Mathematics of the Yoruba People and of Their Neighbors in
Transcription
Mathematics of the Yoruba People and of Their Neighbors in
Mathematics of the Yoruba People and of Their Neighbors in Southern Nigeria Author(s): Claudia Zaslavsky Source: The Two-Year College Mathematics Journal, Vol. 1, No. 2 (Autumn, 1970), pp. 76-99 Published by: Mathematical Association of America Stable URL: http://www.jstor.org/stable/3027363 . Accessed: 24/03/2013 23:30 Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at . http://www.jstor.org/page/info/about/policies/terms.jsp . JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact [email protected]. . Mathematical Association of America is collaborating with JSTOR to digitize, preserve and extend access to The Two-Year College Mathematics Journal. http://www.jstor.org This content downloaded from 138.238.41.254 on Sun, 24 Mar 2013 23:30:41 PM All use subject to JSTOR Terms and Conditions HistoricalCorner Yoruba NumerationSystem Mathematics of the Yoruba People and of TheirNeighbors in SouthernNigeria ClaudiaZaslavsky ClaudiaZaslavskyis the authorof "Black AfricanTraditionalMathematics,"published in the April 1970 issue of The Teacher.She has been interMathematics estedin thehistory ofAfricanmathematics for over a decade. Her work has been describedbyHowardEves as "outstanding andperhapsthefinestin thefield." Thisarticleis partof herforthcoming The editors book on Africanmathematics. electedto printtheentireselectionrather thannarrowtherangeof itscontent,even though the article includes some nondigressions. mathematical The author would like to express her gratitude to the people who offeredvaluableinformation: J. F. A. Ajayi, University of Ibadan, Nigeria;J. A. Akinpelu,Universityof Ife, Nigeria; R. G. Armstrong,Universityof Ibadan, Nigeria; Donald W. Crowe, Universityof Wisconsin;Jim Karns,Ohio Universityat Lancaster;OffiaNwali, Nigeria, International Research & Marketing, Inc.; H. M. A. Obayemi, Nigeria; Paul Rosenblum, Cornell University. Dr. Akinpelu, Dr. Nwali, and Mr. Sam Zaslavsky read the manuscriptand offeredmanyexcellentsuggestions. The readerwith an interestin the development of indigenousmathematicsin Africa will find little informationin the mathematics history books except for a treatment of ancient Egypt.Of the few existing accounts of other Africans' mathematical development,one well-knownstoryis that of the Damara people of SouthwestAfrica, now called the country of Namibia; the Damaras wandered in nomadic bands and were among the least advanced, from the point of view of technology,of all Africans. Their tale was firsttold by Sir Francis Galton, the Britishscientist,explorer,and of in his book, Narrative anthropometrist, an Explorer in Tropical South Africa, published in London in 1889. Here it is, as retold in Howard Eves' In Mathematical Circles: . . . the primitive Damaras of Africa, in barteringtwo sticks of tobacco for one sheep as the rate of exchange, became hopelessly confused when a white trader, desiringtwo sheep, offeredfour sticks of tobacco at once. Fraud was suspected by the Damaras, and the transactionhad to be revised and carried out more slowly. First two sticks of tobacco were givenand one sheep drivenaway, thentwo more sticksof tobacco and the second sheep claimed. When shown that the resultcame out the same as the trader's originalproposal, the tribesmenregardedthe trader as one possessed of magicpowers. Eves concludes the narrativewith a telling comment that is omitted frommost other histories: Yet, these Damaras were not unintelligent. They knew preciselythe size of a flock of sheep or a herd of oxen, and would missan individual at once, because they knew the faces of all of the animals.To us, thisform of intelligence, which is true and keen observation,would be infinitelymore difficult to cultivate than that involved in counting. 76 This content downloaded from 138.238.41.254 on Sun, 24 Mar 2013 23:30:41 PM All use subject to JSTOR Terms and Conditions I should like to suggestanotherex- among the Yorubas of Abeokuta the explanation. There is a widespreadfear traordinarysaying, "You may seem very amongAfricans, as well as otherpeoples, clever,but you can't tell nine timesnine", shows how surprisinglythis faculty has that the countingof people and other been developed, considering the general livingcreatureswill lead to theirdestruc- level of savageryin whichthe tribelived. is doneindirectly, tion.Therefore counting correspondence Conant sees the occurrenceof numbersup by settingup a one-to-one betweenthe animalsand some type of to a million among South Africantribesas "remarkableexceptions" to the "law" that countingobject. In thiscase therewas a "the growth of the number sense keeps betweensticks two-to-one correspondence the growthof the intelligencein of tobacco and sheep. The superstition pace with otherrespects." is treatedat greatlengthby aboutcounting Such was the extent of the prejudice A. Seidenbergin his article,"The Ritual against darkskinned peoples that all the Origin of Counting."(Archivefor the of logic were turned upside Historyof the Exact Sciences,Vol. II, principles pp. 1-40).One can recall,too, theBiblical down. One would expect that a scientist, that refutes storyof KingDavid,whoactedagainstthe when confrontedby evidence his "laws," might begin to doubt their adviceof Joabandtheotherarmycaptains in orderinga censusof his people. After validity. This "scientific" attitude is the count had been broughtto him,he analyzed in an unpublished manuscript, realized his error,but it was too late. Science and Africa, by Frank E. Chapman, pestilenceon the Jr., a young black man now servinga life Jehovahvisiteda terrible people,and manydied. Onlythe offering imprisonment. of a sacrificesucceededat last in staying There is so much talk about a "primitive type of mind" and an "advanced type of thehandofJehovah. L. L. Conant'sThe NumberConcept, mind." These conceptualists rarely pause to consider what it is in fact that they are publishedin 1896,is one ofthefewbooks talking about; they neverstop to consider in Englishwhichdiscussthe numeration that this whole businessof "mind types" is systemsof many Africanpeoples. How- merelya collocation of convenientverbaliever,Conant'spointof viewis completely zations; indeed, the scientist'sbehavior is attitudetoward very similarto the "primitive"he is talking coloredby the prevailing about when he verbalizes about "mind Africansas "primitive savages";theywere types." This stifling"mind" concept cripdeemedhardlyhuman.He dismissesthe ples scientific analysis, and only when systemof greater emphasis is put on psychological amazinglycomplexnumeration the Yoruba people of southwestNigeria behavior patterns (in a given social context) will it be understood once and for withthesewords: Nor,on theotherhand,is thedevelopment indexof of a numeralsysteman infallible mentalpower, or of any real approach use ofthe A continued towardcivilization. facultiesmustand tradingand bargaining does resultin a familiarity withnumbers sufficientto enable savagesto perform unexpectedfeats in reckoning.Among some of the WestAfricantribesthishas actuallybeen foundto be the case; and all ... that the differencein psychological make-up is due, more or less, to the differencesin social conditions,whichhave nothing whatsoever to do with "mind types."* There is ample evidence of the Africans' skills in the use of numbers. The Britishtrader,Mr. Clapperton,reportedin *Quoted withpermissionof the author. 77 This content downloaded from 138.238.41.254 on Sun, 24 Mar 2013 23:30:41 PM All use subject to JSTOR Terms and Conditions in 1826 on theuse of cowrieshellcurrency a region that is now part of Nigeria, bedeclaringthat it was veryconvenient of forgery. cause it allowedno possibility He praisedthe "dexterity of thenativesin countingthe largestsums." Einzig states that merchantshad to count in large figures, and theydevelopedthe advanced arithmetical facultyrequiredforthe purpose. MarionJohnsonwrites:"The use of dependson cowriesforlargertransactions a rapidsystemofcounting them." MichaelCrowder,in WestAfricaunder theYorubapeople ColonialRule,mentions Part of the culturethateach specifically. to the succeeding generationtransmitted generation was the abilityto handle the thenin use. Since variouskindsof currency a low-valued wasusedas (cowrie)currency the base, considerable arithmetic skillwas necessaryto conducttradeoutsideof the confinesof the village."Contraryto a generally EuropeanheldopinionthatAfricans could not count beyond ten, the Yorubas could count to a million." Crowderadds that"worksby NegroMuslaw,theology, history, limson philosophy, and medicineexist all over the Western to the regionof West Sudan," a reference Africa justbelowtheSaharaDesert. Let us nowexaminetheYorubasystem of numeration, called by Conant"one of the most peculiarnumberscales in exisof the systemis given tence."A summary by the Rev. SamuelJohnsonin theintroductionto his book, The Historyof the Yorubas.