Games of chance and the prediction of the future
Every game offers an opportunity to study the way of thinking in a communication. Because every playful exchange between parties is a manifestation of intuition, ideas and strategies based on certain rules, leading to an outcome (winning or losing) which can be placed in a historical context (a tournament, a world champion, etc.), it is an excellent way to give an insight in the mechanism of division-thinking (fig. 219).
Fig. 219 – The game as a manifestation of division-thinking. The four-fold is a regular phenomenon. 1. Game board from the graves of Ur with division elements. (SCHMÖKEL, 1957); 2. The Lien Poh is a Hokkien gambling game played in South East Asia. The name means literally ‘turning treasure’. The cube is the Poh or ‘treasure’ and the metal box is the Poh Kam or ‘treasure cover’ (YOUNG, 1886).; 3. An Indian game with four players (GRUZINSKI, 1992). See also: Andrew McFarland Davis (1886). ‘Indian Games: An Historical Research’.
The connection of a game with a religious meaning has a long history. Fig. 220 depicts a Greek votive wheel, devoted to Apollo, and used to worship the gods.
Fig. 220 – A Greek votive-wheel, devoted to Apollo. Museum of Fine Arts, Boston; William Amory Gardiner Fund. In: MEGGS (1983).
A well-known attribute in games is the die. By throwing the dices a decision is forced on a situation and left – so to speak – to the whim of gods (the Roman Fortuna, and its Greek equivalent Tyche, were the goddesses of luck and fate). ‘Luck’ represents, in a quadralectic setting, the uncertainties of the Second Quadrant, while the outcome of the throw produces a (Third Quadrant) certainty (fig. 221).
Fig. 221 – Dice players in classical Rome are seen here as a portrayal on a wall in Pompeii (Italy). Apparently, these players were in conflict about the numbers thrown. In: DILKE (1975).
Throwing the dices is a very old way of decision-making. Originally, a crystal of pyrite was used, because it has the form of a cube. Pyrite (ferrosulfite) was also employed in the old days to make fire. An early connection between the cube and the (holy) light was for this very reason established, giving the game of dice a sacral content.
Unfortunately, the earthly application of the game results sometimes in human misery. Aristotle put out a warning against playing dices, and since ancient times the game (of dice) was associated with greed and crime. Creating visibility in a forceful way, provoking decisions and worshiping the world of opposites has seldom contributed to a peaceful communication between human beings. Nevertheless, it is the material of which a great part of history is made of.
Alongside the cube was – in classical times – a heel bone of a sheep used for a game of chance (knuckle bones). Aristotle mentioned this game, called ‘astragalos’, in the second chapter of his ‘Historia Animalium’. The heel bone is elongated and has four planes of different dimensions. The convex plane is opposite to a concave plane. The individual planes were numbered: 1, 3, 4 en 6. These numeric values had no meaning in a hierarchical sense, because the Greek were not interested in the laws of chance. Four ‘astragaloi‘ were thrown together, resulting in thirty-five possibilities. The combinations were given a specific name, mostly the name of a god or a mythical hero (SAMBURSKY, 1956). Examples were Midas, Alexander, Solon, Aphrodite, and the Romans used further names like Venus, King and Vulture. The highest throw in Greece, counting 40, was the Euripides. The lowest throw was the Dog.
The history of chess is – in the European cultural realm – an instructive game to demonstrate the way division thinking has changed over the years. Originally, the game was played with four players, with each eight pieces: a king, a rook, a knight and a bishop, positioned behind four pawns (MACKETT-BEESON (1968), fig. 222). The name of the game was then ‘chaturanga‘, a Sanskrit word meaning the four parts of an army. In the early versions of chess-with-four-players (in German: ‘Würfelvierschach‘) dices were used to move the different pieces. The dices disappeared in the gradual change to two players.
Fig. 222 – The four participants at the original game of chess, when it was called ‘chaturanga’ (meaning the four parts of an army). The players had eight pieces: a king, an elephant (later a rook), a knight (or a horse), a ship (later a bishop) and four pawns. In: MACKETT-BEESON, (1968). A colored version can be found in: KIEFER (1958).
