Roger Penrose – Why Intelligence Is Not a Computational Process: Breakthrough Discuss 2025

So in this talk we saw the problem um when an engineer is trying to build consciousness you need to bring all the senses together use a lot of energy and try to hope somehow uh they will arise into something akin to emotion. But what if you just cannot do it? What if just computation in a classical world is not enough to become conscious?

So our last speaker is of course Robert Roger Penrose who has been thinking about this for a very long time and we are very lucky that he found some time to come and tell us about it. Well, thank you very much for giving me the opportunity to waffle on a subject which has interested me for a long time. I'm not going to talk about interesting things like octopuses and bats and things like that which is fascinating nor about emotions which is clearly something to do with consciousness but two boring old numbers um mainly to begin with at least natural numbers.

What's a natural number? Well that means 0 1 2 3 4 etc. when I say etc.

you get the idea but I'm not going to say any more about that. Okay. Well, what I want to talk about really goes back to about 70 years ago.

I could have given this talk perhaps 70 years ago at least most of it because it emerges from a course of lectures that I went to when I was a graduate student in Cambridge and I went to three courses of lectures which were nothing whatsoever to do with my subject. I thought three years is a long time and so I can spend my early years doing some other things which weren't connected with my topic which was in pure mathematics. Of course, that was a stupid idea because I didn't finish in time anyway.

But nevertheless, I went to a lecture by Herman Bondi on general relativity. Had a big influence on me later on in life. I wonderful lectures I should say.

Also, I went to a course of lectures by the great Paul Dr on quantum mechanics which also had a great influence on me. But the third lecture course which was nothing to do with what I was supposed to be doing was a course by a man man called Steen on mathematical logic and it was really about numbers one 0 1 2 3 4 etc. And well, you see how do you in mathematics you want to say things not that just 3 + 2 equals 5 or something like that or bigger numbers than that or huge numbers like what computers can do.

No, you want to say something about all numbers. Well, you learn in school, I hope you still do. I'm not quite sure what people learn in school nowadays, but the pro process of mathematical induction.

So you can prove something is true for all numbers by just proving a couple of things. For mathematical induction, you want to show something's true for all n all natural numbers n then you can say if it's true for n then it's true for n + one. That's one thing you show and then you show show it's true for n equals zero and that shows it's true for all numbers.

So I was really fascinated by that idea. You just do a finite number of things and you can show something is true for all numbers all natural numbers let's say when I say natural number I mean a non- negative whole number now this course of lectures talked about this famous result due to Kurt Girdle which I didn't really like the idea of because it seemed to show that there were things in mathematics you couldn't prove I didn't like that idea at all anyway so I went to the course it was fascinating and the first part of the course was really merely about computability very notion of computability which is very much part of what computers do of course well that's the name and uh that was interesting but then he did talk about this famous theorem of go and it wasn't really what I it was something quite different in a way not that there were things you couldn't prove but what was it now suppose you have a certain set of things that you can use in a proof. See a mathematical proof you have certain set of axioms and then you have a certain set of rules of procedure.

So you have these axioms and then you can combine them together in various ways and if you can get the result out that you're trying to show um such as for example well simple example would be if you add two even numbers you get another even number. A not so simple example would be a number due to a proposition a statement a theorem due to lrange interesting theorem because it the great leonhard oiler tried to prove it and couldn't so it's quite interesting that is to say that every natural number is the sum of four square numbers it's a good example and it's telling you about all numbers finite statement and not so easy to prove but nevertheless you can prove it. Now what does the proof mean?

Well, usually it would mean you have your set of axioms and rules of procedure and if you use them correctly and you derive this result from those axioms and rules of procedure then you've got a proof. Now what did Girdle do? He was it was very clever and I won't go into the details of the cleverness.

quite tricky in some ways. But what he showed was that you could make a statement which in effect said I am not provable by those rules and it's a definite mathematical statement you can construct it and the interpretation you see what it means and how it's constructed and it says oh yes it does really mean that if you understand what these things mean it means I am not pro when I say I am the statement talking if you like I am not provable by those rules rules you've given me. Okay.

