References cited in my introductory chapter to the catalogue accompanying an exhibition of Oriental Games curated by the Asia Society, New York, 2004
1. Li Gang (trans. B. G. Doar), "A wei-qi chess set discovered at the Han Dynasty Yangling Mausoleum", China Archaeology and Art Digest, Vol 4 No 4 (Hong Kong, April-May 2002), p. 53. (Return 1)
2. Short story published 1845. (Return 2)
3. Bliss, Sir Arthur, Ballet Suite: Checkmate (Chester Music & Novello & Co, London). It was written at the request of the Sadler's Wells Ballet for their visit to Paris in 1937 and choreographed by Dame Ninette de Valois. (Return 3)
4. "We have focused on four factors influencing the development of the rules during many centuries. They are (1) strategic complexity, (2) beauty, (3) draw ratio, and (4) handicap system [...] Beauty may be related to the symmetry of movement and positions, for instance as exemplified in the initial position of the game." - Iida, Hiroyuki, et al., "Towards a Classification of Games using Computer Analyses", in Proceedings: Board Games in Academia III - An interdisciplinary approach, papers of a Colloquium held in Florence 1999 (p. 140). (Return 4)
5. Shakespeare, As you like it (II, vii, 139). (Return 5)
6. Schiller, Friedrich, Über die ästhetische Erziehung des Menschen in einer Reihe von Briefen, 1795. (Return 6)
7. Caillois, Roger (trans. Barash, Meyer), Man, Play and Games, (Illinois, 2001), p. 83. (Return 7)
8. Sutton-Smith, Brian, The Ambiguity of Play (Harvard, 1997), p. 208. (Return 8)
9. Wittgenstein, Ludwig, Philosophical Investigations (Oxford, 1953), pp. 31-2. See also: Reurich, Lucien, "Towards a philosophical characterization of playing games", in New Approaches to Board games Research, International Institute for Asian Studies, Working Paper Series 3 (Leiden, 1995), pp. 187-8 (Return 9)
10. Berne, Eric, Games People Play - The Psychology of Human Relationships, (Harmondsworth, 1964 (Return 10)
11. Carse, James, Finite and Infinite Games - A Vision of Life as Play and Possibility (Harmondsworth, 1986), p 4. (Return 11)
12. von Neumann, John and Oskar Morgenstern, Theory of Games and Economic Behavior (Princeton NJ: Princeton University Press, 1944); 3rd ed. New York, Wiley, 1953. Of which Caillois writes:
Whenever calculation arrives at a scientific theory of the game, the interest of the player disappears together with the uncertainty of the outcome. All variables are known, as are conceivable consequences... von Neumann and Morgenstern calculate structures requiring a peculiarly more complex mathematical system. [...] The mathematical analysis of games thus turns out to be a game in itself which has only an incidental relationship to the games analyzed. It would exist even if there were no games to analyze. It can and must develop independently, gratuitously inventing ever more complex situations and rules. It does not have the least effect upon the nature of the game itself." (Caillois (2001), p.173, 174). (Return 12)
13. Spariosu, Mihai, Dionysus Reborn - Play and the Aesthetic Dimension in Modern Philosophical and Scientific Discourse (Ithaca, 1989), p.3. Cf also: "My own quite impressionistic view is that a game is a particular way of looking at something, anything." - Abt, Clark C., Serious Games (New York, 1970), p. 5. (Return 13)
14. "All the uses of 'play' are seen to arise naturally from a primary notion 'to exercise, bestir, or busily occupy oneself'" (Oxford English Dictionary, s.v. "play"). Cf German pflegen "to be accustomed [to doing something regularly or repeatedly or habitually]. (Return 14)
15. "Play is free movement within a more rigid structure", observe Katie Salen and Eric Zimmerman in Rules of play (Cambridge, Mass., 2004, p.304) - a profound study of games and play unfortunately not published before this essay reached final proof stage, otherwise many more references would have been made to it. Using a similar analogy, they continue: "The play itself exists only because of the more utilitarian structures of the driving system [of an automobile]. The 'rules' created by these elements make the free movement of play possible". (Return 15)
16. Self-actualization is the highest of Abraham Maslow's posited hierarchy of needs relating to human motivation. Starting from the lowest, they are: physiological needs (food, comfort etc), security, affinitive (sense of belonging with others), esteem, cognitive (knowledge), aesthetic, self-actualization. See Maslow, Abraham, Motivation and personality, (New York 1954); Maslow, A., Lowery, R (ed) Toward a psychology of being (3rd ed.). (New York, 3rd ed. 1998) (Return 16)
17. "All art constantly aspires towards the condition of music" wrote Walter Pater, in "The School of Giorgione" (Fortnightly Review, October 1877, reprinted in Aldington, Richard (ed), Walter Pater - Selected Works, London, 1948, pp. 269-284.) Pater, an abstractionist before his time, argued that most people (including critics) tend to judge works of art excessively by reference to content and insufficiently by reference to form. The same might be said today of games players and critics. Later in the same essay Pater relates play to the arts:
