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Review of Penrose, The Emperor's New Mind - Pg 3
Review of The Emperor's New Mind Concerning Computers, Minds, and the Laws of Physics.The Times Literary Supplement. Oxford University Press
The argument Penrose unfolds has more facets than my summary can report, and it is unlikely that such an enterprise would succumb to a single, crashing oversight on the part of its creator--that the argument could be "refuted" by any simple objection. So I am reluctant to credit my observation that Penrose seems to make a fairly elementary error right at the beginning, and at any rate fails to notice or rebut what seems to me to be an obvious objection. Recall that the burden of the first part of the book is to establish that minds are not "algorithmic"--that there is something special that minds can do that cannot be done by any algorithm (i.e., computer program in the standard, Turing-machine sense). What minds can do, Penrose claims, is see or judge that certain mathematical propositions are true by "insight" rather than mechanical proof. And Penrose then goes to some length to argue that there could be no algorithm, or at any rate no practical algorithm, for insight.
But this ignores a possibility--an independently plausible possibility--that can be made obvious by a parallel argument. Chess is a finite game (since there are rules for terminating go-nowhere games as draws), so in principle there is an algorithm for either checkmate or a draw, one that follows the brute force procedure of tracing out the immense but finite decision tree for all possible games. This is surely not a practical algorithm, since the tree's branches outnumber the atoms in the universe. Probably there is no practical algorithm for checkmate. And yet programs--algorithms--that achieve checkmate with very impressive reliability in very short periods of time are abundant. The best of them will achieve checkmate almost always against almost any opponent, and the "almost" is sinking fast. You could safely bet your life, for instance, that the best of these programs would always beat me. But still there is no logical guarantee that the program will achieve checkmate, for it is not an algorithm for checkmate, but only an algorithm for playing legal chess--one of the many varieties of legal chess that does well in the most demanding environments. The following argument, then, is simply fallacious:
- (1) X is superbly capable of achieving checkmate.
- (2) There is no (practical) algorithm guaranteed to achieve checkmate. therefore
- (3) X does not owe its power to achieve checkmate to an algorithm.
So even if mathematicians are superb recognizers of mathematical truth, and even if there is no algorithm, practical or otherwise, for recognizing mathematical truth, it does not follow that the power of mathematicians to recognize mathematical truth is not entirely explicable in terms of their brains executing an algorithm. Not an algorithm for intuiting mathematical truth--we can suppose that Penrose has proved that there could be no such thing. What would the algorithm be for, then? Most plausibly it would be an algorithm--one of very many--for trying to stay alive, an algorithm that, by an extraordinarily convoluted and indirect generation of byproducts, "happened" to be a superb (but not foolproof) recognizer of friends, enemies, food, shelter, harbingers of spring, good arguments--and mathematical truths!
Chess programs, like all "heuristic" algorithms, are designed to take chances, to consider less than all the possibilities, and therein lies their vulnerability-in-principle. There are many ways of taking chances, utilizing randomness (or just chaos or pseudo-randomness), and the process can be vastly sped up by looking at many possibilities (and taking many chances) at once, "in parallel". What are the limits on the robustness of vulnerable-in-principle probabilistic algorithms running on a highly parallel architecture such as the human brain? Penrose neglects to provide any argument to show what those limits are, and this is surprising, since this is where most of the attention is focussed in artificial intelligence today. Note that it is not a question of what the in-principle limits of algorithms are; those are simply irrelevant in a biological setting. To put it provocatively, an algorithm may "happen" to achieve something it cannot be advertised as achieving, and it may "happen" to achieve this 999 times out of a thousand, in jig time. This prowess would fall outside its official limits (since you cannot prove, mathematically, that it will not run forever without an answer), but it would be prowess you could bet your life on. Mother Nature's creatures do it every day.
I may well have missed a crucial ingredient in Penrose's argument that somehow obviates this criticism, but it is disconcerting that he does not even address the issue, and often writes as if an algorithm could have only the powers it could be proven mathematically to have in the worst case. It will be interesting to see how he would repair this omission. In the meantime I would say that whether or not the Penrose revolution in physics is coming, he has not yet shown the need for the revolution in order to explain facts of human cognitive competence.
