In chess, controlling the center isn’t always a good idea. For example, when you have the opportunity to effectively sacrifice your bishop on h6, or when you’re at risk of getting checkmated, controlling the center ought to be far from your mind. It would seem that, in addition to the heuristic “Control the center,” a computer also needs heuristical methods for choosing which heuristics to apply in a given situation: i.e., “When the sacrifice on h6 doesn’t lead to a win, try to control the center” or “When you’re about to get checkmated, forget about controlling the center.” Notice how each of these second-order heuristics serve to locate the first-order heuristics in a particular context. By contextualizing essentially context-independent chess wisdom like “Control the center” second-order heuristics help raise chess playing machines to a much higher level of play than any collection of first-order heuristics would be capable of. The problem, however, should be evident: which second-order heuristic should be applied at any given time? For example, what if I’m about to get checkmated but I also have a potentially fruitful bishop sacrifice on h6? The answer is, it depends on the context. Does the bishop sacrifice put the other king in check? Just how close are you to getting checkmated anyway? So a third-order heuristic is necessary. Etc.
It may sound like I’m setting up an ad infinitum proof that computers cannot play chess. But that, of course, would be silly, thanks to Deep Blue, who proved such arguments to be deeply suspect. Instead, I’m trying to show that the act of stupefication involves, at least in part, the navigation of and formalization of a potentially infinite recursive stack of heuristics. That the layers of heuristical guidance are not piled infinitely deep and, indeed, that they obviously need not be piled infinitely deep is proof that there exists a discoverable stopping place amidst the recursive descent. After all, we know that a computer can, with a finite stack of recursive rules, accomplish a high level of chess play.
This should indicate to us that arguments which seek to predict “what computers can’t do” and which cite as evidence the infinitely recursive nature of a particular problem domain may need to be reevaluated — given that a finite number of recursive heuristics may be sufficient to emulate human-caliber performance. And any suppositions about a potentially infinite stack of heuristics may be wholly irrelevant.
I mention this because linguistic systems are known to possess potentially unbridled (and largely uncharted) recursive structures. And incidentally, linguistic systems happen to be an important frontier in AI research. So my question (to paraphrase Turing) is, can a machine be programmed with enough heuristics (of various orders) to function at an apparently high level of linguistic competence? If the answer is yes (which is a huge “if”), then perhaps one way to effect such a breakthrough would be to first begin by programming systems to play very simple languages games that have clearly defined winning conditions and clearly defined transition rules (as mentioned in this post.)
More to come regarding language games.
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