Often such moments [listening to music, etc] are really our moments of play, and we are surprised at the unexpected blessedness of what may seem our least important part of time; not merely because play is in many instances that to which people really apply their best powers, but also because at such times, the stress of our servile, everyday attentiveness being relaxed, the happier powers in things without are permitted free passage, and have their way with us. (Return 17)
18. Huizinga, Johan, trans. R F C Hull, Homo Ludens - A Study of the Play Element in Culture (London, 1949). Huizinga's preferred (and preferable) subtitle was A Study of the Play Element of Culture. Hull's pedantic rewording destroys the sense. (Return 18)
19. Carse (1986), p. 4. (Return 19)
20. Huizinga (1949), pp. 76-88. (Return 20)
21. "Capellanus, Andreas", trans. Parry, John Jay, The Art of Courtly Love (New York/London, 1969), pp. 167-177. (Return 21)
22. Caillois (2001), pp 14-26. (Return 22)
23. Huizinga (1949), p. 3. (Return 23)
24. Eigen, Manfred, and Winkler, Ruthild, trans. R & R Kimber, The Laws of the Game - How the Principles of Nature govern Chance (Harmondsworth, 1983), p.3. (Return 24)
25. Einstein's comment about God not playing dice, though repeated as often as his other well-known observation about the universe (E = mc2), is considerably harder to pin down since it does not appear in any of his own published works. It is referred to, in different translations of the German, in Philipp Frank, Einstein, His Life and Times, 1947, and Banesh Hoffman Albert Einstein, Creator and Rebel, New American Library, p73, and is taken for granted by Prof. Stephen Hawking in Public Lectures: Does God Play Dice?. Michio Kaku, in Einstein's Cosmos (London 2004), writes:
In December 1926, responding to Born's paper, Einstein wrote, "Quantum mechanics calls for a great deal of respect. [...] The theory offers a lot, but it hardly brings us any closer to the Old Man's secret. For my part, at least, I am convinced that He doesn't throw dice" (p.127). (Return 25)
26. Abbott, Robert, Abbott's New Card Games (New York 1963), pp. 73-92. (Return 26)
27. Caillois (2001) pp. 27-35 (Return 27)
28. Albertarelli, Spartaco, "1000 ways of playing Monopoly", in Proceedings: Board Games in Academia III - An interdisciplinary approach, papers of a Colloquium held in Florence 1999 (pp 1-7). (Return 28)
29. Carse (1986), p. 8-9. (Return 29)
30. Huizinga (1949), p. 11. (Return 30)
31. Caillois (2001), p. 173. (Return 31)
32. The unpredictability of large-scale multiply-connected outcomes from a relatively slight initial cause is illustrated by, for example, the break of the pack at Pool or Snooker. Sensitive dependence on initial conditions is known as the Butterfly Effect from a talk given by Edward Lorenz at the December 1972 meeting of the American Association for the Advancement of Science: "Predictability: Does the Flap of a Butterfly's Wings in Brazil set off a Tornado in Texas?" (Return 32)
33. Murray, H J R, A History of Board Games Other than Chess (Oxford 1952), p. 4. (Return 33)
34. See Chick, Garry, "Games in Culture Revisited: A Replication and Extension of Roberts, Arth, and Bush (1959)", in Cross-Cultural Research, 32, 2, 185-206 (1998). The reference is to Roberts, J. M., Arth, M. J. & Bush, R. R. (1959). "Games in culture", American Anthropologist, 59, 579-605. (Return 34)
35. Tedlock, Dennis, in his Introduction to Culin, S, Games of the North American Indians - Volume 1, Games of Chance (Nebraska University Press, 1992), p. 23. (Return 35)
36. For an exploration of this phenomenon, see Alexander Cockburn, Idle Passion - Chess and the Dance of Death (London 1975). (Return 36)
37. Parlett, David, The Oxford History of Board Games (Oxford, 1999), p. 243 ff. (Return 37)
38. Zheng Yan'e, "Preliminary remarks on the games of Liubo and Saixi", in China Archaeology and Art Digest, Vol 4 No 4 "Fortune, Games and Gaming" (Beijing, April-May 2002) p.80. (Return 38)
39. Adapted from Gould, Sydney H (trans.) The Book on Games of Chance (New York 1961), p.22. A translation of Girolamo Cardano, Liber de Ludo Aleae (1564). (Return 39)
40. "Of the 82 societies with at least some information on their games, Roberts, Arth, and Bush (1959) retained 50 for their sample. Of these 50, 44 had games of physical skill, 19 had games of strategy, and 19 had games of chance. Five cultures were reported to have no games at all." Chick, Garry, Games in Culture Revisited: "A Replication and Extension of Roberts, Arth, and Bush (1959)" in Cross-Cultural Research, 32, 2, 185-206 (1998). (Return 40)
41. Randolph, Alexander, "Homo Ordinator", in Proceedings: Board Games in Academia III - An interdisciplinary approach, papers of a Colloquium held in Florence 1999 (p.77). (Return 41)
42. Strutt, Joseph, Sports and Pastimes of the People of England (1801), enlarged and corrected by Cox, J. C. (1903), republished Bath, 1969, p. xv. (Return 42 )
