Ifá as an Information and Memory System: What Is Established and What Is Overclaimed

Ifá is a binary addressing system over a very large memorised corpus. That statement is accurate and is worth taking seriously. What follows separates it from the claims that have grown up around it, several of which are false, and one of which is false in a way that does the tradition no favours.

The reader this corpus is written for has usually arrived at Ifá through the observation that it is binary, often via a viral version of the claim that Leibniz took binary arithmetic from Ifá and that Yorùbá diviners therefore invented the computer. That claim is not true, and the chronology refutes it decisively. The real story is more interesting and requires no exaggeration, which is why this file spends as much space dismantling the flattering version as building the accurate one.

Confidence on this file is medium overall, because it mixes well-established mathematics with genuinely contested history. Individual claims are marked.

The mathematics, stated exactly

The combinatorial facts are settled and are set out fully in file 02. In summary:

The atomic unit has two states, single mark or double mark, produced physically by one-or-two nuts remaining or by a shell landing concave or convex up 12. Four positions make a column, giving 2^4 = 16 columns. Two ordered columns make an Odù, giving 16^2 = 256. Bascom states the formula in exactly these terms, invoking 2^n for four tosses and then 16 x 16 = 256 1.

The system is non-commutative: Ọ̀kànràn Ìrẹtẹ̀ and Ìrẹtẹ̀ Ọ̀kànràn are different Odù with different content 1. Order-sensitivity is what raises the count from 136 unordered pairs to 256 ordered ones.

The address space is exactly 256 and no larger. Bascom explicitly refutes the older inflated figures of 4,096 and 65,536 that entered the literature through J. Johnson and Farrow: "As any reader may verify for himself, however, the system permits no more" 1

In information-theoretic terms, one cast carries eight bits, which is one byte. This is a true statement and an arresting one, and it is also where care is needed. Eight bits identifies one of 256 slots. It does not measure the information in what is retrieved, which is a body of verse, nor does it mean the system performs byte arithmetic.

What the eight bits actually do. They are an index, not a payload. The randomising cast selects an address; the content lives in the diviner's memory. This is the correct way to understand the system's information design, and it is genuinely elegant: a compact, uniformly distributed, physically generated address over a corpus far too large to search linearly.

The mnemonic architecture

The problem the system solves is this: how does a society without writing hold something in the order of 150,000 to 200,000 verses 34, keep them accurate across generations, and retrieve the right one on demand?

Several features work together, and they are worth naming as design rather than as custom.

Indexed rather than sequential storage. The corpus is not a list. It is 256 labelled bins. A diviner does not search the corpus; he goes to one address and recites from it. This reduces the retrieval problem by more than two orders of magnitude.

Uniform partitioning. Because each cast is equally likely to produce any Odù, material is distributed across the address space rather than concentrated. Each bin holds a comparable load.

Fixed skeleton, free body. The eight-part verse structure with four obligatory and four optional parts is the key mnemonic device 3. The obligatory parts, the diviners' names, the client, the occasion, and the moral, are rendered in the same form and same language by all priests within a dialect area, while the narration is the individual priest's own 3. This protects verse identity and conclusion against drift while keeping the memory load tractable, since only the skeleton must be exact.

Text before meaning. Trainees memorise verses first, then learn interpretations and offerings afterwards 3. Learning sound before sense prevents a learner's understanding from reshaping the wording.

Distributed redundancy. No one holds the corpus. Initiates hold at least sixteen verses per Odù, so common verses are held by many practitioners and can be corrected in performance, while rare verses are held by specialists 3. The corpus exists as the union across the profession.

Formulaic devices. Repetition and word-play are the characteristic stylistic features 3, and both aid recall. Names in the verses are often descriptive phrases rather than arbitrary labels, which makes them reconstructible.

Ordered learning. Memorisation proceeds from the most senior Odù downward 3, which gives the syllabus a fixed sequence and makes progress checkable.

Abimbola's conclusion is the one the architecture supports: the training "shows that pre-literate societies can transmit bodies of well-codified knowledge from one generation to the other without knowing the art of writing" 3

Eglash and the recursion claim

Ron Eglash's African Fractals (1999) is the source of most contemporary claims about African divination and recursive mathematics, and it is worth reading what he actually argues, because the popular version has drifted from it.

Eglash's mathematical observation concerns Bamana sand divination, not Ifá. His description: the system "begins with four sets of random dashed lines. These are paired off (i.e. summed by addition module two), and the even/odd results recorded with two strokes or one stroke. Four of these binary digits represents one of 16 possible divination archetypes" 5 The recursive step is what interests him: "Although the first four are generated by this random process, the following 12 are created by recursively applying the same pairing operation on the binary digits making up the four symbols" 5

This is a real and specific mathematical claim: a deterministic recursive operation, addition modulo 2, applied to generated symbols to produce further symbols. It amounts to a pseudorandom generator seeded by a physical random process.

