Monday 6 June 2011

Ancient binary symbolism and why it is relevant today

It is a well-known fact the human use of binary strings (or even binary numbers, see Pingala) predates electronics and automatic calculators by thousands of years.

Divination was probably the earliest human application for binary arrays. There are several systems in Eurasia and Africa that assign fixed semantics to bitstrings of various lengths. The Chinese I Ching gives meanings to the 3- and 6-bit arrays, while the systems used in the Middle East, Europe and Africa tend to prefer groups of 4 and 8 bits.

These systems of binary mysticism have been haunting me for quite many years already. As someone who has been playing around with bits since childhood, I have found the idea of ancient archetypal meanings for binary numbers very attractive. However, when studying the actual systems in order to find out the archetypes, I have always encountered a lot of noise that has blocked my progress. It has been a little bit frustrating: behind the noise, there are clear hints of an underlying logic and an original protosemantics, but whenever I have tried to filter out the noise, the solution has escaped my grasp.

Recently, however, I finally came up with a solution that satisfies my sense of esthetics. I even pixelled a set of "binary tarot cards" for showing off the discovery:

For a more complete summary, you may want to check out this table that contains a more elaborate set of meanings for each array and also includes all the traditional semantics I have based them on.

Of course, I'm not claiming that this is some kind of a "proto-language" from which all the different forms of binary mysticism supposedly developed. It is just an attempt to find an internally consistent set of meanings that match the various traditional semantics as closely as possible.


In my analysis, I have translated the traditional binary patterns into modern Leibnizian binary numbers using the following scheme:

This is the scheme that works best for I Ching analysis. The bits on the bottom are considered heavier and more significant, and they change less frequently, so the normal big-endian reading starts from the bottom. The "yang" line, consisting of a single element, maps quite naturally to the binary "1", especially given that both "yang" and "1" are commonly associated with activity.

I have drawn each "card picture" based on the African shape of the binary array (represented as rows of one or two stones). I have left the individual "stones" clearly visible so that the bitstrings can be read out from the pictures alone. Some of the visual associations are my own, but I have also tried to use traditional associations (such as 1111=road/path, 0110=crossroads, 1001=enclosure) as often as they feel relevant and universal enough.

In addition to visual associations, the traditional systems have also formed semantics by opposition: if the array 1111 means "journey", "change" and "death", its inversion 0000 may obtain the opposite meanings: "staying at home", "stability" and "life". The visual associations of 0000 itself no longer matter as much.

The two operations used for creating symmetry groups are inversion and mirroring. These can be found in all families of binary divination: symmetric arrays are always paired with their inversions (e.g. 0000 with 1111), and asymmetric arrays with their reversions (e.g. 0111 with 1110).

Because of the profound role of symmetry groups, I haven't represented the arrays in a numerical order but in a 4x4 arrangement that emphasizes the mutual relationships via inversion and mirroring. Each of the rows in the "binary tarot" picture represents a group with similar properties:
  • The top row contains the four symmetrical arrays (which remain the same when mirrored).
  • The second row contains the arrays for which mirroring and inversion are equivalent.
  • The two bottom rows represent the two groups whose members can be derived from each other solely by mirroring and inversion.
The semantics within each group are interrelated. For example, the third row ("up", "in", "out", "down") can be labelled "the directions". In order to emphasize this, I have chosen a pair of dichotomies for each row. For example, the row of the directions uses the dichotomies "far-near" and "horizontal-vertical", and the array called "up" combines the poles "far"+"vertical". All the dichotomies can be found in my summary table.

The arrays in the top two groups have an even parity while those on the bottom two groups have an odd parity. This difference is important at least in Al-Raml and related systems, where the array getting the role of a "judge" in a divination table must have an even parity; otherwise there is an error in the calculation.

The members of each row can be derived from one another by eXclusive-ORing them with a symmetrical array (0000, 1111, 0110 or 1001). For this reason, I have also organized the arrangement as a XOR table.

The color schemes used in the card pictures are based on the colors in various 16-color computer palettes and don't carry further symbolism (even though 0010 happens to have the meaning of "red" in Al-Raml and Geomancy as well). Other than that, I have abstained from any modern technological connections.

But why?

Our subjective worlds are full of symbolism that brings various mental categories together. We associate numbers, letters, colors and even playing cards to various real-world things. We may have superstitions about them or give them unique personalities. Synesthetics even do this involuntarily, so I guess it is quite a basic trait for the human mind.

Binary numbers, however, have remained quite dry in this area. We don't really associate them with anything else, so they remain alien to us. Even experts who are constantly dealing with binary technology prefer to hide them or abstract them away. This alienation combined to the increasing role of digitality in our lives is the reason why I think there should be more exposure for the various branches of binary symbolism.

In many cultures, binary symbolism has attained a role so central that people base their conceptions of the world on it. A lot of traditional Chinese cosmology is basically commentary of I Ching. The Yoruba of West Africa use the eight-bit arrays of the Ifa system as "hash codes" to index their whole oral tradition. Some other West African peoples -- the Fon and the Ewe -- extend this principle far enough to give every person an eight-bit "kpoli" or "life sign" at their birth.

I guess the best way to bring some binary symbolism to our modern technological culture might be using it in art. Especially the kind of art such as pixel art, chip music and demoscene productions that embrace the bits, bringing them forward instead of hiding them. This is still just a meta-level idea, however, and I can't yet tell how to implement in it practice. But once I've progressed with it, I'll let you know for sure!


Kartturi said...

Interesting! However, it would be nice if you gave the sources for this information.
Okay, there are four items listed at the end of crosstrad-4bit.html
Any others? Do you have read books of Marcia Asher, for example?

Pingala's work I first encountered in Knuth's History of combinatorial generation, still available here:

For a very inspiring set of graphical representations of various ways to organize binary systems, please see the user Lipedia's images at Wikimedia:

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