57 A New Model Of Ifa Binary System BADE AJAYI Department of Linguistics and Nigerian languages, University of Ilorin, Ilorin, Nigeria INTRODUCTION Ifa, the literary corpus of'which has been aptly described by Abimbola 1 as "the store-house of Yoruba culture inside which one can-find-all the traditional wealth and glory of the Yoruba", is associated with Orunmila, the Yoruba god of wisdom and divination. It uses a geomantic system2 of divination to arrive at appropriate signs and employs Ifa verses to interpret .the signs 3. Ifa divinatory literature is used most by the members of the-Yoruba Community an4 evidence of this abounds in the works of Bascom 4, Abimbola 5, Lucas 6, Idowu 7, and Awolalu 8. Ifa literary corpus consists of 256 possibilities called Odu and each Odu also contains superfluous stories called ese. Sixteen of the Odu are the principal ones while the remaining 240 are the mixed or minor Odu. As the name implies each mixed Odu is formed by the combination of two principal Odu. Each of the Odu (both principal and minor) is represented by a specific sign which is binary in nature. Every Odu sign has two arms illustrated by the first two principal Odu.., Eji-Ogbe and Oyeku Meji below: Eji-Ogbe 1 1 1 1 1 1 1 1 Oyeku 11 11 11 11 Meji 11 11 11 11 2 Or 2 2 2 2 2 2 2 We want to state that we shall make use of one arm of every principal Odu to represent the Odu in question. As it would be seen in table 1 in this study, the Odu are in specific hierarchy, The aim of this paper is to show that the hierarchical order of the Odu is very crucial to the interpretation of Odu signs and Ifa message and that the Ifa Odu signs and computer science have some things in common. We also want to emphasise the fact that communication with the Odu is achieved by means of a calculated mathematical framework based on the prescribed course of conduct required from each Odu. The message of Eji-Ogbe, the principal or king of all other Odu, is the cue to tae mathematical basis of Ifa divination. One ese Ifa belonging to this Odu reveals that the ancient Yoruba used the binary system (number to base two) to develop the Ifa literary corpus. Eji eji ni mo gbe, N o gbe enikan mo A dia fun Tayewo, A -bu-fun-keyinde -9- 58 I bless in twos, I do not bless only one Divined for Tayewo, He-that-shares with Keyinde In fact the digital computer uses the binary system, Like the computer, Yoruba anthmomancy is based on binary system 10 and it is therefore a computer oriented science which can be used in mathematical education. The Ifa-6-A- Bits Paper Computer Model N At a divination session several Ibo (instruments for casting lot), may be used to find detail information about a client's problem. The commonest and simplest form of Ibo of Cowry Shells tied together representing types’ (1) and piece of animal bone representing“Iho” This relates to computer language indo today, we need prediction (which is scientific and reliable) more than divination (which is religious and uncertain). Considering the locio in the arms of the opele, the pairs should be punched (d) and there ‘bi’ spairs not punched (0) using this code paper model of Ifa -6-ABits computer model N has been developed. Here is the model worked out by Opele Punches 000000 000001 000010 000100 001000 000011 000101 001001 000110 001010 001100 000111 001011 001110 001110 001111 Odu Name Ogbe (1) Osa (10) Otua (13) Irete (14) Ogunda (9) Irosun (5) Ose (15) Iwori (3) Odi (4) Ofun (16) Owonrin (6) Obara (7) Ika (11) Oturupon (12) Okanran (8) Oyeku (2) This model based on binary system does not take into consideration the traditional system on which the Ifa corpus rests. In actual fact, the importance of hierarchy of the 256 Odu for the interpretation of Ifa message cannot be over emphasized. The Ifa-6-A-Bits paper computer model N has no cultural basis since the tradition hierarchy is ignored in the opele traditional sequence and to my mind this is a major drawback of the model. In what follows an attempt is made to restore the traditional hierarchy in the Ifa -6-A-Bits using a more consistent ordering in the binary system influenced by Ifa divination sequence. 