#1216 - Sir Roger Penrose

Joe Rogan (0:02)

All right, here we go, three, boom, and we're live. How are you, sir?

Roger Penrose (0:09)

I'm fine, pretty good.

Joe Rogan (0:11)

Thank you for doing this, I appreciate it.

Roger Penrose (0:12)

That's fine, my pleasure.

Joe Rogan (0:14)

Who roped you into this?

Roger Penrose (0:16)

Well, I think, I suppose, James Tagg probably.

Joe Rogan (0:20)

I'm a big fan of your work. I've read much of your work. I've seen many of your interviews and videos online. And one of the things that I really wanted to talk to you about that I find quite interesting is consciousness. And your belief that consciousness is not simply calculation, but that there's something more to it.

And what you think this more could possibly be from a scientific perspective, which is unusual, because a lot of people have some theories about consciousness, but they're usually crazy people like myself.

Roger Penrose (0:54)

Well, I mean, we're all conscious, and so we may have theories about it.

But no, the ideas came by somewhat roundabout route.

I went to Cambridge to do graduate work. It was mathematics. I was working on pure mathematical subjects, algebraic geometry, but I thought, you know, we've got three years, I'll spend some of the time going to other talks that might be interesting. So I went to three talks, particularly, which had a big influence on me. One was a talk by Herman Bondy, was a general relativity cosmology. Wonderful talk with very sort of animated presentation he had. And then there was a talk by Paul Dirac, one of the founders of quantum mechanics.

And his talk, well, his completely wonderful talk too, wonderful lectures as well, but in a completely different style. He was very quiet and precise in what he said and everything. Anyway, in the very first lecture, he was talking about the superposition principle in quantum mechanics. So, if you have a particle and it could be in one spot, or it could be in another spot, then you have all sorts of states where it can be in both places at once.

That's sort of strange, but you've got to get used to that idea. And he illustrated with his piece, a piece of chalk, and I think he broke it in two, to illustrate it could be in one spot or in the other.

And my mind sort of wandered at that point. I don't know what I was thinking about, but I wasn't concentrating. And about a few minutes later, he'd finished his description, his explanation, and I had some vague memory of something about energy, but I didn't understand what he said, and I'd been totally mystified by this ever since.

So I suppose if I'd heard what he said, he would have said something to calm me down and sort of accept it in one way or another. But as it was, it seemed to me this was a major issue. How on earth do you have things that don't behave according to what quantum mechanics says, like cricket balls and baseballs and things like that? Anyway, that's two of the talks. The other course was a course by a man called Steen, who talked on mathematical logic, and he explained things like Gödel's theorem and Turing machines, Turing machines being the mathematical notion upon which modern computers are based, or all computers basically, and the thing about Gödel's theorem. You see, I heard, I used to have a colleague when I was an undergraduate, Ian Percival, who also became a scientist later on, and we talked about logic and how you could make these kind of mathematical systems, which worked out logic. And I'd heard about this Gödel's theorem, which seemed to say that there were things in mathematics that you just couldn't prove.

And I didn't like that idea. But when I heard the, when I went to this course by Steen, and he explained what it really says, and what it says, I suppose you've got a method of proving things in mathematics. And when I say things, I mean things with numbers. The one famous example is Fermat's Last Theorem.

There's the Goldbach conjecture, which isn't yet proved, that every even number bigger than two is the sum of two prime numbers. That's the sort of example of the thing. It's just sort of mathematical things about numbers, which you can see what they mean, but it may be very difficult to see whether it's true or untrue. But the idea often is in mathematics, you've got a system of methods of proof.

And the key thing about these methods of proof is that you can have a computer check whether you've done it right. So these rules, they could be adding A and B, it's the same as B and A and things like that. And if you give, you say to the computer, say, here is a theorem like Goldbach Conjecture, and you see whether it can be proved, and you say, maybe I've got a proof, and this follows these steps, and you give it to the computer and it says, yep, you've done it right, it's true. Or maybe we say, you've done it right, and it's not true. Or it may not say anything, it might just go on forever. But these are the sort of outcomes. And the point about it is that if you believe that these procedures do give you a proof, in other words, that if the algorithm says, yeah, it's true, then you believe that it is true, because you've understood all the rules. You looked at the first one and said, yeah, that's okay. You looked at the second one and said, oh, yeah, I see, okay, that's great. And you go all the way down. And as long as you're convinced all those rules work, then if it says yes, that's something you believe. Okay. Now what Gödel shows, as he constructs a very specific sentence, a statement, which is a number thing, like the Fermat's Last Theorem or something, the thing about numbers, which what he shows is if you trust this algorithm for proving mathematical things, then you can see by the way it's constructed that it's true. But you can also see by the way it's constructed that it cannot be proved by this procedure.