The Large, the Small and the Human Mind consists of Roger Penrose's 1995 Tanner Lectures, together with commentaries by Abner Shimony, Nancy Cartwright and Stephen Hawking. Much of the material will be familiar to readers of his earlier books, The Emperor's New Mind and Shadows of the Mind, although some new material is included. Penrose's general claim is that there are a number of situations that pose problems for current science, and whose resolution will demand the development of radically new theories. The kinds of issue he addresses are major ones: for example, the degree of order of the cosmos, the relationship between mathematics and the physical world, whether human mentality can be duplicated by a computer, and whether there is a fundamental connection between quantum mechanics and the human mind.
In the first chapter he uses a formula of Jacob Beckenstein and Hawking concerning black holes to argue that the early universe should have been highly disordered, a result not consistent with the observed uniformity of the cosmic background radiation. He rejects the standard explanation for this uniformity, based on the inflationary model of the big bang, claiming it to be invalid, and suggests that a more advanced and as yet unformulated physical theory may resolve the problem. His candidate for this role is quantum gravity, a theory that would combine the two highly successful theories of the 20th century, Einstein's theory of gravitation and the quantum theory, which have so far defied all attempts at integration into a single whole. This unified theory might explain the observed uniformity by imposing constraints on space-time geometry. But the whole argument hinges on taking the Beckenstein-Hawking formula out of the context in which it was originally demonstrated, and it is far from obvious that it is valid to do this.
Quantum gravity is additionally invoked to explain away the "Schrodinger's cat paradox". Under standard quantum theory, paradoxical states are possible in which two seemingly inconsistent possibilities (in Schrodinger's original exposition, a cat being fully alive and at the same time dead) are actualised simultaneously. The fact that we do not find such states in reality demands explanation.
Penrose's exploitation of quantum gravity to dispose of possibilities such as a paradoxical "dead-alive mixture" depends on a very tenuous line of argument. Nature, he supposes, abhors indefiniteness regarding space and time even more than it abhors superpositions of live and dead cats (space and time are more real to Penrose than cats, perhaps?). In Einsteinian gravitational theory, gravity is equivalent to a distortion of space and time, so it is logical to invoke gravitational influences as an agency that can prevent space and time getting unacceptably "out of step". The gravitational field of a cat turns out to be strong enough for the task, but unfortunately, as in the case of the earlier problem of accounting for the order of the cosmos, no proper mathematical theory is as yet on offer.
Of more general interest than these, perhaps, are Penrose's ideas on the mind. His lectures elaborate upon an idea touched upon in previous writings, involving three worlds, physical, mental, and Platonic, arranged in a triangle that depicts their mutual influence. The mental world, in accord with conventional wisdom, is presumed to be dependent on something physical such as the brain, while the Platonic world, concerned with universal truths such as mathematical truth, is one to which our minds have special access. This Platonic world, by virtue of the striking way that the physical world conforms to mathematical description, is regarded in its turn as the source of the physical.
Non-locality (the idea that some influences act at a distance), and noncomputability (that some physical processes cannot be computed by a finite computer program) enter into the equation as well. The predictions of quantum mechanics, as shown by John Bell, cannot be accounted for by models where there is no action at a distance while, correspondingly, it seems impossible to localise conscious experience in any one place; and so it is natural to imagine that the two might be connected. And, according to Penrose, mathematical thought cannot be reproduced by a computer program, and so must involve some special physics. Quantum gravity comes in as a candidate for such physics since one attempt to produce such a theory, the Geroch-Hartle scheme, involves classifications which are "noncomputable". As an added bonus, the same process which it is suggested might prevent mixtures of dead and alive cats from being found in nature could prevent our conscious minds being overwhelmed by vast numbers of ideas at the same time.
It requires considerable optimism to speculate that in due course all these ideas will come together, resulting in a theory which will not only unite quantum theory and gravity but also resolve the problem of inconsistent combinations of possibilities, as well as including the subtleties of the mind within its scope. Many scientists see Penrose's problems as being really nonproblems, while others have proposed alternative ways of overcoming some of the difficulties. Henry Stapp, for instance, proposes (as is to some extent consistent with Penrose's emphasis on the Platonic world) that it is mind that is not properly included in science, and that it is mind that, by selecting among the alternative possibilities, resolves the problem of mixtures of inconsistent states.
There appears to be widespread agreement among specialists in modelling the mind that Penrose's arguments for the non-computability of mental processes, based on Godel's theorem, are misconceived. What these arguments actually disprove is one version of mind model, namely a piece of code that could be run on a computer to give the correct answer to any mathematical question. To treat the question in such terms is to ignore a distinction made many years ago by David Marr, between a theory of how a process is executed, and a corresponding computer simulation. These two entities may differ from each other in various ways, one being that in general a real computer program only approximates to the idealisation to which the theory refers. A theory of how we acquire mathematical skills might be based on the way networks of neurons can be trained to perform particular skills, and might be correct in the limit of an infinitely large neural network, but only approximate for any finite computer simulation. The Godel-Turing-type arguments that Penrose uses presume a system that has both a finite specification and perfect abilities, and thus simply cannot be applied to that kind of situation.
