Rithmomachy
Encyclopedia
Rithmomachy 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 depend on the numbers inscribed on each piece.
It has been argued 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. The game, Moyer argues, 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."
, 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
.
.
Chess
Chess is a two-player board game played on a chessboard, a square-checkered board with 64 squares arranged in an eight-by-eight grid. It is one of the world's most popular games, played by millions of people worldwide at home, in clubs, online, by correspondence, and in tournaments.Each player...
, except most methods of capture depend on the numbers inscribed on each piece.
It has been argued 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. The game, Moyer argues, 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."
History
Very little, if anything, is known about the origin of the game. But it is known that medieval writers attributed it to PythagorasPythagoras
Pythagoras of Samos was an Ionian Greek philosopher, mathematician, and founder of the religious movement called Pythagoreanism. Most of the information about Pythagoras was written down centuries after he lived, so very little reliable information is known about him...
, although no trace of it has been discovered in Greek literature, and the earliest mention of it is from the time of Hermannus Contractus
Hermannus Contractus
Hermann of Reichenau , also called Hermannus Contractus or Hermannus Augiensis or Herman the Cripple, was an 11th century scholar, composer, music theorist, mathematician, and astronomer. He composed the Marian prayer Alma Redemptoris Mater...
(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
Byzantine Empire
The Byzantine Empire was the Eastern Roman Empire during the periods of Late Antiquity and the Middle Ages, centred on the capital of Constantinople. Known simply as the Roman Empire or Romania to its inhabitants and neighbours, the Empire was the direct continuation of the Ancient Roman State...
or Alexandria
Alexandria
Alexandria is the second-largest city of Egypt, with a population of 4.1 million, extending about along the coast of the Mediterranean Sea in the north central part of the country; it is also the largest city lying directly on the Mediterranean coast. It is Egypt's largest seaport, serving...
.
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'
Anicius Manlius Severinus Boethius
Anicius Manlius Severinus Boëthius, commonly called Boethius was a philosopher of the early 6th century. He was born in Rome to an ancient and important family which included emperors Petronius Maximus and Olybrius and many consuls. His father, Flavius Manlius Boethius, was consul in 487 after...
De institutione arithmetica, for the students of monastery schools. The rules of the game were improved shortly thereafter by the respected monk, Hermannus Contractus
Hermannus Contractus
Hermann of Reichenau , also called Hermannus Contractus or Hermannus Augiensis or Herman the Cripple, was an 11th century scholar, composer, music theorist, mathematician, and astronomer. He composed the Marian prayer Alma Redemptoris Mater...
, from Reichenau
Reichenau Island
Reichenau Island lies in Lake Constance in southern Germany, at approximately . It lies between Gnadensee and Untersee, two parts of Lake Constance, almost due west of the city of Konstanz. The island is connected to the mainland by a causeway that was completed in 1838...
, and in the school of Liège. In the following centuries, Rythmomachia spread quickly through schools and monasteries in the southern parts of Germany
Germany
Germany , officially the Federal Republic of Germany , is a federal parliamentary republic in Europe. The country consists of 16 states while the capital and largest city is Berlin. Germany covers an area of 357,021 km2 and has a largely temperate seasonal climate...
and France
France
The French Republic , The French Republic , The French Republic , (commonly known as France , is a unitary semi-presidential republic in Western Europe with several overseas territories and islands located on other continents and in the Indian, Pacific, and Atlantic oceans. Metropolitan 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
England
England is a country that is part of the United Kingdom. It shares land borders with Scotland to the north and Wales to the west; the Irish Sea is to the north west, the Celtic Sea to the south west, with the North Sea to the east and the English Channel to the south separating it from continental...
, where famous mathematician Thomas Bradwardine
Thomas Bradwardine
Thomas Bradwardine was an English scholar, scientist, courtier and, very briefly, Archbishop of Canterbury. As a celebrated scholastic philosopher and doctor of theology, he is often called Doctor Profundus, .-Life:He was born either at Hartfield in Sussex or at Chichester, where his family were...
wrote a text about it. Even Roger Bacon
Roger Bacon
Roger Bacon, O.F.M. , also known as Doctor Mirabilis , was an English philosopher and Franciscan friar who placed considerable emphasis on the study of nature through empirical methods...
recommended Rythmomachia to his students, while Sir Thomas More
Thomas More
Sir Thomas More , also known by Catholics as Saint Thomas More, was an English lawyer, social philosopher, author, statesman and noted Renaissance humanist. He was an important councillor to Henry VIII of England and, for three years toward the end of his life, Lord Chancellor...
let the inhabitants of the fictitious Utopia
Utopia
Utopia is an ideal community or society possessing a perfect socio-politico-legal system. The word was imported from Greek by Sir Thomas More for his 1516 book Utopia, describing a fictional island in the Atlantic Ocean. The term has been used to describe both intentional communities that attempt...
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
Sorbonne
The Sorbonne is an edifice of the Latin Quarter, in Paris, France, which has been the historical house of the former University of Paris...
.
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 diagonals.
- Triangles: Triangles can move exactly two squares vertically or horizontally, but not diagonally.
- Squares: Squares can move exactly three squares vertically or horizontally, but not diagonally.
- 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, or a Square, as long as they still contain the respective piece, which makes them very valuable.
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.- 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 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 — suggest a connection with the mathematical work of BoëthiusAnicius Manlius Severinus Boethius
Anicius Manlius Severinus Boëthius, commonly called Boethius was a philosopher of the early 6th century. He was born in Rome to an ancient and important family which included emperors Petronius Maximus and Olybrius and many consuls. His father, Flavius Manlius Boethius, was consul in 487 after...
.
- Common Victories:
- De Corpore (LatinLatinLatin is an Italic language originally spoken in Latium and Ancient Rome. It, along with most European languages, is a descendant of the ancient Proto-Indo-European language. Although it is considered a dead language, a number of scholars and members of the Christian clergy speak it fluently, and...
: "by body"): If a player captures a certain number of pieces set by both players, he wins the game. - De Bonis ("by goods"): 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 ("by lawsuit"): 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 ("by honour"): 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 ("by honour and lawsuit"): 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.
- De Corpore (Latin
- Proper Victories:
- Victoria Magna ("great victory"): This occurs when three pieces that are arranged are in an arithmetic progression.
- Victoria Major ("greater victory"): This occurs when four pieces that are arranged have three pieces that are in a certain progression, and another three pieces that are in another type of progression.
- Victoria Excellentissima ("most excellent victory"): 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.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.
- Medieval & Renaissance Games Home Page