This is not how Ifá works, and the distinction matters. In Ifá all eight positions of the Odù are generated by independent physical events, either eight palm-nut manipulations or one throw of the chain with eight shells 12. There is no modulo-2 pairing step, no derivation of later figures from earlier ones, and no recursion in the generative procedure. Eglash himself treats the West African Fa and Ifá systems as related to the geomantic family rather than as the locus of his recursion finding, referring to "the nearly identical system of divination in West Africa associated with Fa and Ifa" as noted by Trautmann 5.

So: recursion is documented for Bamana sand divination, not for Ifá casting. Sources that attribute Eglash's fractal and recursion findings directly to Ifá are transferring a claim from one system to another. This is one of the commonest errors in the popular literature.

What Ifá does have is a self-similar naming structure: sixteen basic patterns, each of which appears as a component of the 256 compound figures, with compound names built from the component names. That is hierarchical and compositional. Whether it is fractal in any technical sense is a stronger claim that I have not found rigorously demonstrated for Ifá specifically. Confidence: contested.

The Leibniz claim, which is false

The popular claim runs: Leibniz derived binary arithmetic from Ifá, or from African geomancy, and therefore the digital computer descends from Yorùbá divination. It fails on chronology, and it fails on what Eglash actually wrote.

The chronology

Leibniz's earliest known document on binary is the manuscript De Progressione Dyadica, dated in his own hand 15 March 1679, held at the Niedersächsische Landesbibliothek in Hanover 6. It sets out the binary numeral system, its properties and its arithmetic, and describes what appears to be the earliest known design for a binary calculating machine 6.

He discussed binary numeration in a letter to his patron Duke Rudolph August in 1697 7. He wrote to the Jesuit Joachim Bouvet describing his binary arithmetic on 15 February 1701 7. Bouvet replied from Peking on 4 November 1701, pointing out the correspondence with the hexagrams of the I Ching and enclosing a woodcut of the Fuxi arrangement; that letter reached Leibniz on 1 April 1703 7. Leibniz published Explication de l'Arithmétique Binaire in the Paris Academy's journal in 1703 7.

The sequence is unambiguous. Leibniz had binary arithmetic in 1679 and encountered the Chinese hexagrams in 1703, twenty-four years later. He did not derive binary from the I Ching, and the same chronology rules out derivation from any West African system encountered later. There is no documented contact between Leibniz and Ifá at any date.

What Eglash actually claimed

Eglash's own route does not run through Ifá to Leibniz. His text: "The modern binary code, essential to every digital circuit from alarm locks to super computers, was first introduced by Leibniz around 1670. Leibniz has been inspired by the binary-based 'logic machine' of Raymond Lull, which was in turn inspired by the alchemists' divination practice of geomancy (Skinner 1980). But geomancy is clearly not of European origin. It was first introduced there by Hugo of Santalla in twelfth century Spain and Islamic scholars had been using it in North Africa since at least the 9th century" 5

So the chain Eglash proposes is: African divination, to Islamic geomancy in North Africa, to Europe via Hugo of Santalla in the twelfth century, to Ramon Llull, to Leibniz. Ifá appears in his argument as a related member of the geomantic family, not as Leibniz's source.

Every link in that chain is weaker than the popular version implies, and two are seriously weak.

The Llull to Leibniz link is real but is not about binary. Leibniz cites Llull's Ars Magna in his Dissertatio de Arte Combinatoria of 1666, and he criticises Llull for the arbitrariness of his categories 8. Llull's art is combinatorial, using rotating figures to generate combinations of concepts; it is not a binary numeral system. Influence on Leibniz's combinatorics is documented. Influence on his binary arithmetic is not.

The geomancy to Llull link is attributed by Eglash to Stephen Skinner's Terrestrial Astrology rather than argued from primary evidence 5.

The Africa to Islamic geomancy link is the contested one, treated in the next section.

Eglash's own confidence has been characterised by later commentators as modest, and one summary of his position notes that his evidence for the spread claim "is not too strong" 5 The popular versions carry none of that hedging.

Correcting the overclaims by name

"Leibniz got binary from Ifá." False. Binary manuscript 1679; no documented contact with Ifá ever 6.

"Leibniz got binary from the I Ching." False, and this one at least has a real historical episode behind it. Bouvet's letter arrived in 1703, twenty-four years after De Progressione Dyadica 67. Bouvet recognised a correspondence; he did not supply the system.

"Ifá is a computer, or the first computer." False as stated. Ifá has an address space and stored content, but no operations defined on addresses, no writing to storage during use, and no computation on values. It is an indexing system, not a computational one.

