Continuing on (from What about chess? What does it tell us about history? [path dependence]) I note that chess has been of interest to cognitive scientists (AI, cognitive psychology) for what it says about the mind, our powers of deduction and inference, our ability to ‘read’ the mind of another. In that previous post I was interested in what chess had to tell us about history, not the mere fact that the game has a history, like everything else, but that the chess-mind is itself a product of history. AlphaZero’s learning regime placed it outside the human history of the game thereby allowing it to explore regions of ‘chess space’ heretofore unknown to us and to exhibit a new (kind of) intelligence about the game.
That’s worth thinking about. The chess world is, as worlds go, austere and minimal, and above all finite. But it is rich enough to support an interesting historical process. But not just any historical process. I’m tempted to say that the historical process it exhibits is one of minds in competition with one another. But that’s not quite right, for I don’t think that AlphaZero qualifies as having a mind. What DOES it have? What was it doing when it played all those games against itself? That’s what gave it the historical evolution that led it to superior chess skills and NOT a superior version of the games human players have played, but a version of the game with new kinds of moves and strategies.
Now, of course, the human history of the game is not one of a single player against themself for match after match. It’s a history of thousands upon thousands of players competing over the course centuries. According to the Wikipedia, the game can be traced back 1500 years to India. The modern game goes back to late 15th century and early 16th century Europe, with the oldest surviving book on chess theory dating back to 1497. Chess clubs began appearing in the 19th century and modern tournament play began with a London tournament in 1851.
And, wouldn’t you know it, there are various schools of chess; the Wikipedia lists seven, but notes as well that “today there is less dependence on schools – players draw on many sources and play according to their personal style.” That is, it has taken time to learn how to play the game and the process is so rich an complex that different approaches have emerged. Chess is a world to be explored.
The notion of implementation comes to mind. The term originates from computing, where implementation is ubiquitous. As I put it some years ago [1]:
The implementation of logical functions in physical circuits is only one side of implementation, the hardware side. Most implementation is on the software side. High-level languages are implemented in assembly language and end-user programs are implemented in high-level languages. Currently one of the most popular languages is one called C, with a sibling called C++. It requires one implementation to run on a “Wintel” machine, one for the Macintosh, another for a Sun Sparcstation, and so forth. The C language is the same in each case; it has the same nouns and verbs. But the assembly language which implements those nouns and verbs is specific to the machine it runs on. Further, the assembly language for a given machine can implement the nouns and verbs of other high-level languages, such as Basic, Pascal, Fortran, or Cobol. The fact that one language is used to implement another is in not the same as asserting that the high-level language is reducible to the lower level language. Each language establishes its own domain, its own realm; implementation is the relationship between one realm and another.
And of course, application programs are implemented in these various high level languages. Word processors, databases, drawing, whatever, all are implemented in some, or even a combination of, computer language.
Well, I’m saying that chess is (something) like that. The rules of the game are like the constructs of a computer language (at whatever level). The game is what happens when humans compete against one another within the constraints imposed by those rules. The game is, in effect, implemented in those rules. The various schools of chess, then, are somewhat different games. All of them, of course, are consistent with the rules, for the rules define the basic constituents of the game. But the different schools have their preferred moves, strategies, and tactics. And all of these had to be invented over the course of game play. They aren’t deduced from first principles. They’re discovered and constructed. That’s a historical process.
Think of chess as being like Lego. The rules are the basic blocks and a game is something constructed of the blocks. Different schools are different patterns of construction. One school likes to make buildings, another prefers ships, yet another is partial to automobiles and airplanes and then along comes AlphaZero with this really wild school that makes dinosaurs – and believe me, it took those guys quite awhile to figure out how to get the T-Rex so wag his tail. All out of the same blocks.
So, to wrap up, basic arithmetic – as defined by Peano’s small handful of postulates – turns out to specify such a rich mathematical universe that mathematicians and computer scientists use it to work out basic ideas with broad implications. Chess, specified by a somewhat larger set of rules, gives us a world in which we can explore how intelligence, if you will, emerges through competitive play in that world.
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[1] William L. Benzon, Pursued by Knowledge in a Fecund Universe, Journal of Social and Evolutionary Systems 20(1): 93-100, 1997, https://www.academia.edu/8790205/Pursued_by_Knowledge_in_a_Fecund_Universe.
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