Editing 20: Sir Roger Penrose - Plotting the Twist of Einstein’s Legacy

'''Sir Roger Penrose:''' Well I can say if I've used the theorem. In at least two different contexts, yes, maybe more. So, I mean, I'm not an expert in that area at all. And it was mainly when I was trying to solve a particular problem... I don't know how much detail you want to go into these things. But it had to do with how to make Twistor Theory work in curved spaces. But I ran up into a question, which had to do, it has to do with Complex Geometry.

'''Eric Weinstein:''' Well if you, I know you're hot on the trail of this, but just to leaven something in, Roman Jackiw at MIT once beautifully said, and I don't think he wrote it down, he said, "We didn't understand the partnership that was possible between Mathematics and Physics, because we the physicists used to talk to the analysts." And he said, "The analysts either told us things that were absolutely trivial and irrelevant, or things that we already understood." He said, "When we talked to the geometers, we started to learn new things that we'd never considered."

'''Eric Weinstein:''' It was just called the Schwarzschild singularity?

'''Eric Weinstein:''' From Princeton, Norman Steenrod.

To say this in a simple way, suppose I happen to see a configuration of stars that happened to be on a circle. Suppose they were concyclic. And then this astronaut passing by me would also see these in a circle. Even though the transformation would not be a rotation of the spheres, the 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 Riemann sphere? This is the plane of points, you see it's the complex plane, or the vessel plane: the points represent the complex numbers. So zero is in the middle if you like, and then you've got one, and then you've got minus one, and i and minus i, they're all on a circle, and you go out and infinity is way out to infinity. But the Riemann sphere folds all this up into a sphere. So infinity is now a point.

'''Eric Weinstein:''' But, if I understand correctly, and maybe I don't, we have another mutual acquaintance, or friend, Raul Bott, 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 Bott Periodicity, from zero to seven, or one to eight, depending on how you like to count, you get these things called low-dimensional coincidences. And so, that they don't recur because of your point earlier about spinors, that spinors grow exponentially, whereas vectors grow linearly. And, but during the first period, where these things are of comparable strength, you get all of these objects where, depending upon, you define in two different contexts you turn out to be the same object. Are you making use of that here?

'''Sir Roger Penrose:''' It is that, it's the, well the Lorentz group—

'''Eric Weinstein:''' What you're really talking about is a very important fork in the road for Physics: Do you wed yourself to the world that we're actually given? And you know, Mach was famous for having said this phrase, "The world is given only once." And so we happen to know that there does exist a world that appears to be well modeled by three spatial and one temporal dimension. And then the key question is, do you wish to have a more general theory, which works in all dimensions, or which works for all different divisions between how many spatial 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 particularizing 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.

'''Eric Weinstein:''' So, very early in this new stagnation post the Standard Model, people like Glashow and Georgi, and Pati and Salaam, put forward these unifying symmetries that remain very odd, because they're so attractive and powerful, the prettiest of them being something called Spin-10, which physicists persist in calling SO(10) for reasons that escape me.  

'''Sir Roger Penrose:''' I was at the time at the University of Texas for a year, and this Alfred Schild had put a lot of people together who were General Relativity experts, hoping that something would come out of it, I guess. And I had an office, next to Engelbert Schücking, whom I learned a lot from. And on the other side, I had an office, that was Roy Kerr's office, and Ray Sachs was a little way down. And, I have to backtrack, because the question is, where did Twistor Theory come from?