* termsare From one to ten, different used, then for 20, 30, 200 and 400; the rest are multiplesand compounds.Thus 11, 12, 13 and 14 arereckonedasten plus one,plustwo,plusthreeandplusfour;15 to 20 arereckonedas 20 lessfive,lessfour, *AII diacriticalmarkshave been omitted fromthisreprinting. less three, less two, less one, and then 20. In the same way we continue 20 and one, to 20 and four,and then 30 less five (25), less four,and so on to 30, and so for all figuresreckonedby tens. There is no doubt that the digitsform the basis of enumerationto a largeextent, if not entirelyso. Five, ten, twenty,i.e., the digitsof one hand, of two, and the toes included, and their multiples form the different stagesof enumeration. Beginningfromthe firstmultipleof 20 we have Ogoji, a contractionof ogun meji, i.e., two twenties(40), Ogota, three twenties (60), Ogorin,four twenties(80), Ogorun, five twenties (100), and so on to ten twenties(200), when the new wordIgba is used. The intermediatenumbers(30 havinga distinctterminology),50, 70, 90, 110, 130 to 190 are reckonedas: 60 less ten (50), 80 less ten (70), a hundredless ten (90), and so on up to 200. The figures from 200 to 2000 are reckoned as multiples of 200 (400, however,whichis 20 X 20, the square of all the digits,has a distinctterminology, Irinwo or Erinwo, i.e., the elephant of figuresmeaning the highest coined word in calculation,the restbeingmultiples).... By a systemof contraction,elision,and euphonic assimilation,for which the Yoruba language is characteristic,the long termOrun-din-ni (Egbeta or Egberinand so on) is contracted to Ede or Ode, e.g. Edegbeta (500) ... and so on.... Summary. Thus we see that with numbersthat go by tens fiveis used as the intermediatefigure-fiveless than the next higherstage. In those by 20, ten is used as the intermediate.In those by 200, 100 is used, and in those of 2000, 1000 is used. The figure that is made use of for calculating indefinite numbers is 20,000 (Egbawa), and in money calculation especially it is termedOke kan, i.e., one bag (of cowries). Large numbers to an indefinite amount are so many "bags" or rather"bags" in so manyplaces. We have here an example of a vigesimal system,one based on twenty,of whichwe find numerousexamples in westernAfrica, as well as in other parts of the world. In 78 This content downloaded from 138.238.41.254 on Sun, 24 Mar 2013 23:30:41 PM All use subject to JSTOR Terms and Conditions Englishwe have theword"score,"and in French quatre-vingt(4-20) represents (4-20-10) is eighty,whilequatre-vingt-dix used forninety.Theunusualfeatureofthe to a Yorubasystemis thatit is subtractive veryhighdegree. I havereliedheavilyfortheanalysisof Yoruba numeralsupon Robert G. Armstrong'sstudy, Yoruba Numerals.Armstrongstates: "It is testimonyto the that Yorubacapacityforabstractreasoning they could have developedand learned whose sucha system."The originalsystem, age is not given,was expandedfor the cowries. purposeofcounting Table I showsthe wordsforthe first ten numbersin thefourprincipalapplications Table I Cardinal 1. okan 2. eji 3. eta 4. erin 5. arun 6. efa 7. eje 8. ejo 9. esan 10. ewa Adjectival 1. kan 2, 3. 4. 5. 6. 7. 8. 9. 10. meji meta merin marun mefa meje mejo mesan mewaa Counting ookan= eni eeji eeta eerin aarun eefa eeje eejo eesan eewaa Ordinal ekin:ni ikin:ni akoko ekeji=ikeji eketa=iketa ekerin ikerin ekarun=ikarun ekefa= ikefa ekeje= ikeje ekejo= ikejo ekesan= ikesan ekewaa= ikewaa The doublevowelwithwhicheach of the countingnumbersbegins is actually a formof thewordowo, meaning contracted "cowrie"or "money." The followingare the names of the forthe as well as thederivations, numbers, series: counting 6 eefa ookan 7 eeje eeji 8 eejo eeta 9 eesan eerin 10 eewaa aarun 11 ookan laa (laa from le ewa = in additionto ten) 12 eejilaa 13 eetalaa 14 eerinlaa 15 eedogun(fromarundin ogun = five reducestwenty) 16 eerindinlogun(20 - 4) 17 eetadinlogun(20 - 3) 18 eeji dinlogun(20 - 2) 19 ookandinlogun(20 - 1) 20 ogun 21 ookan le logun("one on twenty"= 20+ 1) 25 eedoogbon(30 - 5) 30 ogbon 35 aarun din logoji (five less than two = (20 X 2) - 5) twenties 40 ogoji("twentytwos") 50 aadota(20 X 3-10) 60 ogota (3 X 20, or more literally, "twentyin threeways") 100 ogorun= orun(20 X 5) 105 aarundin laadofa(20 X 6 - 10 - 5) 200 igba 1 2 3 4 5 After200 the systembecomesquite are mainand theseirregularities irregular, levels.A fewexamples tainedon thehigher follow: 300 oodunrun= oodun [20 X (20 - 5)] 79 This content downloaded from 138.238.41.254 on Sun, 24 Mar 2013 23:30:41 PM All use subject to JSTOR Terms and Conditions odinmarun orindinnirinwo [400-(20X 4)-5] irinwo egbewa(200 X 10) egbaaji(2 X 2000) egbaawaa(2000 X 10) egbaawaalonanmeji (ten2000s in twoways) (idiomatically egbeegberun 315 400 2000 4000 20,000 40,000 1,000,000 1000 X 1000) of thenumeralsfrom35 The construction in Table II. Of through54 is represented the twentynumerals,only five do not at all, and fiveinvolve involvesubtraction in twocolumns! subtraction venturesthe opinionthat Armstrong the patternoriginatedso that one could of withthefingers countthetennumbers one hand. If the multiplesof ten are understood,and not shown by finger thenone fingerat a timecan be gestures, extendedto denote 21, 22, 23, and 24, Whenthe fifthfingeris exrespectively. from30; andwhen tended,it is subtracted fourfingers the remaining it is retracted, aredeductedfrom30 to give26, etc. alreadydescribed, Besidesthenumerals there is an additionalset for counting is basedon thecowrie cowries.Thissystem 4000 cowries= one in shillings: equivalents The specialnamefor20,000 cowshilling. riesis oke kan = one bag,or fiveshillings. 1000 cowor toro,represents Threepence, of only300 had a value a penny ries,but the time the was system cowries at principleis used adopted.The subtractive constructions: againin thefollowing = (m)eji two (shillings)and threepence le toro two (shillings)and ninepence= (m)eta dintoro(threelessthreepence) is stillusedtoday The cowriereckoning to large numbers:a farmer in referring mightsay he has "shillingthreepence" ratherthan 5000 yam heaps. The term "bag" may be used insteadof "fiveshillings." The idea of "infinity"is expressedin the Yoruba proverb:"Thereis nothingas numerousas thelocusts;theyarefoundat home and in the farm."Althoughsome farmswereas muchas twentymilesfrom lived,the the townsin whichthe farmers locustscoveredeverybit of foliageon the route.Comparethissimilewiththeancient Egyptiansymbolof a tadpoleto represent 100,000; its name,hfn,also means "innumerable."AftertheNilefloodsreceded, in could be seensquirming thesecreatures to be counted. themud,too numerous A traditional folkquerythatreminds us of our highwaysand citysubwaysis: Table II twentyten unit twentyten unit 35 36 37 38 39 40 41 42 43 44 2 2 2 2 2 2 2 2 2 2 0 0 0 0 0 0 0 0 0 0 -5 -4 -3 -2 -1 0 1 2 3 4 45 46 47 48 49 50 51 52 53 54 3 3 3 3 3 3 3 3 3 3 80 This content downloaded from 138.238.41.254 on Sun, 24 Mar 2013 23:30:41 PM All use subject to JSTOR Terms and Conditions -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -5 -4 -3 -2 -1 0 1 2 3 4 "Whichis the verylong coffinthat can accommodate1400 corpses?"The answer is "the path," depictedas a long coffin containingmanybodies arrangedend-toend in singlefile.This picturerepresents who filealongthe thehundredsof farmers pathson theirwayto andfromtheirfarms during"rush"hours!The number1400 is composedof the factors7 and 200, both specialnumbers. considered of Ife, Dr. Akinpelu,of theUniversity for gave me the followingconstructions andforpowers fordoubling, unitfractions, ofa base: ebu = fraction Idameta = one-third(Divided into three) Idamerin= one-fourth Idamarun= one-fifth etc. Ilopomefi= twotimes,or doubling Erinlonamei= 42 (4 in 2 places) Erinlonameta= 43 Erinlonamerin 44 etc. of Ibadan, Dr. Ajayi,of theUniversity has stated: "Yoruba vocabularycovers, a wide rangeof apart fromnumeration, fractions, concepts,including mathematical squaresand squareroots,etc." On methods he writesthat they are of computation, mentally;"sometimes usually performed also markson walls,beansor sticksin a jar, etc. to representlarge units of what is beingcounted;e.g.,a hundredor thousand cowriesor heads of cattle,etc. owed, or yearsof a monarch'sreign.In somekingdoms,censusesof the numberof families in each villageor districtare kept in the samemanner." I have not thus far been able to determinewhat computationalmethods were used in past centuriesby Yoruba inin commercialtransactions merchants volvingmanythousandsof cowrieshells. Nor have I yet foundwhethertheykept writtenrecordsof debts,or whethertrade on a cashbasis. was strictly During the colonial period the lanEuropeanpowers guagesof thedominating wereused in Africanschools,exceptpossibly in the primarygrades. Since they theAfrican however, gainedindependence, peopleshave been eagerto reviveinterest in theirown languagesand culture;hence thereis a newdesireto expandthenative vocabularyto include conceptshitherto AlthoughEnglishis stillused unexpressed. of higher today in Nigerianinstitutions learningas a commonmeansof communication for studentsof extremelyvaried linguisticbackgrounds,the Yoruba languageis beingexpandedto accommodate newideas. the Directorof the Dr. Armstrong, at theUniverStudies Instituteof African a decimal developed sity of Ibadan, has words Yoruba uses which numbersystem all theirregularandeliminates throughout, ities of the traditionalsystem. Thus would becomereadily modernarithmetic accessibleto averagepeopleand to youngsters in the elementarygrades,without thattheylearna languageother requiring reforms than theirown. Dr. Armstrong's operaincludetermsforall the arithmetic decimalfractions, as well as fractions, has tions, and percents.Dr. Armstrong confidencethat these reformswill enin couragepeople to take a greatinterest as theyrealizetheyare citimathematics, zens of an increasinglymathematical world. He concludes:". . . a nationthat could develop and transmitthe comsystemhas plexitiesof their[numeration] obviouslya great deal of mathematical talentandinterest." 81 This content downloaded from 138.238.41.254 on Sun, 24 Mar 2013 23:30:41 PM All use subject to JSTOR Terms and Conditions History ofSouthwest Nigeria developed many centuriesago. Cattletheoccupationof peoplessuchas herding, The developmentof a numbersystem the of Masai of Kenyaand theHottentots dependsupon the need. In a small selfof extensive South Africa, required systems containedeconomy,typicalof largesecas numeration, did large-scale carried trade, tionsof Africa,in whichall ormostofthe necessitiesof life are producedwithinthe on bytheadvancedancientsocieties. It is only by learningthe historyand community,there is little need for an of a people that we can development extensivereckoning system.The namesof understand their We needformathematics. numbersarefrequently connectedwiththe to the of are discover just beginning history objects to be counted,just as we have the southern most Nigeria, densely popuspecialnamesforcertainsets-flock,herd, brace,etc., datingback to a pastoralor lated regionof the whole continentof agricultural society.Fingerandotherbody Africa.Since the peoplesof thisarealeft thekeyto theirhistory records, gesturesmight accompany or be used no written lie in must archaeological excavations, insteadof spokenwords.Gesture-counting of oral works art, traditions, language in themarketplace, is especiallynecessary of and visitors. analysis, reports foreign wherepeople speakingvariouslanguages The recentlydevelopedtechniqueof gatherto exchangegoods. It mightbe radiocarbon datinghas broughtinfinitely customaryto use beads, shells,nuts,or greater to the fieldof archaeoaccuracy pebblesas mediaof exchangeor as countlogical research. By early 1967 thirty-one ing materials(the word calculate is derived known for dates were all of Nigeria.It is from calculus, Latin for pebble), and to estimated that five thousand dates are arrangethemin sets,thus givingrise to for the needed period 500 B.C.