Commentary Magazine

Shadows of the Mind, by Roger Penrose

Thinking Machine

Shadows of the Mind: A Search for the Missing Science of Consciousness.
by Roger Penrose.
Oxford. 457 pp. $25.00.

Roger Penrose, the distinguished mathematical physicist, has again entered the lists to rid the world of a terrible dragon. The name of this dragon is “strong artificial intelligence.”

Strong AI, as its defenders call it, is both a widely held scientific thesis and an ongoing technological program. The thesis holds that the human mind is nothing but a fancy calculating machine—“a computer made of meat”—and that all thinking is merely computation; the program is to build faster and more powerful computers that will eventually be able to do everything the human mind can do and more. Penrose believes that the thesis is false and the program unrealizable, and he is confident that he can prove these assertions.

For Penrose, the task of showing that consciousness is not just computation is of much more than merely theoretical interest. He seems to feel that the pervasive pessimism of the modern age is fed by the haunting suspicion that we are no better than computing machines and that our claims to a distinctive humanity are illusory.

Penrose is also alarmed by the perverse hope, harbored by some AI enthusiasts, that computers will one day be so intelligent that we will turn to them for advice about curing the world of its man-made afflictions. If the age of wise robots should ever arrive, Penrose wonders what further purpose man would serve:

Humanity itself will then have become obsolete. Perhaps, if we are lucky, they might keep us as pets; . . . or if we are clever, we might be able to transfer the “patterns of information” that are “ourselves” into robot form; . . . or perhaps we will not be that lucky and just not be that clever. . . .

Penrose approaches his subject with the passion of one bent on liberating mankind from the spiritual oppression of this grim outlook. It is not an accident that Shadows of the Mind begins with a fanciful prologue, loosely borrowed from Plato’s Republic, in which a scientist imagines himself trying to convince his fellow men that they live in a gloomy cave and that the things they believe in are mere shadows of reality. The scientist is Roger Penrose, and the shadows are the computational models of the mind that currently dominate the cognitive sciences.



Penrose, who is the Rouse Ball Professor of Mathematics at Oxford University, first did battle with strong AI five years ago in his best-selling book, The Emperor’s New Mind.1 Evidently the dragon is not yet dead, for Shadows of the Mind is a restatement and continuation of the earlier book’s argument, a chance to answer its critics, sharpen points that were vague or tentative, and press the inquiry further into unexplored territory.

In Part I of Shadows of the Mind Penrose makes his rigorous case that human consciousness cannot be fully understood in computational terms. Part II is a frankly speculative search for new principles, both in physics and in neurobiology, that might one day accommodate a noncomputational model of human thought. For, unlike some critics of strong AI (notably the philosopher John Searle), Penrose firmly believes that the key to a satisfactory science of consciousness lies in a future physics that will differ substantially from our current conceptions.

How does Penrose prove that there is more to consciousness than mere computation? Most people will already find it inherently implausible that the diverse faculties of human consciousness—self-awareness, understanding, willing, imagining, feeling—differ only in complexity from the workings of, say, an IBM PC. Penrose, while sharing these suspicions, is not content to rest his proof on such vague appeals to introspective experience.

Instead, he is prepared to narrow considerably the ground of the argument in exchange for much greater certitude in the proof. He will show that one small part of human consciousness—a certain type of mathematical understanding—cannot, even in principle, be simulated by a computer program. If that limited result can be established, it is a reasonable inference that other aspects of our mental life are also beyond the reach of computers. “The floodgates will indeed be open!”

Following in the footsteps of the Oxford don John Lucas, Penrose rests his case on a famous theorem of mathematical logic discovered by Kurt Goedel in 1930. Goedel’s theorem applies to any “formal system,” i.e., a set of mathematical rules which we have translated into a code of uninterpreted symbols (e.g., strings of 0’s and l’s) that can be manipulated without regard to their meanings.

Goedel showed that, for any such formal system, no matter how complete we try to make it, there will be true propositions in arithmetic that cannot be demonstrated within it. These “formally undecidable propositions” can still be proved true, but only by going outside the formal system that we have written down.