It is unclear in any case that one needs to go to quantum gravity to find noncomputability. Noncomputability in some sense already arises in what are known as chaotic systems, a point I shall return to shortly. It would appear that Penrose has been led astray by taking chess-playing programs like "Deep Thought" as good models for how one might simulate mental functioning. On the basis of the fact that Deep Thought lacks concepts such as a "pawn barrier", which people can use very readily, Penrose asserts that people must be using noncomputational methods when they recognise the significance of entities such as pawn barriers. This is a misapprehension: it is known in general terms how computers could be programmed to learn to respond appropriately to features such as pawn barriers, but, on account of the amount of programming effort that would be involved in including this type of insight, that kind of skill has not as yet been included in chess-playing programs.
Even if the arguments used to support it are flawed, the noncomputability concept could still be of value, perhaps in a modified form. For example, chaos theory tells us that real systems may sometimes behave in a way that transcends analysis, because we cannot specify their states with sufficient accuracy to be able to do a definitive analysis. Biological systems might be instances of systems of this type. This idea dates back to Niels Bohr, who was later persuaded by Max Delbruck that it was ridiculous. Regrettably, Bohr's giving in under criticism has led to the idea being ignored, but recently I and others have revived it. Penrose's concept of a Platonic mind with capabilities beyond those fitting into conventional models can be viewed as a contribution to this tradition.
Mathematics is not the best context in which to argue the existence of a Platonic realm, since our mathematical skills might be explicable along conventional lines. I have been collaborating with a musical analyst, Tethys Carpenter, to see whether a more clear-cut case can be made in the alternative context of music. Cognitive scientists attempt to explain musical perception in terms of a variety of models, but these models appear to relate more to the question of what sounds like music than to the "aesthetic dimension". In our paper at the first Tucson consciousness conference in 1994, we argued that it was difficult, on the basis of such models, to account for "the specific forms that appear to be favoured in music, and which appear to possess a curious generative capacity or fertility not possessed by arbitrary patterns of (musical) sound". Furthermore, rather than going through some mechanical generative process, composers appear to possess an ability, somewhat similar to the way creative mathematicians work, to perceive the creative potential of particular patterns of sound from the very beginning, using such "germs" as the basis of their entire composition.
One might conclude from such considerations that Penrose may be right to emphasise creativity, noncomputability and the Platonic realm, but perhaps wrong to look for the integrative factor within his own discipline of quantum gravity. The most crucial element may be creativity. In the physical realm, creativity shows itself only in the minimalist guise of "random fluctuations". My collaborator Fotini Pallikari-Viras and I have argued that fluctuations have their systematic elements as well as random ones, and that biological organisms may evolve or develop to make creative use of them. It has proved difficult to put such ideas in mathematical form, but this is perhaps an area where significant new concepts can be developed.
Of the three concluding commentaries, that by Abner Shimony is perhaps of most interest. He argues for a juxtaposition of Whiteheadian philosophy, where mentality and potentiality play a fundamental role, and quantum physics. Physicists have developed, within the ontology of particles and fields, the framework of quantum mechanics which contains abstract concepts such as state, observable, superposition and entanglement. His proposal is that similar concepts be applied to other kinds of ontology such as those of minds, or entities endowed with a "protomentality". This activity might lead to a "quantum psychology" in which it could be the case that (in line with Stapp's proposals) a developed mentality might resolve the Schrodinger cat paradox. Nancy Cartwright also puts the case for going beyond physics in one's thinking, while Stephen Hawking, once a collaborator of Penrose, in his commentary "Objections of an unashamed reductionist", makes strong objections to a number of Penrose's claims.
Penrose's books are ones that most readers either considerably like or considerably dislike. Ideas are presented at a great rate, but are very speculative, and justified by tenuous and sometimes doubtful arguments. This book reads as if it has been transcribed from a recording of the original talks, with little attempt being made to improve the clarity of the arguments by rewriting, as a result of which following the arguments will prove a considerable challenge for the nonexpert, and possibly problematic even for the expert. Nevertheless, it remains a very interesting and stimulating book.
Brian D. Josephson, Nobel laureate in physics, is professor of physics, Universityof Cambridge.
The Large, the Small and the Human Mind
Author - Roger Penrose
ISBN - 0 521 56330 5
Publisher - Cambridge University Press
Price - £14.95
Pages - 185