-A.D. 1500 specialwords. to enable to archaeologists make an adeMany Africansocieties,however,rereconstruction of the of quate the history quiredthe use of largenumbersfortheir country. economies.MostAmericans well-developed In the Nok area of northern Nigeria to learn and Europeansare just beginning have stone been found implements whose of the greatempiresthathave existedin is estimated at more than age 39,000 years. variouspartsof Africasincethe timeof The iron-based Nok culture is believed to ancientEgypt.Kush,withitsiron-working have in existed approximately 900 city,Meroe,flourished just southof Egypt art figures beforethe Christianera. In the western B.C.-A.D. 200; the terracotta of this period are thought to have directly part of the Sudan region,there were influenced the later art of the Yoruba and ancient Ghana, which did an extensive of Benin. tradein gold; the citiesof Timbuktuand Concentrated efforts arebeingmadeto Djenne,centersof advancedlearning;the the oral gather traditions, but the diffiofMali,Songhay,andKanem,to kingdoms culties are On the site of theformer great. namea few.Further southlie theextensive of the Oyo Yorubas one Empire nowfinds ruinsof Zimbabwe,in presentRhodesia. ruined settlements, some deserted during Earlyin the Christianera thisarea was a the invasion of the Nupe fifteenth and source of gold, copper, tin and iron, sixteenth some centuries, sacked the by particularlyfor the Easternworld. The Alafins of in the (kings Oyo) seventeenth of Kitwaraand Kongo,ofNubia kingdoms and ancient Ethiopia were highly and eighteenth centuries and many 82 This content downloaded from 138.238.41.254 on Sun, 24 Mar 2013 23:30:41 PM All use subject to JSTOR Terms and Conditions in- tionlegend,theOba of Beninandtheheads emptied by the nineteenth-century vasion of the Islamic Fulani from the of the six Yoruba kingdomswereall denorth,as well as theDahomeanslaveraids scended from a common ancestor, greetthe Oduduwa.Oranyan,the youngestking,is fromthewest.Lionsoccasionally supposedto have been thefounderof the present visitors to thesesites. century Oyo state,whichby thefifteenth Essentialto everyAfricanroyalhouseempire. a mighty had become historian, whose hold was theprofessional Anotherversionof the creationmyth duty it was to memorizeand recitethe withtheFlood. Olorun,thesupreme begins His function dynasticlistsof thekingdom. his son Oduduwadownon a chain, let god, ofthe was similarto thatoftherhapsodists a handfulof earth,a cockerel,and carrying Homeric age. No doubt the facts were Oduduwascatteredthe earth a nut. palm colored somewhatto please the current the and thecockerelscratched over water, a theselistsconstitute rulers;nevertheless, theland on whichthe it became it so that reliablerecord. fairly its sixteenbrantree spreading grew, palm Toward the end of the nineteenth sixteen is believed The sacred number ches. centurythe Rev. Samuel Johnson(Anla headsof sixteen crowned the to represent underOgun),a YorubaAnglicanminister, Yorubaland. so tookto writedowntheseoraltraditions, By the year A.D. 1300, the Yoruba ofhisfatherland mightnot thatthehistory had built numerouswalled cities people be lost. Although educated Yorubas, by farms.Tradewas carriedon surrounded schooledin the Westerntradition,were the of the north;theyexwith peoples familiarwith the historyof Greece and kola nutsforproducts cloth and changed abouttheirown Rome,theyknewnothing land. Johnsonspent over twentyyears they needed. In turn the Yoruba states stimulation collectinghis materialand recordedit in wereexposedto theintellectual neighborsand of the The Historyof the Yorubas,whichcom- of of the northern Manyhisin Timbuktu. prisesthe myths,history,and customsof IslamicUniversity in Arabic toricalrecordsof Africa,written hispeople. All the traditionsindicate that the and datingback as far as the seventh to giveus haveyetto be translated Yoruba people came originallyfromthe century, of life. African a more picture complete There are to the similarities many east. the the centuries, following During culture in obancientEgyptian religious its dominion until of expanded state Oyo of burial and works art, customs, servances, theinstitution ofdivinekingship; however, extendedover a vast area,includingeven these culturaltraitsare sharedby other Dahomeyto thewest.MeanwhilethekingAfricanpeoples. The town of Ife, also dom of Benin,to the southeast,had beof theYorubasand had called Ile-Ife,was the spiritualcenterand comeindependent into empire.Whenthe a mighty grown it cradle of the Yoruba people, and was to visitthis the first Europeans Portuguese, fromIfethatthepeopleoftheneighboring in the entered Benin of City Africa, part stateof Beningot theirlonglineof kings. fifteenth were truly late they century, At thissitehave been foundthe remarklevel of the culture astounded they by able bronze, stone, iron and terracotta detravelers encountered. Later European worksof art,datingback almosta thouof the methe main streets scribed thirty sandyears. and wide,the longest Accordingto one versionof the crea- tropolis,all straight 83 This content downloaded from 138.238.41.254 on Sun, 24 Mar 2013 23:30:41 PM All use subject to JSTOR Terms and Conditions of whichwas fourmiles in length."The black cityin Africa,a metropolis of more people are as clean as the Dutch, their than1,400,000people,and the seatof the housesshinelikea lookingglass,"reported famous Universityof Ibadan. Although a Dutchvisitor.The Oba's palacealonewas axes datingback to the Stone Age have reputedto be as largeas a Dutch town. been foundin thearea,Ibadanwas onlya Brass-casting by the lost-waxmethodhad smallvillagebuiltarounda centralmarket century.Withthe been introducedfromIfe,makingpossible priorto the nineteenth warsitbecamea settlement forthe the marvelousplaques on the wallsof the internal army,a townfreeof thefearofinvasion, a palace,a history of Beninin artform. of Withthe Europeanscamemissionaries, refugefromstrife.Todaythree-quarters are farmers who livein the gin,firearms, and theintensification of the the inhabitants whichsurround slave trade. Slave raidingand wars with cityand workon thefarms mileswide.Actuallyit is neighboring peoplesalternated withperiods it in a ringtwenty of stabilityand peacefultrade-untilthe a city-village; farmers, craftsmen and traddissolution oftheempires andtheconquest ers live in largecompoundsin the town by theBritishat theend of thenineteenth center. century.A conservativeestimate gives 24,000,000 as the numberof slavesex- Currencyand Trade portedfromWestAfricaand Angola.Dr. The Yoruba people of southwestNigeria W. E. B. DuBois believedthat100,000,000 have been knownfor centuriespast as a Africans werelostin thecourseof theslave nationoftraders; thisreputation extendsto trade. Many revolted,died in battle, both men and women.Marketswere-and jumped overboard,or perishedin the in- still are-held at regularintervals, usually famous"MiddlePassage,"the journeyto every four days, to coincide with the the New World,wherethe institution of traditionalYoruban four-dayweek. The slaverybecamethe foundationforAmeri- locationand the productsof the markets can prosperity.It was also the wealth rotate.Today the clothmarketin Ibadan, producedby theslavetradethathelpedto held everysixteendays,attractscustomers lay the basis for the expansionof the frompointsas distantas Ghana.Sincethe Yoruba empire.Everyyearthe armiesof marketwomencombinethe rolesof food thekingsscouredneighboring territories in producer, traderand customer, theperiodislaveraids.In turn,theYorubatownswere cityofthemarketis a necessity. attackedby otherpeoples withthe same In somepartsof WestAfrica,thenames reprehensible motives. of the days of the week are actuallythe In 1897 a Britishdelegationinsisted namesof the main townsin the area in upon seeingthe Oba of Benin at a time which marketsare held on those days. whenhis religionforbadehimto meetwith AmongtheIbo people,thevillageclusteris Severalof theBritishwerekilled dividedso that the varioussectionshave strangers. in this incident.In retaliation the British theirrestperiodson different dayswithin sent a punitiveexpeditionto burn the the four-dayweek, or withina periodof entirecity. Theyremoved2500 beautiful two weeks,called the "bigweek." On the Beninbronzes;theseare now on exhibitin rest day, the villagersabstainfromfarm the museumsof Europe and the United workto do householdchores,practicetheir States. hobbies,and visit theirfriends.It is on The YorubacityofIbadanis thelargest thesespecialdaysthatfestivals, ceremonials 84 This content downloaded from 138.238.41.254 on Sun, 24 Mar 2013 23:30:41 PM All use subject to JSTOR Terms and Conditions all in the plains that these cowrieswere imported and marketsareheld,frequently same location.Most lbo marketsnow ad- fromthe northinto the westernSudanic schedule. hereto an eight-day kingdoms. Althoughgoods were oftenexchanged When the Portuguesepaid theirfirst the merchants of visitto Beninin thefifteenth by barterarrangements, century, they long found cowrie shells in commonuse. In southern Nigeriahad adoptedcurrency beforethearrivalof theEuropeans.As the 1588 James Welsh, an English trader, numberwordsindicate,thecowriewas the boughttwo gallonsof palmwinein Benin basic unit of currency.These shellshave fortwentyshells.A yearlatertwoLondon been treatedwith disdainby Europeans, merchantsnamed Bird and Newton repartlybecauseof the debasementof their portedthat"prettywhiteshells"wereused How- as Europeansused gold and silver.They century. value duringthenineteenth formof wereable to purchasetwogallonsofhoney ever,theyare trulya sophisticated MarionJohnson