Rithmomachia

Last updated
1554 illustration of a Rithmomachy board and pieces by Claude de Boissiere Ritho.jpg
1554 illustration of a Rithmomachy board and pieces by Claude de Boissière

Rithmomachia (also known as Rithmomachy, Arithmomachia, Rythmomachy, Rhythmomachy, The Philosophers' Game, and other variants) is an early European mathematical board game. Its earliest known description dates from the eleventh century. The name comes loosely from Greek and means "The Battle of the Numbers." [lower-alpha 1] The game is somewhat like chess except that most methods of capture depend on the numbers inscribed on each piece.

Contents

The game was used as an educational tool that teachers could introduce while teaching arithmetic as part of the quadrivium to those in Western Europe who received a classical education during the medieval period. David Sepkoski wrote that between the twelfth and sixteenth centuries, "rithmomachia served as a practical exemplar for teaching the contemplative values of Boethian mathematical philosophy, which emphasized the natural harmony and perfection of number and proportion, that it was used both as a mnemonic drill for the study of Boethian number theory and, more importantly, as a vehicle for moral education, by reminding players of the mathematical harmony of creation." [2] The game declined sharply in popularity in the 17th century, as it was no longer used in education, and potential players were not introduced to it during their schooling.

History

The play he can of Ryghtmadhye
Which dulle wittits dothe encombre
For thys play stant al by noumbre
And hath al his conclusions
Chefly in proporsions
By so sotil ordynaunce
As hyt ys in remembraunce
By thise Philosophurs olde.

John Lydgate,Reson & Sensuallyte
Earliest known English reference
to Rithmomachia, ~1407. [1]

Little is known about the origin of the game. Medieval writers attributed it to Pythagoras, but no trace of it has been discovered in Greek literature. The earliest surviving mentions of it is are from the early 11th century, suggesting it was created in the late 10th or early 11th century. The name and its many variations are from Greek; it is unclear whether this was due to being created by a rare Western European with a classical education that involved learning Greek, or if the game had a genuine origin in Greece and the Greek-speaking Byzantine Empire of the period.

The first written evidence of Rithmomachia dates to around 1030, when a monk named Asilo created a game that illustrated the number theory of Boethius' De institutione arithmetica, for the students of monastery schools. De institutione arithmetica was the standard textbook for instruction in arithmetics in the period for those lucky enough to receive a medieval education. The rules of the game were improved and spelled out more shortly thereafter by another monk, Hermannus Contractus (1013–1054) from Reichenau, and in the school of Liège. In the following centuries, Rithmomachia spread 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 Rithmomachia came to England, where famous mathematician Thomas Bradwardine wrote a text about it. Even Roger Bacon recommended Rithmomachia to his students, while Sir Thomas More let the inhabitants described in the book Utopia play it for recreation. The game was known well enough to justify printed treatises in Latin, French, Italian, and German, in the sixteenth century. Two notices advertising a game set for sale have been found, one in Paris (1556) and the other in London (1563). Nevertheless, no archaeological evidence of the game (such as playing boards) has survived from the medieval and early modern periods, in contrast to many other board games. [1]

Rithmomachia was at its most popular in the 16th century. The Tudor polymath, statesman and publisher of the Geneva Bible, Sir Rowland Hill, published on the game under the title The most ancient and learned Playe, called the Philosopher's Game invented for the honest recreation of Students and other sober persons, in passing the tedious of tyme to the release of their labours, and the exercise of their Wittes in 1562; [3] his house at Soulton Hall also contains a board for the game on a basement parlour or prayer room.

Sir Rowland Hill's headquarters in Shropshire: the tiled floor of a basement room contains a 16th century Rithmomachia board East front of Soulton Hall.jpg
Sir Rowland Hill's headquarters in Shropshire: the tiled floor of a basement room contains a 16th century Rithmomachia board

In 1572 Francesco Barozzi published a version in Venice which was translated into German by Augustus II, Duke of Brunswick. [4] It lost its popularity sharply in the 17th century, virtually disappearing as the style of teaching mathematics changed, and Boethius's mathematics was considered old-fashioned and obsolete. One issue was that the rules were never standardized, with major variations from teacher to teacher. The game partially survived by clinging to the now far more popular chess. Gustavus Selenus included the rules of rithmomachia as an appendix in one of his books on chess, and the game persisted as "arithmetic chess" or "numerical checkers" as a side mention in German chess books for some time afterward, a curiosity but a rarely-played one. The game was rediscovered in the 20th century by historians of board games such as Arno Borst. [1]

Gameplay

Hand-made Rithmomachy set Homemade rithmomachy set.jpg
Hand-made Rithmomachy set

Rithmomachia is 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, and rounds. Pyramids could be formed by stacking pieces. 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.

The rules below describe the most common version of the game, played through much of the Middle Ages and Renaissance. There was also a variant propounded by Fulke in the 16th century, with significantly different (and somewhat more consistent) capture rules. [5]

Pieces

There are four types of pieces: Rounds, Triangles, Squares, and Pyramids.

