The Crossroads chess club provides me with the entertainment of watching chess games, along with the discussion that is natural to accompany such. Only rarely does my excessive kibbitzing force me to accept a challenge to play; though I have been practicing with such books as 1001 Brilliant Ways to Checkmate, my ability is somewhat lacking (too much mathematics, perhaps, which spoils one by allowing one to easily retract errors). My feeling is that chess is like football. It’s relaxing to watch a game but far too much effort to play. If I’m going to endure an hour of aggravation, memorize sequences of play and their likely chance of success, suffer nervous sweat until it drools down from my armpits to my belt, and run up my heart rate, I’d like to reach orgasm at the end of it. And with much better odds than the (under) 50% I achieve at the chess club.
Anyway, while observing a game, Nathan Jermasek (perhaps with the object of quieting my comments) handed me a slim book by F. V. Morley, “My One Contribution to Chess,” the subject of this book review. It should probably be noted that F. V. Morley and his book are supposed to be fictional creations of Stephen Potter in his famous 1952 book on gamesmanship, at least according to Wikipedia’s entry on fictional books:
You can’t buy My One Contribution on Amazon at the moment, but you may be able to find a used copy if you look around a bit. Perhaps eBay once caught a whiff of one.
Does the book exist or not? It’s hard to say, and certainly I’m not going to “correct” wikipedia on this. But the choice of the name F. V. Morley is interesting in that it leads to some mathematics which might vaguely have something to do with the physics we’re working on around here.
The book is purportedly about a modification of the chess board to allow new openings while keeping intact the old openings. The less said about this bad idea the better. Most of the book is about the author’s father Frank Morley, who died in 1937 and was known for his ability at chess. His name is immortalized in mathematics as a series of miraculous equilateral triangles. The book discusses the English mathematics scene between the wars, the Cambridge mathematical tripos and various other topics. But it does have a few things to say about chess:
I started with the notion that chess when studied seriously is no longer an innocent, friendly game. That seemed to me a pity. The philosophy of having innocent fun is not the same as the philosophy of having superior technical equipment and a first axiom of having fun is that a little knowledge is a good thing and too much knowledge isn’t. On that, so far as chess goes, a number of experts and duffers agreed. It seemed to me to illustrate the point to explain how my father and I, who were much in sympathy, and who in other realms created things together, at chess were separated not merely by his superior power, but by his learning. I asked the question why, at chess, should we be so separated. If anybody could have tempered his knowledge to the occasion, Doctors [his father] would have done so. But that is what you can’t do. The second and concealed axiom is that if you can play you must play, and you must play as hard as you can. What emerges from that axiom is that the game may demand from the players perhaps more than the players wish to demand from the game. What emerges is that chess is not merely a game but a dromenon.
That could have been stated without so much elaboration. It is obvious that both parties to a chess game play not merely against the human opponent, but also to make the best abstract use of the position of the pieces. Chess in its lesser part is a matter of traps, temptations, devices against the mortal frailty of your opponent. In greater part it is something demonstrated by both players against the setting of the universe, the chaste stars, the army of unalterable law. It is when the patterns of power, breaking and reforming as in a kaleidoscope, when pressures half revealed and half perceived manifest themselves and melt and shift, when there is imagination, elegance and accuracy not merely in the combinations — accuracy in the relationships which are invariant although the combinations differ — then and then only do the pieces come to life; then and then only to the players make together something which is both a battle and a ballet, and which in its unearthly beauty entirely transcends the little bits of carvings advancing and retreating on the parti-coloured board.
Chess is a dromenon. That’s why it is inexorable. You can’t play down to a weaker opponent.
You can’t really play chess, that is, mutually create a good game, with anyone who is on a different level. A first-class player can’t play chess with a second-class player; second-class can’t play with third; and third can’t play with steerage. More precisely, steerage cannot create a good enough game with third-class, third-class with second, second with first. The players can beat or be beaten, but unless they are of the same class they cannot together create a game of chess which comes alive, which is worthy of ballet and battle in the sight of the chaste stars, the universe, and unalterable law.
While I love and appreciate the above description of chess (and a good definition of “human” is “the creature that plays games” so these lines apply to far more than chess), at the time I read them I did observe a bit of a violation of the conclusion. Moderns have the additional advantage of the clock, and one can span a few classes of players by giving the weaker player more time on the clock.
The Friday I saw the book, the 2007 Washington State Champion and blitz [high speed chess] specialist, Ignacio Pérez, played a half dozen games with a much weaker player, an excellent child prodigy who shows up at the chess club. To even the matches, Ignacio gave himself 30 seconds on the clock to the youngster’s 5 minutes. This was perhaps 2/3 the time required for Ignacio to win, though I did see him make his first 2 moves before his clock had registered the first second.
Getting back to physics, the miracle equilateral triangle (which is obtained as the intersection of the trisectors of an arbitrary triangle) reminds me of triality a little. Draw an equilateral triangle, such as the red triangle illustrated above. Draw another point well outside of the equilateral triangle. This point will be one point of the large triangle. Duplicate the angle subtended by the equilateral triangle on either side. These three angles will, together, make up the large triangle corner and its trisection. It’s easy to see that you can now determine the other points of the larger triangle (if such exists).
In choosing an equilateral triangle, we need one degree of freedom, its length. Placing the first point of the larger triangle uses up two degrees of freedom. We’ve used three degrees of freedom, all the degrees of freedom of an arbitrary triangle. It’s not too surprising that this is necessary and sufficient to define the larger triangle. But it is still surprising to see the construction (which in this way of describing the situation does not require a trisection), walks around the equilateral triangle and returns exactly to the first choice of arbitrary triangle. This is a requirement of self-consistency, can it be so far from the physics we’re discussing here? Kea will know.