From its place of origin India, the game reached Europe, via Persia and Arabia. The Iranian writer Firdausi (940 – 1020 AD.) gave in his ‘Book of Kings’ (Schah-Nameh) in sixty-thousand double verses not only the Old-Iranian heroes-stories, but also a development-history of chess. KIEFER (1958) called chess ‘ein morgenländisches Spiel‘. The influence of the Mores in Spain, around the year 1000, was mentioned as a possible introduction of the game in Europe. By 1283 the game was so well known that Alphonso the Wise (1221 – 1284), Spanish king of Castile and León (1252 – 1284), had a treatise written about the game (WHITE, 1913). The ‘Libro de juegos’ (1283) depicted the ‘ajedrex de los quatro tiempos’ (chess of the four seasons) a game with four players in a conflict with four elements and humors. The chessmen were marked in the colors green, red, black and white and the pieces moved by the roll of dice.
The visibility of games increased with the arrival of the printing press at the end of the fifteenth century (fig. 223). The chessboard was often depicted and well known as a game of the higher classes.
Fig. 223 – A woodcut from Caxton’s book about the game: Game and Play of the Chess (1482). In: ROSS (1976).
Another game with a chequered board and dices was called tremerel, also called nine mens merrils (from the French word merelles, or mereaux, pointing to the jettons or counters, with which it was played) (fig. 224). The leading number in this game is three.
Fig. 224 – The game of tremerel was played in France. Each party had three counters, which were to be placed in a line in order to win the game. The board on this illustration does not suggest a direct resemblance, but there might be a connection with the Nine Men’s Morris game in England and the Mühle (Mills) game in central Europe. In: GAY (1928/1971).
The distribution of card (games) was widespread all over Europe. The basic illustrations on the twenty-two Tarot-cards and the fifty-two (or fifty-three when the joker is included) game-cards changed little over the years (fig. 225). The original division in the playing cards reflected the four classes in the (medieval) society:
————————– 1. hearts – the clergy,
————————– 2. spades – the nobility (from the Italian word ‘spada‘ – sword),
————————– 3. clubs – the agrarian sector (peasantry) and
————————– 4. diamonds – the citizens (burghers).
Fig. 225 – Left: The playing card as a symbol of the four classes. The ‘diamond jack’ printed from a wood block; around 1400 (MEGGS, 1983). Right: Backside of a card of the ‘Verenigte Stralsunder Spielkartenfabriken A.G.’, around 1915. The backside of cards often has a tetragonal symmetry (JANSSEN, 1985).
In every game are four phases:
1. The invisible invisibility. Most games have an invisible, mystical element. Every player knows about the experience of the undefinable forces of luck. Intuition and talent (how to play a game) are mystical commodities.
2. The invisible visibility. Some elements can be qualified, like the rules and the theory of the game. It is – theoretically – possible to reach a higher knowledge and capability to play the game.
3. The visible visibility. The actual playing of the game. The performance provides the moment of truth in this particular type of (regulated) communication.
4. The visible invisibility. Repetition of the game results in experience, which can be used in future games. Experience is an addition and a mirror image of the theoretical knowledge gathered in the second phase. Practical understanding can improve the performance.
Most games are played with the intention of winning. A game consists of a number of actions, performed individually or collectively, following certain rules and agreements, and resulting in a winning and a losing party. The game is a system for achieving superiority (Adler) within a dualistic frame-work.
Robert AXELROD (1984) studied an interesting ‘tetradic’ game in his book ‘The Evolution of Co-operation’. The game is called the ‘Prisoner’s Dilemma‘ and has references to a four-fold way of thinking. Two players get maximum points if they both work together (mutual co-operation) and minimal points if they both work against each other (mutual defection). In the intermediate positions, the one who co-operates is more punished than the one who defects. The following scheme gives the possibilities and valuation of the ‘Prisoner’s Dilemma’-game (AXELROD, 1984; fig. 1, p. 8; NOWAK et al., 1995):
PLAYER II (Column Player)
co-operation I = 3 I = 0 punishment
II = 3 II = 5 reward
both work together
(Row Player) defection I = 5 reward I = 1
II = 0 punishment II = 1
The distribution of the (score)points in the ‘Prisoner’s Dilemma Game’ is given above. The game is an archetypal communication between two players and two possibilities of choice (Player I/II and co-operation/defection).
AXELROD (1984) tried to analyze the traces of Fortuna by organizing a ‘Computer Prisoner’s Dilemma Tournament‘, giving game-theoreticians of different disciplines (economy, psychology, sociology, political science and mathematicians) the opportunity to search for ‘solutions’. As it turned out, the best way to play this game was the ‘tit for tat‘-method, which means that – after an initial co-operation – every move of the opponent was repeated (co-operation on reciprocity).
NOWAK et al. (1995), in their article on the ‘Arithmetics of Mutual Help’, defined the possibilities to win more accurate by looking at the results of the previous round (and not only to the move of the opponent). The computer can generate patterns – in a spatial setting and under specific circumstances – which are similar to the four-fold symmetry of ‘Persian rugs’. LLOYD (1995) described a computer-program, which produced the outcome of the ‘Prisoner’s Dilemma’-game in tetradic-symmetrical patterns.
