TIM BOUCHER RAW!

An entity ‘complete unto itself’ (I) is, ultimately, incomplete until it develops transactional relationships with other entities from which it derives meaning, purpose, value and context. For example: any word, when excised from the context of the language and culture which spawned it, is without meaning. Gibberish. All of existence, it can be said, is a negotiation of co-sovereign beings and forces (I and I): complex transactions, trades, bargains and negotiations taking place simultaneously and continuously up and down all micro- and macroscopic scales.

The business of life, then, might be meaningfully broken down to the determination of how these transactions go. When one perceiving center perceives another, their mutual perception is a kind a trade. I can see you and you see me. If I smile, do you smile back, ignore me, or frown? When you touch someone’s hand, their hand touches you back. There are many kinds of touching: pleasurable, painful, exploratory, grasping… Likewise, when we trade or conduct social transactions with one another, our actions may serve many purposes. We may be benefiting ourselves. We may be attacking or punishing an opponent. We may be giving a gift without expectation of compensation, or asking a favor of a friend (drawing on a previous store of value). We may be mutually entertaining one another. We may be working towards the same goal, and breaking down a complex goal into constituent parts. Whatever the end result, human culture has crafted ritual structures to guide us through the sometimes bewildering but fundamentally essential act of trade.

In a world without shopping malls and mega-stores, the market or bazaar is a place where one can go to buy, sell, barter, trade or exchange. If you grow a quantity of edible crops or brew beer in excess of what your family, friends and neighbors can eat and drink, you can take it to market and trade for things you need but which you can’t – or haven’t – produced yourself. The act of selling and buying, of bargaining and negotiating is a ritual which varies according to local culture and custom. Unlike the big retail chains of North America, other market-cultures thrive on haggling over prices – though there is often a set pattern to the exchange: the seller over-prices initially causing the buyer to low-ball; the seller reconsiders, lowering their asking price; the buyer thinks better, offers slightly more, but still below the asking price; and somewhere in the middle a deal is struck.

As a hub for exchange, the marketplace develops around it a kind of pidgin language: bits and pieces of cultural expressions pulled from each of its participant groups. Chinese culture, for example, developed a system of numerical hand gestures as a means of compensating for dialect differences in the marketplace (also see Colombian numerals). Likewise, concepts of fairness and right-dealing are tested and their boundaries negotiated in the marketplace. In the tabulation of sales, its interesting to note that “Chinese, Korean and Japanese tally marks use the five strokes of [...] the character meaning ‘correct’, ‘proper’ and ‘honesty’.” Some scholars speculate that tally marks are in fact the precursors of writing: that cuneiform evolved out of trade records. Many cultures have also used counting tables to keep track of quantities measured out for trade.

In outdoor markets of those times, the simplest counting board involved drawing lines in the sand with ones fingers or with a stylus, and placing pebbles between those lines as place-holders representing numbers (the spaces between 2 lines would represent the units 10s, 100s, etc.). The more affluent people, could afford small wooden tables having raised borders that were filled with sand (usually coloured blue or green).

The modern term “calculus” actually comes from the Roman calculi, pebbles shifted back and forth on counting tables as measures of quantities traded. In Medieval Europe, you find the jetons, small tokens or coin-like medals used as counters in calculation or as a substitute for money in games: like the poker chips of today.

The abacus, of course, is probably the most widely recognized ancient counting system – though probably the least understood in Western culture today. The Roman counting tables eventually evolved into the Roman abacus, with close parallels to the Chinese abacus or suanpan. The suanpan typically is composed of a frame, through which are strung beads in columns. The beads are separated by a divider into 2 upper or heavenly beads and 5 lower or earthly beads.

The columns are much like the places in Arabic numerals: one of the columns, usually the rightmost, represents the ones place; to the left of it are the tens, hundreds, thousands place, and so on, and if there are any columns to the right of it, they are the tenths place, hundredths place, and so on.

The upper beads count for 5 in their column and the lower beads for 1, and the suanpan can be utilized for hexadecimal or decimal calculations. The Japanese abacus, or soroban, has 1 heavenly bead in each column and four earthly beads. Its method of operation is to slide beads inwards toward the ‘reckoning bar’. So, if you wanted to indicate the number nine, you take the rightmost bead column, and slide downward one heavenly bead and slide upwards four earthly beads. To add one, you perform a carry operation, sliding the beads in the 1’s column back to zero position, and sliding up one earthly bead in the 10’s column to the reckoning bar to indicate a value of ten. Contests are routinely held to test electronic calculator users against soroban users. The results would surprise most Westerners!

Many soroban experts are also proficient in mental calculation, known as anzan (???, “blind calculation”) in Japanese and as ànsuàn in Mandarin Chinese. They do this by mentally visualizing the soroban (or any other abacus) and working out the problem without trying to figure out the answer beforehand. This is one reason why, despite the advent of handheld calculators, some parents send their children to private tutors to learn the soroban. Proficiency in soroban calculation can be easily converted to mental arithmetic at a highly advanced level.

