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57
A New Model Of
Ifa
Binary System
BADE
AJAYI
Department
of Linguistics
and
Nigerian
languages, University of I
lorin
,I
lorin,
Nigeria
INTRODUCTION
Ifa
,
the literary corpus of'which has be
en aptly described by Abimbola
1
as
"th
e store
house of Yoruba cu
ltu
re inside which one can
find
all the traditional
wealth and
glory of the Yoruba", is associated with
Oru
nmila, the Yoruba
g
od of
wisdom and divinat
ion. It uses a geomantic system
2
of divination to arrive at
appropriate signs and employs
Ifa
verses to in
terpret .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
, Abimbol
a
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
Oyeku
Meji
1
1
11
11
2
2
1
1
11
11
Or
2
2
1
1
11
11
2
2
1
1
11
11
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
hie
rarch
y
, The aim of this paper is to show that the
hierarchical order of the
Od
u
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 math
ematic
al 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 gb
e,
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
K
eyinde
In fact
the digital computer uses the binary system, Lik
e the computer, Yoruba
anthmomancy is based on binary system
10
and it is therefore a computer
ori
e
nted science which can be used in mathematical education.
The
Ifa
6
A
Bits Paper Computer Model N
At a divination session several Ibo (instru
ments for casting lot), may be used
to find
detail information about a client's problem. The commonest and simpl
est
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 a
nd 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
A
Bits computer model N has
been developed. Here is the model worked out by
Opele
Pu
nches
Odu Name
000000
Ogbe (1)
000001
Osa (10
)
000010
Otua (13)
000100
Irete (14)
001000
Ogunda (9)
000011
Irosun (5)
000101
Ose (15)
001001
Iwori (3)
000110
Odi (4)
001010
Ofun (16)
001100
Owonrin
(6)
000111
Obara (7)
001011
Ika (11)
001
110
Oturupon (12)
001110
Okanran (8)
001111
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 interpreta
tion 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 draw
back 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 olrd
er the sign in ascending magnitude as in Table 2
below
Table
I
Old Sequence
ODU Name
Sign
1
Ogbe
1111
2
Oyeku
2222
3
Iwori
2112
4
Odi
1221
5
Irosun
1122
6
Owonrin
2211
7
Obara
1222
8
Okanran
2221
9
Ogunda
1112
10
Osa
2212
11
Ika
2122
12
Oturupon
2111
13
Otua
1211
14
Irete
1121
15
Ose
1212
16
Ofun
2121
Table 2.
Ol
d Sequence
Ordered sign
Binary system
1
1111
0000
9
1112
0001
14
1121
0010
5
1122
0011
13
1211
0100
15
1212
0101
4
1221
0110
7
1222
0111
12
2111
1000
3
2112
1001
16
2121
1010
11
2122
1011
6
2211
1100
10
2212
1101
60
8
2221
1110
2
2222
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
1
cycled 1
fixed
0001
9
cycle 2
0010
14
0100
13
cycle 3
1000
12
(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
Sequence
ODU
0000
1
cycle 1
Ogbe
0001
9
cycle 2
Ogunda
0010 The cause of
14
Irete
0100 diversion is the
13*
cycle 3
*
O
tua
1000 fundamental Nos
12
Oturupon
0011
5
cycle 4
Irosun
0101
15
Ose
0110
4
cycle 5
Odi
0111
7
Obara
1010
16
Ofun
1001
3
cycle 6
Iwori
1011
11
Ika
1100
6
cycle 7
Owonrin
11
01
10
Osa
1110
8
cycle 8
Okanran
1111
2
cycle 9
Oyeku
*The only cycle which fails to obey the traditional hierarchy. This
also
features in
Ifa
6
A
Bits paper computer Mo
del 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
00000
Ogbe
1
Cycle 2
000001
Ogunda
9
000010
Irete
14
The
cause
of
divers
ion and
Cycle 3
000100
Otua
13
attention
is
the
fundamental Nos
001000
Oturupon
12
000011
Irosun
5
Numbers
immediately following
62
Cycle 4
000101
Ose
15
the fundamental Nos
001001
Iwori
3
000110
Odi
4
Trying to follow
fundamental
Cycle 5
001010
Ofun
16
numbers
again;
10,100
001100
Owonrin
6
000111
Obara
7
Numbers
immediately following
Cycle 6
001011
Ika
11
those of cycle 5
001101
Osa
10
Cycle 7
001110
Okanran
8
Cycle 8
001111
Oyeku
2
*Cycles that do not obey traditional hierarchy. The rea
son 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 pro
gram 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*** INP
UT 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) = 11
12: 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
FORI =
TO 16: LPRINT BB (I):: NEXT I:LPRINT: LPRINTt: LPRINT
220
REM*** OBTAIN NEW ORDERED SEQUENCE"***
230
LPRINT TAB (5); "NEW ORDERED SEQUENCE IS:"
240
FOR J = 1 TO 3: SS (J)
BB (CJ): NEXT J
250
FOR J = 12 TO 16: SS (J) = BB (
J): NEXT J:SS (10)
BB (11):SS (11)
=* BB(10)
260
FOR J =
-9 TO STEP
1
270
SWAPBB(J),BB(J
1):S>(J)!BB(J)
280
NEXTJ
290
FOR J = 4 TO 5: SWAP BB (J), BB (J + 1): SS (J): NEXT,J;SS
(6)
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: L
PRINTDD(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
121
2
2121
The Ordered traditional Signature
1111
1112
1121
1122
1211
1212
1221
Tabl
e
2
2111
2112
2121
2122
New Ordered Signature is
1111
1112
1121
1211
Table
3
1222
2121
2112
2122
2
211
2212
2221
2222
New
Ordered Sequence in
Binary Base is
0000
0001
0010
0100
1000
0011
0101
0110
64
0111
l010
l
001
1011
1100
1101
1222
2211
2212
2221
2222
2111
1122
1212
1221
1110
1111
w
h
ere necessary, enou
gh 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 o
f
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 Mereerind
i
n
logu
n
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.
8
Awolalu, 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 understan
ding 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 Studie
s 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 o
f
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 Beli
efs and Sacrificial Rites Longman, London
1979 Bascom, W.R.
Ifa
Divination: Communication Between Gods and
Men in West Africa. In
diana University Press 1969
Crystal, David and Derek Davy Investigating English Style.
Longman, London
1969 pp. 175
77
H
an
n
, 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 Resear
ch 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
Ogil
vy, 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