The most sophisticated randomization device for magical divination is the ancient Chinese text, the I Ching, a collection of oracular sayings, scraps of tradition, historical
anecdote, and commentaries organized around sixty-four symbols called hexagrams, graphic images of six lines each.
The original figures of the hexagrams were somehow derived from cracks in turtle shells roasted on an open fire. The lines were first regularized as trigrams of solid or broken lines, then later the Duke of Chou or Zhou created the six-line figures of the hexagrams.
Whether you consult the I Ching by counting off 49 sticks in bunches of four or by throwing three coins six times, you get a single line of a hexagram on each pass and build a complete hexagram with six passes. The stick method is complicated in that each pass through produces a number (9, 8, 6, or 7) and when these are added you know where the line obtained is solid or broken, moving or not. Only the moving lines (or changing lines) have any oracular significance for a reading. The 49 sticks are a primitive mechanical binary computer that generates random binary numbers; a solid line is analogous 1 and a broken line to 0; six combinations of 1 and 0 can produce binary numbers from 1 to 64. The process of counting through sticks or throwing coins is random, but to these random results the Chinese from ancient times assigned specific texts; some of these were believed to be messages of divine origin. There are 6 X 64 line texts from which to choose, or 384 messages in addition to the basic 64, but because some numerical combinations of sticks or coin tosses yield "moving" lines and others do not, the possible combinations are extended enormously. The "sages" who assigned texts to the hexagrams are said to have concluded that the 64 situations, given all these possibilities, were enough to represent all possible human situations. By the time they’d worked out the math they probably figured that this was as good a result as anyone was likely to get
Randomizers of one kind or another have been in use since before the beginning of recorded history. In the west, the most common was the talus or astragalus, the knucklebone or heelbone of a running animal such as a deer or a sheep. This bone when thrown came to rest on one of four more or less equal sides. Astragals have been found in neolithic sites, according to some archaeologists. In ancient Egypt, somewhere around four or five thousand years ago, dice like those we have today were used in gaming and perhaps for divination. Dice games obsessed more than one Roman emperor. Where three dice are used we have some lingering association with divination; the dice were associated in classical imagery with the three graces and these may have been a cosmeticized version of the three fates, who were known with grim irony in the ancient world as "the kindly ones.”
A randomizer is any physical device or system of rules for introducing chance into a series of choices, as in games of chance—shuffling a deck of cards is a randomizer in both senses of the word. All haruspicatory methods are randomizers, but those like dice (bones) and cards and coins are more purely random than tea leaves or entrails or the Ouija board. [FN: although the Ouija board is an interesting special case since it led to the production of James Merrill's very intricate otherworldly poem, The Changing Light at Sandover, which is perhaps the logical extreme of Mallarme's famous modernist poem Un coup de dés jamais n’abolira le hasard (One fall of the dice will never abolish chance).] Given that randomizers are all about chance, their use is perhaps best justified as another version of the surrealist technique of the "exquisite corpse" wherein different artists draw on different parts of a sheet of folded paper, supplied only with information about where the lines end on the previous fold (no peeking!), the final result a composite and possibly synchronistic image.
The connection between randomizers and divination is deep and lasted undiluted until the end of the seventeenth century, when the mathematics of probability were developed. It suggests a worldview, in fact, where nothing is believed to be truly random, but only seemingly so: randomizers held out the prospect of gaining control over impersonal fate while freeing the gamer from individual responsibility. Luck and Fortune were personified as goddesses, and whether or not they were ever seen as anything but allegorical personifications, the idea that luck is a force is on a par with the belief in fate and destiny, or the belief that our lives are ruled by forces so great that we have no power to act freely or make or own decisions or any choices but wrong ones. The problem, of course, is that we must make all our decisions under conditions of relative ignorance. Probability is likelihood considered as a percentage—a measure of likelihood under conditions of chance. (What are the odds?) What is important is that its development gave science a way to make theoretical predictions that did not depend on causality. This means that science is a bet, our best bet some would say. Probability calculations can be used for decision-making in such suboptimal conditions. Even today, business-guru types offer guidance to decision-makers in the form of Bayesian statistical techniques called risk analysis designed to exploit the conditions of ignorance and to offer the illusion—still as ever an illusion—of escape from it. A Bayesian [FN: After Thomas Bayes, an English Presbyterian minister and mathematician opposed to David Hume’s possibly atheistical view of causality.] starts from a position of complete ignorance, chance, where the odds are fifty-fifty, and feeds results of calculations forward into the next trial of statistical calculations, and soon the odds have turned in your favor. How could this be?
