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 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!

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Unified Cross-Traditional Semantics for 4-bit Binary Arrays

By Ville-Matias Heikkilä a.k.a. viznut/pwp; supplements the blog post at Countercomplex.

The Symmetries

Shape ••



Modern binary 0000 (0) 1111 (15) 0110 (6) 1001 (9)
Visual interpretations group of people/things, maximum number of things road, path, single, half crossroads, joining of two figures enclosure, prison cell, link in chain
Unified semantics HOME: stay at home, family (-> people), no change (-> permanence, stability, longevity), enough wealth (-> satisfaction, yin), receiving guests. ROAD: travel (-> messenger), change, exploration (-> new, expanding, yang), being a stranger (-> incompleteness, solitude, sibling). MEET: encounter (-> trade, business, external relations, problems with strangers), join (-> alliance, copulation, children). JAIL: reclusion (-> privacy, secrecy, introspection; -> avoidance, self-restriction, postponing), protection (-> security), chain (-> heritage, unchangeable essence).
4-way grouping + stability separation + movement grouping + movement separation + stability
Greek (unknown) (unknown) (unknown) prison, watch
Greek trigram sun (000) moon (111) hermes / mercury (010) kronos / saturn (101)
Ilm-al-raml assembly road unity, meeting deception, link
Geomantia people, congregation, diurnal moon way, nocturnal moon union prison
Sikidy abundance solitude, death, journey slave, bad thoughts, weights and measures, protection from thieves and enemies vagabond protection, house, food
Ifa double longevity, good journey good visitor children, end of good luck bad visitor, avoid journey
Igbo Afa double bad condition reappear, twice worthless, destructive miss the target
Igbo Afa single home, family, conflict journey, visitor, coming, death, messenger, market birth, death, waste, illness ancestor, mother, anger, underworld
I Ching trigram earth, receptive, yielding, yin (000) heaven, creative, expanding, yang (111) water, abyss, danger, rapid rivers, moon (010) fire, radiance, clinging, rapid movement, sun (101)
I Ching hexagram field, receptive, acquiescence, flow (000000) force, creative, strong action, key, god (111111) great exceeding, critical mass (011110) swallowing, jaws, comfort/security (100001)
I Ching hexagram (alt.) small exceeding (001100) center returning, inner truth (110011)


The Contrasts





Modern binary 0011 (3) 1100 (12) 0101 (5) 1010 (10)
Visual interpretations beam of lights from the sun, emptied container blessings growing from earth, full container, knife incoming arrow, two emptied bowls outgoing arrow, two bowls
Unified semantics POOR: poverty (-> hunger, desire), temporary help from outside (-> debt, gift), lost greatness (-> modesty, obstruction). RICH: wealth (-> power, success), long-term independent success (-> stability, rich family), gained greatness (-> victory, difficult beginning), knife (-> right hand, blood, lineage, death). GONE: arrow (-> danger, risk, destiny; -> poison, medicine, illness), loss (-> something outside grasp, leaving for dangerous journey, sacrifice). DONE: avoided arrow (-> safety after risk), gain (-> money, something within grasp, new friends/enemies).
4-way lack + passivity satisfaction + activity lack + activity satisfaction + passivity
Greek incoming fame outgoing fame outgoing things incoming things
Greek trigram (no counterpart) (no counterpart) (no counterpart) (no counterpart)
Ilm-al-raml victory leaves victory comes incoming arrow outgoing arrow
Geomantia minor fortune, aid coming in, minor adventure, diurnal sun major fortune, aid going out, major adventure, nocturnal sun loss gain
Sikidy chiefs, elderly, pride, domination, food, anger fire, creator, most sacred tears, land, enemy protection, boss, child money, misfortune
Ifa double poverty longevity, slander good wife, journey, prosperity share, be alert
Igbo Afa double pay a debt knife, right hand see suffering
Igbo Afa single food, greed, gift blood, violence, war, lineage, wealth, animal sacrifice joy, sacrifice, poison, medicine suffer, escape, alcohol
I Ching trigram (no counterpart) (no counterpart) (no counterpart) (no counterpart)
I Ching hexagram obstruction, standstill, stagnation, selfish (000111) pervading, peace, greatness (111000) not yet fording, before completion (010101) already fording, after completion (101010)

The Directions


Modern binary 0001 (1) 1000 (8) 1110 (14) 0111 (7)
Visual interpretations arch, fountain, rainbow, mountain broken arch, stake being driven into ground, thunder cloud, tornado new moon's crescent old moon's crescent
Unified semantics UP: high thing (-> mountain, high building, immovability, stability), high status (-> king, government, god, keeping up), high mood/state (-> joy, happiness, good luck, prosperity), going up (-> rising, appearing, future; -> seeing far, wisdom). DOWN: opposition (-> evil, struggle, revolution), low mood/state (-> sorrow, suffering, accident, bad luck), going down (-> disappearance, destruction, past), low things (-> earth, foundation) IN: appearance (-> beginning), internal (-> internal problems, internal authorities, self-sufficiency), inner circle (-> secrets, relatives) OUT: going out/away (-> disappearance, retreat, end), external (-> outsider, outside influence, sudden unexpected change)
4-way away + vertical near + vertical near + horizontal away + horizontal
Greek upward-moving downward-moving the lintel when coming in (unknown)
Greek trigram aphrodite / venus (001) ares / mars (100) zeus / jupiter (110) zeus / jupiter (011)
Ilm-al-raml joy, beard bearded, reversed inner threshold outer threshold
Geomantia joy sadness, small transversion dragon's head (ascending lunar node) dragon's tail (descending lunar node)
Sikidy king, strength spouse, stubbornness, tears evil thoughts, arguments, trials, bad destiny, wars, children slave, cold words, a type of fate
Ifa double coming of good luck accident, honor difficulties in work sudden trouble/wealth
Igbo Afa double forest difficulties thing struggled for villain thing standing outside
Igbo Afa single future, high, joy, authority, god relatives, war, truth, firmness breath, life, survive, escape authority, visitor, nature force
I Ching trigram mountain, stillness, immovability (001) thunder, arousing, excitation, revolution, division (100) lake, swamp, joy, satisfaction, stagnation (110) wind, gentle, gentle penetration, flexibility (011)
I Ching hexagram stripping, splitting apart, flaying (000001) returning (100000) displacement, resoluteness, break-through (111110) coupling, meeting (011111)
I Ching hexagram (alt.) viewing, looking up (000011) nearing, approach, forest (110000) great invigorating, power of great, great maturity (111100) retiring, retreat, yielding (001111)

