Roger Penrose is physicist, mathematician, and philosopher at University of Oxford. He has made fundamental contributions in many disciplines from the mathematical physics of general relativity and cosmology to the limitations of a computational view of consciousness.

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OUTLINE:
0:00 - Introduction
3:51 - 2001: A Space Odyssey
9:43 - Consciousness and computation
23:45 - What does it mean to "understand"
31:37 - What's missing in quantum mechanics?
40:09 - Whatever consciousness is, it's not a computation
44:13 - Source of consciousness in the human brain
1:02:57 - Infinite cycles of big bangs
1:22:05 - Most beautiful idea in mathematics

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The following is a conversation with Roger Penrose, physicist, mathematician, and philosopher at University of Oxford.

He has made fundamental contributions in many disciplines from the mathematical physics of general relativity and cosmology to the limitations of a computational view of consciousness.

In his book, The Emperor's New Mind, Roger writes that, quote, "'Children are not afraid to pose basic questions "'that may embarrass us as adults to ask.' "'In many ways, my goal with this podcast is to embrace the inner child that is not constrained by how 1 should behave, speak, and think in the adult world.

Roger is 1 of the most important minds of our time.

So it's truly a pleasure and an honor to talk with him.

This conversation was recorded before the outbreak of the pandemic.

For everyone feeling the medical, psychological, and financial burden of the crisis, I'm sending love your way.

Stay strong, we're in this together, We'll beat this thing.

This is the Artificial Intelligence Podcast.

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And now, here's my conversation with Roger Penrose.

You mentioned in conversation with Eric Weinstein on the Portal podcast that 2001 Space Odyssey is your favorite movie.

Which aspect, if you could mention, of its representation of artificial intelligence, science, engineering, connected with you?

There are all sorts of scenes there which are so amazing.

I mean, people say, oh no, Interstellar, it's this amazing movie, which is the most scientific movie, but I thought it's not a patch on 2001.

I mean, 2001, they really went into all sorts of details and regarding getting the free fall well done and everything.

And also things like the scene where at the beginning they have these sort of human ancestors, which are sort of apes becoming humans.

Yes, and well it's the 1 where he throws the bone up into the air and then it becomes this, I mean that's an amazing sequence there.

Does it have any scientific or philosophical meaning to you?

This kind of thing that sparks innovation?

So Hal 9000 decides to get rid of the astronauts because he, it, she, believes that they will interfere with the mission.

That's right, yeah, well there you are, it's this view.

I don't know whether I disagree with it, because in a certain sense it was telling you it's wrong.

See, the machine seemed to think it was superior to the human, and so it was entitled to get rid of the human beings and run the show itself.

What do you think Hal did the right thing?

Or if we think about systems like Hal, would we want Hal to do the same thing in the future?

Well, you're basically touching on questions, you see.

Is 1 supposed to believe that Hell was actually conscious?

I mean, it was played rather that way, as though Hell was a conscious being.

Because Hell showed some pain, some, hell appeared to be cognizant of what it means to die.

And therefore had that, an inkling of consciousness.

Yeah, I mean I'm not sure that aspect of it was made completely clear, whether Hal was really just a very sophisticated computer, which really didn't actually have these feelings and somehow, but you're right, it didn't like the idea of being turned off.

How does it change things if Hal was or wasn't conscious?

Well, you might say that it would be wrong to turn it off if it was actually conscious.

I mean, these questions arise if you think.

I mean, AI, 1 of the ideas, it's sort of a mixture in a sense.

You say, if it's trying to do everything a human can do, and if you take the view that consciousness is something which would come along when the computer is sufficiently complicated, sufficiently whatever criterion you use to characterize its consciousness in terms of some computational criterion.

So how does consciousness change our evaluation of the decision that Hell made?

Well I guess I was trying to say that people are a bit confused about this.

Because if they say these machines will become conscious, but just simply because it's a degree of computation, and when you get beyond that certain degree of computation, it will become conscious, then of course you have all these problems.