Penrose next draws on the work of Alan Turing, the father of digital computing, to show that a formal system in mathematics is precisely equivalent to an algorithm, i.e., a computational procedure that might be programmed into a generic computer (a Turing machine). On this basis he concludes that no computer program is capable of reaching all the mathematical truths accessible to human understanding.

But if our thoughts proceed noncomputationally, then so must the brain with which we think, and if the brain, then also the atoms and molecules of which the brain is composed. Here the argument reaches its dramatic peak. For Penrose maintains that all current physical theories are basically computational in nature. That is, any physical process governed by such theories can, at least in principle, be effectively simulated by a digital computer. Even quantum physics, with its mysterious “indeterminacy,” merely adds an element of randomness and cannot, at least in its present form, provide a home for noncomputational processes. So Penrose’s proof that thought transcends computation compels us to seek radical changes in the basic laws of physics itself.

It testifies to the originality of this book and to the audacity of its author that, in his quest to find a home for mind in nature, he is ready to contemplate profound changes in fundamental physics. Few scientists today have the breadth of knowledge and interest such an inquiry requires, while those professional philosophers who do take up the “mind-body problem” often stand in such awe of mathematical physics that they are afraid to challenge any of its tenets.



Part II of Shadows of the Mind initiates the reader into the profound mysteries of quantum physics. Penrose distinguishes the puzzles of the theory, exotic features of reality that we will just have to get used to, from its even stranger paradoxes, which to Penrose are signs that the theory itself is still incomplete. A typical puzzle is the Einstein-Podolsky-Rosen phenomenon of “nonlocal entanglement,” in which objects separated by vast distances can act as if still in communication with each other. The best-known paradox is that of “Schroedinger’s Cat,” which, if connected to a lethal quantum-mechanical device, would allegedly enter a “superposition” of states, simultaneously dead and alive.

Penrose believes that the non-computational features of consciousness will become consistent with physics only when the paradox of Schroedinger’s Cat has been eliminated from quantum physics altogether. What is needed is a criterion that would govern when the superpositions typical of the quantum world (e.g., particles in different places at once) collapse into the single states typical of the objects of ordinary experience (e.g., cats either dead or alive but not both). Penrose speculates daringly that the criterion for this “state vector reduction” will be found in the arcane field of quantum gravity, where minute changes in the curvature of space-time might, in some genuinely noncomputable way, precipitate the collapse of the quantum superposition.

Penrose turns, finally, to neurobiology to ask where in the brain such quantum-gravitational effects might play their role in consciousness. His answer: not in the networks of neurons that AI enthusiasts see as the seat of consciousness, but in the tiny subcellular microtubules, which may provide a sheltered environment within which quantum phenomena like non-local entanglement could occur coherently on a large scale. It is here that Penrose expects future scientific research to find the key that will liberate the mind from the “straitjacket of computation.”



After enjoying such a rich intellectual feast it may seem ungrateful of me to complain that the much-anticipated final course is, after all, rather meager.

By this book’s end we are asked to believe that, while we think, deep inside the microtubules of our brain cells, at the borderline between gravity and quantum physics, there are large-scale nonlocally entangled quantum-coherent oscillations collapsing—and in a genuinely noncomputable manner to boot! But Penrose has had remarkably little to say about what it would really mean for this process, or human consciousness for that matter, to be noncomputable.

He does tell us what would not qualify as noncomputable: neither a random process, nor a chaotic one, nor one dependent on the environment will do. He suggests that a noncomputable process could still be deterministic (as in classical physics), but he does not pursue this provocative claim, perhaps because he is just not prepared to confront the idea of free will or genuine spontaneity in human thought and action. Straining to come up with an example of a non-computable process, Penrose skates perilously close to science fiction, invoking a kind of relativistic time-travel in which the future could retroactively influence the past.

We are left with the impression that Penrose has trouble even conceiving of something noncomputable. To do so, he might have to be willing to open his mind to aspects of human experience other than the mathematical. Perhaps Penrose himself, despite his ambition to lead us out of the computational cave, still finds it hard to turn away from its familiar shadows.


1 Reviewed in COMMENTARY by Jeffrey Marsh, June 1990.—Ed.

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