Missing Refutations

It looks like the opposing all-human team is winning the exhibition game of me and my it's-not-chess engine (as White) versus everyone in the office who (unlike me) actually knows something about chess (as Black). I mean, naïvely, my team is up a bishop right now, but our king is pretty exposed, and the principal variation that generated one of our recent moves (16. Bxb4 Bf5 17. Kd1 Qxd4+ 18. Kc1 Ng3 19. Qxc7 Nxh1) looks dreadful.

Real chess aficionados (chessters? chessies?) will laugh at me, but it actually took me a while to understand why Ng3 was in that principal variation (I might even have invoked the engine again to help). The position after Ng3 looks like

    a b c d e f g h
 8 ♜       ♜   ♚   
 7 ♟ ♟ ♟     ♟ ♟ ♟ 
 5           ♝     
 4   ♗   ♛         
 3 ♙           ♞   
 2   ♙ ♕     ♙ ♙ ♙ 
 1 ♖ ♘ ♔     ♗   ♖ 

and—forgive me—I didn't understand why that wasn't refuted by fxg3 or hxg3; in my novice's utter blindness, I somehow failed to see the discovered attack on the white queen, the necessity of evading which allows the black knight to capture the white rook, and preparation for which was clearly the purpose of 16. ..Bf5 (insofar as we—anthropomorphically?—attribute purpose to a sequence of moves discovered by a minimax search algorithm which doesn't represent concepts like discovered attack anywhere).

It's the little things like this that reinforce my suspicion that human cognition doesn't really work most of the time, that to the extent that we have a technological civilization with nice things in it, it's a matter of a bunch of apes, some of whom are just barely generally-intelligent, happening to stumble into patterns of coöperation that happened to scale, and not a matter of anyone within the system actually understanding much. It's the current year, and the current year turns out to be not only congruent to 0 mod 2, but furthermore to 0 mod 4, which means outrage season is brewing again. I'm mostly pretty good at ignoring it, except for the undercurrent of contempt that I can't help but feel at how almost everyone seems to think it's okay for important decisions to be made in this way.

The thing about chess is that it's a very simple game. There are these thirty-two figurines on an eight-by-eight grid, and you take turns moving the figurines subject to a few rules with a well-specified objective in mind. Simple. If you're lazy like me, you can even write a computer program to do it for you. And if you hadn't already spent many, many hours of study and practice mastering the game yourself, what such a program will surely show you (as it showed me, though I expected as much) is that your unaided attempts to make good moves will get it wrong. The novice thinks: checkmate is the goal, giving check is good, capturing material is good; I should look for moves that do those things. And the novice will lose, badly. What you actually need to do is look for your best move given your opponent's best reply given your best counterreply given your opponent's best countercounterreply, and so on as far forward as you can afford to compute. It's not magic and it's not impossible, but it's subtle and it takes work.

And the thing about the real world is that it is unimaginably complicated. There are seven billion humans on this radius-6.37·106 m planet, all haphazardly pursuing their own objectives subject to no rules except whatever high-level generalizations about the underlying fundamental physics strike you as sufficiently robust to be worth reifying as a rule. Unimaginable. And I feel like those appealing to the masses seeking leadership positions in the reigning institutions of governance don't properly appreciate this. You hear them or their boosters talk about how "we" obviously need to make college or healthcare free, or crush our terrorist foes, and to me it just sounds like so many shouts of "fxg3!" or "hxg3!". The goals are noble: of course we want America to be great, and for its people to be healthy and wealthy and knowledgeable and safe, just as a chess player wants to checkmate the opposing king. But the interventions that sound intuitively appealing aren't necessarily the same as the interventions that will actually work! "We" should hope for leaders with the courage and skepticism and competence to say, "No, wait, that won't work because of ...Bxc2," and continue the search for better alternatives for our nation and its children.

But if I can predict that that's not what "we" are going to choose, maybe I should continue searching for better alternative ways to spend my time than complaining about it.

4 thoughts on “Missing Refutations

  1. I'd just like to say that I love your blog and am glad that you continue to post in it.

  2. "It's the current year, and the current year turns out to be not only congruent to 0 mod 2, but furthermore to 0 mod 4"

    This irks me. You are deliberately making your writing understandable to fewer people just to show off your clueless-math-nerdiness. It's bad writing. It's bad communication. It's even bad signaling, except to a sorry parochial few.

    This post is a important message. Isn't it worth *some* effort on making it less than maximally unappealing and incomprehensible to people who don't already agree with it? Just how strong do you want your ivory tower's gate reinforced?

  3. @Grognor - This blog is meant to appeal to a certain subset of people, and I personally like it that way. This entire post is centralized around programming ideas, and that "0 mod 2" makes it clear. There are other concepts presented which are programming-based which you didn't notice. "minimax search algorithm" and "generally-intelligent" are obviously based around this idea, but perhaps more important is the underlying idea that there is a certain emergent complication arising from the simple rules of chess which is difficult to build a computer program for (the it's-not-chess engine), and that this relates to the complication of the world in which everybody is making their decisions naively similarly to the way that he does in his chess algorithm.

    It's not that there is a deliberate attempt to make the writing difficult to understand, it's that these ideas make the concept easier to understand to a particular subset of people. The facts that you think this is "maximally unappealing and incomprehensible" and that you didn't comment on the subtler ideas which are not clearly represented to the general public show that you yourself didn't completely understand the messages in the writing. This blog just isn't for you.

    There are many different types of people and many different types of blogs. This isn't a communist dictatorship; there isn't a need to make everything appeal to everyone. If you were right in what you were saying that he was deliberately making the writing less understandable without purpose, I'd agree and say that there needn't be pointless barriers to understanding. However, in this case, that "0 mod 2" serves to filter out the people like you that don't understand the deeper meanings of the text.

    I don't say these things to put you down; I say these things so that the author doesn't feel discouraged in his excellent writing. I like the way he writes and know that I wouldn't as much if these ideas were presented in a different, more generally-understandable way.

  4. @Grognor
    If a math blog isn't about math, that's bad blogging. If it says "Algorithm" in the name and doesn't live up to that, then that is bad communication.

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