"Ifá has 4,096 or 65,536 Odù." False. Bascom traces these to J. Johnson and Farrow and refutes them: the system permits no more than 256 1.

"Eglash showed Ifá is fractal and recursive." Misattributed. Eglash's recursion finding is about Bamana sand divination 5. Ifá's casting has no recursive step.

"Ifá proves Africans invented binary before Europeans." Unsupportable as framed, in both directions. It presumes a single inventor and a single line of descent for a notion, two-state notation, that has arisen independently in many places. What can be said is that a two-state notation with a 256-element ordered address space was in documented use in West Africa, and that European binary arithmetic is documented from 1679 6. These are separate facts and neither requires the other.

Why this matters. A reader who was told Yorùbá heritage was worthless, and who then discovers a compensating story in which it secretly founded computing, has swapped one distortion for another. The overclaims are also fragile: anyone who checks the Leibniz dates finds the story collapses, and the collapse can take the genuine achievement down with it. The genuine achievement is a 256-address randomised retrieval system over a corpus of a hundred thousand-plus verses, held in memory, with quality control, in a society without writing. That needs no help.

Ifá and geomancy: the honest state of the question

The relationship between Ifá, the Islamic geomancy ʿilm al-raml (science of the sand), and European geomancy is genuinely unsettled, and it is one of the more interesting open problems in the history of divination.

What is established. The systems share a formal structure. Sixteen figures, each of four binary positions, generated by a randomising physical procedure. European geomancy uses the same sixteen four-position figures with different names and meanings. Bascom found that the names of the Ifá figures are standard across Yorùbáland, the Fọ̀n, the Ewe, Cuba and Brazil 1.

Arabic geomancy is documented in texts from the ninth century, with the earliest systematic descriptions in Arabic and some rudimentary material earlier 9. It entered Latin Europe through translation in twelfth-century Spain, the Ars geomantiae translated by Hugo of Santalla being the oldest divinatory handbook of Western geomancy 9.

What is disputed. The direction of transmission. Trautmann assumed geomancy originated in Arabic society 5. Eglash argued the reverse, that African divination spread to the Muslim world and thence to Europe, on the grounds that base-2 calculation was ubiquitous in ancient Egypt while surrounding traditions favoured base 10, that doubling recurs across African knowledge systems, and that number bases have long historical persistence 5. He offers this as a plausibility argument, not as demonstration.

The most careful recent treatment I found is Ayodeji Ogunnaike's work on the spread of geomancy in Africa, which rejects both simple directions. His position is that Yorùbá Ifá likely appropriated the structure and figures of geomancy and grafted them onto a pre-existing divinatory tradition, and that influence subsequently ran both ways, with indigenous traditions reshaping local Islamic geomancy in turn 10. His supporting points include that al-Zanātī, author of a foundational geomantic text, was probably Berber; that early figure names show Berber origins; that African societies already practised binary and recursive systems; and that Ifá's two divination methods suggest the four-position structure was a later technological addition to something older 10.

That last point deserves attention because it is a structural argument rather than a documentary one. If the tetragram framework were original to Ifá, one would expect the instruments to be built around it from the start.

How to hold this. The most defensible summary is that Ifá and Arabic geomancy are formally related and historically connected, that the connection is old, that transmission was probably not one-directional, and that no one has demonstrated which system's four-position structure came first. Anyone stating flatly that Ifá derives from Arabic geomancy, or that Arabic geomancy derives from Ifá, is asserting more than the evidence supports.

Confidence: contested. This is the correct marking for the current state of the field rather than a hedge.

Note also that this question does not bear on the Leibniz claim at all. Even if African priority in geomancy were established, Leibniz's 1679 manuscript would still predate any contact, and his documented sources would still be Llull's combinatorics rather than any geomantic figure system 68.

What is genuinely remarkable

Set the overclaims aside and the following remain, each documented:

A physical randomisation procedure with a rejection rule, discarding draws that yield zero or more than two nuts, which converts a messy manual process into a clean two-state output 12.

Two instruments of different speed producing informationally identical results, with the fast one used for routine work and the slow one reserved for public and ritual occasions 12.

An address space of exactly 256, ordered rather than unordered, with a naming scheme that lets any practitioner name any address from its marks and reconstruct the marks from the name 12.

A corpus of the order of 10^5 verses held in distributed memory with no written record, indexed by those 256 addresses 34.

A verse format that separates invariant from variable parts, protecting identity and conclusion while leaving performance free 3.

A retrieval protocol that deliberately withholds the query from the operator and delegates relevance-matching to the client 3.

A training pipeline of ten to twenty years to a documented entry standard of 4,096 verses with their interpretations and prescriptions, followed by specialisation and lifelong continuation 3.

Considered as information design, that is a serious body of work. It is what the evidence supports, and it is enough.