quotesan anony- anda honeycomb fora sumofone hundred currency. mous Dutch gentlemanwritingin 1747: cowries. About the year 1700 a Dutch trader Cf...those who are pleased to show a contemptof them(cowries)don't reflect told of the royalmonopolyof theOba of thatshellsare as fitfora commonstandard Benin.No specificdutieswereimposedon buttherewasan annual of pecuniary valueas eithergoldor silver." importsor exports, of trading. Picturesof cowrieshellsappearon the tax in cowriesfortheprivilege governorwas requiredto man. Each territorial wallsofcaves,executedbyPaleolithic consideredthecow- raisea specifiednumberof bagsof boesies The ancientEgyptians rie a magicagent,a talismanof fertility, (cowries)forthe Oba's use,whileofficials in of lower rank deliveredproducefor the and in some cases used it as currency foreign exchange. Archaeologistshave royal household. There were no poor foundmillionsof themin thetombsof the people in the land; the wealthywere centuryAfrica obligatedto see thatnonewenthungry. Pharoahs.By thethirteenth fromthe Cowrieshellswereintroduced had been floodedwiththesesmallshells. Large quantitieshave been excavatedin Maldivesof the Indian Ocean by Arab caravans,whichbroughtthemfromEgypt ancientIfe. Accordingto one of the Yoruba across the Sahara to the westernSudan legends,Oranyan,the founderof Oyo,was region.Withthem came the sexagesimal to thetheory the youngestof King Oduduwa'sgrand- systemofcounting, according He bases this conclusion children.When the King died, all his of Dr. Jeffreys. fortunein cowrieswent to the Oba of upon the Ibo systemof countingcowries Benin,whileOranyanwasleftwithnothing by sixes, as well as the fact that the but the land. But cleverOranyancharged Mandingo"hundred"was actuallysixty. rentforthe use oftheland,andeventually Jeffreys' by theory,however,is discounted acquiredall the wealthfromhis brothers. otherauthorities. A latermethodof entry fromTangier, was by way of the GuineaCoast portsof Ibn Battuta,thetraveler in North Africa,reportsin the book he WestAfrica,withtheDutchandEnglishas wrotein themid-fourteenth century:"The middlemen. of cowbuyingand sellingofits(Gao's) inhabitants An analysisof therelationship and the sameis rie currencyto thenumeration is done withcowry-shells, systemsof the case at Malli." The editor'snote ex- the variouspeoples of West Africais a 85 This content downloaded from 138.238.41.254 on Sun, 24 Mar 2013 23:30:41 PM All use subject to JSTOR Terms and Conditions study.Here we shall consider fascinating Nigeria.How onlythepeoplesof southern werethesesmallshellshandled?How does theirvaluecomparewiththatof European I have reliedmostheavilyon currencies? MarionJohnson'sfineanalysis,"The Cowof WestAfrica"andon A. H. rieCurrencies excellentarticle,"The M. Kirk-Greene's History." inNigerian MajorCurrencies partsoftheregion,the In thenorthern cowrieshellswerecountedoutin groupsof five, while along the coast they were in strings piercedand threaded,generally of forty.The Ibo method was an exception;therethe basic unitwas six cowcowrieswere ries.It is not knownwhether strungat the time the Portuguesefirst began to trade. We know they were namedgalinhas countedin unitsof forty, (Portuguesefor "hens"). Laterthisname or was appliedto a bunchof fivestrings, two hundredshells,no doubt to correspond to the devaluationof the cowriein termsof its purchasingpower. As the commercial languagechangedfromPortuguese to English,later equivalentswere givenin English. In areaswherecowrieswerenotstrung, theiruse dependedupona rapidmethodof higherunits. themin successively grouping thatin Nigeriatradewas Let us remember carriedon by both men and women,and thatcowrieshad to be countedup intothe they high denominations.Furthermore, werecountedout by both the buyerand the seller!Certainlythisshouldhave discouldbarely pelledthemyththatAfricans countto ten. The earlyYorubasystemwasbasedon a combinationof vigesimaland decimal counting:20, 200, 2000, and 20,000 (oke kan = one bag). The systemat Lagoswas north: lateradoptedfurther 40 = 1 string 2000 = 1head= 50 strings 20,000= 1 bag= 10 heads. However,the 200 unitwas recognized;a discountof two cowrieswas allowedon everyfivestrings. whowas sold The Yoruba,Osifekunde, earlyninein the Brazil into slaveryin in the youth his teenthcenturyhad spent recollecHis Lagos. of Ijebu area,northeast tions of life in his homelandincluded of the currencyvalues.He remembrance cowrieequivalents: gavethefollowing = 40 cowries ogoji= string = 200 ogwao= bunch(of fivestrings) cowries = 2000 egwegwa= head(of tenstrings) cowries oke = bag (of ten heads) = 20,000 cowries. The only fixedmeasurehe knew was a standardunitof gold dustcalledochouon, worthapproximately about a thimbleful, 1000 cowries.An averagepricefora slave at thattimewastwobags. Nigeria,the roti, In partsof northern or pound (originallyof copper),was the equivalentof 32 cowries.Each timea roti was countedout, an additionalshellwas set aside as a tally, so that threerotis approximatedone hundredcowries.Perhapsthismethodwas an attemptto reconsystemwiththatof the cile the northern south,wheretwo hundredwerethreaded of of fortyeach,threestrings in fivestrings sixty-six,or two stringsof one hundred witha discountof one percent. All largetradingcentersin thewestern Sudan area employed cowrie counters. Imagine having to count daily up to 300,000 of thesesmallcurvedshells,parwherethey ticularlyin theinlandregions, An attemptby theNiger werenot strung. measure Expeditionof 1841 to substitute for numberprovedto be unpopular.Perhaps the sellerfearedhe wouldbe cheated! 86 This content downloaded from 138.238.41.254 on Sun, 24 Mar 2013 23:30:41 PM All use subject to JSTOR Terms and Conditions In the 1880'scowriesat Lokoja,on the NigerRiver,werestrungin bunchesofone The thousand,witha valueof one shilling. stationto womanemployedby thetrading count them was paid ten shillingsa Womenof West month-inmerchandise. Africaare notabletradersto thisday,and in someIbo marketsthewomen'scouncils set the rate of cowrieexchange.Yoruba women have a reputationfor knowing whereto buy cheapand selldear.Theygo directlyto the farmsseveralmilesfrom town, or wait on the farm paths to purchaseproduceon its way to the local market. In the 1860's thecowrietableand the Britishequivalentsread (with variations upontimeandplace): depending = 40 cowries= one string 3/4- 5 strings= one bunch = 3 10 bunches= one head = lings - 1 penny 6 pence 13Y4- 2 shil- 10 heads = one bag = 14- 18 shillings. By the end of the century,one thousand cowrieswereworththreepence in silver, for buta copperpennycouldbe exchanged only300 cowries. During the early nineteenthcentury the largerZanzibar cowrieswere introduced; European merchantsfound they could scoop themup by the ton and sell Withtheadded themat a handsomeprofit. weightof the shells,and thedepreciation in value owing to the introductionof European currency,by the end of the to transcenturyit was hardlyworthwhile port them.On the lowerNigerRiverthe cowriebecamemerelya measureofvalueprices were quoted in so many cowrie units. It had become impracticalto use themas a mediumof exchangeexceptfor smallpurchasesin the local markets.The in thevalueofthecowriesand fluctuations the need to convertto Britishunitsmust of have taxed the skillsof the shrewdest As an example,in 1902 therate merchants. at Ilorin,in was fourthousandto a shilling the northernYoruba region,while at Sokoto, in northernNigeria,a shilling wouldfetchonly1200 shells,sincecoinage was harderto come by away fromthe Coast.Importsof cowrieswerebannedby Proclamationin 1904 and coinage was However, introducedby the government. since the smallestunit was a threepenny piece,cowriescontinuedto be usedin local of the anini, tradeuntil the introduction ofa penny. worthone-tenth The cowrie units remainusefulas a means of expressinglarge numbers.A farmermightsay his farmhas "threepence" (1000) yamheaps.In earliertimes it was recordedthattheKingofDahomey was beatenby the Yorubaswitha loss of and twenty", "two heads,twentystrings, or 4820 soldiers.The enemywere the who famousDahomeanwomenwarriors, were "advancingin the orderof battle, marchingsteadily and solidly onward, ignoringthe fireof the Egbas (Yorubas) and payingno attentionto thoseamong themselveswho fell, but kept marching stolidlyonward.They neverfiredbut at andwhentheydid, thewordof command, By thiswe theirvolleysweredemoralizing. can see thatthe Dahomeansoldierswere disciplinedtroopssuch as the Egbas had neverfaced before.... Whenthose who actuallyenteredthetownwerecaughtand slain,... then the Egbas knewthatthese terriblefighterswere the Amazons!" So runs the account of the Rev. Samuel the Johnson.He continues:"Immediately newsspreadamongall ranksthattheyhave with women,and for very been fighting shameall the Egba menwereexasperated beyond measureand rushedupon them withone accord and compelledthemto in 1851. Thisbattlewas fought retreat." 