The conclusions in the game-theory confirm the behavior of the goddess Fortuna: only the reduction of the four-division (of the initial setting) to a two-division (‘tit for tat‘) creates an environment to ‘win’.
This same element (of reduction to a dual concept) is present in the world of prediction. Prediction is always closely related to division thinking, of choosing positions and view points and – finally, for the time being – believing in the position of the observer. There must be a mutual trust and confidence in the acceptance of the boundaries within a communication if a prediction will be valuable.
The form and function of prediction in a society are an indicator of the way trust/belief is handled and worth studying. There were times when the rulers had great confidence in the words of soothsayers when important political events or wars were eminent. However, in other epochs, like the present one in Europe, the importance of detailed predictions is played down and regarded as ‘unscientific’. Despite this overall feeling, there is a lot of planning going on, in particular in big hierarchic organizations. Many civil servants are engaged in government-sponsored planning-offices, producing figures and graphs to assist the never-ending task of political decision taking. Figures are a necessity as political power tools.
In other cultures – like the Chinese – the element of belief has never faded away. Prediction – ritualized in acts of worship – is still alive as a means to communicate with a godhead. The more worldly derivatives of certain games of chance and gambling-in-general enjoy a long history in the Chinese culture (fig. 226/227). Lillian Lan-ying TSENG (2004) wrote an excellent article on the TLV mirror, which brought these subjects together.
Fig. 226 – Prediction was a holy and spiritual exercise in the Chinese Han Dynasty of the second century AD. Priests employed the so-called TLV-mirror to read the future. The mirror is believed to represent a square earth and a round heaven. This illustration gives a detail from the ‘Tomb of the painted Basket’, Harada – Lo Lung, China. Drawing (detail) by W.P. Yetts in: HADINGHAM (1983).
Fig. 227 – Implements from the game of Liubo. Late third century B.C.E. The pattern found on the surface of Liubo boards is associated with the TLV mirrors, which were common in the Han Dynasty. Fig. 6 in: TSENG, Lillian Lan-ying (2004).
The connection between game, prediction and belief is long established. Alternatively, like WHITEHEAD (1926) put it: ‘Religion and play have the same origin in ritual. (…) A holy day and a holiday are kindred notions.’ He distinguished four elements in the manifestation of religion: ritual, emotion, belief and rationalization. The aim of religion is an increase of emphasis.
Whitehead’s division is, in quadralectic terms, an expression of the four quadrants: 1. belief (I); 2. ritual (II); 3. rationalization (III) and 4. emotion (IV). Whitehead (1926; p. 18) saw the ritual as the primary religious factor, followed by emotion. And he continued: ‘Perhaps it is true to affirm that the later factors are ever wholly absent. But certainly, when we go far enough back, belief and rationalization are completely negligible, and emotion is merely a secondary result of ritual.’ He pointed to loneliness as the cornerstone of every devout experience: ‘The great religious conceptions which haunt the imaginations of civilized mankind are scenes of solitariness.’
The (Second Quadrant) ritual offers the first insight in a ‘full communication’: an invisible god (I) is worshiped by rules and customs (II), supported by attributes (III), which are emotionally experienced by the worshiper (IV).
Fig. 228 – Left: An African divination tray of the Yoruba. Ifa-tribe, Ekiti, twentieth century. Wood, diameter 19 inch. See also: William Russell Bascom’s book ‘Ifa divination: communication between gods and men in West Africa’ (BASCOM, 1969). Right: Scheme of the positions of a plate by ‘babalawo‘ (father or master of the mysticism) Kolawole Ositola; Ijebe, Nigeria. A drawing by H.J. Drewal. In: DREWAL & PEMBERTON III (1989).
In certain parts of Africa, in particular by the Western African tribe of the Yoruba, the divination tray is used to predict the future (fig. 228). These trays are utilized by the diviner, who draws three lines (‘paths’) on the surface at the outset of a divination to ‘open’ channels of communication. The lines connect the countless competing forces of the universe as crossroads. Subsequently, the diviner reads their significance for an individual or group (DREWAL & PERBERTON, 1989). The holy act to establish a better awareness of the position in the universe has all the ingredients of a ritual game.