Capturing

There were a variety of capture methods. Pieces do not land on another piece to capture it, but instead remain in their square and remove the other. If a piece is captured, it changes sides. [6]

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 were recommended for more skilled players. Proper victories required placing pieces in linear arrangements in the opponent's side of the board, with the numbers formed by the arrangement following various types of numerical progression. The types of progression required — arithmetic, geometric and harmonic — fit with the mathematical and numerological teachings of Boethius.

Notes

  1. The first word is a combination of αριθμός, arithmós, number, and ρυθμός, rythmós, rhythm; the second word is μάχια, máchia, battles. So a literal translation might be "Number-Rhythm Battles". [1]

Related Research Articles

Chess strategy is the aspect of chess play concerned with evaluation of chess positions and setting goals and long-term plans for future play. While evaluating a position strategically, a player must take into account such factors as the relative value of the pieces on the board, pawn structure, king safety, position of pieces, and control of key squares and groups of squares. Chess strategy is distinguished from chess tactics, which is the aspect of play concerned with the move-by-move setting up of threats and defenses. Some authors distinguish static strategic imbalances, which tend to persist for many moves, from dynamic imbalances, which are temporary. This distinction affects the immediacy with which a sought-after plan should take effect. Until players reach the skill level of "master", chess tactics tend to ultimately decide the outcomes of games more often than strategy. Many chess coaches thus emphasize the study of tactics as the most efficient way to improve one's results in serious chess play.

<span class="mw-page-title-main">Queen (chess)</span> Chess piece

The queen is the most powerful piece in the game of chess. It can move any number of squares vertically, horizontally or diagonally, combining the powers of the rook and bishop. Each player starts the game with one queen, placed in the middle of the first rank next to the king. Because the queen is the strongest piece, a pawn is promoted to a queen in the vast majority of cases.

<span class="mw-page-title-main">Chess piece</span> Game piece for playing chess

A chess piece, or chessman, is a game piece that is placed on a chessboard to play the game of chess. It can be either white or black, and it can be one of six types: king, queen, rook, bishop, knight, or pawn.

<span class="mw-page-title-main">Pawn (chess)</span> Chess piece

The pawn is the most numerous and weakest piece in the game of chess. It may move one square directly forward, it may move two squares directly forward on its first move, and it may capture one square diagonally forward. Each player begins a game with eight pawns, one on each square of their second rank. The white pawns start on a2 through h2; the black pawns start on a7 through h7.

<span class="mw-page-title-main">Rules of chess</span> Rules of play for the game of chess

The rules of chess govern the play of the game of chess. Chess is a two-player abstract strategy board game. Each player controls sixteen pieces of six types on a chessboard. Each type of piece moves in a distinct way. The object of the game is to checkmate the opponent's king; checkmate occurs when a king is threatened with capture and has no escape. A game can end in various ways besides checkmate: a player can resign, and there are several ways a game can end in a draw.

<span class="mw-page-title-main">Checkers</span> Board game

Checkers, also known as draughts, is a group of strategy board games for two players which involve forward movements of uniform game pieces and mandatory captures by jumping over opponent pieces. Checkers is developed from alquerque. The term "checkers" derives from the checkered board which the game is played on, whereas "draughts" derives from the verb "to draw" or "to move".

<span class="mw-page-title-main">Shatranj</span> Old form of chess

Shatranj is an old form of chess, as played in the Sasanian Empire. Its origins are in the Indian game of chaturaṅga. Modern chess gradually developed from this game, as it was introduced to Europe by contacts in Muslim Al-Andalus and in Sicily in the 10th century.

Mak-yek is a two-player abstract strategy board game played in Thailand and Myanmar. Players move their pieces as in the rook in Chess and attempt to capture their opponent's pieces through custodian and intervention capture. The game may have been first described in literature by Captain James Low a writing contributor in the 1839 work Asiatic Researches; or, Transactions of the Society, Instituted in Bengal, For Inquiring into The History, The Antiquities, The Arts and Sciences, and Literature of Asian, Second Part of the Twentieth Volume in which he wrote chapter X On Siamese Literature and documented the game as Maak yék. Another early description of the game is by H.J.R. Murray in his 1913 work A History of Chess, and the game was written as Maak-yek.

A fairy chess piece, variant chess piece, unorthodox chess piece, or heterodox chess piece is a chess piece not used in conventional chess but incorporated into certain chess variants and some chess problems. Compared to conventional pieces, fairy pieces vary mostly in the way they move, but they may also follow special rules for capturing, promotions, etc. Because of the distributed and uncoordinated nature of unorthodox chess development, the same piece can have different names, and different pieces can have the same name in various contexts as it can be noted in the list of fairy chess pieces.