There are two schools of thought about probability. Frequentists believe that each new trial has the same odds, a view which corresponds well to the results of successive coin-tosses or die-casts. Frequencies apply to physical systems, such as dice or roulette wheels, where the results even out over the long run. No convinced frequentist will be tempted by the other school, the subjectivists (usually Bayesians), who want to evaluate evidence and therefore have to include beliefs in their calculations. It is easy to see that the probability of belief is intrinsically and ineluctably subjective . . . and a lot of applications, from annuities to poker games, turn out to be about beliefs (anything that can be described as a bet). The I Ching is frequentist in the way it constructs hexagrams, which is wholly mechanical, but subjectivist—in the extreme—in the way it approaches interpreting results.
The rise of probability and statistics in the west was a long process of freeing the mind from its dependence on the belief that every event has a cause, and this development—primarily in mathematical thinking—paralleled a long decline in the belief in similitudes as the underlying causes of all creation. Prior to the New Science, the book of Nature was written by God in the form of similitudes: every leaf of every tree was a page from the book of nature, expressing somehow the divine will, and the overall pattern of things represented, one might say, movements in the mind of God. Spinoza still thought this way about nature, although at an extremely abstract level. Galileo in contrast believed that the Book of Nature was written in the language of numbers.
The idea that there is something divine in similitudes—the idea that every resemblance expresses a divine thought—seems to be at the root of all divination and what is striking is that even randomizers are somehow expressions of something like the divine, call it fate, luck, or the will of heaven. The I Ching is most often read as a Confucian or Taoist work, but it also has a Mohist aspect in its insistence on accord with the law of heaven. The Superior Man, or gentleman, or noble person who is its ideal may be a Confucian sage, a Taoist magician, or a Mohist logician.
When it first reached readers in the West it was soon picked up by C. J. Jung, who offered his theory of “synchronicity,” as he called it, an “a-causal connecting principle.” Jung was proposing that the division of the sticks or the fall of the coins was controlled not by the laws of probability but by some kind of action at a distance that connected the metaphysical world with the mundane.
Jung’s synchronicity is a kind of theory of meaning; coincidences are interpreted as meaningful. The texts (especially the commentaries) in the I Ching supply possible meanings, obscure enough to require imaginative interpretation. The thing about synchronicity (like luck) is that another power does it for you. (It can be treated as a tool for opening the mind to novel trains of thought.) For a mind like Jung’s, probabilities are a bridge between visible and invisible worlds. Since probability itself is already an a-causal connecting principle, it is unclear how synchronicity differs from it; things synchronically connected, no doubt, connect only by chance, unaided by gods, ancestors, or fate. Synchronicity also looks something like the “97anthropic” principle of quantum theory, according to which our observations create the very events we observe.
Now that I think about it, what Jung
was talking about may just be a fancy word for serendipity, where things
come together in a way that
makes us feel good.
Thanks to Jung, we have a word for events that arrive together and in some sense rhyme. Subways and buses run at the convenience of new lovers, eager to meet up somewhere, or one encounters a friend just when one needs to ask a question he is most likely to know the answer to. When things are in harmony, we incline to believe that the harmony is not an accidental combination of random events but one that was somehow determined at another level of reality, where things that belong together are directed to occur together. We all know what it feels like, and it is a very good feeling to be positioned, even for the fractional moment when the dice are in the air, in the center of the universe.
David Rollow’s coauthored paper written with Montgomery Link of the Suffolk University Department of philosophy, on relations in Wittgenstein's Tractatus, has been accepted by the International WIttgenstein Symposium.
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