TABLETOP TIME MACHINE
The Philosophers’ Game is now known only as a curiosity appealing to mathematical minds, but for 500 years it was rated at least as high as Chess, if not more so in its own academic milieu. First recorded in northern Europe in the mid 11th century, it was still being written about as a ‘live’ game until somewhere in the 16th, after which it appears in print only as an afterthought. Historians still consider it one of the greatest games of medieval Europe.
To the medieval mind, a ‘philosopher’ meant an academic, a man of learning, which in effect meant a cleric. Rithmomachy is an anglicisation of Rithmomachia, a Greek concoction meaning The Battle of Numbers. It was usually played on a double chessboard of 8x16 squares, by two players sitting opposite each other on the longer sides, with each one’s ‘home’ board on their right.
Many game descriptions survive, but no two agree in every detail. The two most significant are by John Shirwood, Bishop of Durham (1482), and Augustus II, Duke of Brunswick (1616), translated from an Italian original of 1472. The following description is a simplified mash-up based on various sources.
Each side has a theoretical twenty-four pieces, eight each of rounds, triangles, and squares, each bearing a number. White’s are based on the even numbers 2-4-6-8, Black’s on the odd series 3-5- 7-9. The remaining numbers derive from its four base numbers by an arcane algorithm, based on Boethian arithmetic, purportedly showing how all numbers are logically generated from unity.
Each piece is double-sided, with its opposite colour on the reverse, so that a piece when captured is drafted into the capturer’s army. White’s square 91 is replaced by a pile of six additional pieces totalling 91, namely rounds one and four, triangles nine and 16, and squares 25 and 36. Black’s square 190 is replaced by a pile of five pieces totalling 190, namely round 16, triangles 25 and 36, and squares 49 and 64. Rounds move two spaces, triangles three, and squares four (but counting the starting square as the ‘one’). Pieces can be captured by blockade, when so surrounded as to be immobile, or by being involved in an arithmetical relationship (addition, subtraction multiplication or division) by one or more enemy pieces.
The aim of the game is to form a ‘triumph’ on the enemy side of the board, and/ or to demolish the opponent’s pyramid. A triumph is three pieces with numerical values forming an arithmetical, geometrical, or harmonic progression, and arranged in a symmetrical pattern, such as in a row, column, or diagonal, with an equal number of unoccupied squares lying between the central piece and those on either side, or forming three points of a square.
Arithmetical games are not everyone’s cup of tea (though I prefer them to fantasy games), and the reason why this one died out is that it was only ever played by an elite community of clerics and academics. By the 16th century universities had ceased to favour the arithmetic promulgated in Boethius’s De Arithmetica (c.500) and the intellectual aristocracy turned to the new and exciting form of chess dominated by an all-powerful queen.
There are many online descriptions of the game, but its history is best recorded in Anne E Moyer,
The Philosophers’ Game: Rithmomachia in Medieval & Renaissance Europe (Univ Michigan Press, 2002).