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Hello and welcome to this series on physics and philosophy from the University of Oxford Artificial Intelligence.

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The term conjures up apocalyptic visions of armies of robots taking over the world and enslaving the human race.

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Technology today is indeed progressing at an ever growing rate.

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A pocket calculator can solve problems in a matter of seconds that a human would take much longer today.

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Many of our mundane and repetitive jobs are now being taken care of by machines.

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But could a computer ever truly replace a human? Could it enjoy the Northern Lights or fall in love and write a poem?

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I'm on guitar and Evan and I'm speaking to Sir Roger Penrose, emeritus professor of mathematics and fellow of Wadham College, Oxford.

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Although a mathematician at heart, he has made extensive contributions in the fields of physics, philosophy and even art.

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He is the recipient of many awards and prizes, including the 1988 Woolf prize for his work in Black Holes.

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His book, The Emperor's New Mind and its sequel, Shadows of the Mind,

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explored the idea of artificial intelligence and whether the human mind could ever be fully replicated by a computer.

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So do you think that the human mind can ever be replicated by a computer?

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I don't, actually. But we have to be careful about the terminology.

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I mean, I think that the conscious aspects of the human mind I mean, mind you may include unconscious activities also,

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but what's involved in consciousness is not to do with computation,

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and that no matter how complicated the computation is, it would not evoke consciousness,

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nor would it be able to do the things that I believe consciousness actually is used for.

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So I think of consciousness is something which actually does affect our behaviour.

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Some people refer to an epi phenomenon, which means that it just happens to tag along.

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If you have a computational action, for example, or some kind of action and consciousness sort of comes along as a passenger, I don't take that view.

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It's a more active role that it plays. I'm not quite sure I could define that in any way that would make a philosopher happy.

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But nevertheless, I do think it's an active role and it's serving a purpose.

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So that's the evolution of consciousness in in us and in other animals is in my, in my view, something which had a strong selective advantage.

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So that's why we have it, if you like. But that is not something that a computer does.

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And the reasons I have believing this mainly come from mathematical logic.

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So although there's arguments which I've been trying to make for a long time,

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first in the Emperor's New Mind and more in more detail in my later book, Shadows of the Mind.

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But in many other writings, I have tried to make the case that I think it's actually a strong case,

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that there is something quite different that we use our consciousness for, which is not something that could be actually done by a computer as such.

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To clarify that a little bit. I don't necessarily mean that some device made by some mad scientist or a same scientist,

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some latter day Frankenstein say who could construct some entity out of maybe inanimate materials,

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which might conceivably be conscious, but it would not be a computer in the sense that we use that word today.

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So what exactly would the difference be? What is it about a computer that it cannot have consciousness?

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Well, this is the centenary year of Alan Turing, so it's nice to be able to relate this discussion to Turing's work.

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You see,

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Turing in the 1930s put forward a very interesting concept which was basically making clear what a lot of other logicians were doing at the time,

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which was what is a computation. There were some mathematical problems or classes of problems which had been proposed as you can.

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You find an automatic way of solving all these problems.

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And in order to address that question, Turing had to make clear what it meant to say an automatic process.

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And he also showed that there are mathematical problems which lie outside the scope of any automatic process.

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This was part of his initial thesis. This was more or less known already to gerdau and famous logician.

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But I think, as Goodall himself appreciated,

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Turing's way of looking at it made it much clearer that his way was actually encompassing what you really mean by computation.

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Now, the idea is that a computation is something which needs no means to do it.

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It just goes on automatically. It has rules which it follows.

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And these rules are made very clear. And we they are the basis of what we now understand by a general purpose computer.

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So a Turing machine, the notion that Turing introduced in whenever it was 1935 or something, the idea.

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Is basically what we now understand by a general purpose computer or an ordinary or a laptop idealised in basically three ways.

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One is it has unlimited storage space, so it can keep on you can keep on adding memory, if you like,

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and unlimited storage space that it can go on indefinitely without ever wearing out and that it never makes mistakes.

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So it's idealised in those ways.

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But when you've idealised it in those ways, you could actually see the limitations as Turing himself was very clear about.

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So initially, he he, I believe, tried to explore how you might go beyond his ideas.

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I think that perhaps his his experiences at Bletchley Park with decoding and realising the power of electronic computers.

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He shifted his view and went around to the view that maybe we are just computers in some very sophisticated code.

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But I would dispute that. Let me paraphrase Girls Famous Incompleteness Theorem in a slightly different way.

