War Games: A History of War on Paper

Notes

Notes Unless otherwise indicated, all quotations from German-language sources are translated by Ross Benjamin. Preface 1. As early as in the 1950s, Vera Riley and John P. Young came to this conclusion, exploiting the potential of the war game for the then-new scholarly discipline of operations research. Riley and Young trace the relevance of the war game back to two essential factors: first, the success it afforded the German military, which probably made “the greatest use of the war game, in the past half century” (1957, 8). Second, they cite John von Neumann’s game theory, which had already been presented in 1928 and which after the Second World War made possible a far-reaching theorization of tactical and strategic games (9). 2. Clausewitz 1976, 119. 3. See, for example, Booß-Bavnbek and Høyrup 2003 or Mehrtens 1996, 87–134. 4. This is how Bernays describes the fundamental suspicion toward the specialized field of logic (1976, 1). Chapter 1 1. See Ries 1522. 2. For a persuasive historical study of zero and nothing, see Rotman 1987. 3. Through the systematic investigation of medieval sources, medievalist Arno Borst managed to rescue from oblivion the history of the Battle of Numbers and make the Rithmomachia legible beyond a small circle of specialists. Borst’s authoritative publications on the Battle of Numbers are Das mittelalterliche Zahlenkampfspiel (1986) and “Rithmimachie und Musiktheorie” (1990, 253–288). 4. Borst summarizes the genesis of the word and its various spellings. See Borst 1990, 256, 261, 281. 5. Borst 1990, 258. 146 Notes 6. Not until the early Scholastic period do commentators begin to designate the Battle of Numbers as a game. See Borst 1990, 256, 285. 7. The Battle of Numbers was first called by name in 1070 at the cathedral school in Lüttich (Borst 1990, 276). 8. Duke August II of Braunschweig-Lüneburg, who will be discussed further in chapter 2, took up instructions for the Rithmomachia as a curiosity in his famous chess book. See Selenus 1978. 9. See Borst 1986, 96. 10. Gottfried Friedlein was most likely the first to have alluded to this situation. See Friedlein 1863, 298. 11. Werner Bergmann points out that the abacus takes on the calculation of geometric figures and thereby moves away from arithmetic, which stresses numerical concepts and relations. See Bergmann 1985, 117. 12. See Borst 1986, 55. 13. See Friedlein 1863, 327, and Borst 1986, 473. 14. See Borst 1986, 278. 15. Borst on the new, stratifying format of the composite manuscript: “[the] intellectuals concerned with the Battle of Numbers were obsessed with commentary: they could scarcely hear or read something without immediately writing about it. The genre responsible for such short written preliminary notes was the composite manuscript” (1986, 276). 16. Borst 1986, 326. 17. Borst 1986, 277. 18. See Busch 1998, 126. 19. See Knobloch 1989, 243. 20. See Bischoff 1967, 256, 259. 21. Bischoff 1967, 255–259. 22. See Friedlein 1863, 313. 23. Translation based on Friedlein 1863, 299. 24. See Borst 1986 for Greek numerals in the Battle of Numbers: 132–134, 147, and for Arabic numerals, 117. 25. See Bergmann 1985, 210. 26. Bergmann 1985, 209. 27. See Vossen 1962, 139. See also Bergmann 1985, 196–197. 28. See Vossen 1962, 141–142, though the question of whether the reference is to gobar digits or Greek letter-numbers remains open. See also Bergmann 1985, 210. 29. Borst speaks out against Walther as the founder of the Battle of Numbers. Compare Borst 1986, 42–43. See also Vossen 1962, 145. Moritz Cantor, on the other hand, presumes Walther to be the founder of the game (Cantor 1922, 1:851–852). 30. Walther von Speyer, quoted in Vossen 1962, 52. 31. Illmer et al. 1987, 48–57. 32. See Borst 1986, 69. Notes 147 33. Huffmann 1993, 419. 34. Domaszewski asserts, “The formulaic character of these phrases makes them recognizable as technical expressions, which are taken from the command language of the Roman military” (1885, 5–6). 35. Erdmann 1935, 30. 36. Voltmer 1988, 188–189. 37. Borst 1986, 72. 38. Borst 1986, 86. 39. Upton-Ward 1992, 89, Rule 317. 40. Fleckenstein 1980, 19–20. Chapter 2 1. See, for example, Furttenbach 1663. 2. See Knobloch 1973–1976, 56, and Krämer 1988, 107. 3. Thus asserts Leibniz, in old age, looking back at his project in a letter to Pierre Rémond de Montmort...