The attention to the game as an independent means of communication was raised around the year 1500 and clearly expressed in the work of Hieronumus Cardanus (1501 – 1576). His book on the games of chance – ‘Liber de ludo aleae’ (GOULD, 1953/1961; ORE, 1953) – was written around 1520, when he was a rector at the university of Padua. Cardanus’ life was an example of the ‘pivotal’ times in which he lived. His autobiography provided a good insight in the dualistic character of the European cultural history. He wrote ‘De Vita Propria Liber’ in 1575, a year before his death.
The year 1539 was a turning point in Cardanus’ life. He reached the state in which he ‘ceased to be poor because he had nothing left to lose’ (STONER, 1962), but then fortune came his way. He personified his time as a physician, philosopher, mathematician, astronomer and oneirocritic (FIERZ, 1977), with the attraction of extremes as the central theme.
Aristotle’s’ warning against gambling (in the ‘Ethica‘) was never taken seriously and particular with the arrival of the printing press and the cheap availability of playing cards – games of chance became a widespread pastime. GOULD (1953/1961) stated: ‘in times of great fear and sorrow, when even the greatest minds are much disturbed, gambling is far more efficacious in counteracting anxiety than a game like chess.’
Henry Cornelius AGRIPPA von Nettesheim (1486 – 1535) gave – in his book ‘De Occulta Philosophia’ (1531; 1651/1986) – a methodical description of the cabalistic system. This body of knowledge had its roots in the (dualistic) Jewish culture, but found a fertile feeding-ground in the twelfth and thirteenth century, when the European culture itself was searching for an identity. Southern France – with the Cathars, carrying a rejuvenated form of dualistic thinking – and Spain – with the intermingling of Arab and Jewish ideas in a spirit of dualism – furnished the mind-material to (gradually) break down the reign of tetradic thinking.
The Book ‘Zohar‘ was written in Spain at the time of Raymond Lull (around 1280/90) and became the main text of the Cabala. Four-fold aspects were present, but they were derived from a dynamic two-division, rather than a tetradic environment. The Book ‘Zohar’ mentioned, for instance, four cabalistic principles:
A possible explanation of the four phases in cabalistic thinking from a quadralectic point of view is given as follows:
1. The ‘En-Sof‘, the infinity, or boundless nothingness, is here compared with the First Quadrant. Four emanations are envisaged to develop from the ‘En-Sof‘:
—————————– a) Atsiluth (emanation)
—————————– b) Beriah (creation)
—————————– c) Yetsirah (formation)
—————————– d) Asiah (action)
These characteristics resemble the characteristic dynamic principles of the four quadrants (in quadralectic thinking);
2. An original unity emerges from the Nothingness, identified as the Crown (the Will) above the wheel of life. This unity differs from the (quadra-lectic) Second Quadrant, which is a distinct area of pluriformity (ideas), of which unity (in its ‘Third Quadrant’, II,3) is only a subdivision;
3. The Division of Opposites results in the First Man (Adam Kadmon). This visibility coincides with the (quadralectic) Third Quadrant;
4. The Union of Opposites takes place in the fourth phase. This stage is comparable with the Fourth Quadrant, but there is – again – a reversal from uniformity to pluriformity. The Unity (of the fourth phase) should be placed in the ‘Third Quadrant’ of the Fourth Quadrant (IV,3). Unity is symbolised in the ‘Sefiroth‘ – a ten-division – offering a view of the celestial man. ‘The Sephiroth of the Cabala are really Divine Names as creative principles’ (YATES, 1966; p. 178).
The cabalistic system puts an emphasis on boundaries and, subsequently, projection of the boundaries into the future is a tempting option. Divination is a logical outcome of a dynamic communication, when a belief (in division) is combined with a certainty (future).
In the same period as Cardanus lived the French apothecary and seer Michel de Nostredame, also known as Nostradamus (1503 – 1566). The first complete edition of his predictions dated from 1568 (CENTURIO, 1977/1985). The – often cryptic – description of future events, combined with a chaotic sequence of the quatrains, allowed a great variety of interpretations. Maybe this is one of the reasons, that his work has shown such a remarkable historical resilience.
Nostradamus envisaged in the early twenty-first century the biggest battle of all times against a yellow invasion from Asia. We will be saved by Henry the Happy of France, ‘the phoenix of the good king Henry IV’ and a united Europe will enjoy seventy-five years of peace. To quote dr. Centurio:
‘If the beginning of this period is placed around 2040, then our future offspring will reap the harvest of peace of the seeds which we and the next two generations scattered in blood and tears’.
In the meantime, Henry the Happy lives in the area of Le Mans, where he was born on Thursday the 21th January of 1981… (fig. 229).
Fig. 229 – Location Le Mans (France, September 2001).
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