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. Ibadan, Nigeria 1976
Awon Oju Odu Mereerindmlogun Ibadan Oxford University press 1977.
Abraham, W.E. The Mind of Africa Chicago: The University of Chicago Press
1962. Adetoro, J.E, Introduction to the History, Science and Philosophy
of Numbers and the Role of 7 University of llorin Press. 1986
Awolabu, Omosade J. Yoruba Beliefs and Sacrificial Rites Longman, London
1979 Bascom, W.R. Ifa Divination: Communication Between Gods and
Men in West Africa. Indiana University Press 1969
Crystal, David and Derek Davy Investigating English Style. Longman, London
1969 pp. 175-77
Hann, A. Education for,Open Society Boston: Allynsucori4nc. 1962
Horton, R. "African Traditional Thought and Western Science" African Vol. 37
No. 1 & 2 pp 50-70 1967.
Idowu, Bolaji Religion A Definition C.M.S. London 1973
Lassa, P.N. "Toward a Research Model IN Mathematics Education". Abacas Vol.
7 No. pp 146-63 March 1986
Luca*, J.O. The Religion of the Yoruba Lagos C.M.S. Bookshop 1948
McClelland, E.M. "The Significance of Number in the Odu of Ifa"
African XXX W4 pp 424-30 1966
Ogilvy, C.S. and Anderson, J.T. Excursions in Number Theory H.y. Oxford
University Press 1966 :
Bozegha, W.B., M.A. Ikbiejugba, P. Onumanyi and F.M. Aderibigbe “Number
generation in number bases” ABACUS Vol. 17 No. 1 pp 202-217 March
1986