The Societies

Shape ••




Modern binary 0010 (2) 0100 (4) 1101 (13) 1011 (11)
Visual interpretations clashing swords, turned glass glass, scales of justice vulva, woman with exaggerated breasts, execution cross, mouth sword, erect phallus, scarce beard, fish, drop of water
Unified semantics WAR: violence (-> death, blood, red), campaign (-> march, booty, managing to escape), aggressive feelings (-> anger, passion, feelings overcoming wisdom, settle disputes by force). LAW: wisdom (-> intelligence, knowledge, careful planning, wisdom overcoming aggressive feelings), superficial harmony (-> purity, white), justice (-> punishment, captured criminals, legal trouble). PEACE: harmony (-> innocence, passivity, beauty), unity of people (-> fellowship, consensus, shared wealth), peaceful talk (-> settle disputes by talking, truth, talk, storytelling). CRIME: rebellion (-> robbers, misfortune, illness), young men (-> workers, passion, aggression) water (-> rain, river, fish, harvest, accumulating)
4-way rough + unfair rough + fair gentle + unfair gentle + fair
Greek redness of war (unknown) minor, male scarce, female
Greek trigram (no counterpart) (no counterpart) (no counterpart) (no counterpart)
Ilm-al-raml redness whiteness solid beardless
Geomantia red white, shining white girl, measure from face boy
Sikidy joy, ghost, riches, clothes diviner, crowd, heartbreak, thievery riches, love, favorable day, land/earth robber, misfortune, workers, harvests
Ifa double health, prosperity accept advice peace, consensus prosperity despite enemies
Igbo Afa double run, escape handcuffed, in trouble (bad) talk accident
Igbo Afa single run, escape, journey, war trouble, female, wisdom talk, story water, river, struggle, tears
I Ching trigram (no counterpart) (no counterpart) (no counterpart) (no counterpart)
I Ching hexagram grouping, holding together, alliance (000010) leading, army, troops (010000) great possessing (111101) concording/gathering people, fellowship with men (101111)
I Ching hexagram (alt.) enthusiasm, excess (000100) humbling, modesty (001000) small accumulating/harvest, taming power of small (111011) treading, continuing (110111)
I Ching hexagram (alt.) clustering, finished (000110) ascending, pushing upward (011000) great accumulating, taming power of great, potential energy (111001) without embroiling, innocence, pestilence (100111)

Fields explained

Shape: The "lines of stones" representation of the four-bit binary array.

Modern binary: The bottom-up translation of the array into modern binary notation. Single markers are interpreted as 1, double markers as 0.

Visual interpretations: Some possible visual interpretations for the binary array.

Unified semantics: My own non-scientific guess of an "original" or "defiltered" meaning of the combination. Derived from the rest of the fields in this table. I've aimed at sensible pairs of opposites whenever possible.

4-way: A simplification of the meaning using a set of two dichotomies. Each row is assigned a dichotomy pair of its own.

Greek: The associations of the shape from Greek manuscript 2419, as given by van Binsbergen.

Greek trigram: The associations of the corresponding three-bit combination from Codex Harleianus 5596, as given by van Binsbergen.

Ilm-al-raml: The associations of the shape in the Arabic Ilm-al-raml system, as given by van Binsbergen.

Geomantia: The associations of the shape in European Geomancy, as given by van Binsbergen.

Sikidy: The associations of the shape in the Madagascan Sikidy system, as given on the website

Ifa double: The associations of the double nybble in the Yoruba Ifa system, as given by Manfredi.

Igbo Afa double: The associations of the double nybble in the Nri-Igbo version of the Afa system, as given by Manfredi.

Igbo Afa single: Common associations of the single nybble in the nybble pairs of Igbo Afa and some other related systems. Derived by myself from the 256-entry table given by Manfredi.

I Ching trigram: The associations of the corresponding three-bit combination from the Chinese tradition.

I Ching hexagram: The I Ching associations of the corresponding six-bit combination, using the interpretations listed in Wikipedia.


van Binsbergen, Wim: The astrological origin of Islamic geomancy, 2004.

Manfredi, Victor: Afa, the Nri-Igbo counterpart of Ifa, 2010.

Wikipedia: List of hexagrams of the I Ching (as accessed in 2011-05-25).

Serena's Guide to Divination: Sikidy (as accessed in 2011-05-25).