The mathematics of the system, the mnemonic architecture that makes a corpus this large holdable, and a careful separation of the documented claims from the popular ones.
The Yorùbá wey dem quote, the proverbs, oríkì, ẹsẹ Ifá, word list headwords, Odù names and citations dey exactly as the corpus record dem, for every language.
Ifá na binary addressing system on top very large corpus wey people memorise. Dat statement dey accurate and e make sense make person take am serious. Wetin dey follow go separate am from di different claims wey people don carry join am, wey plenti of dem dey false, and one of dem false for way wey no even help di tradition at all.
Di reader wey dem write dis corpus for normally dey reach Ifá through di observation say e dey binary, and many times through di viral version of di claim say Leibniz carry binary arithmetic from Ifá and say na Yorùbá diviners come invent computer. Dat claim no true, and di timeline of history clear am out completely. Di real tori sweet pass dat one and e no need make person hype am, na why dis file spend plenti space to scatter di sweet lie as e dey build di correct one.
Confidence on top dis file na medium overall, because e mix well-established mathematics with history wey people dey genuinely drag about. Dem mark each individual claim.
Di combinatorial facts don clear and dem state everything well-well for file 02. In summary:
Di smallest unit get two states, single mark or double mark, wey dey come out physically wen one or two nuts remain or wen shell land facing up or facing down . Four positions dey make one column, wey give 2^4 = 16 columns. Two columns wey follow order dey make one Odù, wey give 16^2 = 256. Bascom state di formula exactly like dis, as e use 2^n for four tosses and den 16 x 16 = 256 .
Di system na non-commutative: Ọ̀kànràn Ìrẹtẹ̀ and Ìrẹtẹ̀ Ọ̀kànràn na different Odù with different content . Because order dey matter, dat na wetin make di count jump from 136 pairs wey no get order go 256 pairs wey follow order.
Di address space na exactly 256 and e no pass dat. Bascom strictly reject di older inflated numbers of 4,096 and 65,536 wey enter literature through J. Johnson and Farrow: "As any reader may verify for himself, however, the system permits no more"
For information-theoretic terms, one cast dey carry eight bits, wey be one byte. Dis na true statement and e dey catch attention, and na also place wey person need take care. Eight bits dey identify one out of 256 slots. E no dey measure di information inside wetin dem bring out, wey be collection of verses, and e no mean say di system dey do byte arithmetic.
Wetin di eight bits dey actually do. Dem be index, dem no be payload. Di cast wey dey randomise dey select address; di content dey inside di diviner memory. Na dis be di correct way to understand di system information design, and e fine well-well: e be compact address wey share equally and come out physically on top corpus wey big pass wetin person fit search line by line.
Di problem wey di system dey solve na dis: how society wey no get writing take hold something wey reach around 150,000 to 200,000 verses , keep dem accurate across generations, and bring out di correct one wen dem need am?
Different features dey work together, and e make sense to call dem design instead of just custom.
Storage wey use index instead of line-by-line list. Di corpus no be list. Na 256 bins wey get label. Diviner no dey search di corpus; e just dey go one address and recite wetin dey inside. Dis one reduce di wahala to find verse by more than two orders of magnitude.
Uniform partitioning. Because each cast get equal chance to produce any Odù, di material spread across di address space instead of make e pack for one place. Each bin dey carry load wey match each other.
Fixed skeleton, free body. Di eight-part verse structure wey get four compulsory parts and four optional parts na di main mnemonic tool . Di compulsory parts, di diviners names, di client, di occasion, and di moral, all priests within di same dialect area dey recite dem for di same form and same language, while di narration na each priest own personal way . Dis one dey protect di identity of di verse and di conclusion make e no shift, while e still make di memory load easy to carry, since na only di skeleton must dey exact.
Text before meaning. Trainees dey memorise verses first before dem come learn interpretations and ebo afterwards . To learn sound before meaning dey prevent learner understanding from changing di wording.
Distributed redundancy. Nobody dey hold di whole corpus. People wey dem initiate dey hold at least sixteen verses per Odù, so many practitioners dey hold common verses and dem fit correct dem wen dem dey perform, while specialists dey hold verses wey scarce . Di corpus dey exist as di combination across di whole profession.
Formulaic devices. Repetition and word-play na di main stylistic features , and di two dey help memory. Names inside di verses na often descriptive phrases instead of just random names, wey dey make am easy to recall.
Ordered learning. Memorisation dey start from di most senior Odù go down , wey come give di syllabus fixed sequence and make progress easy to check.
Abimbola conclusion na wetin di architecture support: di 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"
Ron Eglash book African Fractals (1999) na di source of most modern claims about African divination and recursive mathematics, and e make sense make person read wetin e actually argue, because wetin plenti people dey talk don shift from wetin e write.
Eglash mathematical observation dey about Bamana sand divination, no be Ifá. Di way e describe am: di 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" Di recursive step na wetin interest am: "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"
Dis na real and specific mathematical claim: one deterministic recursive operation, addition modulo 2, wey dem apply to symbols wey dem generate so dat e go produce more symbols. E be like pseudorandom generator wey physical random process start.