87 This content downloaded from 138.238.41.254 on Sun, 24 Mar 2013 23:30:41 PM All use subject to JSTOR Terms and Conditions words up to 96,000,000, and compares thesenumerals to the decimalsystem used by the same people for non-cowrie counting. Althoughthe use of cowriesas ordinary currencyhas been discouragedor outlawed,thesesmallshellshavea function as special-purpose money-as bridewealth and forvariousceremonial payments. Most Africansocietiesrequirea materialconsiderationto legitimizeand stabilizethe marriage,recompensethe bride'sparents for the loss of theirdaughter,and guarantee that the husband will fulfillhis ofthebrideprice, obligations. The payment whichmay take severalyears,permitsthe man to claimhis children;otherwise they wouldbe retainedby themother'sfamily. If thewifedies withoutchildren, or if the couple separates,the bridepricemustbe returned.Europeansmightconsiderit a dowryin reverse. At thetimeSamuelJohnsonwrotehis 6 Nkpulu(singleshells) = 1 Ekpetti= book,wealthyfamiliesrequiredmorethan 6 cowries ten heads of cowries(over 20,000), as 10 Ekpetti= 1 Ukwu = 60 cowries withearliertimeswhena token compared 20 Ukwu = 1Akpa = 1200 cowries. payment of one head was considered The personwho countsfirstseparatesout ample. Today the bridepriceis generally groupsof six,and thenmakespilesof ten tenderedin cash. Withthe government's suchgroups. introductionof general-purpose money, In some partsof the land Ibo people brides "entered the market."This has refusedto sell forany currency but cow- createda moralproblem,contributing to ries.Ironically,the value rose after1900, the modernAfrican's"identitycrisis."In when the government outlawedtheirim- 1969 maximumbrideprice payments were in some partsof the purchasing set by the government portation.Furthermore, out of powerof thecowriewas greaterthanthat Nigeria,sincethematterwasgetting of metal coinage.Cowriesdistinctly had hand-the higherthe girl'seducation,the thebrideprice! the advantageovercoins,due to custom, greater Amongthe Yoruba ceremonialoccaand utilityforotherpurposes.Smallwonderthatpeoplehoardedthemfordecades! sionswhichrequirecowriepaymentsare initiation intosecretsocieties,and The completecowrienumeration sys- funerals, certainfines.As decorationcowriesare temof theUmundri(Akwa Ibo), basedon unitsof six and sixty,is givenby Dr. D. W. seen everywhere-onclothing, drums, diviningchains,headdresses, ritualmasks, in "The CowryShell" in a 1938 Jeffreys publicationof Nigeria.He lists number andfurniture. By no means did cowrie shells disintroappearafterthe Britishgovernment ducedcoinage.Cowriesarean integral part of dailylifein manyregionsof Africa,for use as decoration,religioussymbols,and special-purpose currency. Evenas ordinary moneytheywerestillusedin recenttimes. In the 1920's theIbo peoplekeptthemin in theinlandareas. circulation, particularly In Yoruba and Nupe territory they reappearedduringthe severedepressionof the 1930's,wheneventheanini(one-tenth of a penny) was too large a unit of exchange.As late as 1942 paymentsin some partsof Nigeriawere expressedin cowriesratherthanin coinage. AmongtheIbo peopleof southeastern Nigeriaa unique systemof cowrieequivalents was in use. Cowrieusage was still widespreadin 1920, whenG. T. Blasden wrote Among the Ibos of Nigeria. He states: 88 This content downloaded from 138.238.41.254 on Sun, 24 Mar 2013 23:30:41 PM All use subject to JSTOR Terms and Conditions The Rev. Johnsonreportsthat We are accustomedto thinkof money attributes. it is whenone wenton a longjourney,he took at leastthreefunctions: as embodying a measureof value,a mediumof exchange, beadsinsteadofcowries. Of all the currenciesin use in the and a methodof storingwealth.We take onlygunsand alcohol century, thatcoinsandpapernoteshave nineteenth forgranted value. The tradi- achievedany stabilityof exchangerates, functional no inherently tionalAfricanattitudewas quitedifferent, accordingto the AfricanhistorianK. O. and theAfricanfelt,forexample,notthat Dike. Bottlesof gin passedfromhand to but hand for years without having been yamswerebecomingmoreexpensive, that cowrieswere gettingcheaper.The opened, and mightrepresentthe entire had to meetthe de- wealthof a chief.Basdenreportedseeing Europeanmerchants mand for currencyobjects that had in- huge collectionsof emptygin bottles-a recordofpasttransactions! value. trinsic We shall mentionbrieflythe various SacredNumbers articleswhichhave been used as currency andcultural that The cityof Ife is the spiritual in Europeantradewiththeterritories archaeHere people. of the Yoruba center todaymakeup Nigeria.In 1510 one could masks heads, beautiful have found ologists buya slaveforeightor tencoppermanillas terraand brass in cast groups figure and (Portuguesefor "bracelet"). There were to back in dating stone, and figures cotta, patternsof manillasin Nifivedifferent the stands still Here century. the thirteenth geria,each acceptedonlyin certainareas, By the "staff of Oranyan", the stone obelisk and in use intothepresentcentury. five century, stan- markingthe burialspot of the legendary end of the nineteenth bottle of gin. founderof the Yoruba kingdomof Oyo. one dard manillasbought werein great Here one findstheancientshadowclocks, and brass rods Copper,iron thatservedto tellthetime into stonemonoliths manufactured demand; they were Here the datesforfestivals. and fix of day and of weapons art, ornaments,works burial, token of given was Benin the Oba The currency. tools, and special-purpose Rev.Johnsoncomplainsthat"soon doubts even thoughthe kingdomof Benin had will beginto be expressedas to whether achieved independence from Yoruba The influenceof thereligious iron domination. Yorubaseverknewtheartof smelting of Ife spreadto Benin,to theIbos, beliefs rise to fromthe ores!" The ironbar gave elsewhere. and the Nupe, to or "a tobacco" "a bar of the terminology are heldto be sacred, numbers Certain the Nigeria Ogoja bar of rum".In southern occupiestheprincipal four number the and worth was iron bar, penny,a Y-shaped Thuswe findthata them. among position of a Basden speaks about a half-penny. among the is traditional week four-day Ibo of the in one part currency unique the Among Nigeria. of southern people arrowwith of iron pieces region,tiny shapedheads,used in oldentimesforthe Yorubas each day is dedicatedto one of acquisitionof slaves. "How manythou- the fourmajordeitiesor itslocal countersandshad to be countedwhenmakingsuch part: Shango (Sango, Jakuta),an early as thegod king,laterworshipped The mythical a purchasebafflesone's imagination." by the doubleused in thisareawasbrass of thunder,is represented highercurrency bolt;Obatala rods. Beads were widelyreportedas cur- axe symbolof thelightening the creativegod, corency, and valued for their decorative (Orisala,Orisha-nla), 89 This content downloaded from 138.238.41.254 on Sun, 24 Mar 2013 23:30:41 PM All use subject to JSTOR Terms and Conditions workerwiththe supremegod Olorun,the god of purity,is protectorof the town gates and patron of the physicallydeformed;Orunmilais the oraculardeityof the Ifa diviningsystem;and Oduduwa (Ogun), the legendaryfounderof Ife, is In god of warand patronof iron-workers. began each region in the week past, the withthenameof themostpopulargod of that area. More recentlythe day of the thenamesof thedays: marketdetermined second day," "market's day", ''market is market "tomorrow day," third "market's day." "market another day,"andfinally "The world has four corners"is a widespreadYoruba expression;similarly, the approachto the earthfromtheouter thefourgates.Thisimage worldis through is carriedout in thefourgatesof thewalls of each town.One of theYorubadeitiesis being,whose OloriMerin,the four-headed place in imagewas set up in a prominent one of faced the town so thateach head the four points: east, north,west and south.The fourmajordeities,whosenames weregivento the days of theweek,were linkedwiththesepoints;Shangowiththe east, Obatala with the north,Orunmila with the west, and Oduduwa with the quadsouth.Each of the fourdirectional rantswas dividedagain into fourparts, each beingunderthe patronageof one of the sixteendeitieswho were responsible oftheearth. fortheformation Of greatimportarethepowersoffour: 16, or 42, and 256, or 44. Thesenumbers known are centralto theartof divination as Ifa. numbersare 40 (4 X Otherimportant 41 as theirsuccessors as well 10) and 200, latter the of significance The and 201. numbersmay be due to theYorubapractice of includingthe firstof the sequence Thus,some cyclically. twicewhencounting have a Yorubas the that state authors week;thefirstday of theweekis five-day and at the countedboth at the beginning end. oftheBini(people The sacrednumbers of Benin),accordingto PeterIdehen,are "20, 2, 4, 7, 14, 40, 200 and 201. The in Binisusuallygivekolanutsto strangers twos,or fours.If the numberof peopleis great,theygive7, 14 or 20. If thenumber is greater,as forexample,a wholevillage, they give 200 or 201. Whenthey offer sacrificesto theirgods, they followthe same order.Onlyveryrichpeople or the Oba can offer200 or 201 kolanutsor victims." sacrificial The Yoruba people are renownedfor theirIfa diviningsystem,the means of consultingthe oraculardeity Orunmila. The adviceof the god is solicitedpriorto a decision. step involving everyimportant The apparatusincludessixteennutsof the is uniquein palm tree,whoseimportance nut the lifeof the people. A seventeenth mightlie nearbyin a ringof cowrieshells, called "money of Ifa." The divinerfirst shakesthe sixteennutsin his two hands; this processis called "beatingthe palm nuts."He thenplaces themall in his left hand, and tries to pick up as manyas possiblewithhis righthand.If exactlyone nutremainsin thelefthand,he tracestwo strokeson the powderedsurfaceof the decoratedIfa tray;if two nuts beautifully remain,he makes one strokeon the Ifa tray.A recordis madeonlywhenexactly one or twonutsremainin thelefthand. This whole processis repeateduntil eightsingleor double strokeshave been recordedin two columnson thetray.One mightbe: arrangement I ,! 90 This content downloaded from 138.238.41.254 on Sun, 24 Mar 2013 23:30:41 PM All use subject to JSTOR Terms and Conditions , Orunmila says each should take his name Each columnhas a distinctive own row; I say each should take his own and since theremay be and significance, row; he says that Forty Cowries takes his eitherone or two strokesin eachposition, own row but cannot finishit. arrangements thereare 24, or 16 different I say, "Well then, my father Agbonin each column. The names vary from nire,2who can completehis row?" He says by Bascom,four FiftyCowries alone can complete his row, regionto region.As giver. because we cannot count money and forget are: arrangements Ogbe Oyeku Iwori Edi FiftyCowries. Ifa says he will not allow the personfor whom this figurewas cast to be forgotten. This person wants to do something;he will "complete his row" in the thinghe wants to do. 1. The row refersto a row in the fields to be hoed or weeded. Here, and elsewhere used in a broader male,andis in these verses,it is often The right columnis considered sense to mean any undertaking,so that more powerfulthan the left,or female, "completing one's row" means being succolumn. Each of these double-column cessfulin a givenventure. 2. Agbonnire is a shortened form of is calleda "roadof Ifa" or an arrangements anothername forOrunmila Agbonniregun, X thereare 24 24, or256 Odu. Altogether or Ifa.