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The book of chess


Magnus Carlsen has now openly accused Hans Niemann of cheating. (See background here). I know nothing about this subject per se, but I’ll note that Carlsen’s evidence seems rather thin: he points out that Niemann has improved at an unusually rapid rate, and that he didn’t seem tense or nervous or even concentrating that hard, in Carlsen’s estimation, when he beat Carlsen. That’s . . . not really evidence exactly. It sounds more like paranoid conjecture, with the only reason to think it isn’t being that its basically impossible to imagine a chess champion having a paranoid personality.

I’ll leave further discussion of the merits of the matter to LGM’s chess maven community, which the previous thread revealed was quite large and opinionated.

In the rest of this post I want to talk about the question of whether computers are thinking when they’re playing (or “playing”) chess. To me it’s transparently obvious that the answer is “no,” and that this is even a question illuminates some fascinating blind spots in the ideology of both contemporary AI in particular and the sort of scientism that takes a radically reductive approach to consciousness in general.

Let’s begin with a simple observation, which is that any game that features perfect information must have, conceptually speaking, a total strategy which is — or would be with enough time and computing power — available. A total strategy means a complete guide to how to play every possible instantiation of the game in the optimal way. Another way to put this is that there are a finite number of possible games of chess, which means that if you were to specify all of them you would know exactly what move would be optimal at any moment in any of them, which means you would be, for the purposes of chess, God.

OK, how many games of chess does God have to memorize in order to be the perfect chess player? To be the God of Tic Tac Toe you have to memorize the 255,168 possible variations of the game that exist (Actually you don’t since a very simple algorithm, that can be taught to a small child, yields a perfect strategy, without having to memorize the 255,168 individual variations. Is there an analogous algorithm for chess? I know the answer and have noted it in the margin of the post but will explicate it later).

Chess is more complicated than Tic Tac Toe, so the total number of possible games is larger. Limiting games to only those that feature legal moves, the total number is ten to the 40th power, which is a number approximately half the square root of the size of the number of atoms believed to exist in the observable universe.

Since the total number of games is finite, this means that, as in the case of Tic Tac Toe, a complete strategy for chess is available in theory, although symbolizing it in textual form would require a document whose physical manifestation, in order to be visible to humans, would probably have to be the size of a galaxy or two (You do the math).

This would be the Book of Chess, and it would give you the answer to the question of exactly what the optimal move would be in any situation in any game of chess that can be played.

Now we reach our question, which is, does this book play chess? And the answer could not be more obvious which is of course this book doesn’t play chess because it’s a book. Now here’s the question: why would anyone imagine that digitizing the contents of the book into a searchable computer program, which would yield the answer to any chess question much more conveniently for any user of this tool than consulting the galactic-sized volume, would turn that program into a chess player, any more than our hypothesized book is a chess player?

We also know of another superstition o f that time: that of the Man of the Book. On some shelf in some hexagon (men reasoned) there must exist a book which is the formula and perfect compendium of all the rest: some librarian has gone through it and he is analogous to a god. In the language of this zone vestiges of this remote functionary’s cult still persist. Many wandered in search of Him. For a century they have exhausted in vain the most varied areas. How could one locate the venerated and secret hexagon which housed Him? Someone proposed a regressive method: To locate book A, consult first book B which indicates A’s position; to locate book B, consult first a book C, and so on to infinity … In adventures such as these, I have squandered and wasted my years.

It does not seem unlikely to me that there is a total book on some shelf of the universe ; I pray to the unknown gods that a man thousands of years ago! —- just one, even though it were may have examined and read it. If honor and wisdom and happiness are not for me, let them be for ot hers. Let heaven exist, though my place be in hell. Let me be outraged and annihilated, but for one instant, in one being, let Your enormous Library be justified. The impious maintain that nonsense is normal in the Library and that the reasonable (and even humble and pure coherence) is an almost miraculous exception. They speak (I know) of the “feverish Library whose chance volumes are constantly in danger of changing into others and affirm, negate and confuse everything like a delirious divinity.” These words, which not only denounce the disorder but exemplify it as well, notoriously prove their authors’ abominable taste and desperate ignorance.

Borges, The Library of Babel

ETA: As many commenters have pointed out, my argument is very similar to the one John Searle makes in his Chinese Room Thought Experiment. I believe Searle’s argument definitively refutes the claims of what he calls strong AI, which nevertheless many people still cling to when they argue that “computers” are beating humans at chess. It would be more accurate to say that some humans are using computers to beat other humans at chess, and that computers themselves are no more great chess players than the calculator in your smartphone is a better mathematician than Gauss or Newton.

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