Most machines have predictable output. The mill, the clock,
the engine, each has a cycle that is unvarying and expected. Even in
prehistoric times, however, people built a different kind of machine, devices
that were generative: they produced original results not explicitly intended by
their creators. One very early example is the family of divination systems used
throughout Africa called geomantic systems. These are still in wide use today,
and we know from inclusions in burials that they were already old when the
Egyptian dynasties were just beginning. They were largely virtual machines, or
software: a set of rules that if followed exactly would provide a result,
rather than a physical apparatus that applied those rules.
The “hardware” of these systems is extremely simple: a grid
of squares drawn in the dirt with a stick, or an array of pits dug into wood or
stone, along with a handful of different colored markers. There are many variations throughout Africa and the Middle East, with layers
of complexity built up over time. A typical example of their use would go
something like this: the fortune-teller takes a handful of seeds and drops a
few into each pit. The seeds are removed from each pit in pairs, leaving either
one or two seeds in each pit. This binary code is recognized by name and used
to pick out an answer to the query from a memorized structure. The code is
sometimes related to the appearance of the symbol string. For example, in one
system the pattern 2-1-1-1, bearing a resemblance to a flag on a flag-pole,
carries a meaning of exultation (in the table below this pattern is labeled
Caput Draconis, perhaps because of its resemblance to the head of the
constellation Draco).
These simple patterns composed of four binary symbols are
generated in groups, and the elements are recombined to derive new patterns,
such as taking the first symbol from the first pattern, the second symbol from
the second pattern and so forth to form a derived daughter pattern from the
original mother patterns. The daughter patterns then could be recombined using
addition (mod 2) to form yet another new pattern, whose meaning modifies that
of the original pattern. The details are strictly passed down within a
tradition, but variants exist across Africa and the Middle East. The patterns
are associated not only with an interpreted meaning, but with the planets, the
elements, the gods, the points of the compass, the signs of the zodiac, and so
forth.
Where did such a system come from? Anthropologists can only
speculate, but the same block of pits and seeds is also used for other purposes
in these societies. For an illiterate population, it is a way of performing
addition, subtraction, multiplication and division in a concrete way that all
parties can verify, by literally reenacting the event being calculated with a
single seed standing for a single item.[1] It performed functions of rewritable
memory that had previously only been possible within the brain. Before the
invention of writing or numbers, it was a system of symbols that represented
other goods, that remapped time and space into an abstract world, with its own
discrete units of space and time.
modified from Games of the Gods by Nigel Pennick, p. 55-63
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I am the revealer of secrets; in me are marvels of wisdom and
strange and hidden things. But I have spread out the surface of my face out of
humility, and have prepared it as a substitute for earth.… From my intricacies
there comes about perception superior to books concerned with the study of the
art.
From this inscription we can see that
the device was personified, yet was presented without pretence as a machine.
Whether using a mechanical device or simply following a set of rules, the petitioners
believed that a mechanical process could behave in an intelligent way. This was
their central discovery: that ideas could be held in objects, and by
manipulating those ideas mechanically, one could learn something new.
The connections with modern computers are more than coincidences.
The same features that made a pitted board useful for tracking heads of cattle
also made it ideal for playing a game and for divination: external symbols that
both players could refer to. Regarding this relationship between games and
divination devices, anthropologist Wim van Binsbergen writes:Another use of the same type of pits and seeds was the board
game Mancala. In Mancala, the pits are said to represent fields and the markers
represent seeds being sown. In this use as well, we see the board acting as a
model of another activity, a simplified model with continuous space and time
replaced with discrete divisions. The seeds and pits resemble the paper tape
and marks along it that Turing imagined in his seminal paper on computation.
Both material divination systems and board-games are formal
systems, which can be fairly abstractly defined in terms of constituent
elements and rules relatively impervious to individual alteration. Both consist
in a drastic modeling of reality, to the effect that the world of everyday
experience is very highly condensed, in space and in time, in the game and the
divination rite. The unit of both types of events is the session, rarely
extending beyond a few hours, and tied not only to the restricted space where
the apparatus (e.g. a game-board, a divining board or set of tablets) is used
but, more importantly, to the narrowly defined spatial configuration of the
apparatus itself. Yet both the board-game and the divination rite may refer to
real-life situations the size of a battle field, a country, a kingdom or the
world, and extending over much greater expanses of time (a day, a week, a year,
a reign, a generation, a century, or much more) than the duration of the
session. In ways which create ample room for the display of cosmological and
mythical elements, divination and board-games constitute a manageable miniature
version of the world, where space is transformed space: bounded, restricted,
parcelled up, thoroughly regulated; and where time is no longer the computer
scientist’s “real time” — as is clearest when divination makes pronouncements
about the past and the future. Utterly magical, board-games and divination
systems are space-shrinking time-machines. [2]
Considered as a way to predict the future, any existing form
of divination will be little better than chance. Its interest for our purposes
lies not in its accuracy, but in the way it brought people to confront the
issues of artificial generation of meaning millennia before the invention of
computers. As a way of holding information and allowing it to be manipulated,
these techniques provided a way of working out possibilities in a safe space.
[1] The first abaci were drawn
in the sand and used pebbles as counters, and later used pits and grooves
carved in wood. The word abacus comes
from the Hebrew abaq, meaning “dust.”
The pebbles (calculi) used in the
Roman abacus are the origin of words such as calculate.
[2]
Wim van Binsbergen, Board-games and
divination in global cultural history (web page), 1997
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