I mean, you might say, well, 1 of the reasons you're doing AI is because you understand the device out to some distant planet, and you don't want to send a human out there because then you'd have to bring it back again and that costs you far more than just sending it there and leaving it there.

But if this device is actually a conscious entity, then you have to face up to the fact that that's immoral.

And so the mere fact that you're making some AI device and thinking that removes your responsibility to it would be incorrect.

so this is a sign of flaw in that kind of viewpoint.

I'm not sure how, you know, people who take it very seriously.

I had this curious conversation with, I'm going to forget names, I'm afraid, because this is what happens to me at the wrong moment.

But I didn't agree with his conclusion from Godel's theorem, I think he got it wrong.

Well, I'll just tell you my story, you see, because I'd never met him.

And then I knew I was going to meet him at the occasion I realized he was coming in.

He wanted to talk to me and I said, that's fine.

And I thought in my mind, well, I'm going to paint him into a corner, you see, because I'll use his arguments to convince him that certain numbers are conscious.

You know, some integers, large enough integers are actually conscious.

And this was going to be my reductio ad absurdum.

So I started having this argument with him.

He didn't even need to be painted into it.

He took the view that certain numbers were conscious.

I thought that was a reductive and absurdum, but he seemed to think it was perfectly reasonable point of view.

Interesting, but the thing you mentioned about Hal is the intuition that a lot of the people, at least in the artificial intelligence world, had and have, I think.

They don't make it explicit, but that if you increase the power of computation, naturally consciousness will emerge.

But basically that's because they can't think of anything else.

I think most of what you actually call computation is done by the cerebellum.

I mean, this is 1 of the things that people don't much mention.

I mean I come to this subject from the outside and certain things strike me which you hardly ever hear mentioned.

I mean you hear mentioned about the left-right business, the move your right arm that's your left side of the brain and so on and all that sort of stuff.

If you have these plots of different parts of the brain, there are 2 of these, these things called the homunculi, which you see these pictures of a distorted human figure, and showing different parts of the brain controlling different parts of the body.

And it's not simply things like, okay, the right hand is controlled and both sensory and motor on the left side, left hand on the right side.

And it's as though it's about the worst organization you could imagine.

And this is made more pronounced when you think of the cerebellum.

The cerebellum has, when I was first thinking about these things, I was told that it had half as many neurons or something like that, comparable.

And now they tell me it's got far more neurons than the cerebrum.

The cerebrum is this sort of convoluted thing at the top people always talk about.

Cerebellum is this thing just looks a bit like a ball of wool right at the back underneath.

It's got more neurons, it's got more connections.

Computationally, it's got much more going on than the cerebrum.

But as far as we know, although it's slightly controversial, The cerebellum is entirely unconscious.

So the actions you have a pianist who plays an incredible piece of music and you think of and he moves his little finger into this little key to get it hit it just the right moment.

Does he or she consciously will that movement?

It's probably to do with the feeling of the piece of music that's being performed and that sort of thing which is going on.

But the details of what's going on are controlled.

I would think almost entirely by the cerebellum.

That's where you have this precision and the really detailed...

Once you get, I mean, you think of a tennis player or something, does that tennis player think exactly how to, which muscles should be moved in what direction and so on, no, of course not.

But he or she will maybe think, well, if the ball is angled in such a way in that corner, that will be tricky for the opponent.

And the details of that are all done largely with the cerebellum.

That's where all the precise motions, but it's unconscious.

So why is it interesting to you that so much computation is done in the cerebellum and yet it is unconscious?

Because it doesn't, it's the view that somehow it's computation which is producing the consciousness.

And here you have an incredible amount of computation going on.

And as far as we know, it's completely unconscious.

Why is the cerebrum, all this very peculiar stuff that very hard to see on a computational perspective, like having everything have to cross over onto the other side and do something which looks completely inefficient.

And you've got funny things like the frontal lobe and the, what do we call the lobes?