Well, you can say, well, maybe it's false. But if it's false, then it is provable by the rules, and therefore it has to be true. It has to be true, but it's not provable by the rules.

Now, this is very strange. You've got something which is true. You know it's true.

How do you know it's true? Not by using those rules, because it's not provable by those rules. You know, it's true because you understand why the rules only give you truths.

And I think that's really very remarkable. It's your understanding of why the rules work gives you more than using the rules. What does that mean?

What does understanding what the rules mean mean? Well, it's this awkward word understanding. What is understanding?

Well, it's something that involves consciousness. You see, it's a sort of in the ordinary use of language. You say an entity, does it understand something or not?

Well, it rather implies by the use of the word understanding that it's at least aware of what it's trying to do. Can something understand something without even being aware of it? Well, not in ordinary usage.

I mean people might quibble about that but the ordinary usage of the term understanding means at least it it's aware of what it's thinking about or doing or something awareness awareness consciousness so it does seem to imply that this is something to do with consciousness and I found this very striking as I say about 70 years ago I could have given that much of my talk and I began to think Well, I'm a physicalist, too. So, I believe whatever's going on in our heads must be in accordance with the laws of physics. So, there's whatever the laws those laws are, they have to be something.

Well, could be they be something you could put on a computer. Well, then they would be computable and then you would be back in the trouble of the girdle thing. And it seems to me it's got to be something in the physical laws.

As I say, I'm a physicist. It's not something magic which comes in when whatever that it is something to do with the organization of this stuff which is going in our heads or in the octopus's head or whatever. There's something going on there which is acting in accordance with the laws of physics but is not really something computable.

As I say the beginning of the course I went to by ste involved the notion of computability and all that stuff and so I understood vaguely what that meant. more or less it means what you could put on a computer. Now this says that there is something beyond the understanding of what what you're doing seems to be something beyond what you could put on a computer.

Now of course people might argue about that. Now I think it's a strong case to show that there are things which are not computable which are going on in the physical world and that includes this phenomenon of consciousness. But then I began to wonder what in the physical world could possibly be non-computable?

Well, I mean, you put things on computers, Newtonian mechanics, sure, you can go ahead and do that. What about uh well, Maxwell's equations? You have a little bit of a problem with these things.

You have to worry a little about, which I think is a genuine worry because these laws of physics depend on the continuum. They're not just about the the natural numbers 0 1 2 3 4. They depend on filling in the gaps between the natural numbers if you like and that's not a trivial issue.

I just take the view which I still take the view but it's not that's not really the problem. You can put things well enough on a computer even if they're not exactly the continuum. You can approximate them.

I think there is a possible lacuna in the argument there which I have often wondered about. But let's take the root which I'm taking here. It's not that you can get closely enough to uh the na to the continuum with your natural numbers to put your computer to work.

And well that that time computers weren't so good at doing general relativity. The general relativity the Einstein's theory of gravity and space and time and all that stuff. that theory you can put it on the computer and you're doing the approximations in a normal sort of way and nowadays you can do wonderful things with these computers the LIGO detector you can know that there are black holes colliding and producing gravitational waves and the signals are very calculated very well calculated and you know exactly what's going on.

So this is very much a computational issue that's not where it lies. So it's not to do directly with these theories of the continuum or something. What about quantum mechanics?

Well, quantum mechanics was a little bit unclear there. How about the Schrodinger equation which I I said I went to DA's lectures and I learned about um how how these equations work. Simply differential equations.

They can be difficult to use because there are many variables and so on. can be quite tricky to use uh but still it's still computation in the same sense except that what is quantum mechanics well it consists of two parts people don't quant emphasize this very much um Einstein and Schroinger certainly did they say that well even Drq as I learned later said that quantum mechanics is not complete in some sense I'm going to be a bit rudest than that it's not just not complete it's not quite right. Why do I say it's not quite right?

