The Yoruba numeral system, which is genuinely unusual among the world's number systems in how heavily it subtracts and how many ways it lets you say one number, plus counting practice, measurement, and what can honestly be said about mathematics in Ifá.
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.
The Yoruba number system na the strongest proof say Yoruba culture get special mathematical identity, and e no need help from any of the claim dem wey people dey usually make on top am. Na base-20 system wey dey form numbers with subtraction reach level wey hard make you see for almost any other place; e come from how dem dey count cowries instead of hand finger alone; and e get one structural feature wey expert dem find genuinely remarkable: dem fit often express the same number for many different correct ways, wey dey show say dem dey see number as arrangement of combinations instead of position for line.
Dat one na real and specific finding about one real and specific system. E dey far more interesting pass the popular claims about Ifá and binary, wey dis corpus don already examine and mostly reject inside 05-ifa/07. Dis file dey refer to dat treatment and e no repeat the exaggerated claims.
Base twenty. The base na ogún, twenty, or score . Twenty get two lexical forms with distinct grammatical roles: dem dey use okòó for word beginning when dem dey add put or remove from twenty, and dem dey use ogún with the multiplication parts when dem dey form numbers .
One to ten na simple single words: ení or ọ̀kan (1), èjì (2), ẹ̀ta (3), ẹ̀rin (4), àrún (5), ẹ̀fà (6), èje (7), ẹ̀jọ (8), ẹ̀sán (9), ẹ̀wá (10) .
Eleven to fourteen dey use addition. Ọ̀kanlá (11), èjìlá (12), ẹ̀tàlá (13), ẹ̀rìnlá (14), wey dem form as ten plus one reach ten plus four .
Fifteen to nineteen dey use subtraction, and na here the system take separate from most others. Ẹ̀ẹ́dógún (15) na twenty minus five, ẹ̀rìndínlógún (16) na twenty minus four, ẹ̀tàdínlógún (17) na twenty minus three, èjìdínlógún (18) na twenty minus two, ọ̀kàndínlógún (19) na twenty minus one . The element dín, to reduce or be less by, na the subtraction operator and e dey show clear inside the words.
Notice ẹ̀rìndínlógún, sixteen, wey also be the name of the sixteen-cowrie divination system and the number of principal odù. Sixteen for Yoruba literally mean "four less than twenty".
The decades. Ogún (20), ọgbọ̀n (30), ogójì (40, two twenties), àádọ́ta (50), ọgọ́ta (60, three twenties), àádọ́rin (70), ọgọ́rin (80, four twenties), àádọ́rùn-ún (90), ọgọ́rùn-ún (100, five twenties) .
The pattern make sense to see clearly. The even decades na multiples of twenty: 40 na two twenties, 60 na three twenties, 80 na four twenties, 100 na five twenties. Dem dey form the odd decades by subtracting ten from the next even decade: 50 na (20 × 3) − 10, 70 na (20 × 4) − 10, 90 na (20 × 5) − 10 . So Yoruba speaker dey reach fifty by going to sixty and coming back.
Higher numbers. Igba (200, twenty tens), irinwó (400), ẹgbẹ̀wá or ẹgbàá (2,000, two hundred tens), ẹgbàawàá or ọ̀kẹ́ kan (20,000, literally one bag) . Dat last one na the clear sign: twenty thousand na one bag, because twenty thousand cowries na one bag of cowries.
Worked examples of the compounding. Na these ones dey make the structure clear :
Three hundred na twenty times fifteen, and fifteen on its own na twenty minus five, so 300 na 20 × (20 − 5). Dat one na nested subtraction inside multiplication, wey dem express inside single ordinary word wey Yoruba speakers dey use without stress.
The system stand on top counting cowrie shells, wey serve as currency for the region for centuries . Dis one matter for three reasons and na the key to the whole structure.
E dey explain the base. People dey usually say twenty as base come from counting fingers and toes, and dat one fit be part of am, but the higher units for Yoruba na cowrie-trade units. As dem dey call twenty thousand one bag na the decisive evidence: the number words na counting-house words.
E dey explain the object forms. Reach thirty, Yoruba get distinct numeral forms specifically for counting objects, wey come from counting cowries . Oókàn, one, na short form of owó ọ̀kan, one cowrie . The counting vocabulary carry the word for money inside am.
E dey explain the subtraction. If you dey count physical objects into heaps, e dey quicker to make heap of twenty and remove three pass make you count seventeen one by one. Subtractive naming na wetin physical counting practice with standard heap sizes dey produce. The system na description of procedure with the hands, no be abstract notation wey dem invent for desk.
Dem also arrange cowries in arrays, and dem don describe the arrangement say e function like abacus . Mann 1887 report to the Journal of the Anthropological Institute describe the activities of wetin im call the magician-calculator, the specialist wey dey do fast computation with cowries . Dis na the earliest substantial European description of the system.
Two properties make the system remarkable to specialists, and dem suppose state am in the terms wey specialists dey use.
Unusually heavy subtraction. Subtractive number formation dey exist inside many languages, including Roman numerals and Latin undeviginti, but normally e dey marginal. For Yoruba, e dey structural and pervasive: e dey control 15 to 19, all the odd decades, and large share of compound numbers. Yoruba numbers get more than typical amount of subtractive formation, an operation wey dem describe as back-counting .
Combinatorial flexibility. Na dis findin go far pass normal curiosity. Yoruba numbers get serious flẹksibiliti for how person fit form dem, wey dey allow make dem call one particular number for many different correct ways wey plenty pass normal; person fit call 19,669 for eleven different ways . Overmann interpretation na say dis one dey show say Yoruba people dey see numbers like group of different ways to combine things, no be like points for straight line di way Western number line dey see dem, and she join dis idea wit di way dem dey arrange cowries visually for groups .