No be so Ifá dey work, and dis difference dey important. For Ifá, na independent physical events dey generate all di eight positions of di Odù, either eight times wey dem control palm-nut or one throw of di chain wey get eight shells . No modulo-2 pairing step dey, dem no dey derive later figures from earlier ones, and recursion no dey di way dem dey generate am. Eglash sef treat di West African Fa and Ifá systems like say dem relate to di geomantic family, no be say na dem be di exact place wey him recursion finding come from; e talk about "the nearly identical system of divination in West Africa associated with Fa and Ifa" just as Trautmann note .
So: dem document recursion for Bamana sand divination, no be for Ifá casting. Sources wey dey carry Eglash fractal and recursion findings give Ifá direct dey carry claim from one system go put for another system. Dis na one of di most common mistake for popular literature.
Wetin Ifá get na self-similar naming structure: sixteen basic patterns, wey each of dem dey show as part of di 256 compound figures, with compound names wey dem build from di component names. Dat one na hierarchical and compositional. Whether e be fractal for any technical sense na stronger claim wey I never see say dem rigorously demonstrate for Ifá specifically. Confidence: contested.
Di popular claim dey talk say: Leibniz derive binary arithmetic from Ifá, or from African geomancy, and because of dat, digital computer come from Yorùbá divination. E no match di chronology, and e no match wetin Eglash actually write sef.
Di earliest document wey people know say Leibniz write about binary na di manuscript De Progressione Dyadica, wey him use him own hand write date 15 March 1679, wey dey Niedersächsische Landesbibliothek for Hanover . E explain di binary numeral system, di properties and di arithmetic, and e describe wetin be like say na di earliest design wey people know for binary calculating machine .
E discuss binary numeration for one letter wey e write give him patron Duke Rudolph August for 1697 . E write give Jesuit Joachim Bouvet dey describe him binary arithmetic on 15 February 1701 . Bouvet reply from Peking on 4 November 1701, point out how e match di hexagrams of di I Ching and e put one woodcut of di Fuxi arrangement inside di letter; dat letter reach Leibniz on 1 April 1703 . Leibniz publish Explication de l'Arithmétique Binaire for di Paris Academy journal for 1703 .
Di sequence dey clear well-well. Leibniz don get binary arithmetic for 1679 and e see di Chinese hexagrams for 1703, twenty-four years later. E no derive binary from di I Ching, and dis same chronology show say e no derive am from any West African system wey e encounter later. No record dey at all say contact happen between Leibniz and Ifá for any date.
Eglash own route no pass through Ifá go Leibniz. Wetin e write: "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"
So di chain wey Eglash propose na: African divination, to Islamic geomancy for North Africa, to Europe through Hugo of Santalla for twelfth century, to Ramon Llull, to Leibniz. Ifá appear for him argument like related member of di geomantic family, no be like wetin Leibniz use as source.
Every link for dat chain weak pass wetin di popular version dey talk, and two among dem weak well-well.
Di link from Llull go Leibniz dey real, but e no concern binary. Leibniz mention Llull Ars Magna for him Dissertatio de Arte Combinatoria of 1666, and e criticise Llull say him categories no get strong basis . Llull art na combinatorial, e dey use figures wey dey rotate take generate combinations of concepts; e no be binary numeral system. Influence on Leibniz combinatorics get record. Influence on him binary arithmetic no get record.
Di link from geomancy go Llull, na Stephen Skinner Terrestrial Astrology Eglash quote, instead of say e go argue am from primary evidence .
Di link from Africa go Islamic geomancy na di one wey people dey contest, and dem treat am for di next section.
Later commentators describe Eglash own confidence say e modest, and one summary of him position note say him evidence for di spread claim "is not too strong" Di popular versions no carry any of dat kind carefulness.
"Leibniz get binary from Ifá." No be true. Binary manuscript na 1679; no record dey say e ever get contact with Ifá .
"Leibniz get binary from di I Ching." No be true, and dis one at least get real historical event behind am. Bouvet letter reach for 1703, twenty-four years after De Progressione Dyadica . Bouvet notice say dem resemble each oda; no be him give am di system.
"Ifá na computer, or di first computer." No be true as dem state am. Ifá get address space and content wey dey stored, but no operations dey defined on addresses, e no dey write to storage when dem dey use am, and no computation on values dey. Na indexing system e be, no be computational one.
"Ifá get 4,096 or 65,536 Odù." No be true. Bascom trace dis numbers go meet J. Johnson and Farrow and e refute dem: di system no allow pass 256 .
"Eglash show say Ifá na fractal and recursive." Dem give credit to di wrong person. Eglash recursion finding na about Bamana sand divination . Ifá casting no get any recursive step.
"Ifá dey prove say Africans invent binary before Europeans." Dis talk no get backing as dem arrange am, for both sides. E dey assume say na one person invent am and na one single line of descent produce idea, two-state notation, wey don come up on im own for many different places. Wetin person fit talk be say two-state notation wey get 256-element ordered address space dey on record say dem use am for West Africa, and say European binary arithmetic dey documented from 1679 . Dese na separate facts and none of dem depend on di other.