Many classical techniques exist the world over in which one can use one’s fingers to count not just from 1 to 10, but up to 99, or even up to 1,023. A Korean finger-counting system called chisanbop elegantly reflects the Japanese-style soroban abacus. In Chisanbop, the right hand is essentially the ones column of the abacus. The fingers (but not the thumb) each stand for one – like the earthly beads. The thumb stands for five, like the heavenly beads. So, to indicate the numeral 3, one uses three fingers. To indicate 7, one uses the index and middle finger with the thumb. Once 10 is reached, the index finger on the left hand is used and the fingers and thumb on the right relax. So, to indicate 66, one would hold up the index fingers and thumbs on both hands.

Counting on the fingers (and toes; ie, digits) is so elemental a human activity that most people don’t give it a second thought. But imagine living in a pre-literate culture with no concept of numerals, no 1 through 9, no zero. Objects being counted in such an ethnomathematic system would not be assigned an abstract figure. Instead, each new item reckoned would be another tally mark, another stick in the pile, another calculus, another jeton, another finger…

Many West African languages base their number words on a combination of 5 and 20, derived from thinking of a complete hand or a complete set of digits comprising both fingers and toes. In fact, in some languages, the words for 5 and 20 refer to these body parts (e.g., a word for 20 that means “man complete”).

Fingers and hands, meanwhile, are the instruments of the execution of our will in the world, of our deftness and dexterity in the manipulation of objects and the practical tools of exchange in the marketplace. Money passes from hand to hand. In finger-counting games like Morra (or its cousin, rock-paper-scissors), the number of fingers displayed by competitors may be used to settle disputes, make wagers, for entertainment or as a selection method (similar to drawing straws or the casting of lots – sortes in ancient Rome; see also: Eeny-meeny-miney-mo and other counting-out rhymes).

In another version one person is designated the “odds” player while the other is labeled “evens”. Players hold one hand out in front of them and count together to three (sometimes chanting “Once, twice, thrice, SHOOT!” or “One, two, three, SHOOT!”). On three (or “shoot”), both players hold out either one or two fingers. If the sum of fingers shown by both players is an even number (i.e. two or four) then the “evens” player wins; otherwise the “odds” player is the winner. Since there are two possible ways to add up to three, both players have an equal chance of winning. In New York City and Long Island in the 1950s, the game was called “choosies,” and would be invoked to resolve a playground dispute by one antagonist saying, “let’s shoot for it.” In Boston at about the same time, the term in use was “bucking up.” Some variants of Morra involve money, with the winner earning a number of currency units equal to the sum of fingers displayed.

Divination, determination of the will of the gods, by the casting of lots is called cleromancy. It’s use is mentioned many times in the Bible, notably:

In the Book of Joshua 7:11-22, God commands that a thief be found by casting lots, first among the tribes of Israel, then among the families of that tribe, etc. Achan, the person identified in this way, confesses his guilt, and shows where he has buried the loot.

In the First book of Samuel 10:17-24, the people of Israel demand God to set a king over them, and God decrees a king to be found by a procedure similar to the above, leading to the selection of king Saul.

The Old Testament objects known as Urim and Thumimm, said to be stones in the breastplate of the high priest are thought to have been similar tools for divination. Along the same lines, many ancient divination tools had overlapping usage as gaming or gambling devices. Consider the astragalus, a bone in the ankle or hock of a sheep, referred to erroneously as knucklebones, and played throughout the world.

The game was usually played like the modern game of “jacks”: one threw the knucklebones in the air and attempted to catch as many as possible. They were also used like modern “dice.” Each of the four long sides of the knucklebone had a value: the convex side was worth 3, the concave 4, and the two flat sides 1 and 6.

The Mongolian version of the same practice is called shagai and may be done for entertainment or fortune-telling. In Malaysia, the game of batu seramban occupies the same cultural position (even being played in zero-gravity by a Malaysian astronaut). A variant of this game called five stones continued through to at least colonial America, and the game of jacks is basically the same pattern. The use of games allows both children and adults to practice, experiment and play with behaviors and emotions typical to the marketplace and thereby society: trading, valuation of goods, tabulation of quantities, rule-following (legality), distribution and hoarding of wealth, strategy, skill and chance.

In especially African traditional cultures (such as the practices of the South African sangoma), we hear about “throwing the bones” as a means of understanding constellations of energies, natural forces and the activities of unseen beings such as gods and spirits.

The divining bones are not strictly all bones but comprise shells, money, seeds, dice, domino-like objects or even dominos themselves, and other objects that have been appointed by the sangoma and the spirit to represent certain polarities (for instance a miniature car to represent a journey). Animal bones from lions, hyenas, anteaters, baboons, crocodiles, wild pigs, goats, antelopes and others form the large majority of the objects in the sangoma’s bag, and there are bones for all psycho-socio-spiritual polarities. The bones represent all of the forces that affect any human being, anywhere, whatever their culture.

