Penrose's triangles: The large, the small, and the human mind

At 4 p.m. on May 11, 1997, “the truly impossible occurred,” as Newsweek reported (May 26, 1997, 84). The computer Deep Blue defeated the world chess champion and one of the greatest chess players of all time, Garry Kasparov. In the process, his confidence, bolstered by his impressive previous victories over computers, was shattered along with the confidence and hopes of much of the chess world. Indeed, the defeat was taken by some, including by Kasparov, as a humiliation. It appears to have been especially humiliating because it was inflicted on a great chess mind, capable of the most complex tactical and strategic thinking, by the raw power of computation. A great chess mind was defeated by crude number-crunching—a much inferior form of thinking or, in this case, not even thinking. Such minds have always been seen as able to circumvent and transcend protracted computational routines, and as entities whose own workings are themselves inaccessible to computational analysis.

In the last installment of his ongoing argument against the possibility of artificial intelligence, The Large, the Small, and the Human Mind, Roger Penrose uses chess to illustrate the difference between the computational approach used by digital computers and non-computational thinking, which, according to him, fundamentally defines the human mind and gives it ultimate superiority over computers or computer-like computational intelligence (103–5). Penrose gives examples of two chess problems that are easily solved by even mediocre human players but have defeated a computer (in this case Deep Thought, the forerunner of Deep Blue). Penrose’s lectures (given in 1995 and published earlier this year) preceded the latest chapter of the story of computer chess just described, and he may even have been inspired in part by Kasparov’s previous decisive victories over computers and by the seemingly unquestionable ultimate superiority of chess players or, one might say, chess thinkers over chess computers.

This latest episode of this, by now long, history does not prove the opposite. Nor does it prove the ultimate superiority of any one form of thinking over another, or of (human) thinking over (computer-like or other) non-thinking. That is, assuming that human thinking is indeed non-computational—a claim that, however appealing or likely, remains hypothetical, as Penrose admits. Everyone acknowledges that Deep Blue cannot think—leaving aside here the complexity, if not impossibility, of the latter concept itself. Nor does the episode prove that artificial intelligence is any more likely now than it was before. What it does prove is that computational thinking or (even more humiliatingly for its opponents) computation without thinking, number-crunching, can be taken to a level high enough to supersede non-computational thinking in certain specific cases. The fact that this is possible in some cases is in part (there are more general conceptual reasons) what drives the idea—which is more or less the idea of artificial intelligence—that it may be possible in any given case. Much else, it is further extrapolated, would be possible as well for computational devices. It may, for example, be possible for machines to perform any given task that human thinking can perform, or conceivably even to think or have consciousness or even to feel, just as humans do. Or—a rarely, if ever, discussed but interesting and radical possibility—it may be possible to perform even the most complex tasks better than humans without thinking and, thus, in a certain sense without intelligence. Or, as I said, it might also be possible to assume that at bottom the human mind is itself only a computational device, a number-crunching machine. These are the types of possibilities that are pursued in the field of artificial intelligence and related endeavors and that are argued against by, among others, Penrose.

At a certain level, at stake here is still the power of creative...