And the place where they come together, you have the different parts, the control, you see 1 to do with motor and the other to do with sensory.

And they're sort of opposite each other rather than being connected by, it's not as though you've got electrical circuits.

So it's just the idea that it's like a complicated computer just seems to me to be completely missing the point.

There must be a lot of computation going on, but the cerebellum seems to be much better at doing that than the cerebrum is.

So for sure, I think what explains it, it's like half hope and half we don't know what's going on and therefore from the computer science perspective you hope that a Turing machine can be perfectly, can achieve general intelligence.

Well you have this wonderful thing about Turing and Godel and Kirch and Currie and various people, particularly Turing and I guess Post was the other 1, these people who developed the idea of what a computation is.

And there were different ideas of what a computer, it developed differently.

I mean Church's way of doing it was very different from Turing's, but then they were shown to be equivalent.

And so the view emerged that what we mean by a computation is a very clear concept.

And 1 of the wonderful things that Turing did was to show that you could have what we call a universal Turing machine.

You just have to have a certain finite device.

Okay, it has to have an unlimited storage space which is accessible to it, but the actual computation, if you like, is performed by this 1 universal device.

And so the view comes away, well, you have this universal Turing machine, and maybe the brain is something like that, a universal Turing machine and it's got maybe not unlimited storage but a huge storage accessible to it.

And this model is 1 which is what's used in ordinary computation.

It's a very powerful model And the universalness of computation is very useful.

You could have some problem and you may not see immediately how to put it onto a computer, but If it is something of that nature, then there are all sorts of sub-programs and sub-routines when all the, I mean, I learned a little bit of computing when I was a student, but not very much.

But it was enough to get the general ideas.

And there's something really pleasant about a formal system like that.

Where you can start discussing about what's provable, what's not, these kinds of things.

And you've got a notion, which is an absolute notion, this notion of computability.

And you can address when things are, mathematical problems are computably solvable and which aren't.

And it's a very beautiful area of mathematics and it's a very powerful area of mathematics and it underlies the whole sort of, what would 1 say, the principles of computing machines that we have today.

Could you say what is Gato's incompleteness theorem and how does it, maybe also say is it heartbreaking to you and how does it interfere with this notion of computation and consciousness?

Sure, well the ideas, basically ideas which I formulated in my first year as a graduate student in Cambridge.

I did my undergraduate work in mathematics in London and I had a colleague, Ian Percival.

We used to discuss things like computational and logical systems quite a lot.

I was a bit worried by the idea that it seemed to say there were things in mathematics that you could never prove.

And so when I went to Cambridge as a graduate student, I went to various courses.

I was doing algebraic geometry of a sort, a little bit different from what my supervisor and people were doing.

And I was interested, I got particularly interested in 3 lecture courses that were nothing to do with what I was supposed to be doing.

1 was a course by Herman Bondi on Einstein's general theory of relativity, which was a beautiful course.

He was an amazing lecturer, brought these things alive, absolutely.

And now there was a course on quantum mechanics given by the great physicist, Paul Dirac.

Very beautiful course in a completely different way.

He was very kind of organized and never got excited about anything, seemingly.

But it was extremely well put together and I found that amazing too.

Third course, it was nothing to do with what I should be doing, was a course on mathematical logic.

I got excited, as I say, my discussions with Ian Percival.

Was the incompleteness theorem already deeply within mathematical logic space?

I was introduced to it in detail by the course by Steen.

And he, it was 2 things he described which were very fundamental to my understanding.

1 was Turing machines, and the whole idea of computability and all that.

So that was all very much part of the course.

And it wasn't what I was afraid it was, to tell you there were things in mathematics you couldn't prove.

It was basically, and he phrased it in a way which often people didn't, and if you read Douglas Hoff's status book, he doesn't, you see.

But Steen made it very clear, and also in a sort of public lecture that he gave to a mathematical, I think it may be the Adams Society, 1 of the mathematical undergraduate societies, and he made this point again very clearly, that if you've got a formal system of proof, so suppose what you mean by proof is something which you could check with a computer.

