To Twentieth Century Urban Man Number Is a Tool, 8 Scale for Enumeration, a Gage for Measurement, a Code for Iden%Ification

To twentieth century urban man number is a tool, 8 scale for enumeration, a gage for measurement, a code for iden%ification. It ie a mathematical ab- etraction, an abstraction of order and quantity. It was not always eo. To nun-mathematical rnan numberrf is no abstraction for he does not necesearily diatinguish betweon number and that which fs numbered. Number cm be far more than a conventional aymbol; It can be rn entity with characteristics and propertiee of its Basjc to Pythagoras ' (582-500 B.C. ) philcsophy is the idea that numbers can be isofated and endowed with both biological and moral properties.2 For ByLhetgoras number was more than a symbol of quantity, more than a symbol of reality, it --w~s reality. Just ae other Greek philosophers had postulated fire, earth, and water as the element8 of exis- tence, Pythagoras idenllfied numbers ss the elements of reality. A less aetonishing and more recent case fox the non-mathematical significance of numbers was mdu by Carl ,lung (1875-1.961). This modern peychologist proposes that number is one of the fundamental categories of the human psyche, or - in hie terminology -- an archetype. Shortly before he died, he wrote, The very numbers you use in counting are more than you take them to be. They are at the aame time mythological elements (for Pythagoras, they were divine) ; but you are certainly unaware of this when you use numbers far a practical purpose.3 But are numbers, In fact, anything more than codes for the man who uses them in calclLLators and computers? A street number, a Social Security code, a driver'e license are certainly in no way symbolic. me price on a pound of meat and the monthly telephone bill are codeft, nothing more. Yet, many an urban American avoirTrs the thirteenth fl.oor of hi^ apartment house. He at- tends church every seventh day and io recognized as an adult at twenty-one. Whether superstition, symbol, or ~impleconvention, certain numbers do play a decidedly important ro1.e irn his 1-lfe. Rrh~p~Jung over-stated the case by eiving numberrs archetypal significance; nevertheless he did point out an important fact: numbere used aon-mathematicaUy do foUw certain patterns of ueage. Freud was correct when he asserted that man uses numbers in a way which ha8 been strictly determined, more determined than might aeem possible. 4 Numbers are not ueed at random, but; according to a consistent, ascertainable pattern. When euch a pattern appear8 among the Yoruba of southwestern Nigeria, it is not because the Yoruba are unacquainted with the mathematical uses of numbers. Unlike many other African peoples, the Yoruba have long been an urban, mer- cantile nation; the city and mrtrk~tare centuries old inetitutions in Yoruba- . land. The demandis of trade and urban buxeaucracy long ago made numbere fami- liar tools of calculation. It ia m Inarult among ,the Yoruba of Abeokota to Bay, "0 daju danu, o ko mg essan mesaan [YOU don't know 9 x 91. "5 (Americans w set their standards of Ignorance much lower: "~ecan't put two and two together.") Moet Yorubars would probably sneer at Pythagoras hotion that numbers are divine. Of courare %he Yoruba we of numbare ia not confined to tho market and the afin. The eame women who shrsdly bargain in the marketplace axe part of the community which tells and listens to traditional rtories, poeme, and songs. Number is an element, akthough not a predominant one, in thir lore. The quertions posed here are: How is number used in this tradition? Are rpecific numbers aseociated with particular genre8 or cantexCs? Do any numbers evince symbolic associations of any rort? And, parhaps most significantly, why are certain numbers wed consistently in the folklore in preference to otherr? To attempt to anawer these quertions working only wia translated materials might seem romewhat spsciour. Numbers, however, pore far fewer problems of inaccurate or misleading translation than moat other elements of language. The words used for numbers arc most often unambiguous, single forme without synonyms or other linguistic asaociations. Although number-words probably owe their origin to some specific activity or object, these early associations near always drop away and numbers become isolated, easily identifi- able form63 Furthermore, number i18 a concept common to nearly every cul- ture and, aa a result, parallel linguistic forms make number translation a relatively simple matter. Number, in short, is among the elements of language least likely to be distorted by tranalation. Although individual Yoruba numbers have parallel forms in the European lan- guages, the traditional number ryrtem of the Yoruba is in some ways quite different from the European decimal eyetem. A survey of this traditional syatem ir prerequisite to understanding the ure of number in Yoruba society. It may well be that the structure of the number syatem affects, perhaps