Did African Ifá Give Leibniz Binary Code?

There is no evidence that Gottfried Wilhelm Leibniz knew anything about Ifá. The claim circulates widely — usually as "binary code came from Africa" — and it appears to be a conflation with a different and genuinely documented episode involving a Chinese text.

The real story is more precise, and the thing it displaces is better: Ifá is an eight-position binary system with 256 addressable states and an enormous memorised literature attached, and it needs no borrowed credit from European mathematics.

What actually happened with Leibniz

Two facts, in order, because the order matters.

First: Leibniz developed binary arithmetic himself. Manuscripts show him working with base-2 representation well before any contact with Chinese material — he was exploring it in unpublished notes in the 1670s and 80s. Binary was his own work, arrived at from his interest in a universal formal language and in the theological elegance of generating all numbers from 1 and 0.

Second: in 1701 he learned about the I Ching, through correspondence with Joachim Bouvet, a French Jesuit stationed in Beijing. Bouvet sent him the Fuxi arrangement of the sixty-four hexagrams — the ordering sometimes called the "natural" or binary sequence.

Leibniz recognised his own system in it. Read a broken line as 0 and an unbroken line as 1, and the Fuxi sequence runs 0 through 63 in binary order.

He published "Explication de l'Arithmétique Binaire" in 1703, with a note on the Chinese figures, and treated the correspondence as striking confirmation.

So even the I Ching claim needs care. The I Ching did not give Leibniz binary. Leibniz already had binary and found it reflected in the I Ching — which he took as evidence for the universality of the system, and, being a Jesuit correspondent's correspondent, as a possible bridge for missionary argument.

There is no equivalent episode involving Ifá. No letters, no manuscripts, no intermediary.

Why the confusion is understandable

Because Ifá genuinely is binary, and it is a larger system than the I Ching.

The babaláwo casts either the opele — a divining chain of eight halved seed-shells — or manipulates sixteen ikin palm nuts. Either method produces eight positions, each resolving to one of two states, marked as a single or double stroke.

Two states, eight positions: 2⁸ = 256.

Each of those 256 figures is a named odù, and each odù carries a body of memorised verses called ese — myths, precedents, prohibitions, prescriptions, and the record of who consulted this sign before and what happened to them. Hundreds of verses per odù.

That is plausibly the largest body of oral literature on Earth, held in human memory, indexed by a random binary draw.

How the system actually works

This is the part that gets flattened by "it's an ancient computer," and the reality is more interesting than the metaphor.

The diviner does not interpret. He casts, identifies the odù, and recites its verses. The client listens and recognises their own situation in the stories. The prescription follows from the precedent.

So the structure is closer to case law than to computation: a vast indexed archive of precedents, retrieved by a randomising mechanism, applied by analogy. The randomiser removes the diviner's judgment from the selection, which is the point — it is not the babaláwo who chooses which precedent applies.

To hold a working practice, a babaláwo must memorise a substantial portion of the corpus. Training takes many years, and the tradition is exacting about accuracy.

UNESCO inscribed the Ifá divination system on its list of Intangible Cultural Heritage in recognition of exactly this.

The genuine open question nobody teaches

Here is the puzzle that deserves the attention the Leibniz claim is stealing.

Four divination systems share a binary structure and a family resemblance:

The Arabic, European, and Malagasy systems all use sixteen figures generated by binary marks, and Ifá's sixteen basic odù — which pair to make 256 — sit in the same numerical family.

The relationships between these are genuinely debated and not settled. Some scholars argue for transmission along trans-Saharan and Indian Ocean trade routes, in one direction or another. Others argue for independent invention from a natural starting point — marking odd or even counts is an obvious randomiser once you have the idea of divination by lot.

Malagasy sikidy is particularly interesting because Madagascar was settled from Southeast Asia and has centuries of Arab and East African contact, so it sits at a genuine crossroads.

That is the real question, and it is unresolved. It is a live problem in the history of mathematics and the anthropology of divination, and it is considerably more substantial than a misattributed anecdote about a German philosopher.

The fact that stands on its own

Strip out the borrowed credit and here is what remains:

While Fibonacci was introducing Hindu-Arabic numerals to Europe, West African diviners were operating an eight-bit system with 256 addressable states, each indexing a substantial body of memorised text, retrieved by a randomising mechanism, and transmitted through a formal multi-year training.

That is a fact about the history of information systems, and almost nobody teaches it.

Two things not to say

"Ifá is an ancient computer." It is not, and the claim cheapens what it actually is. A computer executes operations on data. Ifá indexes and retrieves a literature. The binary structure is an addressing scheme, not a processor. Calling it a computer invites a correction that then discredits the true part.

"Africa invented binary before Europe." This overstates in a way that is easy to dismantle and unnecessary. Binary representation has been arrived at independently many times — it is what you get whenever you record two-state outcomes. The remarkable thing about Ifá is not that it is binary. It is the scale of the literature attached to it and the fact that the whole thing runs in memory.

What to say instead

Leibniz did not get binary from Ifá — and he did not get it from the I Ching either. He developed it himself, then recognised it in the Fuxi hexagrams via Bouvet in 1701. But Ifá is an independent eight-position binary system with 256 states and hundreds of memorised verses attached to each one. And the real open question is why West African Ifá, Arabic geomancy, Malagasy sikidy, and the Chinese I Ching all share a binary structure. Nobody has settled that.

Every clause survives a specialist reading it, and the closing question is one they would find genuinely interesting.