59 Steps leading to our Model: 1. Given the Odu and the corresponding sign in Table 1 2. We olrder the sign in ascending magnitude as in Table 2 below Table I Old Sequence 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 ODU Name Ogbe Oyeku Iwori Odi Irosun Owonrin Obara Okanran Ogunda Osa Ika Oturupon Otua Irete Ose Ofun Sign 1111 2222 2112 1221 1122 2211 1222 2221 1112 2212 2122 2111 1211 1121 1212 2121 Table 2. Old Sequence 1 9 14 5 13 15 4 7 12 3 16 11 6 10 Ordered sign 1111 1112 1121 1122 1211 1212 1221 1222 2111 2112 2121 2122 2211 2212 Binary system 0000 0001 0010 0011 0100 0101 0110 0111 1000 1001 1010 1011 1100 1101 60 8 2 2221 2222 1110 1111 3. (i) We start counting the binary numbers with 0000; 0001,0010 corresponding to the Old traditional sequence 1,9,14,. (ii) The three fundamental numbers 0010, 0100 and 1000 correspond to 14, 13 and 12 respectively in the old traditional sequence. Thus, we have: 0000 0001 1 9 cycled 1 - fixed cycle 2 0010 0100 1000 14 13 12 cycle 3 (iii) We then return to the beginning of the binary system trying to count but omitting numbers already assigned in steps 3 (i) and 3 (ii). We also maintain the hierarchy in their corresponding old traditional sequence. Thus we have the following cycle of numbers in the binary system of Table 2. 0011 5 Cycle 4 0101 15 (iv) Repeat step (iii) but omitting numbers already assigned. Thus we obtain the succes- sive cycles: 0110 4 0111 7 cycle 5 1010 16 1001 3 cycle 6 1011 11 1100 6 cycle 7 1101 10 1110 8 cycle 8 1111 2 cycle 9 - fixed Thus we obtain a new Ifa divination model below:- 61 Table 3. New Model Old Traditional 0000 0001 Ogunda 0010 The cause of 0100 diversion is the 1000 fundamental Nos Oturupon 0011 Irosun 0101 0110 0111 Obara 1010 1001 1011 1100 Owonrin 1101 1110 Okanran 1111 Oyeku Sequence ODU 1 9 cycle 1 cycle 2 Ogbe 14 13* 12 cycle 3 5 cycle 4 15 4 7 cycle 5 16 3 11 6 Irete Otua * Ose Odi Ofun Iwori Ika cycle 6 cycle 7 10 8 cycle 8 Osa 2 cycle 9 *The only cycle which fails to obey the traditional hierarchy. This also features in Ifa-6-A-Bits paper computer Model N in addition to other cycles which fail to obey traditional hierarchy. (See Table 4 below:) Table 4. IFA - 6 - A - Bits Paper Computer Model N Cycle 1 Cycle 2 diversion and Cycle 3 fundamental Nos 00000 000001 000010 Ogbe Ogunda Irete 1 9 14 The 000100 Otua 13 attention Oturupon Irosun 12 5 Numbers 001000 000011 immediately following cause is of the 62 Cycle 4 000101 001001 000110 Ose Iwori Odi 15 3 4 the fundamental Nos 001010 Ofun 16 numbers 001100 000111 Owonrin Obara 6 7 Numbers immediately following Cycle 6 001011 001101 Cycle 7 001110 Cycle 8 001111 Ika Osa Okanran Oyeku 11 10 8 2 fundamental Cycle 5 10,100 Trying to follow again; those of cycle 5 *Cycles that do not obey traditional hierarchy. The reason for this is due to the fact that in the Ifa-6-A-Bits, from cycle 4 onwards, emphasis is placed on the binary system alone regardless of the hierarchy in traditional sequence. NEW MODEL COMPUTER PROGRAM IN BASIC LANGUAGE Below is the computer program in basic language used to produce the numbers in Tables 1, 2 and 3. 10 REM*** PROGRAM: NUMERALS 20 REM*** This program converts Ifa ordered signature into binary scale. 