The Emperor's New Mind: Concerning Computers, Minds, and the Laws of Physics (Oxford Landmark Science)

by Roger Penrose

One cannot imagine a more revealing self-portrait than this enchanting, tantalising book … Roger Penrose reveals himself as an eloquent protagonist, not only of the wonders of mathematics, but also of the uniqueness of people.’

Stimulated by science fiction read in their youth, and convinced that our minds are simply ‘computers made of meat’ (as Marvin Minsky once put it), they take for granted that pleasure and pain, the appreciation of beauty and humour, consciousness, and free will are capacities that will emerge naturally when electronic robots become sufficiently complex in their algorithmic behaviour.

Penrose’s book is the most powerful attack yet written on strong AI. Objections have been raised in past centuries to the reductionist claim that a mind is a machine operated by known laws of physics, but Penrose’s offensive is more persuasive because it draws on information not available to earlier writers.

Penrose also has the courage to affirm, contrary to a growing denial by a small group of physicists, a robust realism. Not only is the universe ‘out there’, but mathematical truth also has its own mysterious independence and timelessness.

Like Newton and Einstein, Penrose has a profound sense of humility and awe toward both the physical world and the Platonic realm of pure mathematics.

Many pages in Penrose’s book are devoted to a famous fractal-like structure called the Mandelbrot set after Benoit Mandelbrot who discovered it. Although self-similar in a statistical sense as portions of it are enlarged, its infinitely convoluted pattern keeps changing in unpredictable ways.

Even this achievement has been eclipsed in recent years by Penrose’s construction of two shapes that tile the plane, in the manner of an Escher tessellation, but which can tile it only in a non-periodic way. (You can read about these amazing shapes in my book Penrose Tiles to Trapdoor Ciphers.) Penrose invented them, or rather discovered them, without any expectation they would be useful.

Penrose’s achievements in mathematics and physics–and I have touched on only a small fraction–spring from a lifelong sense of wonder toward the mystery and beauty of being. His little finger tells him that the human mind is more than just a collection of tiny wires and switches.

The Adam of his prologue and epilogue is partly a symbol of the dawn of consciousness in the slow evolution of sentient life. To me he is also Penrose–the child sitting in the third row, a distance back from the leaders of AI–who dares to suggest that the emperors of strong AI have no clothes. Many of Penrose’s opinions are infused with humour, but this one is no laughing matter.

As part of the aim of this book, I try to set forth, as clearly as I can, a good deal of the profound progress that physicists have made towards an understanding of the workings of the physical world.

Most particularly, I argue that the phenomenon of consciousness cannot be accommodated within the framework of present-day physical theory.

I do my best to express, in a dispassionate way, my scientific reasons for disbelieving this perception, arguing that the conscious aspects of our minds are not explicable in computational terms and moreover that conscious minds can find no home within our present-day scientific world-view.

Nevertheless, it is not my contention that we should look outside science for an understanding of mentality, merely that existing science has not the richness to achieve what is required.

One thing that I had not adequately anticipated while writing this book was the vehemence that my thesis would evoke, mainly from those who strongly support the computational model of the mind, but also from some who ...

No doubt, a person’s philosophical position with regard to the mind can—like a person’s religion—be a touchy subject. But just how touchy a subject it can be was...

My reasoning, as presented in this book, has two main strands to it. The first of these endeavours to show, by appealing to results of Gödel (and Turing) that mathematical thinking (and hence conscious thinking generally) is something that cannot...

The second strand of the reasoning is to demonstrate that there is an important gap in our physical picture of the world, at a level which ought to bridge the submicroscopic world of quantum physics to the macro-world of classical physics. My viewpoint demands that the missing physics falling within this gap, when found, will play an essential part in the physical understanding of the conscious mind. ...

What Gödel’s theorem tells us, in a nutshell, is the following (which is not controversial). Suppose that we are given some computational procedure P for establishing mathematical assertions (let us say, assertions of a particularly well-defined type, such as the famous ‘Fermat’s last theorem’ (cf. pp. 76–7)). Then if we are prepared to accept that the rules of P are trustworthy—in the sense that we accept that the successful derivation of some mathematical assertion by use of the rules of P provides us with an unassailable demonstration of the truth of that assertion—then we must also accept as unassailably true some other assertion G(P) which is beyond the scope of the rules of P (cf. p. 135

But many critics have remained unconvinced and have pointed to various possible loopholes in this deduction. In my follow-up book Shadows of the Mind,1 I responded to all these criticisms in some detail and provided a number of new arguments to counter these criticisms.

One of the reasons that people sometimes have difficulty in seeing the relevance of Gödel’s theorem to our mathematical understanding is that, according to the way in which the theorem is usually presented, G(P) seems to have little relevance to any mathematical result of interest.

The numbers appear to be ever increasing, and it would be natural to suppose that this will continue indefinitely. However, this is not so; for Goodstein’s remarkable theorem tells us that no matter what positive whole number we start with (here 581) we always eventually end up with zero!