determines, the use of numbers in the lore. It is difficult to diaeociate the European number nyotem from the written numerals which represent it. The Yoruba number r atem, on the other hand, posses~eano commonly accepted written ahorthand.7 Number is a verbal, not a written, form in West Africa. Merchandising, for example, is a verbal procesa, not a matter of ladgera and account booke. This is an important point of difference between the European and Yoruba systeme. The limits of mental calculation and verbal expreeaion impose certain conventions on the Yoruba system, conventions which will be deacribed below. Yet, the Yoruba eystem is by no means less complex than the decimal system. In fact, the Yoruba syetem is considerably more difficult to practically emplay than the re1ative.b nirnple European system. Some anthropologiste assume that the Yorub number system, like nearly all known systems, began with digital counting8 ; man almost certainly began counting with hir fingers and tocde .\9 In the Yoruba system the bsaic numbers correspond to the finger8 the numbers one through ten. here is no mathematical concept of zsro.16) Theas numerals -- simple, unambiguous, and uncompounded forms -- are ten of the fourteen root numbers, or radical forms, from which all other numbere arc compounded. The number eleven, for example, in a compound form meaning one in addition to ten (1+10). The numbers eleven through fourteen are formed by adding the appropriate radical to ten. Fifteen through nineteen are formed not through addition, but subtraction. Fifteen, for example, is a compound meaning twenty minus five (20-5). Why the Yoruba emplay both addition and subtraction in these ele- mentary forms poaes an interesting problem. The numbers one through twenty could have bean counted simply enough on all the flngera and toes (as among the neighboring Vei). Why thie more complex system? Robert Armrtrong proposes an interesting hypothesis to answer this question: he euggesta that by using both addition and subtraction a man is able to count ten and its multiples on the fingers of one hand.?.= Ths accompanying drawings show how auch a counting opnvention might have worked. Uning the free hand to count off units of ten, a man might extend finger counting well beyond its apparent limits. Armstrong's proposal is, of course, only hypothetical, for Yoruba mathematical akill~long ago developed well beyond such basic counting. Twenty, ogun (not to be confused with the oriaha bgh), is a most important root number, a radical basic to the form of most of the firat 200 numerale. Even multiples of twenty are formed aimply by multiplying ogun by another radical. Forty, for example, is 2 x 20. Other multiples of tan, not exact multiples of twenty, are formed by multiplication and subtraction. Fifty, for example, is a compound meaning (20 x 3)-10. he number thirty is an exception here; it is a radical form, although little used in compounds. ) Intermediate forme not multiples of ten are compounded according to the pattern of addition and eubtraction set by eleven through nineteen. This pattern of regular compounding is illuatrated below. Thus, in contrast to tho European decimal system which forma compounds with addition and multiplication, the Yoruba eyatem cmpounde with addition, multiplication, and aubtraction. The result ia complex numeral form. Such a number system, although somewhat awkward with large numbera, would be more than satisfactory for a rural population with a barter economy. This system or one very sirnil-ar to it probably oufficed the Yoruba during their early history; but once the Yoruba nation adopted a currency as the means of exchange, this eystem proved inadaquate. Adopted by the Yoruba and some neighboring tribes, the cowry shell (cypraea moneta) was s true currency, portable, durable, and a universal medium of exchange among the Yoruba peoplea. Like all money, shell money demands quantification; to be ran effective money, the cowries had to be numbered, their value determined. The cowry count became so important that a special number form developed for just that purpose: bkan (I), for example, developed an alternate form, ookan (one cowry). Okbwo (okoC a string] owo[of cowriee] ),a number form re- presenting twenty cowrie8 eesme to indicate that c~wryshells were strung in groups of twenty. However, other sources (eources such as S. Johnson, the Yoruba historian) state that the 8hel.l~were strung in group6 of thirty- two, forty,12 sixty-six, or even 100.13 The number of cowries in theee initial groupbgs or strings Beeme, in short, to have been quite variable. Nonetheless, certain conventions of cowry usage did develop which suggested a way, using th baeic logic of the lower numerals, to expand the baeic number system.lt Unstrung covriea aeem to have been counted out in small groups of twenty or forty; when enough cowrie8 were thus counted, the small piles were puehed together into a heap of 200.

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