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This is more the Turing way. Suppose you're trying to prove certain statements in mathematics.

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Now, these are statements which have to do with in the infinite in some way.

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They always have to do with the infinite. You might say, how can we know about the infinite?

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Well, let me give you a statement, which I think you would agree is pretty obviously true, even though it talks about the infinite.

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If you add two even numbers together, you always get another even number.

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You never get an odd number. There is no odd number, which is the sum of two even numbers.

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Now that's a statement about all numbers, no matter how absolutely, fantastically enormous they might be.

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And yet we can perceive for various reasons why that's true.

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If you add even numbers together, you get another even number. Okay.

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There are much more sophisticated statements like that.

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Like the famous Fermat's Last Theorem, which is another example of something of a similar character.

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Now let's just take simple statements.

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When I say this simple, that may be very difficult to prove that statements like that,

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which are to do with natural numbers, the numbers zero one, two, three, four, etc.

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So we know what we're talking about. They're not some highfalutin concept.

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But the statements about these numbers, such as the still unproved goldbach conjecture,

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every even number greater than two is the sum of two prime numbers.

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So if you know the prime numbers, it's a fairly clear statement. Nobody knows whether that's true or not.

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It's just people suspect it is true. But there is no known proof.

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Okay. Now, how would you expect to be able to prove statements like this?

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Well, you might have some kind of system rules, axioms, rules of procedure, which if you follow them properly, you come up with yes or no.

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Now the key point about these rules is that they are computationally checkable so that if I produce.

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An alleged proof. I can put this on the machine and it says, Yup, you've done the rules right?

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Or You made a mistake there. So that's what I mean by computationally checkable.

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Okay. So you can put that on the computer. I don't say that it knows what it's doing.

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It just can check whether or not the rules have been correctly followed.

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Now, here is the girl Turing statement. This is Turing's version of girl statement.

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Whatever those rules are, let's call them a capital R.

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So when these rules rules are the rules. If I know what they are, I can construct a statement of the kind that I'm talking about.

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Right. Some of the prime numbers and so on. I can construct a statement which has the following two properties.

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First of all, it's true, provided the rules do not enable me to prove that two equals three.

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If I trust the rules to the extent that I know they will never enable me to prove two equals three, then this other statement is certainly true.

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Yet that other statement cannot be proved using the rules.

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So our understanding inside can.

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Supersede or transcend any system of rules whatsoever.

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If you give me a system of rules which are meant to be the way mathematicians prove these statements,

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I can go away and construct in a very clear cut way a statement which I can show is beyond the scope of the rules.

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Yet it's still true. And the key point is knowing that it's true comes from my trust in the rules.

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So it's my very trust in the rules which enables me to transcend the rules.

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Now, that's very remarkable statement. It shows that we don't work by rules.

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Okay. There are various objections you might make to say, well, we don't know what we are, we don't know what calculations we do and so on.

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I don't believe any of those objections really get to the point.

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Turing's answer. He knew perfectly well that statement. Turing's answer was, Well, human beings make mistakes.

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And that's where our superiority lies. Okay, maybe that I really don't think that is what makes us superior to computers.

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You can make computers, make mistakes. It's easy to see. So I don't believe that that's.

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Why? We can do certain things that computers can't, and we do them because we understand what we're doing.

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Now, I don't know what understanding really is, but whatever it is, it's something which computers don't have.

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When we use computers and we do it also, we can make them play chess.

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We can make them do calculations to do wonderful simulations in science and so on.

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But the computer doesn't know what it's doing. It doesn't know it churns out an answer.

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It may say yes or no. It may say it takes note, but it hasn't the faintest idea what it's doing.

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It doesn't understand what it's doing.

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It's the understanding that enables us to transcend the rules if we understand the rules enough to believe them.

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That same trust in the rules enables us to transcend the rules.

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Now, that's very clear. But God approved.

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And Turing's version, he said, is in terms of computation, it's the same girls there.

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I could even prove it to you. It's not that hard to prove this statement.

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It's a little bit contorted how you do it. It's not that hard to prove.

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Now, when I learned about this, not quite in the form.

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I've said it here when I was a graduate student at Cambridge.

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Before that, I probably would have believed that we were all computers in some form.

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You see, I was, you know, I was that much of a materialist, if you like to use that word.

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But after hearing about the Gardner Theorem, after hearing this from a logician,

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a lecturer we had in Cambridge, it seemed clear to me, okay, there's something else going on in our heads.