Well, you see what is quantum mechanics? How do what what is the subject? Well, you have a thing called the wave function, the state vector, if you like, and the Schroinger equation tells you how that state vector or wave function evolves in time.

If you know what it is now, you will know what it is in 10 minutes. You'll know what it is in a 100 years. So according to the Schroinger equation, it's a deterministic equation.

You could put it on a computer, do any precision you like, but the world doesn't satisfy the shing equation. I'm saying that quite brutally when I say quantum mechanics isn't quite right. This is what I mean.

Why is that? Well, because the theory of quantum mechanics depends on something else than the Schroinger equation. It's a thing which is rather impolitely called the collapse of the wave function.

Schroinger tells you how the wave function evolves. But the world doesn't quite do that. Every now and again it does something else.

What do I mean by every now and again? Well, Schroinger who made the sort of emphasis by this and by talking about his famous cat. People often re misinterpret that in my view.

They say well it's really shows if you had a really subtle system which which you could actually have your cat in it and you could calculate exactly what happened according to the Schroing equation. Then you could make a cat which is dead and alive at the same time. That's not what Schwinger was saying.

He was saying this is an absurdity. There's something wrong. And I believe he was right to say there is something wrong.

There's something wrong. You see what is what is the collapse of the wave function? Well, people usually interpret it as say well you look at the wave function or something.

You measure it. You do a measurement on it. And this means you adopt a different procedure.

You don't follow the Schroing equation. You follow another procedure which you gives you a sequence of probabilities and it's the probability of this or this or this or this. And that's what you do at that stage.

you do something else in the Schroinger equation. You collapse the wave function. You make a measurement.

Okay. Well, there are theories which tell you how that if the system gets involved with the environment, it gets so complicated use a different procedure. I won't go into all that.

There's famous theorem due to Landau and vonman which tells you if you take the environment into consideration then this you follow a certain procedure and you get this sequence of probabilities. If you look at it carefully, you see it actually involves what I call a double well a double cheat or I say cheat which is an ontology switch. That is you have a certain view about how the theory relates to the real world and then you change your view to something different.

Technically, it's you change from the wave function to what's called a density matrix and then you change it back again to probability mixture of different wave functions. And that's where you're cheating. You do a double cheat.

It's a very good cheat. I would say it's the sort of thing which gives you the right answer. And it's a really very impressive thing to do.

I'm not saying that what Landon von Nolman did was was rubbish. Absolutely not. It was very clever.

But it does involve this double ontology shift to cheats if you like that to do a big good physicist you know how to cheat properly. I think that's that's part of the idea and uh okay that's fine part of the game but it's more important to see what's going on what's really going on there. Now I took the view because of this part first part of my talk that what's going on has to be something which is not computable.

Now that's was not a normal view about these things. People often would say about me well I waffle about consciousness and all my really talking about this teensy weasy little thing which has to do with um mathematics in a particular area or something like that. And what's that got to do with the main problems like uh well feelings and goodness knows and what do I have to say about the different impression that blue and pink have sure they look completely different they feel completely different I don't have anything whatsoever to say about that I mean of course there are various things with certain conditions in the brain you get confused about which is blue and pink and all that stuff I don't happen to have that problem but um I I have nothing to say.

I have no idea. The little tiny wensy thing that I do have something to say about is this issue of computability which tells me that there is something going on in consciousness in understanding in this very particular way in which consciousness is being employed. an important way because it involves understanding and in understanding in the world of a world at some level or another is absolutely crucial.

I'm sure it's true for the octopuses we just heard about. They understand something about what's going on and that's very important to them. Now, what does understanding mean?

Well, you have to be conscious of it. But I mean that's going one way around and it's not saying much about our feelings and blue and purple and whatever it is. But it is saying something about something which the point I'm making is this is telling it that is that the consciousness thing that we're trying to search for seems to depend on something that goes beyond any of these theories I've talked about.

