Rithmomachy

Rithmomachy (or Rithmomachia, also Arithmomachia, Rythmomachy, Rhythmomachy, or sundry other variants; sometimes known as The Philosophers' Game) is a highly complex, early European mathematical board game. The earliest known description of it dates from the eleventh century. A literal translation of the name is "The Battle of the Numbers". The game is much like chess, except most methods of capture depends on the numbers inscribed on each piece.

History

Very little, if anything, is known about the origin of the game. But it is known that medieval writers attributed it to Pythagoras, although no trace of it has been discovered in Greek literature, and the earliest mention of it is from the time of Hermannus Contractus (1013–1054).

The name, which appears in a variety of forms, points to a Greek origin, the more so because Greek was little known at the time when the game first appeared in literature. Based upon the Greek theory of numbers, and having a Greek name, it is still speculated by some that the origin of the game is to be sought in the Greek civilization, and perhaps in the later schools of Byzantium or Alexandria.

The first written evidence of Rythmomachia dates back to around 1030, when a monk, named Asilo, created a game that illustrated the number theory of Boëthius' "De institutione arithmetica", for the students of monastery schools. The rules of the game were improved shortly thereafter by the respected monk, Hermannus Contractus, from Reichenau, and in the school of Liège. In the following centuries, Rythmomachia spread quickly through schools and monasteries in the southern parts of Germany and France. It was used mainly as a teaching aid, but, gradually, intellectuals started to play it for pleasure. In the 13th century Rythmomachia came to England, where famous mathematician Thomas Bradwardine wrote a text about it. Even Roger Bacon recommended Rythmomachia to his students, while Sir Thomas More let the inhabitants of the fictitious Utopia play it for recreation.

The game was well enough known as to justify printed treatises in Latin, French, Italian, and German, in the sixteenth century, and to have public advertisements of the sale of the board and pieces under the shadow of the old Sorbonne.

Gameplay

The game was played on a board resembling the one used for chess or checkers, with eight squares on the shorter side, but with sixteen on the longer side. The forms used for the pieces were triangles, squares, rounds, and pyramids. The game was noteworthy in that the black and white forces were not symmetrical. Although each side had the same array of pieces, the numbers on them differed, allowing different possible captures and winning configurations to the two players.

Pieces

There are four types of pieces, which are Rounds, Triangles, Squares, and Pyramids.
*Rounds: Rounds move one square in any of the four spaces next to it.
*Triangles: Triangles can move three squares in any direction, including the diagonal.
*Squares: Squares can move four squares in any direction, including the diagonal.
*Pyramids: Pyramids are not actually one piece, but more than one piece put together. The White Pyramid is made of a "36" Square, a "25" Square, a "16" Triangle, a "9" Triangle, a " 4" Round, and a "1" Round, which totals up to the Pyramid's value of 91. The Black Pyramid is made up of a "64" Square, a "49" Square, a "36" Triangle, a "25" Triangle, and a "16" Round, which adds up to the Pyramid's value of 190. These irregular values make it hard for them to be captured by most of the capturing methods listed below, except for Siege. Pyramids can move like a Round, a Triangle, and a Square, which makes them very valuable.

Capturing

There were a variety of capture methods. It is notable that pieces do not land on another piece to capture it, but insteads remain in their square and removes the other.
* Meeting: If a piece could capture another piece with the same value by landing on it, the piece stays in its location and the opponent's piece is taken from the board.
* Assault: If a piece with a small value, multiplied by the number of vacant spaces between it and another larger piece is equal to the larger piece, the larger piece is captured.
* Ambuscade: If two pieces' sum is equal to an enemy piece that is placed between the two, the enemy piece is captured and removed from the board.
* Siege: If a piece is surrounded on all four sides, it is removed.

Victory

There were also a variety of victory conditions for determining when a game would end and who the winner was. There were common victories, and proper victories, which is recommended for more skilled players. Proper victories requires placing pieces in linear arrangements in the opponent's side of the board, whose numbers formed by the arrangement is in various types of numerical progression. The types of progression required, arithmetic, geometric and harmonic, suggest a connection with the mathematical work of Boëthius.
*Common Victories:
**De Corpore: If a player captures a certain number of pieces set by both players, he wins the game.
**De Bonis: If a player captures enough pieces to add up to or exceed a certain value that is set by both players, he wins the game.
**De Lite: If a player captures enough pieces to add up to or exceed a certain value that is set by both players, and the number of digits in his captured pieces' values are less than a number set by both players, he wins the game.
**De Honore: If a player captures enough pieces to add up to or exceed a certain value that is set by both players, and the number of pieces he captured are less than a certain number set by both players, he wins the game.
**De Honore Liteque: If a player captures enough pieces to add up to or exceed a certain value that is set by both players, the number of digits in his captured pieces' values are less than a number set by both players, and the number of pieces he captured are less than a certain number set by both players, he wins the game.
*Proper Victories:
**Victoria Magna: This occurs when three pieces that are arranged are in an arithmetic progression.
**Victoria Major: This occurs when four pieces that are arranged have three pieces that are in a certain progression, and another three pieces are in another type of progression.
**Victoria Excellentissima: This occurs when four pieces that are arranged have all three types of mathematical progressions in three different groups.

Popularity

From the seventeenth century onwards the game, which at its peak rivaled chess for popularity in Europe, virtually disappeared until the late 19th and early 20th century when rediscovered by historians.

ee also

* The Glass Bead Game - a novel by Hermann Hesse

References

* The Philosopher's Game, Ann E Moyer, University of Michigan Press, ISBN 0-472-11228-7
* Das mittelalterliche Zahlenkampfspiel, Arno Borst, ISBN 3-8253-3750-2
* Numerology, or What Pythagoras Wrought, Chapter 17, Underwood Dudley, Mathematical Association of America, ISBN 0-88385-524-0
* The Boardgame Book, R.C. Bell, pg 136, ISBN 0-671-06030-9

External links

* [http://www.stargraphics.com/ambush.htm] Ambush, a modern computer game loosely based on Rithmomachia
* [http://www.functologic.com/applet/Rhythmomachia.html] A Java applet implementing 'Rhythmomachia'.
* [http://www.kuro5hin.org/story/2002/9/18/01924/0267] Rithmomachia: The Game for Medieval Geeks
* [http://www.gamecabinet.com/rules/Rithmomachia.html] A translation of the rules established by Claude de Boissière in 1556.
* [http://jducoeur.org/game-hist/ Medieval & Renaissance Games Home Page]