What all this shows is that the quality of understanding is not something that can ever be encapsulated in a set of rules. Moreover, understanding is a quality that depends upon our awareness, so whatever it is that is responsible for conscious awareness seems to be coming essentially into play when ‘understanding’ is present.

Thus, our awareness seems to be something that involves elements that cannot be encapsulated in computational rules of any kind; there are, indeed, very strong reasons to believe that it is an essentially ‘non-computational process’.

The possible ‘loopholes’ to this conclusion, referred to above, are that our capacity for (mathematical) understanding might be the result of some calculational procedure that is unknowable because of its complication, or not unknowable but no...

If we accept that there is indeed something outside purely computational procedures in our capacity for understanding and, therefore, in our conscious actions more generally, then the next step would be to seek where, in physical actions, any ‘essentially non-computational behaviour’ might be found. (This is assuming that we also accept that ‘physical action’ of some kind is where we must look in order to find the origin of conscious phenomena.)

Hence, we must look for a relevant place where there is an important gap in our theories. This gap, I claim, lies in the bridge between the ‘submicroscopic’ world where quantum physics holds sway and the macro-world of our more direct experiences, where classical physics works so well.

The term ‘non-computational’ refers to specific types of mathematical action of the kind that has been mathematically proved to be outside the scope of computation.

Non-computable processes can be completely deterministic. This is something of a fundamentally different character from the complete randomness that features in our present-day interpretation of quantum mechanics, when a small-scale quantum effect is magnified to the classical level—the procedure referred to as ‘R’ in the present work.

I also argue that this missing theory is the same as the missing link between quantum theory and Einstein’s general relativity. The term used in conventional physics for this unified scheme is ‘quantum gravity’.

Is the Mandelbrot set like non-recursive mathematics?

Natural selection of algorithms? The non-algorithmic nature of mathematical insight

‘Now is there anyone in the audience who would like to initiate our new Ultronic Computer System by asking it its first question?’

CAN A COMPUTER HAVE A MIND?

OVER THE PAST few decades, electronic computer technology has made enormous strides. Moreover, there can be little doubt that in the decades to follow, there will be further great advances in speed, capacity and logical design. The computers of today may be made to seem as sluggish and primitive as the mechanical calculators of yesteryear now appear to us.

If machines can one day excel us in that one important quality in which we have believed ourselves to be superior, shall we not then have surrendered that unique superiority to our creations?

The question touches upon deep issues of philosophy. What does it mean to think or to feel? What is a mind? Do minds really exist? Assuming that they do, to what extent are minds functionally dependent upon the physical structures with which they are associated? Might minds be able to exist quite independently of such structures? Or are they simply the functionings of (appropriate kinds of) physical structure?

In any case, is it necessary that the relevant structures be biological in nature (brains), or might minds equally well be associated with pieces of electronic equipment?

Are minds subject to the laws of physics? What, indeed, are t...

My own guesses will have important roles to play in what follows, but I shall try to be clear in distinguishing such speculation from hard scientific fact, and I shall try also to be clear about the reasons underlying my speculations.

My main purpose here, however, is not so much to attempt to guess answers. It is rather to raise certain apparently new issues concerning the relation between the structure of physical law, the nature of mathematics and of conscious thinking, and to present a viewpoint that I have not seen expressed before.

I can at least state that my point of view entails that it is our present lack of understanding of the fundamental laws of physics that prevents us from coming to grips with the concept of ‘mind’ in physical or logical terms.

I should make clear that my point of view is an unconventional one among physicists and is consequently one which is unlikely to be adopted, at present, by computer scientists or physiologists.

Most physicists would claim that the fundamental laws operative at the scale of a human brain are indeed all perfectly well known.

Yet all these issues seem as remote as one could imagine from the ‘everyday’ scale (or a little smaller) that is relevant to the workings of a human brain. And remote they certainly are!

We shall need some idea of the status of artificial intelligence. We shall need to know what a Turing machine is, and to understand the meaning of computability, of Gödel’s theorem, and of complexity theory. We shall need also to delve into the foundations of mathematics, and even to question the very nature of physical reality.

Thus, part of the task for the computer’s programmers is to make the computer appear to be ‘stupider’ than it actually is in certain respects. For if the interrogator were to ask the computer a complicated arithmetical question, as we had been considering above, then the computer must now have to pretend not to be able to answer it, or it would be given away at once!

In any case their point of view often tends to be that it will not be too long before a computer will be able actually to pass the test – say by the year 2010.

The kind of thing I do have in mind is that at some time in the future a successful theory of consciousness might be developed – successful in the sense that it is a coherent and appropriate physical theory, consistent in a beautiful way with the rest of physical understanding, and such that its predictions correlate precisely with human beings’

The objectives of AI are to imitate by means of machines, normally electronic ones, as much of human mental activity as possible, and perhaps eventually to improve upon human abilities in these respects.

Nevertheless, it would be fair to say that, although many clever things have indeed been done, the simulation of anything that could pass for genuine intelligence is yet a long way off. To convey something of the flavour of the subject, I shall first mention some of the (still quite impressive) early achievements, and then some remarkable recent progress with chess computers.