But you see the clue I claim in quantum mechanics because it's incomplete or as I my rud phase not quite right it's wrong in a certain sense that when a system gets big enough that these superp positions being here at the same time something like that well that was what Dak was saying he I didn't quite gather the explanation he gave I think I was staring out of the window I know I missed it which was probably a good thing because that meant I I never understood what he said and probably what he was said was to something to smooth it over and stop you worrying about the problem. I'm sure it was something like that and I didn't get that bit. So I did worry about the problem for ever since which is what on earth is going on.

is something which is not in current physics and it involves the collapse of the wave function which is a physical process and the laws of which are something we don't know and which I'm claiming are not computational that's if you like the only place that I could see it can seriously be in there little possibilities it could be that I think this is the easily the most likely that it's in the collapse of the wave function that we have something beyond our present understanding which allows us to understand things or some way go beyond pure computability and I guess people won't like this very much because modern computers of course they're doing because they don't do the infinite things you see well at the beginning of my talk I was saying you could talk about the infinite you can talk about in a serious way in a rigorous way and it doesn't matter your computer can I Some of these very early results I remember learning about skews skews theorem which was something which was those times it was some number which was absolutely huge way beyond what any computer even today could get anywhere close to and you had to get beyond this number to see that this result happened to be true. this happened to be a number thing in number theory I won't bother you with um anyway so the the point of view I had was this quality of understanding it'sn't be anything to do with mathematics that's just a way you see it you see the role of being something beyond our physical understanding now all this is old hat when I say I could have been talk maybe not 70 years ago but maybe about 50 years ago I could have given that talk but There are certain ideas about this which are much more recent. I've tried to understand a bit more about the collapse of the wave function and how it relates to relativity and it has a very curious relation to relativity.

Let me give you a sort of example of this. I think in the early days people used to worry about the wave function and they said is it real in some sense? Mathematicians who know what a wave function is said no it's complex.

Oh, that's not what I mean. It's is it really there or is it just some kind of artifact that we use in our calculations? And Einstein put forward a rather impressive condition.

He said something is real if you can make a measurement on it and if this measurement gives you yes with certainty and without disturbing the system then it gives you a reality. What I'm trying to say now is that it does give you a reality but it's a kind of reality which is a little peculiar. It's what I'm calling quantum reality.

And I make the point that there are different kinds of reality. There's classical reality and there is quantum reality and they're not quite the same. The main difference is that classical reality you can ascertain it.

I could take my sticks here and I say hello stick. What's your shape? Well, I can it it will say I'm more or less cylindrical up to here.

I'm another slightly smaller cylinder and I've got a little spike on the end and all that sort of stuff. and it can describe the shape exactly. Well, close enough.

So that's what classical reality is like. You can say hello state and what what is your state like? And it can just give you this description.

Quantum reality is not like that. And I give you a good example. The spin of an electron that's an example of a spin half particle.

The spin of an electron. The state of that can be described by taking some direction. say the direction of my thumb and it is spinning right-handed about that direction.

Every state of spin is spinning right-handed about some direction. Now that is quantum reality. If I find a state and I want to know say hello state, which way are you spinning?

It looks at me blankly and says I don't answer questions like that. Suggest a direction. So I might say I know because I know this state came about from some complicated experiment it would be spinning that about that direction and I can I can ask the I can confirm by saying are you by any chance spinning about right-handed about that direction and the spin then says yep you got it right every time you got it right and that is quantum reality but if I say tell me which direction you're spinning in it says nope I don't answer that kind of question that's the difference so it's true about Einstein's idea of reality but it's quantum reality and this kind of reality is important to understand because it behaves very peculiarly with regard to time and I did study this and I wrote an article about this once and you think is that the fact that you can't ascertain It is important.

You can confirm it but not ascertain it. And there are experiments there things that call EPR experiments, Einstein, Pedoski, Rosen experiments and things like this which seem to be very curious. They seem to indicate that signal can be sent from well it's always Alice and Bob are the two.

Alice has a spin half particle. Bob has another one. They start from a stage of spin zero and then they they sort of spin oppositeely to each other.

and Alice makes a measurement instantaneously Bob's state is going the other way. It's worse than that. It's before backwards in time his thing goes the other way.