And from another source:

P.H. used the bones for everything. He would make a throw first thing in the morning, before he was even out of bed, to see what the day would bring. He would see how many people would be coming that day for treatment, if they were male for female, and what their ailments were. He would then throw the bones to diagnose with more detailed information once the patient arrived. The threw the bones to find out how to work with me, and on a daily basis what our lessons would be. Throwing the bones for P.H. was his main source of communication with his ancestors, his helping spirits.

Fortune-telling and gambling are inextricably intertwined in that they rely on unpredictable, random or chaotic patterns and processes. The I Ching indicates trends implicit in the balance of yin and yang energies at any given moment and points towards strategies likely to yield success. The gambler rides the knife-edge of the moment, intuitively divining the proper course of action from tells on the other players, his cards, the odds and the amount to be won or lost. As in life, at the enclosed ritual space of the gambling table, the gaming board, he may win it all or he may be brought back down to nothing, to zero* (*0 is a gift from Hindu mathematicians, to be discussed shortly). The very Daoist Rota Fortuna of the Tarot Deck, which finds a place again on the gaming tables:

In some European countries, the design of the [Nine Men's Morris] board was given special significance as a symbol of protection from evil,[1] and “to the ancient Celts, the Morris Square was sacred: at the center lay the holy Mill or Cauldron, a symbol of regeneration; and emanating out from it, the four cardinal directions, the four elements and the four winds.”

Aside from condemning divination as witchcraft and sorcery, Medieval European Christian culture was careful to separate games according to those of chance, such as dice, and those of skill – chess being the prototypical example of the latter category. Folk culture, however, inextricably combined the two at all times and in all ways. Variants of chess exist, in fact, in which the die is used to determine which pieces may be moved (also see: tic-tac toe chess).

The Libro des los Juegos is a medieval “…treatise that addresses the playing of three games: a game of skill, or chess; a game of chance, or dice; and a third game, backgammon, which combines elements of both skill and chance.” Further,

These games are discussed in the final section of the book at both an astronomical and astrological level. Extrapolating further, the text can also be read as an allegorical initiation tale and as a metaphysical guide for leading a balanced, prudent, and virtuous life [...]

Among its more notable entries is a depiction of what Alfonso calls the ajedrex de los quatro tiempos (“chess of the four seasons”). This game is a chess variant for four players, described as representing a conflict between the four elements and the four humors. The chessmen are marked correspondingly in green, red, black, and white, and pieces are moved according to the roll of dice.[2] Alfonso also describes a game entitled “astronomical chess”, played on a board of seven concentric circles, divided radially into twelve areas, each associated with a constellation of the Zodiac.

[See also: Napier's bones, and the Napier Chessboard Calculator.]

The Hindu culture which created the eminently useful zero as a placeholder was built upon the strong foundation of Vedic mathematics. The Vedas, five thousand year old storehouses of cultural and spiritual information, contain mathematical sutras written in verse “to ensure that information would be preserved even if written records were damaged or lost.” Within the context of the Vedas, “…mathematical formulas and laws were often taught within the context of spiritual expression (mantra). Thus while learning spiritual lessons, one could also learn mathematical rules.” And by cultivating “…transcendental knowledge, one can also come to understand the intricacies of the phenomenal world. By the process of knowing the absolute truth, all relative truths also become known.”

In ancient India, mathematics served as a bridge between understanding material reality and the spiritual conception. Vedic mathematics differs profoundly from Greek mathematics in that knowledge for its own sake (for its aesthetic satisfaction) did not appeal to the Indian mind. The mathematics of the Vedas lacks the cold, clear, geometric precision of the West; rather, it is cloaked in the poetic language which so distinguishes the East. Vedic mathematicians strongly felt that every discipline must have a purpose, and believed that the ultimate goal of life was to achieve self-realization and love of God and thereby be released from the cycle of birth and death. Those practices which furthered this end either directly or indirectly were practiced most rigorously. Outside of the religio-astronomical sphere, only the problems of day to day life (such as purchasing and bartering) interested the Indian mathematicians.

Aside from spiritual focus and direction, the benefits of the ancient Vedic maths is comparable to the mental calculation skills gained by masters of the Japanese soroban abacus:

Utilizing the techniques derived from these sutras, calculations can be done with incredible ease and simplicity in one’s head in a fraction of the time required by modern means. Calculations normally requiring as many as a hundred steps can be done by this method in one single simple step.

Compare that level of knowledge and practical mathematic skill to that of the average American, who can barely calculate change out of a twenty for a Happy Meal, or the grocery stores which don’t trust their cashiers enough to let them count out pennies – instead replacing that essential human functionality with counting machines. It occurs to me, in the study of these various maths and techniques mostly lost to Western culture that we have given up, offloaded and unnecessarily mystified basic parts of not just our mental operation, but of our own physicality as countable beings in the world. Now someone else is doing the counting and we have become chips on their board: corporate goods to be bought, sold, shuffled around and wagered upon in an invisible marketplace to which we weren’t invited, except as chattel, chained and bound to someone else’s valuation of our lives. It is essential, therefore, that we as humans go back and reclaim our natural latent genius – lost maths, forgotten algorithms, hidden systems – and become our own masters.

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