* from to 1 different odus,whichareranked With 256 in the orderof theirimportance. each odu thereis associateda numberof verses,each versebeingrelatedto a problemin reallife,butcouchedin theoblique of Yoruba. As languageso characteristic the divinerrecitesthe versesassociated with the odu, the client listensfor the words appropriateto his own situation. The priestsare also renownedas skilled physicians. thattheIfa The Rev. Johnsonsuggests the oracle at that of systemresembles a indicates verse The following Delphi. it to present-day psychoanalysis; similarity givesthe suppliantthe confidencenecessary to carry out the desired undertaking-andexactsa price. Orunmila says each should take his own row;' I say each should take his own row; he says that TwentyCowriestakes his own row but cannot finishit. Orunmila says each should take his own row; I say each should take his own row; he says that ThirtyCowries takes his own row but cannot finishit. A simpler system of divination, used for minor decisions, calls upon Opele, a lesser deity. For this purpose the oracle casts a divining chain on which eight half-pods or coins are strung at regular intervals,with a greaterspace between the fourthand fifthsymbol. The divinerpicks up the chain in the middle and lets it fall upon a flat surface in a two-column arrangement.The appropriateodu is determined by the sequence of convex and concave surfacesof the half-pods,or heads and tails on the coins, and the interpretationis exactly as with the palm nuts. Some authors, including Ojo, claim that there are 163, or 4096 odus (roads of Ifa), while others state that there are as many as 164, or 65,536. Bascom maintains thatthe numberis precisely256. * beFrom Ifa Divination:Communication tweenGodsandMenin WestAfrica,by William Bascom. Copyright? 1969 by Indiana University Press.Reprintedby permissionof the publisher. 91 This content downloaded from 138.238.41.254 on Sun, 24 Mar 2013 23:30:41 PM All use subject to JSTOR Terms and Conditions For centuriesthe Yoruba rulershave At of Ifa diviners. a hierarchy maintained powerful a held oracles one time these of the state, positionin the government for even to the responsibility the deposition of the reigningAlafin. Europeans the practiseof Ifa at reportedwitnessing year1705. The cult the as back far as least has spread far and wide-to Dahomey, Togo and partsof Ghana. Ifa geomantic divinationhas been preservedamongthe Yoruba descendentsin Cuba and Brazil, and whereit has mergedwithCatholicism, a Yoruba templewas recentlyopened on SeventhAvenuein NewYorkCity. the number As mentionedpreviously, sixteen occurs in one of the creation legends,that of the palm tree with its the sixteen sixteenbranchesrepresenting kingsof theYoruba. In Ile-Ife,therestandsan ancientsunmonolitharoundwhich clock,a triangular a circle has been drawn.This circle is dividedintosixteenparts,andtheposition of the shadow in relationto the circle indicatedin earlierdays the timeforthe ofcertainfestivals. observance The statefuneralof Lt. Col. Adekunle 1967 wasmarkedbythe FajuyiinJanuary, dirge.At chantingof the Ekititraditional cried: one pointthesinger was madeto the sacrednumber Reference 200: 200 persons "The one whoenlightened is yourfather." Included in the giftswhicha young man presentsto his betrothedare forty kola nuts.Ritualrequiresthattheybe split and dividedamongthe guests,indicating The thebetrothal. thattheyhavewitnessed symbolicimage associatedwith Ori, the householddeity,is a crownof forty-one cowries. The Yorubas recognize many subsidiary gods, or orishas (orisas), each associated with a specific functionor event.The Rev. Johnsonstates401 as the other supremenumberin the hierarchy; claim201, 401, or 1600. authorities thedeityof The worshipof Orisha-nla, place in Yoruba purity,has an important life.The god's responsesare thoughtto be kola by castingthefour-valved interpreted nut. It can fall in one of fivedifferent positions,each carryinga certainsymbolism. Sacrificeto this Orishaincludes sixteensnails,sixteenroastedrats,sixteen driedfish,and sixteenkola nuts. In anthe priests other phase of the festivities strip 201 leaves from the branchesof certaintrees. The numbersevenoccursin connection I callyou,won'tyou pleaseanswer? with the seven-dayharvestfestival,and I callyoufivetimes,sixtimes! with the Egugun celebration,which is I callyouseventimes,eighttimes! dedicatedto departedancestorsand obI callyousixteentimes.... festivities. servedwith greathomecoming to Later the crywas repeatedin a different One versionof thecreationmythrefers of Oduduwa,who form: the sevengrandchildren subsequentlybecame the rulersof the Your fathercalls you fivetimes,six Yoruba and Beninpeoples.Initiationinto times! of the worshipof Shango, He calls you seventimes,eighttimes! the mysteries He callsyousixteentimes requiredthepayment the god of thunder, growall Wherethe Olubije-mushrooms of sevenhead of cowries(14,000 shells), overtheroad! to Johnson. according He callsyouwithoutstopping! subjectis theoriginand A fascinating calls too. you Yourmother 92 This content downloaded from 138.238.41.254 on Sun, 24 Mar 2013 23:30:41 PM All use subject to JSTOR Terms and Conditions meaningof the symbolscarvedinto the obeliskto the founderof Oyo, the "staff of Oranyan,"stillstandingin Ile-Ife.The Rev. Johnsonwritesthatthe symbolsare i A, The PhoenicianlettersResh Yod the (read fromrightto left),representing name "Oranyan."Preciselythese letters wereused in classicalHebrew,whichwas derivedfromPhoenician,as symbolsfor The thenumerals200 and 10,respectively. sacrednumber200 again! If we go further back to theEgyptian we discoverthat the letter hieroglyphs, Reshcan be tracedto theimageof a head, while Yod representsa hand. Are these letterspossiblylinkedwithRa, thesun-god of the Egyptians,and with Yahweh,the forbiddenname of the Hebrewgod? Redashcold wateron any centinvestigations such speculative interpretation.The eminent authorities,WilliamFagg and FrankWillett,in their1960 article"AncientIfe", state thatthereis "no justifiof the cationat all forthe interpretation reliefcarvingon the Opa Oranmiyanin termsof Hebrewof Egyptiancharacters, nor for any explanationsoffered to account for the iron nails." They claim that the sketch of Oranyan'sstaffin Johnson'sThe Historyof the Yorubas to theoriginal, and bearslittleresemblance thatthe numberof ironnails driveninto the granitemonolithdoes not agreewith It may thatgivenin Johnson'sdescription. take many more turns of the archaeologist'sshovelto discoverthetruegenesis of theobelisk. andsignificance colonial powers.The anthropologists and linguists studiedAfrican lifeandlanguages, thusenablingtheadministrative officers to set up the most efficaciousgoverning apparatus.The missionaries introduced salvation throughChristianity and Western education, and in return,the Africans servedas police,soldiers,and lowerlevel clerks in the employ of the colonial powers.Africawas the"Dark Continent," to which the Europeanswere bringing light. AndtheEuropeansdid an excellent job of brain-washing. "Africansocietiesfrequentlyhad a philosophyof greatdepth andvalueandbeauty,theyhad poetry,and above all had dignity.It is thisdignity that all African but lost in the many peoples colonial period, and it is this that they mustnow regain."So statestheIbo writer ChinuaAchebe.WhenChristianity cameto the Ibos, he says further, Nigeriandances wereoutlawed,and thepeopleused cheap insteadofthebeautiimported enamelware ful Ibo clay pots and bowls. Anything Ibo-madewasbrandedas inferior. EducatedAfricans weretaughtto scorn theirown cultureand languages.The Rev. Johnsonwrotehis Historyforthebenefit of his Yoruba compatriots;they were about ancientGreece and knowledgeable but Rome, ignorantof theirown past. Thesepeoplebecamean elite,ideologically separated from their uneducated (by Western fellowAfricans. standards) I havein mypossessiona paperentitled "How the Binis Count and Measure," written student byPeterIdehen,a Nigerian AfricaComesintoIts Own in a teacher-training course in Abudu, Untiljust a few yearsago most of the Nigeria.One realizesthe extentto which about the continent Africans availableinformation havebeenrobbedoftheirheritage of Africa originated from European whenone readsin thisessay:"It was said mission- thethePortuguese sources-anthropologists, linguists, taughttheBinis(people eachwith of Benin) how to carve and do brass ariesand administrative officers, his own axe to grindin theserviceof the work." This was writtenat a timewhen 93 This content downloaded from 138.238.41.254 on Sun, 24 Mar 2013 23:30:41 PM All use subject to JSTOR Terms and Conditions of the his comprehension and artistshad firmlyes- base. Apparently archaeologists to cope withthe tablishedthe Africanoriginsof the tech- languagewas insufficient andelisions. niquesforcreatingthesebeautifulworks. contractions With the developmentof the new Later Idehen statesthatthe Bini had no precisemeasuringunits. "This condition Africannations and the rise of native staffedby Africans,the true was a bit improvedwhen the Europeans universities cameto Beninin especiallythePortuguese Europeanand storyof Africais emerging. bottles Americanauthorscan afford-andare reTheyintroduced the 16thcentury. whentheybroughttradeginto thecoun- quired-tobe moreobjective.How can the and try.Theybroughtkegsof gun-powder imageof Africabe strippedof the stereomanyothercontainers.... They use the the Dark Contypes,the misinformation, kegsfordrymeasure; tinentprejudicesdevelopedoverthe cenemptygun-powder thistheycalledEpipa." Indeedsomething turies?To this end, I recommendthe for!In relationto counting reportissuedby UNESCO of themeeting to be thankful in theirmothertongue,Idehenwrites:"In in Parisin 1968, dealingwitheducational schools teachersoftenstop at 30 or 50 methodsdesignedto combatracialprejuto an educator interest do notknowhow becausetheythemselves dice. Of particular Con"Recommendations to count." Idehen himselfhad to seek is thestatement, in Educationon Race assistancein writingthe highernumerals. cerningTerminology Questions,"byMr.A. Babs Fafunwa,Dean yearsago,L. L. Conant,in Seventy-five of The NumberConcept,called theAfricans of the Facultyof Education,University "savages."More recentauthorshaveattri- Ife, at Ile-Ife.Aftera brief,but pointed, to