, depending
on how you like to camp,
you get these things called low
dimensional coincidences. Oh yes.
And so that they don't recur because
of your point earlier about spinners
that spinners grow exponentially
whereas vectors grow linearly
and, but during the first period where
these things are of comparable strength,
yes,
you've get all of these
objects where depending upon,
you defined in two different contexts,
you turn out to be the same object
you're making use of that. Here
It is, it's the with the Lawrence group
Where like, you know that the
rotations of space and time,
which we might call [inaudible] or son
three double cover would be equal to
something else called [inaudible],
which would mention complex numbers even
though there's no complex numbers to be
seen in space and time. Yeah. It depends
On that. One of those coincidences
where it's triple coincidence.
I think you certainly
get a coincidence there.
Which one is depending
upon in this description,
but the point I'm making here
is that in a certain sense,
relativity, it's described when
you do it in the two spinner form,
which is really expressed in this fact
that it's the transformation of the
Raymond sphere to itself, which
is a complex transformation.
This is the most general
transformation of the sphere to itself.
When you think of that
sphere as a reman sphere.
So it's a complex one
dimensional space, you might say,
surely it's two dimensional. Well,
it's two dimensional in real numbers,
but one dimensional in complex
numbers cause the complex,
each complex numbers carries the
information of two real numbers.
So for example,
mathematicians would call what most
people call the complex playing.
They might call it a complex line.
It's complex line. That's right.
And so the language again is intended to
make things very hostile to the newbie.
Yes, that's true.
But you have to get used to the idea
that when you're thinking complex,
when you think of it sort of really
sort of concretely and in the real terms
that you have to double the number of
real dimensions to get the number of
complex. I want my audience,
but I don't want them to feel
stupid for making a mistake.
You have the number. Of course,
we have the complex numbers
playing a fundamental role in
relativity. That's really point I want
to make and it's the complex fear. Sorry,
the remand sphere,
which is this one
dimensional in complex sense,
two dimensional in the real sense
object which is fundamental.
Now this remains fear appears
in the most basic way in quantum
mechanics to you think
of the Mo, the spin.
Now that's the practically
the most direct complex,
the most direct quantum mechanical
thing in a certain sense where you see
quantum mechanics playing a
real role as quantum mechanics,
which is hard to grasp
normally, but you can see it.
Here is the geometry
really works. You see,
if you have an object of a spin half,
that's the smallest non-zero spin.
You can have such an electron. So
think of an electron. It has spin half.
Now what that means is
that it's basically two
States of spin, which people
call it spin up and spin down.
What does that mean? Right? Hey,
put your thumb up like that.
Right-Handed spin is where your
fingers go and that's spin up means
right-handed about up spin down.
His right hand is about dyno
is left-handed about that.
And those are the two basic States.
But what's special about up and down?
Nothing. So you think of what about
right? Left, forwards, backwards.
All those are combinations of up and down.
And they're complex combinations
through these complex numbers,
which lie at the basis
of quantum mechanics.
But here you can see in a visual
way what they're doing. You see,
you can say up,
down what's left and right where
these are combinations of up and down.
So you add this much of up to
that much of down and you get
to the, to the right, right?
And, and you minus it,
you're getting to the last two times
you're good forwards, whichever it is.
And the complex numbers come
in to describe these possible
directions of spin and it's
the reman sphere again. So,
but you were relating these complex
numbers of quantum mechanics do the
directions in space.
So you have a connection between
these rather abstract numbers,
which are fundamental to quantum mechanics
and the much more concrete picture of
the directions in space.
I think you're both,
well let me be challenging
slightly, slightly go on. Yes.
What you're really talking about is
a very important fork in the road for
physics.
Do you wet yourself to the
world that we're actually given?
And you know, mock was famous
for having said this phrase,
the world is given only once.
And so we happened to know that there
does exist a world that appears to be well
modeled by three spacial
and one temporal dimension.
And then the key question is do you
wish to have a more general theory,
which it works in all dimensions
or works works for all different
divisions between how many spacial
and how many temporal dimensions?
And what I see you as having done,
which I think is incredibly noble,
brave and scientifically valid,
is to work with
mathematics that are really
particularly using themselves to the
world we're given rather than sort of
keeping some kind of,
I mean like you're getting married to
the world we live in in a way that other
people are just dating it and
wishing to keep their options open.
I think you've hit on a very crucial
point. That's absolutely right.
I mean, for example with
string fair and all that,
people talk about 26 dimensions
or 10 special ultimate or 11 or
12 and things like that,
and sure the mathematics,
we've got mathematics to handle these
things and maybe that's important to the
way the world works,
but I was never attracted by
that for basically two reasons.
One was the reason I'm just
trying to describe here,
and it's exactly what you're saying,
that I'm looking for a way in
which you find a mathematics to
describe the world,
which is very particular to
the dimensionality we see.
So the three space dimensions
and one time dimension is
described in this formalism very
directly and if you're going to try and
talk about other numbers
Of dimensions of space and time,
it doesn't work as much as I really like
to stick it to the string theorists.
That's not exactly their problem
either because 26 is really,
because it's two more
than 24 and 10 is really,
because it's two more than eight and an
eight you have something special called
triality and so what they
were really doing was
figuring out how to build different
theories around different highly
specific targets, but you see there
it's the beauty and the mathematics,
which sure is a good guide,
but it has to be well they play with
some theories and they never grow up to
playing with reality. That's
the sort of thing, I mean it's,
it's perfectly good to explore all these
different things and it's very valuable
but I'm trying to follow a route which
is viewed I think in many quarters is
very narrow.
I'm looking for a route which
is work specifically for
the number of space, time,
dimensions that we have and
is if I'm there aspects of
twisted theory, which do
work in other dimensions,
but they run out very quickly and
you can see analogs of these things.
But that kind of
is wrong version of the
anthropic principle,
which is that if there weren't a
beautiful mathematics to, to catch you,
I mean in some sense, despite the fact
that you're in your late eighties,
it's like you're stage diving at a punk
concert where you're kind of hope that
the mathematics catches you because
you're willing to actually marry at a very
deep level. The world that we do observe.
And I find that what,
what's very disturbing to me is
that the political economy of
science means that fewer people
are willing to make strong
speculations, strong predictions,
to explore things that don't give them
the flexibility in case things that
don't work out to say well it could
be like this, it could be like that.
And so in part I see you
as part of a dying breed of
people who are willing to go down with a
ship for the privilege of commanding it
as it's captain. Well, you can
use it that way if you like.
My claim isn't, the ship isn't actually
sinking. You might think. No, no, no,
I'm not. I'm not claiming.
I think that one of the things that's
happened is has been that yours has
been one of the most important
idiosyncratic programs that in fact
got a huge lease on life
from the fact that it has
positive extra now is because it
was absolutely solid mathematics.
It turned out that even if it doesn't
give us a fundamental description of the
world,
it is at least a deep insight into how to
transform one problem into another to
allow solutions that wouldn't have been
easily gleaned in the in the
original formulation. Yeah.
I'm not saying that it's, it's knocked
out of the park for a fundamental theory,
but I don't actually know whether,
do you believe twisters are a more
fundamental description of the world?
Well, I do, yes. I mean, I don't
know me to say that out loud,
but now you put me in a position. Yes.
No, I don't think that's fucking great.
I mean, in other words, it's like
you have to say this, I believe in,
in general, people won't say it.