30 DIM NN (18), SS (1B), DD (18) 40 REM*** INPUT OLD SEQUENCE**** 50 NN (1) = 1111: NN (2) = 2222: NN (3) = 2112: NN (4) = 1221: NN (5) = 1122: NN (6) = 2211 60 NN (7) = 1222: NN (8) = 2221: NN (9) = 1112: NN (10) =*, 2212: NN: 2122 70 NN (12) = 2111: NN (13) = 1211: NN (15) = 1212: NN (16) = 212 80 REM 111 PRINT OUT OLD SEQUENCE *** 90 LPRINT TAB |(5); “OLD SEQUENCE IS:”:LPRINT 100 FOR J = 1 TO 8: LPRINT NN (J):: NEXT J: LPRINT 110 FOR J = 9 TO 16: LPRINT NN (J):: NEXT J: LPRINT: LPRINT: LPRINT 120 REM *** ORDER OLD SEQUENCE AND PRINT OUT*** 130 LPRINT TAB (5): “THE ORDERED OLD SEQUENCE IS:”:LPRINT 140 FORI = 1 TO 15: FOR J = I TO 16 150 IF NN (I) NN (J) 170 160 GOTO 180 170 SWAP NN (I), NN (J) 180 NEXTJ 190 BB (I) = NN (I); NEXT I: BB (16) 200 FOR I = 1 TC B:LPRINT BB (I):: NEXT I: LPRINT 63 210 220 230 240 250 FORI = TO 16: LPRINT BB (I):: NEXT I:LPRINT: LPRINTt: LPRINT REM*** OBTAIN NEW ORDERED SEQUENCE"*** LPRINT TAB (5); "NEW ORDERED SEQUENCE IS:" FOR J = 1 TO 3: SS (J) - BB (CJ): NEXT J FOR J = 12 TO 16: SS (J) = BB (J): NEXT J:SS (10) - BB (11):SS (11) =* BB(10) FOR J =-- 9 TO STEP -1 SWAPBB(J),BB(J-1):S>(J)!BB(J) NEXTJ FOR J = 4 TO 5: SWAP BB (J), BB (J + 1): SS (J): NEXT,J;SS (6) 260 270 280 290 W(6} 300 FOR I = 1 TO 8:LPRINT SS (1);; NEXT I: LPRINT 310 FOR I = 9 TO 16:LPRINT SS (I):: NEXTI LPRINT: LPRINT: LPRINT 320 REM *** NOW TRANSLATE INTO BINARY NUMBERS AND PRINT OUT *** 330 FOR J = 1 TO 16: DD (J) = SS (J) -1111: NEXT J 340 LPRINT TAB (5) ;"NEW ORDERED SEQUENCE IN BINARY BASE IS:": LPRINT 350 FORK = 1 TO8: LPRINTDD(K);: NEXTK: LPRINT 360 FOR K = 9 TO 16: LPRINT DD (K);; NEXT K: LPRINT: LPRINT 370 LPRINT "WHERE NECESSARY, ADD ENOUGH ZEROES ON THE LEFT TO MAKE FOUR DIGITS" 380 END 381 Result. traditional signature 1111 2222 2112 1221 1122 2211 1222 2221 Table 1 1112 2212 2122 2111 1211 1121 1212 2121 The Ordered traditional Signature 1111 1112 1121 1122 1211 1212 1221 1222 Table 2 2111 2112 2121 New Ordered Signature is 1111 1112 1121 2122 1211 2211 2111 2212 1122 2221 2222 1212 1221 2221 3 2222 Table 1222 2121 2112 2122 2211 New Ordered Sequence in Binary Base is 0000 0001 0010 0100 1000 2212 0011 0101 0110 64 0111 l010 l001 1011 1100 1101 1110 1111 where necessary, enough zeroes are added on the left to make four digits ENDNOTE 1 Abimbola, W. "An Exposition of If a Literary Corpus", Ph.D. Thesis. University of Lagos Lagos 1971 p. 487 2 Similar system could be found in some West African ethnic groups such as, among the Bariba, Edo, Ewe, Fon, Ibo, Igbira and Nupe. 3 For a detailed information on this, read Bascom, W.R., Ifa Divination: Co mm imitation Between Gods and Men in West Africa, Indiana University Press 1969 and Ablm-bola,W. Sixteen Great Poems of Ifa UNESCO Publication 1975. , . 4 Bascom, W.R. 1969 5 Abimbola, W. IFA; An Exposition of Ifa Literary Corpus O.U.P, Ibadan Nigeria. 1976; AwonOju Odu Mereerindinlogun Ibadan Oxford University Press 1977. 6 Lucas, J.O, The Religion of the Yoruba Lagos C.M.S. Bookshop. 1948. 7 Idowu, Bolaji African Traditional Religion - A Definition C.M.S., London 1973. 8Awolalu, Omosade J.Yoruba Beliefs and Sacrificial Rites Longman London, 1979. 9 Part of Ese Ifa collected from Awo Adebayo Kehinde, Elepc-Onipele Compound Iseke, Oyo on August 23rd, 1987. 10 My understanding of binary system has benefited greatly from long discussion with Dr. P. Onumanyi of Department of Mathematics. University of llorin. He has read passed useful comments on an earlier draft of this paper. 11 Opeola, Modupe S. '.'could African Studies Guide High School Science Curriculum Improvment in Nigeria" Mimeograph 1986 p. 16 12 I also acknowledge the assistance of Mr. F. Aderibigbe (programmer) who produced the computer program in basic language. 65 REFERENCES Abimbola, Wande "An Exposition of Ifa Literary Corpus" Ph.D. Thesis University of Lagos, Lagos 1971 p. 487 Sixteen Great Poems oflfa UNESCO Publication 1975 IFA: An Exposition of Ifa Literary Corpus O.U.P. 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