the explanationof the threefactorsthatconbutedeveryAfricanaccomplishment to thedevelopment ofracialprejutributed Europeans,to theArabs,to theIndians,to the Mesopotamians,to ancient Egypt, dice betweenthe 16thand 20thcenturiesand colonialismwhose people they classifiedas "Cau- the slavetrade,religion, of the casian" in spite of evidencethat many Mr. Fafunwagivesthisdescription "good" Africanof recentyears:"one who short,to Egyptiansweredark-skinned-in themselves. was only Africanin blood, Christianby any sourcebut blackAfricans Not only does one encountera racist religion,and Britishor Frenchin culture aboutAfrica;in biasin seekinginformation and intellect.He mustshunthingsAfrican and anthropologists local attire,Afrisuch as images,artifacts, addition,missionaries, misinterpreted can moresand customs-allin thenameof colonialofficers frequently or failedto understand aspectsof culture Christianity and civilization."The suband language.Ojo findsit necessaryto stance of Fafunwa's report lay in an criticizeEllis and Dennettfortheirinter- analysisof themanytermswhichcontinue sensein relation pretationof the Yoruba calendar.The to be used in a derogatory errorsare compoundedas the samemater- to Africa,wordssuch as "tribe,""primiial appearsin variousbooks.For example, tive," and "vernacular"(insteadof "lanConant translatesthe Yoruba word for guage"). "eleven" as "great ten"; no doubt this The poignantstoryof thepublication errorappearedin the sourcefromwhich of the Rev. Samuel Johnson'shistoryof Conant obtained his material.In fact, the Yoruba people furnishes yet another Migeod classifiesthe Yoruba numeration exampleof racism.It is best told in the systemas havingten, not twenty,as its words of the editor, Dr. 0. Johnson 94 This content downloaded from 138.238.41.254 on Sun, 24 Mar 2013 23:30:41 PM All use subject to JSTOR Terms and Conditions attained to reachthelevelof achievement by FrankE. Chapman,theauthoroftheas A singularmisfortune,whichhappilyis book Scienceand Africa. not of everyday occurrence, befell the yet unpublished fromChapman's excerpts following The original manuscripts of this history, in throwsome light on the consequence of which the author never autobiography lived to see in printhis more than twenty miseryof his existenceand his determinayearsof labour. tion to devotehis life to "the searchfor The manuscriptswere forwardedto a forthisis myonlytruereligion." truth, well-knownEnglish publisherthroughone October5, 1961, I was sentenced On of the great MissionarySocieties in 1899 and fiftyyearsfor to life imprisonment and-mirabile dictu-nothing more was murderand robbery.I was nineteenyears heard of them! ofageat thistime. The editor who was all along in colwhichled to my The circumstances laboration with the authorhad occasion to greetedmethedayI presentimprisonment visit England in 1900, and called on the of publisher,but could get nothingmore from was born,and are shapingthe destinies millionsof black men and womeneven him than that the manuscriptshad been of matermisplaced, that they could not be found, now.Thesearethecircumstances poverty.... and that he was preparedto pay forthem! ial andspiritual of eleven chilI was the first-born This seemed to the editor and all his dren.... WhenI was about six or seven friendswho heard of it so strangethat one years old, my father,an unskilledblack could not help thinking that there was more in it than appeared on the surface, worker,turnedthief,desertedthe family escapade(stealing, especially because of other circumstances and wenton a hustling confidencegames,gambling,etc.), across connected with the so-called loss of the I intensely loved thecountry. Nevertheless, manuscripts.However, we let the subject of the family my fatherand his desertion rest there. The author himselfdied in the hurtme deeply.Althoughmymotherwas following year (1901), and it has now leftalone to provideforus, and although fallento the lot of the editorto rewritethe a greatdeal fromlack of food we suffered whole history anew, from the copious and clothing,I neverhated myfatherfor notes and rough copies left behind by the anyof this.I just hatedthewaywe hadto author. live.... (Ajagbe Ogun), brotherof the author: Due to other tragic circumstances, the book did not appear until the year 1921. Aftermore than fortyyears of labor, The Historyof the Yorubaswas published; it has since become a major source of informationfor all scholars in the field of Yoruba historyand culture. Can we evaluate the loss in human progressdirectly attributableto the consequences of racism? An attempt at such an evaluation staggersthe imagination.Not only were the peoples of Africaconsidered less than human; the same racist attitude has prevented the black people of the United States from fulfillingtheir aspirations. Few are able to overcomethe almost insuperable obstacles imposed by society, By thetimeChapmanwas elevenyearsold he had been arrestedfiftyor sixtytimes. Then followed severalstintsin reform schools. Duringall thistime,I had acquireda real, genuinehatredforsociety.I hatedgoingto school,and stayinghome.I hatedbeingon welfare,and my motherhavingto beg people forfood so we could eat. I never whenI was a childwhy could understand so muchandwhy mymotherhad to suffer she had to beg "bigshotwhitepeople"for food and clothingfor her children.But rebelledagainst deep withinme I violently thishumiliation whichhad becomea way of lifeformy family.I was powerlessto eliminateour poverty,but I was not powerlessto hate. Then there was the 95 This content downloaded from 138.238.41.254 on Sun, 24 Mar 2013 23:30:41 PM All use subject to JSTOR Terms and Conditions brutalityof racism. Every time I came in touch with white people, I was abused and spat on because of my so-called "Niggerhood".... When I was enrolled in Soldan High School in February 1957 (at the age of fourteen),I had a personal interviewwith one of the assistantprincipalsby the name of De Shields. He told me that while in Booneville [State ReformSchool], I made an excellent academic record for myself and that I could possiblywin a scholarship if I applied. For the firstcouple of weeks,I enjoyed school work,and I was becomingabsorbed in science, history, and literature stud- ies.... Then one night around 1:30 police banged on our door and threwtheirflashlights in my face demanding "Are you Frank Chapman?" I was taken to the Page and Union police station and chargedwith car theft. The police knew that I didn't steal the car but they wanted to clean up the books, and I was a likely suspect because I had just gottenout of Booneville for car stealing.... 1957 was a decisive year in my life because this was the year I gave up all hope of ever livinga so-called normal life. I rationalized that with my past record,the police would neverlet me alone anyway,so I mightas well make the most of it. Chapman proceeded to "make it" in the only way he knew. Between crimes were several sojourns in the juvenile home and the state hospital for the mentallyill. At last he made his way to Chicago early in 1960, wherehe obtained a job in a hospital and was marriedat the age of seventeen. AfterI got marriedI wantedto make it work. I got a job in Evanston, Illinois workingas an assistantprinter.I averaged about eighty-seven dollars every two weeks. This was just not enoughmoney to support my family.... We separated. Our separationhad nothingto do withthe way we felt toward each other; it was simplya matterof survival.On the nightwe separated, I felt total despair,because this was one thing in life I wanted.... I returnedto St. Louis penniless and desperatein February1961. My plans were to organize a stick-upringand rob until I accumulated enough money to supportmy familycomfortably. I forget on just what day in March 1961 it was, but I rememberit was dreary and raining.I was at a fellow'shouse I had just recentlymet, drinkingwine, when he suddenly suggestedto me, "Let's stick up that shoe shop and get some money." I replied "Okay." I walked into the shoe shop with a loaded twenty-twopistol. An old white man about seventyyearsold was sittingon a bench. When I said, "This is a stick-up," he leaped from the bench and grabbed me by the arm and the hand the pistol was in. In the process of wrestling, the gun went off and a bullet enteredthe head of the old man. To this day, I can't rememberall the thingsI did rightafterI killed this man. I know I ran for blocks before I regained control of myself.The man I committedthis crime with,I hardly knew, for we had only met two days beforethisincident.... On April 6, 1961, I was apprehended by the police in Evanston, Illinois for suspicion of drug addiction. Two weeks later I was in St. Louis facinga charge of first-degree murder. Presently,I am in prison,confinedin a box-like cell, which is about six feet in width,seven and a half feet in length,and ten feet high.... Prison is a place where a few men acquire new dreams and new hopes, and where most men lose even the ability to hope for anything except a successful crime career.... But I left the courtroom with this conviction; I must know the truth about myself, I must become conscious of whateverforceshave shaped my lifeand made me what I am. On that day life forme took a new and sudden turn. I wanted to live only to know myself better,and the world. I wanted to discover formyselfmy own humanity. In many respects prison is almost an ideal place for study, for one has a great deal of leisure time.... First I enrolled in school, in the eighth grade. In a few months I graduated. This was the second time I had graduatedfromgradeschool. As soon as I thoroughlyrefreshedmyselfon the fundamentals,I began to study seri- 96 This content downloaded from 138.238.41.254 on Sun, 24 Mar 2013 23:30:41 PM All use subject to JSTOR Terms and Conditions ously. The first subject I attacked was mathematics.In a couple of months I was doing advanced algebra. I read and studied such books as Eric T. Bell's Development of Mathematics,Lancelot Hogben's Mathematics for the Million, and Mathematica Principiaby BertrandRussell and AlfredN. Whitehead.AfterreadingMathematicsfor the Million, I had little difficultyin understandingthe otherbooks. mination of