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And I do believe that something in our heads, it's not something which comes mystically from outside.

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I mean, some people might think that no, I believe it's something to do with the goings on inside our heads, which is not computational.

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Now. I had believed this for many decades, but when it came to, I had the idea that someday I would write a book for the general public.

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You see, I just had this ambition. Maybe long after I'm retired.

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I will have time to do this, you see. But I heard a radio talk where Marvin Minsky, who is a very strong person, he believes we're all computers and.

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And Edward Fradkin was another of the same beliefs.

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And they were arguing things which seem to me to be quite extreme.

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Like if you walk from one end of the room, the other end of the room,

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there are two computers communicating with each other in the time you walk from one end of the room to the other.

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They have communicated more things to each other than the human race has ever done in its whole existence.

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You see. So I said, Well, I see where you're coming from. If you take the view that what we do is computations.

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Yeah, I suppose I could see your logic. I don't believe it, because I don't think that's what we do.

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I think understanding is something which is not a computational process.

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And that's what makes us different from computers. Yes. Well, there are lots of things that make us different.

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I think, you know, feelings, emotions and artist appreciation.

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But I'm only concentrating on this one quality, which is understanding.

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And there I think you can make a good case that what we do is not computational.

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So do you think that science can fully understand the mind?

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I think it's possible. Now, you see, here's where it's much more speculative.

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I think the girl statement, despite the fact that many people argue with me and you be surprised how many rude things they say.

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But it seems to me the argument when presented clearly is absolutely clear.

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Okay. They say, well, we don't know what algorithm we follow in our heads.

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And all this is some very complicated algorithm which gets to mathematics.

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I find that completely incredible because you have to say, how did we come about?

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Well, natural selection. Natural selection didn't favour people who are doing sophisticated mathematics.

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It's quite other things. It favoured understanding. It favoured consciousness.

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Consciousness, in my view, is a crucial ingredient to understanding.

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But if you ask me, do I think science will ever come to grips with that question,

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I think quite possibly whether we would properly completely come to grips with it, I don't know.

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But I think we shall make progress on that. But I think that the progress will come.

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From trying to understand what in physics there could be which lies outside computation.

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Now, this is where I get you know, people have trouble agreeing with me.

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Sometimes they say, well, we know all about physics, enough about the hand of the brain,

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where we know all the equations and Newton and Einstein and Schrodinger and so on, and these equations.

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Okay, we don't know the full details, but there are things we could put on a computer,

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we could make a computer and maybe a bigger one than we have now and fit all the equations in and make it so we just compute it.

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Help me. So I say, Well, it's true.

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Although there are little problems here, there are little problems which I'm going to say are not probably the important one.

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One of them is. The very notion of computation depends on the sweetness.

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You have bits which can be this way or that way, whereas almost all the equations of physics we know about are continuous.

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They depend on continuous parameters. Newton. Still true, Einstein, still true.

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Schrödinger, Maxwell. All those equations depend on continuous functions.

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I'm saying, okay, that's true. But maybe that's not really the point.

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It could be. But I do not believe it.

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I think that you can simulate with discreet ness close enough to the continuous that probably that's not the answer.

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Is there anything else we don't know in physics? Yes.

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There's this also, when I was a graduate student at Cambridge doing something quite different from my real research at that time,

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I learned from Dirac about quantum mechanics. The Great Quantum mechanics physicist, and it stayed with me.

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There's a big paradox in quantum mechanics. It involves two completely different procedures.

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Let's call one the Schrödinger equation, which it is. I use the letter U for that.

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That's unitary evolution. That's the word they used. And the other is what you do when you make a measurement.

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And then you have to do something quite different,

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which is called the collapse of the wave function or the reduction of the state vector for reduction.

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So you and A of the two processes, if you look at them carefully, they're strictly speaking mutually inconsistent.

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If the world works according to you, you can't have any. Ah.

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You do how? To me, that says the equations are right.

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Okay. They're very, very good, but they're not quite right.

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And when they apply to big enough structures, there's something new comes in.

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And Schrödinger himself was very clear when he made it. He talked about his cat.

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You know, he said, well, I could I won't do it because I'm a nice, humane person.

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But I could have an experiment in which a cat is put in a superposition of being alive and dead.

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And that's absurd. I mean, he didn't quite put it like that.

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But basically what he was saying is my equation when I say I'm shooting and you see Schrodinger's equation doesn't explain what happens to cats.

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There's something missing. And I agree there is something missing.

