This week we consider what the abrupt disappearance of a medieval board game can tell us.
To play a game is voluntarily to restrict your own liberty. It is a form of moral discipline. You agree to abide by certain rules which, most likely, you had no part in drawing up and will not trouble yourself to question.
And it would seem that, unlike other forms of moral discipline, the pay-off is more or less immediate, if also more or less superficial. Not only are the outcomes minimally deferred, but the exercise of skill and the distribution of luck occur conspicuously, and in the here-and-now.
However, a game is not a wholly closed or self-contained system. Learning to play chess or cricket or snooker well requires you to think about the game when you are not playing it – in other words to practice, to watch others, to analyse your own performance. And it requires you, moreover, to participate in the history of the game.
Games, like everything else, have a history, and if there are more extinct species of game than there are survivors, this is because their fitness for survival is tied to the wider historical context in which they grow up. A case in point is rithmomachia, the great game of the intellect of the Middle Ages.
Very often in medieval or renaissance art, what appears to be a game of chess is a game of rithmomachia.
Rithmomachia was played on a chequered board, like chess, but the board was rectangular, not square. Also like chess, it was a game of territory and capture, and an emblem of intellectual prowess.
But unlike chess, it was a game in which the building of harmonious and pleasing patterns was not merely a side effect of the play: it was the whole object. The game was rooted in Boethian number systems, a neo-Pythagorean doctrine of great influence in the Middle Ages, according to which numbers were philosophical entities which lay, in various important and profoundly interrelated sequences, at the heart of everything.
Each player had counters marked with numbers disposed according to various of these sequences – square numbers, triangular numbers, hexagonal numbers and so on – the numbers on each row derived in increasingly arcane fashions from those on the row above:
The object of rithmomachia varied depending on the skill of the opponents. There were eight possible Victories, as they were known – five Common and three Proper. It was agreed at the outset which Victory would be played for. The Common Victories involved counting pieces captured, value of pieces captured, and so on. The Proper Victories were more esoteric, requiring the player to align sequences of numbers in arithmetical, geometrical and so-called harmonic progressions. The highest Victory of all – the so-called Victoria Praestantissima or Victoria Excellentissima – invited players to align four pieces in a row in such a way that all three progressions were expressed therein (examples, for what it’s worth, would be (2,3,4,6), (7,8,9,12) and (12,15,16,20)).
Thus rithmomachia, partly a mnemonic and intellectual aid and partly the proper occupation of a magus or scholar, was bound intimately into its intellectual world. And for this reason, it was rapidly and almost entirely extinguished by the collapse of Boethian number theory, which was ousted by advances in trigonometry and algebra towards the end of the sixteenth century.
We do not exhaust the possibilities of games. The game merely ceases to be relevant. In 1943 Hermann Hesse published his last novel, The Glass Bead Game, in which, in some ill-defined future (perhaps, he suggested, at the outset of the 25th century), philosophers and aestheticians withdraw into monastic communities the better to pursue an ultra-intellectual game, the counters of which are the totality of cultural and scientific– and especially mathematical and musical – knowledge.
Hesse is describing the distaff as he perceived it between action in the world and stoical withdrawal from it; all cultural and intellectual life, he seems to be saying, are a closed system, one in which your manifest excellence is no preparation for an actual life. But the history and especially the disappearance of rithmomachia tell us the reverse: that a game is bound utterly to the wider conditions of its existence. A game is an oblique form of inquiry, not simply an object of knowledge. And sooner or later we will cease to inquire into what no longer interests us, no matter how interesting the form of that inquiry.