Demonstrating errors in fundamental methodology while containing a wealth of empirical data; the book: 'THE PHILOSOPHER'S GAME: Rithmomachia in Medieval and Renaissance Europe' (2001) by professor Ann E. Moyer [with an edition of Ralph Lever and William Fulke, 'The Most Noble, Auncient, and Learned Playe (1563)] "is at times as much about the history and significance of the teaching of Boethius's ARITHMETIC as it is about the game itself." (p. 13)Indeed, the book appeared to be mis-titled as the author seemed to digress away from Rithmomachia and onto Medieval and Renaissance European reaction to Boethian mathematics via the Philosopher's Game.
Anicius Manlius Severinus Boethius (d. 524 A.D.) whose two major texts, the ARITHMETIC (a loose translation of writings by the second century scholar Nicomachus of Gerosa); and the DE MUSICA (which was heavily based on the "Pythagoreo-Platonic concept of numerical ratios of the musical scale"); were the main text sources for the Quadrivium, the curriculum of monastic schools, cathedral schools, and somewhat in the newly formed universities (studia generalia). It is Dr. Moyer's contention that "rithmomachia had arisen with the promotion of the quadrivium in 11th century-education, so the game's disappearance helps mark the end of this long era of European learning and culture". (p. 123)
Yet a few problems of consistency arose within THE PHILOSOPHER'S GAME which impaired her thesis; as Dr. Moyer stated in her proem that "Rithmomachia was played as long as Boethius's ARITHMETIC was taught; the game and the curriculum disappeared together" (p. 13) which contrasted sharply with her observation of Renaissance Italy where "Boethius's ARITHMETIC did not hold there the place it had held traditionally in northern Europe ... Boethian influence remained as only one aspect among many of mathematics and related studies." (p. 123)
The Renaissance Italians, first exposed to Rithmomachia in Florence "in the social gatherings at the Racellai gardens" (p. 115), were entirely ignorant of Boethian proportions and his text, the ARITHMETIC; and felt "the key to correct proportion is Pythagora's system of musical harmony." (Wittkower, 'Architectural Principles' p. 33). Rithmomachia was played in Italy (and England) as the 'Pythagora's Game', and Francesco Barrozi (c. 1560), modified the rules by Boissiere by totally eliminating Boethian proportion to expedite the beginner to the game. Obviously, in contrast to the author's assertion that the game was played as long as the ARITHMETIC was taught, it is apparent that Rithmomachia was sometimes played in total ignorance of the ARITHMETIC, or independently of Boethian mathematics, and well beyond the life of the Quadrivium curricula.
Depending heavily on a secondary source, Arno Borst, to claim that Rithmomachia, the 'battle of numbers' was invented c. 1030 in a German monastic school by a monk named Asilo, who "made use of Gerbert's SCHOLION on Boethius's ARITHMETIC in comprising his rithmomachia" (p. 20), Dr. Moyer made no effort to document another possible inventor, Herman Contractus, simply understating his contribution. With Dr. Moyer's emphasis of the interest also taken in chess, she took no consideration of the indigenous games of Northern Europe and their possible influence on Rithmomachia. For example, the Viking game 'Halatafl' (fox & geese) dating back to before 400 A.D. and played until the 17th century, where the geese are to capture the fox by surrounding him on all sides so it cannot move, is 'a fortiori' reminiscent of 'Ambuscade' found in the Philosopher's Game!
Therefore the book THE PHILOSOPHER'S GAME is not a definitive work, and contained a number of non-sequiturs, unreferenced claims, foot-noted digressions, 'cum hoc' fallacies, a resort to determinism, and internal inconsistencies. Despite the large number of useful sources, the author would have made her work more rigorous if she included in her bibliograhy translated copies of her secondary sources along with William Fulke's manual.
A work which should be read in conjunction with Professor Ann Moyer is: ARCHITECTURAL PRINCIPLES IN THE AGE OF HUMANISM (1962, 1971) by Rudolf Wittkower, where in chapter four is found a scholarly in-depth treatise of Renaissance Italy's dependence on Plato's 'Timaeus'; Pythagorean number theory; and Plato's musical scales, for the practical application of Renaissance architectural ratio and proportion, without Boethius's ARITHMETIC; while, unintentionally, providing clear and precise explanations of the ratio formulas and proportions found in the rules of Rithmomachia.
This good work: THE PHILOSOPHER'S GAME by Dr. Ann Moyer, is useful to anyone studying the historical influence which the Boethian text, ARITHMETIC, had on a Quadrivium education; but (at $65.00 and 205 pages) might disappoint the serious player of Rithmomachia.