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And it's that missing thing which has to be involved in our mental processes, in consciousness.

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It's not just that quantum mechanics is involved in brain action.

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It's the missing. Boundary between quantum and classical mechanics, which we don't understand.

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And when we have that, we might see that it's a non computational process and maybe we can see how it works in the brain.

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Maybe we can see what relates to our feelings and other things about consciousness.

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So I think it's possible we will make genuine progress. I think we're enormously far from it right now.

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In your second book, Shadows of the Mind, you talk about microtubules in the brain.

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Do you think that any new physics, perhaps not computational new physics, might play a role in microtubules and how these work?

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And do you think research in this field may take a little closer to understanding consciousness?

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I don't know what this new physics is that will go beyond colour codes, but I do make a guess.

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When I wrote The Emperor's New Mind, I couldn't think of any place for this new physics to play a role.

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I wrote my book anyway, thinking that by the time I'd written it I would see what the answer was.

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No, I didn't. However, I was expecting young people maybe to be stimulated by my book.

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I'm not sure how many were, but occasionally a scientist would be.

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And Stewart Hamer of. I had never heard of him before.

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Told me he wrote me a letter. They used to write letters in those days in which he pointed out that there was something evidently he didn't know,

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namely microtubules these as little tubes, which in and also in almost all cells, not quite.

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They have a special role to play in neurones, he says, and he knows about them because he puts people to sleep.

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He's an anaesthesiologist.

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But unlike many of his colleagues who just put people to sleep and wake them up again, he's interested in what he's actually doing.

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What is he doing to the brain when he puts it to sleep?

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So he wants to know what qualities of the brain, what structures in the brain do the general anaesthetics actually affect?

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And he comes up with a view that the microtubules neurone or microtubules, which have a different kind of organisation from other cells.

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And I was most impressed by this. I'd never heard of them stupidly.

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And it seemed to be, well, here's a chance. There are structures with great deal, almost crystalline structure, highly organised tubes.

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I thought there's a much better chance than the neurone propagation which gets lost in the environment.

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That's hopeless. The microtubules, maybe. Now, this has been in a maybe state for a long time, but only within the last couple of years.

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An Indian scientist who shares your name and your Ben Bandyopadhyay,

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who has worked in Japan for many years with some Japanese colleagues, has been doing experiments on live microtubules.

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These are actually pig brained microtubules. I don't think it's some problem they have getting human ones.

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But anyway, pig brain microtubules and.

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He has exhibited some very remarkable quantum properties.

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So they have very strange properties, high conductivity at very specific frequencies.

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You measure the resistance with a certain frequency input and suddenly they become very conductive.

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And there are different frequencies. There are about eight different channels or frequencies, all working together in some complicated way.

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But he argues that this has to be a quantum mechanical process.

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You can't understand this from purely classical ideas.

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This is the beginning of some research, but it's a new area which I think could be extremely exciting.

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And maybe tell us something very important about what's going on in brain activity, which could be related to what's really going on in consciousness.

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And is this non computational that's very hard to tell at this stage.

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We would only be looking for coherent quantum effects in order for there to be any chance for the new physics that I claim is there to come in.

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You need many, many microtubules actually acting in concert.

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There's not enough displacement of mass. So the criterion that, as I say, this is a done deal.

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She and I have independently put forward a proposal that if you have enough displacement of mass between two states,

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then that gives you a lifetime for how long that superposition can live.

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So if you have a superposition, two states, you can work out a lifetime.

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It can't last for longer than, so it becomes one or the other. Now that lifetime for a single microtubule will be enormously long.

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So that can't be in itself. What gives consciousness?

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Because you aim conscious actions occur in matters of fractions of a second.

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So one is looking for many microtubules acting together in some coherent process.

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So you would need lots of them acting together. But it's a beginning.

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You can't tell from just that experiment that there's anything non computational going on.

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It's not even at the level where the new physics would come in is at a level where quantum physics seems to be playing a role at a level where people

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thought couldn't happen because the temperature is too high and you need low

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temperature or isolation or both in order to get coherent quantum effects.

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And he seems to be seeing coherent quantum effects at high temperatures.

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Body temperature higher than body temperature. And there's a good step.

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A beginning. It's only a beginning. You need lots of microtubules coherently.

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You need to understand about the structure of the brain. You need to understand all sorts of things.

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It's a huge story, I'm sure, but at least it's a perhaps a little window into what's going on.

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Yes. Thank you very much.