Dis na claim about how brain dey reason mathematics, no be just about vocabulary, and na di most interesting tin wey anybody don talk about Yoruba numeracy. Make we mark am say na interpretation instead of measurement: Overmann dey use language structure bring out how di mind dey reason, wey be reasonable inference but no be proof. Confidence: medium.
Helen Verran related work look Yoruba number from different angle, as e check how Yoruba counting practice dey work for real life instead of just for theory, and na di oda major academic work be dat . Wetin concern Verran na wetin dey happen wen Yoruba and English counting practice meet for classroom, and her argument touch whether di two systems dey actually do di same tin.
E hard? Mathematics literature point out say di system hard small for middle numbers, and dem ask correct question whether dis complexity get any special advantage, since complex arithmetic dey require person to remember plenty things for head . Na honest observation be dat and e correct make e dey here. System wey dey call 45 as twenty-in-three-places-minus-ten-minus-five no dey clearly better for calculation pass one wey dey call am forty-five, and wetin people dey do today don clear: educated Yoruba speakers today dey often use English numbers for arithmetic, price of things and date, while dem still dey use Yoruba numbers for normal talk and inside traditional settings. Di system dey face real pressure from dat competition.
Counting groups. Di four-day week and how four, eight and sixteen dey repeat for Yoruba arrangement dey inside 09-social/09-time-and-the-calendar, wey explain di four-day ọ̀sẹ̀, di market cycle wey e dey control and di cosmological reason wey dem give for am. Dat file na di reference for how Yoruba people dey calculate time and dis one no dey repeat wetin dey there. Wetin suppose dey here na di observation say di counting system base na twenty, while di time and divination arrangement dey run on four and di way dem dey double am. Na two different modular structures inside di same culture be dis, and dem no come from each other.
Length. To measure how long tin dey, dem use parts of di body, like arm span, forearm, hand span and pace, just like most societies before metric system start. Dis compiler no find any standard Yoruba unit for length wey get documented value, and e no add any.
Volume and quantity. To measure things for market trade, dem count units and dem use standard containers: calabash, basket, and heap. Market practice dey measure plenty goods by heap instead of weight, and e still dey do so till today, wey be system of standard customary quantity instead of exact scientific measurement. 09-social/06-economy-and-the-market cover market practice.
Weight. Dis compiler no see any evidence of Yoruba balance-and-weight system wey match Akan gold-weight system, where dem dey use brass weight wey get standard mass together wit balance scale take weigh gold dust. E good make we talk say dis system no dey, because sometimes people dey generalize Akan system give whole West Africa. Yoruba trade run on cowries wey dem count, and to count na different technology from to weigh.
Value. Cowrie na di unit of account and di number system dey built on top am, as e dey above. Dem dey count big money for bags, ọ̀kẹ́, wey be twenty thousand.
Dis corpus don already treat dis matter well-well inside 05-ifa/07-ifa-as-information-system, wey separate wetin don dey proven from wetin people just dey claim. Di main points, wey we link instead of to write dem again:
Wetin be true. Ifá na binary addressing system over one very big corpus wey dem hold for memory. Each odù get eight binary positions, wey dey give 2⁸ = 256 addresses, and dem dey bring out di verses through dat address space. Dat na accurate description and na serious achievement for information management inside society wey no dey write.
Wetin no be true, and di corpus talk am. Di claim say Leibniz copy binary arithmetic from Ifá no correct based on time line: him write date for his own De Progressione Dyadica wit his own hand say na 15 March 1679, and no record dey at all say Leibniz and Ifá ever get any contact at any time. Di claim say Eglash show say Ifá na fractal and recursive put another finding for wrong place: Eglash recursion result concern Bamana sand divination, where later figures dey come from earlier ones through addition modulo two, and Ifá casting no get dat kind step, since all eight positions dey come from independent physical events.
Wetin make dis file no dey argue am again. Reader wey wan see di full argument, di dates, di sources and di assessment of di transmission debate suppose go check 05-ifa/07. Wetin matter for section on Yoruba science na di methodological point: di real achievement na di 256-address randomised retrieval system over a corpus of more dan one hundred thousand verses wey dem keep for memory wit quality control, and e no need any borrowed credit from di history of European computing. Di number system wey we describe above na better example of Yoruba mathematical distinctiveness because nothing about am dey exaggerated.
Yoruba number system dey base on twenty-twenty (vigesimal), e comot from how dem dey count cowrie, e dey use subtraction well-well in special way, and e get unusual flexibility to take arrange the same number in different correct ways . Dem document am for European literature start from Mann 1887 report go front , and standard survey book on African mathematics treat am . E truly special among the number systems for the world on top subtraction and flexibility matter, and na the assessment of specialists wey dey study numeral systems, no be just ordinary person claim.
Yoruba measurement follow traditional custom pass metrological standard, and no standard weight system wey match the Akan one dey documented. To talk am like this no cost anything and e dey protect every other thing wey dey the file.
What is and is not documented about Yoruba star knowledge, the agricultural year and how it was kept, and the soil and land classification which has been tested against laboratory soil science and largely held up.
What laboratory analysis of Yoruba iron, glass and dye actually shows, including the Igbo Olokun glass which turned out to be made rather than imported, and how the reducing chemistry of an indigo vat and a soap ash lye works.
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 four-day week and its orisa, the lunar month and the thirteen-month year, how festivals were dated, and how a four-day week now coexists with a seven-day one.
An analysis of the traditional Yoruba vigesimal and subtractive numeral system, cowrie currency computation, and anthropomorphic and relational units of measurement.
What the Yoruba word for medicine covers, how physical and spiritual causation work together inside one diagnostic act rather than in separate compartments, and why calling this system "traditional" as opposed to "scientific" describes it wrongly.