Martian Chess is an abstract strategy game for two or four players invented by Andrew Looney in 1999. It is played with Icehouse pyramids on a chessboard. To play with a number of players other than two or four, a non-Euclidean surface can be tiled to produce a board of the required size, allowing up to six players.

<span class="mw-page-title-main">Makruk</span> Chess variant

Makruk, or Thai chess, is a strategy board game that is descended from the 6th-century Indian game of chaturanga or a close relative thereof, and is therefore related to chess. It is part of the family of chess variants.

<span class="mw-page-title-main">Chu shogi</span>

Chu shogi is a strategy board game native to Japan. It is similar to modern shogi in its rules and gameplay. Its name means "mid-sized shogi", from a time when there were three sizes of shogi variants that were regularly being played. Chu shogi seems to have been developed in the early 14th century as a derivative of dai shogi. There are earlier references, but it is not clear that they refer to the game as we now know it.

<span class="mw-page-title-main">Chaturaji</span> Chess variant

Chaturaji is a four-player chess-like game. It was first described in detail c. 1030 by Al-Biruni in his book India. Originally, this was a game of chance: the pieces to be moved were decided by rolling two dice. A diceless variant of the game was still played in India at the close of the 19th century.

<span class="mw-page-title-main">Jetan</span> Chess variant

Jetan, also known as Martian chess, is a chess variant first published in 1922. It was created by Edgar Rice Burroughs as a game played on Barsoom, his fictional version of Mars. The game was introduced in The Chessmen of Mars, the fifth book in the Barsoom series. Its rules are described in Chapter 2 and in the Appendix of the book, with an actual game partly described in Chapter 17.

Dai shogi or Kamakura dai shogi (鎌倉大将棋) is a board game native to Japan. It derived from Heian era shogi, and is similar to standard shogi in its rules and game play. Dai shogi is only one of several large board shogi variants. Its name means large shogi, from a time when there were three sizes of shogi games. Early versions of dai shogi can be traced back to the Kamakura period, from about AD 1230. It was the historical basis for the later, much more popular variant chu shogi, which shrinks the board and removes the weakest pieces.

<span class="mw-page-title-main">Circular chess</span> Chess variant played on a circular board

Circular chess is a chess variant played using the standard set of pieces on a circular board consisting of four rings, each of sixteen squares. This is topologically equivalent to playing on the curved surface of a cylinder.

In chess, an exchange or trade of chess pieces is a series of closely related moves, typically sequential, in which the two players capture each other's pieces. Any type of pieces except the kings may possibly be exchanged, i.e. captured in an exchange, although a king can capture an opponent's piece. Either the player of the white or the black pieces may make the first capture of the other player's piece in an exchange, followed by the other player capturing a piece of the first player, often referred to as a recapture. Commonly, the word "exchange" is used when the pieces exchanged are of the same type or of about equal value, which is an even exchange. According to chess tactics, a bishop and a knight are usually of about equal value. If the values of the pieces exchanged are not equal, then the player who captures the higher-valued piece can be said to be up the exchange or wins the exchange, while the opponent who captures the lower-valued piece is down the exchange or loses the exchange. Exchanges occur very frequently in chess, in almost every game and usually multiple times per game. Exchanges are often related to the tactics or strategy in a chess game, but often simply occur over the course of a game.

<span class="mw-page-title-main">Outline of chess</span> Overview of and topical guide to chess

The following outline is provided as an overview of and topical guide to chess:

<span class="mw-page-title-main">Infinite chess</span> Variation of chess

Infinite chess is any variation of the game of chess played on an unbounded chessboard. Versions of infinite chess have been introduced independently by multiple players, chess theorists, and mathematicians, both as a playable game and as a model for theoretical study. It has been found that even though the board is unbounded, there are ways in which a player can win the game in a finite number of moves.

References

  1. 1 2 3 4 Stigter, Jurgen (2007). "Rithmomachia, the Philosopher's Game". In Finkel, Irving L. (ed.). Ancient Board Games in Perspective. The British Museum Press. pp. 263–269. ISBN   9780714111537.
  2. Ann E. Moyer, "The Philosopher's Game: Rithmomachia in Medieval and Renaissance Europe." Isis, Vol. 95, No. 4 (December 2004), pp. 697–699. David Seposki
  3. Anton Schmid (1847). Literatur des Schachspiels, [a bibliogr.] gesammelt, geordnet und mit Anmerkungen (in German). Oxford University.
  4. Bazzarini, Antonio (1834). Ortografia Enciclopedica Universale Della Lingua Italiana: PO - R; Con Appendice. 2,6 : Dizionario Enciclopedico Delle Scienze, Lettere Ed Arti (in Italian). Bazzarini, Antonio.
  5. Fulke, "Of these partes in the fyrst kynd of playng"
  6. Suzuki, Jeff (2009). Mathematics in Historical Context. Mathematical Association of America. p. 144. ISBN   978-0-88385-570-6.

Bibliography