I have left no doubt about the difficulty of this book, and I must balance that impression by noting that it is nevertheless a pedagogical tour de force, with some dazzling new ways of illuminating the central themes of science. I was struck as never before by the gleeful staircase of human artifices--diagrams, mappings, formalisms--piled one on top of the other over the years, permitting our species so much as to entertain such audacious hypotheses about the world we live in. His discussion of phase spaces, for instance, and his development of the rationale for the second law of thermodynamics, are particularly refreshing. His exemplary candor, particularly in the chapters on cosmology and quantum physics, provides the uninitiated reader with a vivid experience of the way gut intuitions and aesthetic reactions call the tune in science until someone figures out a conversation-stopping proof, mathematical or experimental. And along the way he makes important points that have been overlooked by the believers in strong AI, even if they can be incorporated into it. For instance, he closes the book with a speculation about time I believe is exactly right:
I suggest that we may actually be going badly wrong when we apply the usual physical rules for time when we consider consciousness! . . . My guess is that there is something illusory here. . .and the time of our perceptions does not 'really' flow in quite the linear forward-moving way that we perceive it to flow (whatever that might mean!). The temporal ordering that we 'appear' to perceive is, I am claiming, something that we impose upon our perceptions in order to make sense of them in relation to the uniform forward time-progression of an external physical reality. (p.443-4)
This is, in my opinion, the key to removing the last, harmful vestiges of Cartesian thinking from our standard vision of how consciousness relates to the brain, but you don't need quantum magic or quantum gravity to get there. A clear statement of the point has been given by Douglas Snyder Endnote 1, and I myself have more recently been developing the case for this claim from an entirely conservative--indeed an "engineering"--base, as the best way for Mother Nature to handle the synchronization problems that arise in a brain that must cope with events that sometimes occur on a time scale faster than its own internal transmissions. Endnote 2
A philosophy professor once said to his class, "I want you to believe the things I tell you, but not because you believe me; I want you, rather, to believe them because you yourself see that they must be true." This is Penrose's ideal, and indeed it should be every teacher's ideal, but we all fall short; the semester (or life) is too short, and at some point we fall back on "Take it from me: that idea just doesn't work." Penrose is positively heroic in his attempts to live by this standard. The reader is warned, after weathering over two hundred pages on the lambda calculus, the class of NP-complete problems, Maxwell's equations, the Lorentz equation, special and general relativity, and much more, that in the next chapter, on quantum mechanics, things are going to get "a bit technical. In my descriptions I have tried not to cheat, and we shall have to work a little harder than otherwise." (p.227) But although matters do then get still more technical, uninitiated readers cannot "work harder"--because we simply do not know the rules. If we are to "see for ourselves" the truths of quantum physics, we must be active and skeptical, but the world of quantum physics is so alien that we can no longer trust our untutored judgments of what counts as a telling objection and what is merely a misapplied maxim or analogy drawn from more familiar territory. I suspect that nothing short of extended immersion in the actual use of the mathematics to solve particular problems can give one a confident sense of how this game is played, and why the rules are what they are. We get assured by Penrose that various hard-to-swallow options make sense while others are just not on, and we have to take his word for it. His brilliant exposition up to this point gives us ample reason to respect his obiter dicta once they start to flow, but, contrary to his best intentions, his readers at this point must cease being participants and start being spectators.
This raises a perplexity about Penrose's intentions in writing this book. He repeatedly acknowledges that his colleagues, who already understand the difficult materials he is teaching us much better than we ever will, do not yet accept his idiosyncratic vision. But if he can't convince them, pulling out all the stops, what good will it do if he convinces us with a relatively elementary version? What then? Are we supposed to join in a Children's Crusade to persuade his colleagues to get in step? This cannot be his intention.
I suspect he has a more subtle strategy in mind. When experts talk to experts, they are careful to err on the side of underexplaining the fundamentals. One risks insulting a fellow expert if one spells out very basic facts. There is really no socially acceptable way for Penrose to sit his colleagues down and lecture to them about their oversimplified and complacent attitudes about fundamentals. So perhaps educated laypeople are only the presumptive audience for this book, hostages to whom he can seem to be addressing his remarks, so that the experts--his real target audience--can listen in, from the side, without risk of embarrassment. I think this is a wonderful strategy, perhaps the only way of getting experts who are talking past each other to refresh their mutual understanding of the fundamentals. (It is especially valuable in philosophy.) It may leave the non-experts in the role of spectators, but at least it gives them ringside seats.
Endnotes
1. "On the Time of a Conscious Peripheral Sensation," Journal of Theoretical Biology, 1988, 130, 253-254.
2.In "The Autocerebroscope," at a symposium in memory of Heinz Pagels, The Reality Club, Alliance Française, New York City, February 1, 1989; "Temporal Anomalies and the Architecture of Consciousness," Cognitive Science Colloquium, Indiana University, February 28, and the Gildea Lecture at Washington University School of Medicine, May 2, 1989.