Wetin make dis matter. Reader wey dem don tell say Yorùbá heritage no get value, and wey later find one compensating story say na am secretly start computing, don change one lie for another lie. Di overclaim sef no strong: anybody wey check di Leibniz dates go see say di story scatter, and di way e scatter fit bring down di real achievement join am. Di real achievement na 256-address randomised retrieval system over corpus of hundred thousand-plus verses, wey dey for memory, with quality control, for society wey no dey write. Dat one no need help.
Di relationship between Ifá, di Islamic geomancy ʿilm al-raml (science of di sand), and European geomancy still never settle at all, and e be one of di more interesting open questions for di history of divination.
Wetin dey established. Di systems share formal structure. Sixteen figures, each with four binary positions, wey dey generated through physical procedure wey dey randomize things. European geomancy dey use di same sixteen four-position figures with different names and meanings. Bascom find out say di names of di Ifá figures na standard across Yorùbáland, di Fọ̀n, di Ewe, Cuba and Brazil .
Arabic geomancy dey documented for texts from di ninth century, with di earliest systematic descriptions for Arabic and some early basic material before dat . E enter Latin Europe through translation for twelfth-century Spain, di Ars geomantiae wey Hugo of Santalla translate being di oldest divinatory handbook for Western geomancy .
Wetin dey disputed. Di direction of transmission. Trautmann assume say geomancy start from Arabic society . Eglash argue di opposite, say African divination spread go di Muslim world and from there enter Europe, based on say base-2 calculation dey everywhere for ancient Egypt while surrounding traditions dey use base 10, say doubling dey show up plenty for African knowledge systems, and say number bases dey last long for history . E present dis one as argument say e possible, no be say e don prove am completely.
Di most careful recent work wey I see na Ayodeji Ogunnaike work on di spread of geomancy for Africa, wey reject both simple directions. Im position na say Yorùbá Ifá likely take di structure and figures of geomancy join onto divinatory tradition wey dey before, and say influence come run both ways afterwards, with indigenous traditions reshaping local Islamic geomancy in turn . Im supporting points include say al-Zanātī, author of foundational geomantic text, likely be Berber; say early figure names show Berber origin; say African societies already dey practice binary and recursive systems; and say di two divination methods of Ifá dey suggest say di four-position structure na later technological addition to something wey older .
Dat last point deserve attention because e be structural argument instead of documentary argument. If to say di tetragram framework na original part of Ifá from start, person for expect say di instruments go dey built around am from day one.
How to hold dis. Di summary wey make sense pass to defend na say Ifá and Arabic geomancy get formal relationship and historical connection, say di connection old well well, say transmission likely no be one direction, and say nobody don show clearly which system first get di four-position structure. Anybody wey just talk point-blank say Ifá come from Arabic geomancy, or say Arabic geomancy come from Ifá, dey talk pass wetin evidence support.
Confidence: contested. Dis na di correct way to mark di state of di field as e dey now, no be say person dey dodge talk.
Make you note also say dis question no affect di Leibniz claim at all. Even if dem establish say Africa first start geomancy, Leibniz 1679 manuscript go still come before any contact, and im documented sources go still be Llull combinatorics instead of any geomantic figure system .
Drop di overclaims comot and di following ones remain, each of dem documented:
Physical randomisation procedure with rejection rule, wey dey troway draws wey bring zero or pass two nuts, wey dey turn rough manual process to clean two-state output .
Two instruments wey get different speed wey dey produce di same information result, with di fast one wey dem dey use for everyday work and di slow one wey dem keep for public and ritual occasion .
Address space of exactly 256, wey dey ordered instead of unordered, with naming scheme wey dey allow any practitioner call any address name from im marks and build di marks back from di name .
Corpus of verses wey reach 10^5 wey dey inside distributed memory without written record, wey dem index with dose 256 addresses .
Verse format wey separate di parts wey no dey change from di parts wey dey change, wey protect di identity and conclusion while leaving performance free .
Retrieval protocol wey deliberately hide di query from di operator and leave di work of matching wetin relevant to di client .
Training process of ten to twenty years to documented entry standard of 4,096 verses with dia interpretations and prescriptions, wey specialisation and lifelong practice dey follow .
If person look am as information design, dat one na serious work. Na wetin evidence support be dat, and e plenty enough.
Each Odù is two columns of four marks, every mark single or double, giving four bits per column, eight bits in total, and exactly 256 possible signatures.
All 256 Odù listed with signatures, the 16 principal Odù in the competing ranking orders, and an honest account of where the sources disagree.
How the sixteen-cowrie system, kola divination, and the Fon, Ewe, Cuban and Brazilian relatives relate to Ifá, and why formal similarity is weaker evidence than it looks.
The verses filed under each Odù are case reports in verse, built to a described eight-part structure, held collectively across practitioners rather than by any one person.
Ifá is a Yorùbá system for reaching a decision by casting a signature, retrieving the memorised verses filed under it, and reasoning from the precedents they contain.
What the instruments are, how a consultation runs from the client's whispered question to the prescribed offering, and which decisions belong to the diviner and which do not.