So to say whether you've got it right or not, you've got a lot of steps.

Have you carried this computational procedure, well, following the proof, steps of the proof correctly, that can be checked by an algorithm, by a computer.

Now what you have to, now you see, is this any good?

If you've got an algorithmic system, which claims to say, yes, this is right, you've proved it correctly, this is true, if you've proved it, if you made a mistake, it doesn't say it's true or false, but if you've done it right, then the conclusion you've come to is correct.

Now you say, why do you believe it's correct?

Because you've looked at the rules and you said, well, okay, that one's all right, and that one's all right, what about that?

I'm not sure, oh yeah, I see, I see why it's all right.

Okay, you go through all the rules, you say, yes, following those rules, if it says, yes, it's true, it is true.

So you've got to make sure that these rules are ones that you trust.

If you follow the rules and it says it's a proof, is the result actually true?

And that your belief that it's true depends upon looking at the rules and understanding them.

Now what Gödel shows is that if you have such a system, then you can construct a statement of the very kind that it's supposed to look at, a mathematical statement, And you can see by the way it's constructed and what it means that it's true, but not provable by the rules that you've been given.

And it depends on your trust in the rules.

Do you believe that the rules only give you truth?

If you believe the rules only give you truth, then you believe this other statement is also true.

I thought, my god, You can see that this statement is true.

It's as good as any proof, because it only depends on your belief in the reliability of the proof procedure, that's all it is, and understanding that the coding is done correctly, and it enables you to transcend that system.

So whatever system you have, as long as you can understand what it's doing and why you believe it only gives you truths, then you can see beyond that system.

What is it that enables you to transcend that system?

Well it's your understanding of what the system is actually saying and what the statement that you've constructed is actually saying.

So it's this quality of understanding, whatever it is, which is not governed by rules.

So this idea of understanding is not going to be within the rules of the, within the formal system.

Yes, you're only using those rules anyway because you have understood them to be rules which only give you truth.

I mean people say, well okay, this is 1 set of rules as good as any other.

You have to understand what the rules mean.

And why does that understanding of the mean give you something beyond the rules themselves?

And that's what it was, that's what blew my mind.

It's somehow understanding why the rules give you truths enables you to transcend the rules.

So that's where, I mean, even at that time, that's already where the thought entered your mind that the idea of understanding, or we can start calling it things like intelligence or even consciousness, is outside the rules.

Yes, see, so I've always concentrated on understanding.

You know, people say, people, somebody's pointing out, well, we know, but what about creativity?

That's something a machine can't do, is create.

And I don't know, you know, somebody can put some funny things on a piece of paper and say that's creative, and you could make a machine do that.

I don't know, you see, I worry about that 1.

I sort of agree with it in a sense, but it's so hard to do anything with that statement.

You can make, go see that understanding whatever it is, and it's very hard to put your finger on it.

Can you try to define, or maybe dance around a definition of understanding?

To some degree, but I don't, I'm often wondered about this, but there is something there which is very slippery.

And it's got to be something, you see, it's also got to be something which was of value to our remote ancestors.

Because I sometimes, there's a cartoon which I drew sometimes showing you how all these, there's a, in the foreground you see this mathematician just doing some mathematical theorem.

There's a little bit of a joke in that theorem but let's not go into that.

He's trying to prove some theorem and He's about to be eaten by a saber-toothed tiger who's hiding in the undergrowth, you see.

And in the distance, you see his cousins building, growing crops, building shelters, domesticating animals.

In the slight foreground, you see they built a mammoth trap and this poor old mammoth is falling into a pit, you see, and all these people around him are about to grab him, you see.

And well, you see, those are the ones who, the quality of understanding, which goes with all, it's not just the mathematician doing his mathematics, this understanding quality is something else, which has been a tremendous advantage to us, not just to us.

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Roger Penrose: Physics of Consciousness and the Infinite Universe | Lex Fridman Podcast #85