Wednesday, August 21, 2013

Excerpt 8: Divination and Games

This same pattern played out again and again, in China, Europe, Babylonia and the Americas as well as Africa: games of chance and skill, with their discrete states and physical markers, were invariably associated with divination.
Upon comparing the games of civilized people with those of primitive society many points of resemblance are seen to exist, with the principal difference that games occur as amusements or pastimes among civilized men, while among savage and barbarous people they are largely sacred and divinatory. This naturally suggests a sacred and divinatory origin for modern games, a theory, indeed, which finds confirmation in their traditional associations, such as the use of cards in telling fortunes.[1]
When we think of divination as a kind of game, as a way of generating new sentences from thin air, the problem of predictive accuracy is marginalized. The system was generally set up so that whatever sentence was generated would be a true sentence, because the truths encoded in the system were general truths, applying universally.
…The experiential (both recreational and revelatory) value of divination and board-games is that they create an unlimited variety of vicarious experiences, i.e. stories. Spinning relevant, even illuminating and redeeming stories out of the raw material which the fall of the apparatus in combination with the interpretative catalogue provides, is the essence of the diviner’s skill and training; and in the same way board-games can be seen as machines to generate stories. [2]
Nearly all of the ancient board games were associated with divination at one time or another.
Senet: Senet was a board game played in Egypt from around 3500 BC. Tomb paintings show the importance that Egyptian society placed on the game. A successful player of Senet was assumed to be under the protection of Ra and Thoth, since the chance fall of the throwing sticks was believed to be under their control. (For this reason Senet boards are of found among the items buried to be taken into the afterlife.)

The Royal Game of Ur: Dating to about 2600 BC, this game was played in Mesopotamia. Like Senet, it was a race game something like Backgammon. This game had certain squares thought to bring good fortune.
Go: The most prominent Chinese board game, Go was invented by the third century BC. The Go board was also used for divination, by casting the black and white stones and analyzing the patterns of how they fell. As Ban Gu described in The Essence of Go in the first century AD, “The board must be square and represents the laws of the earth. The lines must be straight like the divine virtues. There are black and white stones, divided like yin and yang. Their arrangement on the board is like a model of the heavens.” As in Mancala, the patterns were associated with a model of the world.

Chess: There are multiple theories on the origin of chess, but one possibility is that it stems ultimately from Chinese divination methods. Chess historian Joseph Needham writes:
The game of chess (as we know it) has been associated throughout its development with astronomical symbolism, and this was more overt in related games now long obsolete. The battle element of chess seems to have developed from a technique of divination in which it was desired to ascertain the balance of ever-contending Yin and Yang forces in the universe…. It appears that the pieces on the board in this divination technique represented the sun, moon, planets, stars, constellations, etc. The suggestion is that this “game” passed to 7th-century India, where it generated the recreational game conceived in terms of battling human armies… “Image-chess” derived in its turn from a number of divination techniques which involved the throwing of small models, symbolic of the celestial bodies, on to prepared boards. Thus there was a dice element as well as a move element, and there were many intermediate forms between pure throwing and placement followed by combat moves. All these go back to China of the Han and pre-Han times, i.e. to the -4th or -3rd century, and similar techniques have persisted down to late times in other cultures.[3]
Dr. John Dee, astrologer to Queen Elizabeth II, invented a four player chess variant called “Enochian Chess,” which was designed explicitly for use in divination. Unlike random divination, it was thought that players could influence the outcome of fate through their actions on the board.

Cards: Playing card games are associated with the development of fortune-telling via Tarot cards (from which the common playing card is a simplified derivative). In the 1500s in Italy, a dealt hand of cards was used as a kind of random poetry generator. The poet would need to fit the images on the cards or their meanings into his poem. This practice was known as “tarocchi appropriati.” The fortune telling aspect of Tarot cards seems to have evolved from this game.

Divination and Mathematics
These games and divination systems are remarkably old. Consider the die used in most games of chance: the reason it has pips instead of numbers on the faces is that the form of the die settled into its present form before the invention of Arabic numerals.
Divination drove the development of mathematics: much of Mayan, Egyptian, and Babylonian mathematics were used for astrological purposes. For example, our measurement of time and angles come from Babylonian astrologers’ division of the heavens in their base 60 system.[4] The most advanced mechanical computers from Greek and from Arab inventors in the ancient world were complex representations of the heavens, used for navigation and astrology. The Antikythera mechanism (often called the first mechanical computer) is the best known of these, as few others have been preserved. Found in a shipwreck and dating from around 200 BC, it showed the position of all the known planets, the sun, and the moon, requiring over 30 gears to do so. Modern scientists, who find such a device fascinating for the level of mechanical sophistication it displays, seem reluctant to admit that the only practical use such a device could have had was casting horoscopes and determining auspicious days. Watching how the planets move back and forth around the wheel of the zodiac on a recreation of this device, it is not hard to see how such an irregular motion would give the impression of an intelligent and willful plan being acted out. Early attempts by archaeologists to understand the device focused on the words inscribed on it, and were unsuccessful. It was only when an attempt was made to understand the gearing system that the meaning of the device was recovered.
Later, it was the analysis of games of chance that led to the development of probability theory and statistics, which are key components of most modern AI systems, since absolute reasoning is often too brittle to deal with real-world situations.
The combinatoric principles of the I Ching[5] and the geomantic divination (introduced at the beginning of this chapter) inspired the 17th century philosopher Gottfried Leibniz to develop binary notation. These binary codes are found in other divination systems around the world, such as the African Ifa or Sikidy systems of divination. In recent years, the fields of “ethno-mathematics” and “ethno-computation” have begun studying these cultural artifacts to explore the mathematical ideas of non-Western cultures. [6]
Elements of recursion play a large role in these games and divination systems, where the state resulting from a series of actions is the beginning point for the same series of actions, performed again and again. In Mancala, for example, the game is played by choosing one pit, scooping up all the seeds from the pit, and planting one in each of the following pits. The object of the game is to be the first to get all of one’s seeds into the final pit. One strategy to do this is to find a pattern that persists over time, so that the seeds in multiple pits move together in a train. These patterns were discovered and used by experienced players across Africa. In the field of cellular automata, this is known as a “glider.”[7] As a form that maintains itself as it moves through a space divided into discrete cells, it is an important component in the study of these computational systems, a study which only began in the 1940s as computers were invented.
These connections to mathematics are a natural extension of the representational nature of the tokens and spaces used in board games and divination. As a simpler system than the real world, it provided a fertile ground to begin development of mathematical ideas.

[1] Stewart Culin, Gambling Games of the Chinese in America, 1891
[2]Wim van Binsbergen, ibid.
[3] Thoughts on The Origin of Chess by Joseph Needham, 1962
[4] Because 360 is a nice round number near to the number of days in the year in base 60, the ancient Babylonians divided the sky into 360 degrees. (This is easy to accomplish using a compass and straightedge.) The fact that we use 24 hour days and 60 minute hours also derive from this way of dividing up a circle.
[5] The I Ching or Book of Changes is a Chinese method of divination that involves casting small sticks that can land in one of two possible ways. Based on the binary pattern formed by several of these casts, a fortune can be looked up in a book (thus the name).
[6] Viznut, “The Mystery of the Binary,” [Alt] Magazine, 2003
[7] Ron Eglash, African Fractals, 1999 

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