Does that contradict relativity? No. Because it's quantum reality.

Bob can't ask his state which way you spinning. He can say do you happen to be spinning this way? And then give you an answer.

It's important to know that distinction because quantum reality behaves very peculiarly with regard to time. It doesn't quite go backwards in time, but it does something rather like that. And I think it's important perhaps to relate this to things I I when I wrote my book, The Emperor's New Mind, um this was my first toying with these ideas and sort of writing a semi-popular book and uh I thought it would might inspire young people.

I only got uh commentaries from old retired people who were old enough to to spend enough time to read my book. But then I did get a message. Well, I have got some people from young people later.

That's good. From Stuart Hammerov who did read my book and he got back to me and said, "You evidently don't he was a bit more polite than that. Evidently, you never heard of microtubules, have you?

" You see, I'd learned about the Hodskin Huxley theory of nerve propagation and I realized that's hopeless. If you want to preserve quantum quantum states, it doesn't doesn't do it. I mean that it disturbs the environment too much and that's not what you want.

If consciousness couldn't be just by nerve propagation, there had to be something else. And he said, well, how about microtubules? Well, I won't go into that story and I think it's an important story.

Seems to me there is a reasonable chance that there is something in the microtubules which requires quantum reality notions and there could be something more. In fact, there are certain ideas which Stuart has gone into. I don't really follow all these things now but there are certain lay layer of the brain you see one thing that I learned about I learned sort of elementary things about neurohysiology not and one things they were sort of blatantly obvious things one is things that the cerebrum and the cerebellum are different the cerebrum is has this stupid crossing over some people say oh it's a mistake or something no it's not a mistake the other is the cerebellum which didn't make that mistake mistake no cerebellum is right hand side goes the right way and the left hand side um is sp controls and is controlled by the left hand side.

There's no none of this stupid crossing over. So the cerebrum does all this crazy stuff. It's doing it for a reason.

I don't know what the reason is but there is obviously something else going on than just nerve propagation. And I think he's right in that. And I didn't know there anything which is different between these two parts of the brain.

And then he points out well there's certain cells called parameal cells where the microtubules have all different organizations and things like I don't want to go into that I don't understand it myself but the claim is that you could maybe you see the the issue which I was worry about another issue is it seems to be that things happen I I I think in my book the emperor's new mind I did refer to these experiments to Benjamin Libbit which seem to indicate something very curious about temporal uh when you actually experience something when does a conscious feeling of something or other happen and it seems the time is all messed up in some peculiar way that it's not somehow it goes almost as though it's retroactive and maybe it is in some sense because the classical I mean quantum reality can do that classical reality can't. You got to be damn careful that you don't get causality problems. But if it's quantum reality, it's not going to cause you a problem.

I don't want to talk about this in any detail because first of all, I don't understand it in any detail. And secondly, it would confuse everybody else. But I do want to say that there could well be something in what's going on in the brain which involves this quantum reality notion and these very curious in experiments made by Benjamin Libbit which seem to indicate that there is something very puzzling about the timing of conscious experience and it relates to the way see you think of a pingpong player I used to try and playing ping pong in my youth and it's clearly you have to make it you've got to want to make a decision am I going to flick the ball to the right or to the left well I judged where my opponent is and I think if I flip it this way it's more likely it will unexpected to my opponent and that thought sort of very rapid kind of thought according to current views is much too quick to be done consciously it has to be unconscious but I thought no no I was thinking it consciously but the view is that you could do this maybe if you realize that there's something about quantum reality involved at conscious experience I'm only putting this out as a sort of slight feel of some mind.

I don't have any theory of this but I am indicating that it could be much more subtle issue certainly than a computer. There's something much more subtle going on which could involve this difference in notion between quantum reality and classical reality which is something there in the real world. It's in the real world, but it's very peculiar certainly in relation to temporal um orderings and things like that.

Thank you very much.