all his constructiveachievements.... Reflectionsof this nature have led me to the conclusion that the most pressing task of Africanphilosophers,scientists,and political leaders is the layingof ideological foundations by assessing the nature of Africa's role in the modern world, and thereby arrivingat some concrete conception of her historical mission. . . . My Science and Africa deals with only one of The study of mathematicsled Chapman to the many significanteffectsof European imperialism.After conquering the world, natural science, then to philosophy and the white man has falselyclaimed that he Africancultureand history. and he alone is the benefactorof human civilization.In this book I tryto destroy, I was determinedto know everythingthe human race had done, as well as everything theoretically,the white man's racial monopoly in the fieldof naturalscience; and to it is doing. the extent that I succeed I will have In 1964 I decided to write a book demonstratingthe scientificcontributions contributed to the happiness and wellof African peoples to mankind. In June beingof mankind. I sent the manuscriptto John Clarke, 1964 I wrote a briefsynopsisof my ideas, editor of Freedomways in the summerof article in the form of an it and submitted 1966. Freedomways published some exentitled"Mathematicsin Antiquity"to the cerptsfromScience and Africa.... editors of Freedomways Magazine in New Throughknowledgeand understanding, York.... Mr. John H. Clarke, an editorof I have freed myself from my past errors Freedomways,got the articleaccepted by a Parisian magazine entitled Presence Afri- and have created for myselfa brightand beautiful future.My greatambition in life caine. After my article was accepted, I is to tryto keep othersfromrepeatingthe beganto work on my book.... mistakes I have made and to free my Within a year Science and Africa was finished.Upon finishingI wrotethe follow- brothersand sistersfrom the humiliation I cannot ing: I would be the firstto admitthat this of being black and poor.... is a stupendous task for anyone to under- accept the argumentthat I and I alone am responsible for what happened, for the take, but it is a little more than that for a crimes I committed. If that be the case, man in prison endeavoringto write and carry on scientificresearch under severe then the major premise of modern sociology and psychiatryis false. However, and tryingcircumstances;yet, I was and what I wish to bringout is the fact that I am determinedto get the job done, and I am a new man, with new interests,dreams am confidentthat this work (Science and Africa) will provide a useful and socially and ambitions. ... I am not trying to conceal anything constructiveoutlet for the outpouringof I have done behind glitteringgeneralizathat social energyI have inherited.I have tions; I only want the reader of these cold spared no effortin the endeavor to make and lifeless words to understandthat ours myself fully cognizant of the impact the modern world has had on me and my is not the storyof just a solitaryman who presentlydestroyedhis chances to be a fine fellow human beings. And out of this has fellow, but a man born into a social been born an outlook which has enabled situation that chokes and cripples man's me to link up my own individual social experience of mankind.... Such an out- infinite capacity to produce and create. Therefore,what I have done, and what has look is not merelyborn out of dreamsand been done to me, is in no way purely fantasticlongingsfora betterway of life;it is born out of man's effortsto grapplewith unique. To tell the truth,my storyis the story his objective existence and it is the cul- 97 This content downloaded from 138.238.41.254 on Sun, 24 Mar 2013 23:30:41 PM All use subject to JSTOR Terms and Conditions of millions.One black brotherhas appropriatelycalled us "The Wretchedof the Earth". Ojo, G. J. Afolabi. Yoruba Culture. London: Universityof Ife and Universityof London Press, 1966. Seidenberg, A. "The Ritual Origin of Counting," Archive for the History of the Exact SciencesII 1-40. Undauntedby failureto haveScience and Africa published,Mr. Chapmanhas of SouthwestNigeria continuedto work on the subsequent History volumes,Science,Societyand Truth,and Aderibigbe,A. A. B. "Peoples of Southern Nigeria," In J. F. Ade Ajayi and Ian Race and Society.We can onlyhope that Esprie (eds.), A Thousand Years of West such geniuswill soon receivethe recogAfrican History,2nd ed. Ibadan: Ibadan nitionit deserves,and thatMr. Chapman UniversityPress, 1968. will be able to enjoytherelativefreedom Apple, R. W. Jr."Singsong Voices, Bright oflifeoutsideofprison. Caps Mark Ibadan's Yorubas," The New Bibliography Yoruba NumerationSystem Ajayi, J. F. Ade. Universityof Ibadan. (personal communication). Akinpelu, Jones A. (personal communication). Armstrong,Robert G. Yoruba Numerals. Ibadan, Nigeria: OxfordUniversityPress, 1962. Chapman, Frank E., Jr.Science and Africa. Unpublishedmanuscript. Conant, Levi Leonard. The Number Concept. New York: Macmillan,1896. Crowder, Michael. West Africa Under Colonial Rule. Evanston, Ill.: NorthwesternUniversityPress, 1968. Delano, Chief Isaac 0. Conversationsin Yoruba and English. New York: FrederickA. Praeger,1963. Einzig, Paul. Primitive Money, 2nd ed. Oxford: PergamonPress,1966. Eves, Howard. In Mathematical Circles. Boston: Prindle,Weber& Schmidt,1969. Hodgkin, Thomas. Nigerian Perspectives. London: Oxford UniversityPress, 1960. Johnson,Marion."The Cowrie Currencyof West Africa,"Journalof AfricanHistory XI, 1 (1970): 17-49. Johnson,Samuel. The History of the Yorubas. London: Routledge and Kegan Paul, 1921, 1966. Menninger,Karl. Number Wordsand Number Symbols. Cambridge, Mass.: The M.I.T. Press, 1969. Murdock,George P. Africa: Its People and their Culture History. New York: McGraw-Hill,1959. York Times (June 14, 1969). Babayemi, S. 0. "Oyo Ruins," African Notes. Institute of AfricanStudies, Universityof Ibadan, Vol. 5, No. 1 (1968). Crowder, Michael. The Story of Nigeria. London: Faber & Faber, 1966. Davidson, Basil. African Kingdoms. New York: Time-LifeBooks, 1966. DuBois, W. E. B. The Worldand Africa. New York: International Publishers, 1965. Hodgkin.NigerianPerspectives. Johnson,Samuel. Historyof the Yorubas. Lloyd, P. C.:, Awe, B.; and Mabogunje, A. L. The City of Ibadan. Cambridge UniversityPress, 1967. McCall, Daniel F. Africa in Time Perspective. New York: Oxford University Press, 1969. Shaw, Thurstan."Radiocarbon Dates from Nigeria," Journal of the Historical Society of NigeriaIII, 4 (June 1967). Shinnie, Margaret.Ancient African Kingdoms. London: Edward Arnold, 1965. andTrade Currency Abraham, Roy C. Dictionary of Modern Yoruba. London: Universityof London Press,1958. Apple. "SingsongVoices, BrightCaps." Basden, G. T. Among the Ibos of Nigeria. New York: Barnes & Noble, 1921, 1966. Bohannan, Paul. Africa and Africans.New York: The AmericanMuseum of Natural History,1964. Conant.Number Concept. Einzig.PrimitiveMoney. Herskovits,Melville J. Economic Anthropology. New York: Alfred A. Knopf, 1952. 98 This content downloaded from 138.238.41.254 on Sun, 24 Mar 2013 23:30:41 PM All use subject to JSTOR Terms and Conditions Hodgkin.NigerianPerspectives. Ibn Battuta. Travels in Asia and Africa, 1325-1354, trans. and ed. H. A. R. Gibbs. New York: Robert M. McBride, 1929. Jeffreys,M. D. W. "The Cowry Shell," Nigeria,Lagos, No. 15, 1938. Johnson,M. "Cowrie Currency." Johnson,S. Historyof the Yorubas. Kirk-Greene,A. H. M. "The Major Currencies in Nigerian History,"Journal of the Historical Society of Nigeria, II, 1 (December 1960). Lloyd, P. C. "Osifekunde of Ijebu." In Philip Curtin (ed.), AfricaRemembered. Madison: Universityof WisconsinPress, 1967. Murdock. Africa: People and CultureHistory. Ojo. Yoruba Culture. Ryder, A. F. C. "Dutch Trade on the Nigerian Coast during the Seventeenth Century,"Journalof the HistoricalSociety of NigeriaIII, 2 (December 1965). Smith,Homer W. Man and His Gods. New York: Grossetand Dunlap, 1952. Ukwu, Ukwu I. "The Development of Trade and Marketingin Iboland," Journal of the Historical Society of Nigeria III, 4 (June 1967). Sacred Numbers Armstrong,R. G., Olayemi,V. and Adu, B. "Ekiti Traditional Dirge of Lt. Col. Adekunle Fajuyi's Funeral," African Notes. Ibadan, Vol. 5, No. 2 (January 1969). Bascom, William. Ifa Divination. Bloomington: Indiana UniversityPress, 1969. Crowder.Storyof Nigeria. Crowe, D. W. "Mathematicsin the Everyday Environment,"Entebbe Mathematics Workshop,1962. Dennett, R. E. Nigerian Studies. London: Frank Cass, 1910, 1968. Fagg,William,and Willett,Frank. "Ancient Ife," Odu, Ibadan, No. 8 (1960). Forde, Daryll. The Yoruba-Speaking Peoples of South WesternNigeria. London: International African Institute, 1951. Frobenius, Leo. Voice of Africa. New York: BenjaminBlom, 1913, 1968. Idehen, Peter. "How the Binis Count and Measure." Unpublishedpaper writtenfor a teacher training course at P.T.T.C., Abudu, Nigeria, 1962 (sent to the author by Jim Karns, Ohio University,Lancaster,Ohio). Johnson,S. Historyof the Yorubas. Leuzinger, Elsy. Africa, the Art of the Negro Peoples. New York: Crown Publishers,1960. Menninger.Number Words and Symbols. Morton-Williams, Peter. "An Outline of the Cosmology and Cult Organizationof the Oyo Yoruba," Africa,No. 34 (1964). Ojo. Yoruba Culture. Parrinder,Geoffrey.Religion in an African City. London: Oxford UniversityPress, 1953. Smith.Man and His Gods. Stevens, Phillips. "Orisha-nla Festival," Nigeria, Lagos, No. 90 (September 1966). AfricaComesintoItsOwn Achebe, Chinua. "The Role of the Writer in a New Nation," In Barbara Nolen (ed.), Africa is People, New York: E. P. Dutton, 1967. Conant.Number Concept. Crowder. WestAfrica underColonial Rule. Fafunwa, A. Babs. "Recommendations ConcerningTerminologyin Education on Race Questions." In Final Report of Meeting of Experts on Educational Methods Designed to Combat Racial Prejudice,UNESCO: Paris, 1968. Idehen. "How Binis Count and Measure." Johnson,S. Historyof Yorubas. Migeod, W. L. Languages of WestAfrica. London: Kegan, Paul, Trench,Trubner& Co., 1911. Ojo. Yoruba Culture. lc:(0oJ1 99 This content downloaded from 138.238.41.254 on Sun, 24 Mar 2013 23:30:41 PM All use subject to JSTOR Terms and Conditions