chimakonam-metric system in igbo thought final-libre

8/12/2019 Chimakonam-metric System in Igbo Thought Final-libre

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Paper presented at The 11th Annual Conference of the Igbo Studies Association on Ohaka: The Community is

Supreme Held at Modotel, Enugu, Nigeria June 27-29, 2013

METRIC SYSTEM IN IGBO THOUGHT LONG BEFORE THE ARRIVAL OF THE

EUROPEANS: A SYSTEMATIZATION

Jonathan Okeke Chimakonam Ph.D

Department of Philosophy

University of Calabar

[email protected]

ABSTRACT

Among the Igbo of today it is often mistaken that our fore-fathers lived in darkness, knew

nothing and did nothing of worth. Any mention of the past was readily greeted with one scornful

remark or another. The Igbo man of the pre-colonial era was a bush man, primitive, untamed,

untutored and uncivilized. He had no civilization of his own and he had learned none from the

outside world. However, Igbo scholars in the recent times have unearthed so much to contradict

these false positions. In this work, we investigated the metric system of the Igbo some of which

have been in practice for centuries. It was our goal to unearth and systematize the Igbo metric

system that lies suppressed and hidden since colonial times in order to falsify the claim that prior

to the coming of the Europeans the Igbo were a primitive, uncivilized people with no high

cultures and a system of thought but, far beyond this, it was also our goal to push through these

discoveries into the modern historical place for the sake of posterity and our invaluable identity.

Introduction

It is a common intellectual dogma in our time that the pre-colonial Africans (including

Igbo people) lived in darkness knew nothing and did nothing of worth. Any serious academic

reference to that portion of history was readily greeted with one scornful remark or another. The

Igbo man of the pre-colonial era was a bush man, primitive, untamed, untutored and uncivilized.He had no civilization of his own and he had learned none from the outside world. Issues like

this make Gordon Hunnings in his work Logic, Language and Culture to assert that

According to this view1 the study of African traditions is largely an antiquarian exercise of

1The view that the bulk of African traditions can be classed as mystical and consequently

dismissed from serious consideration in the twentieth century.


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interest to social anthropologists, except that obstinate addiction by Africans to their traditional

culture is an obstacle to progress; the removal of this obstacle (therefore) becomes the principal

aim of higher education throughout the continent (3). As appalling as this may sound, Hunnings

wants to make the point that Western education was aimed at weaning the black man of his tail

in hope that he could become civilized. This is because the African culture and its appurtenances

are presumed to lack the stain of rationality. For this, Hunnings again, posits that The second

argument which has tended to inhibit the serious and systematic study of African culture is that

the corpus of traditions which it embodies is not only mystical but pre-logical and so lacking the

elements of rationality (4). This sort of opinion is held by historical ignoramibus like George

Hegel (cf. Phenomenology of the Spirit) and misinformed anthropologists like Lucien Levy

Bruhl (cf. Primitive Mentality). However, Igbo scholars in the recent times have unearthed so

much to contradict these false positions. Paul Dike, Adiele Afigbo, Angulu Onwuejeogwu etc.,

in Igbo history and Culture; C. Agbodike and C. Acholonu in Igbo archeology; C. Acholonu and

A. Animalu in Igbo linguistics; W. Umezinwa and C. Achebe in Igbo culture; A. Animalu and J.

Chimakonam in Igbo scientific thought; A. Asouzu, T. Nwala etc., in Igbo philosophy; J.

Chimakonam in Igbo Thought System and Logic. Indeed the list is endless, these champions and

many more not mentioned here smothered the argument that the Igbo were a primitive race,

uncivilized and without any system of thought or high culture before the coming of the west.

In this work, the author wishes to investigate the idea of Igbo metric system which was in

use long before colonial times. In 1799 the International System of Units, a French construct was

inaugurated and promoted for all cultures. Before then, different nations had their standard. But

for the reason of universal convenience, a single standard was thought to be inevitable, that was

what the French offered in 1799. Many nations of the world adopted it. In USA, it was

sanctioned in 1866 but to this day is still practised together with the traditional American system.

The same goes for Britain grudgingly swing between the French system and their native Imperial

System of Measure. Other countries like Liberia and Burma are yet to adopt the French System.

The campaign to universalize the French system was wedged by the French until 1875 when the

General Conference for Weights and Measures was form. The latter has carried on the project

ever since and now aims at achieving the universal single system by 2014. It should be pointed


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that through the passage of time the project of one universal system of measure has sought to

take inputs from different systems in lieu of a universal system. In all of these eclectics,

references were not made to Africa. The reason is not far-fetched. Hegel had declared that Africa

had no high cultures before colonization and had made no contribution to world civilization2. So

there was no need looking into Africa for any form of ideas. Hence, our objective here is to give

reasons to denounce any internationally agreed decimal system of measurement by the proposed

2014 which does not include ideas from Africa. The Igbo metric system which we discuss here is

yet another important fragment in the big body of rational knowledge which has been suppressed

since the colonial times. Since we are going to make use of figures, we shall discuss briefly Igbo

philosophy of mathematics and paint a little picture about Igbo thought system and logic. This

will give a firm foundation to the work as it progresses. We shall be making ample use of

diagrammes in order to drive home every point we take up at each turn. One of our goals is to

establish that a cultural system that developed technical appurtenances in metric system was

logically sophisticated.

On the whole we shall look at the Igbo ideas of the Counting set, Set correspondences,

Linear measurement, Capacity Measurement, Area measurement, Mass and weight, Temperature

Measurement, Plane angle measure, Igbo Calendar Year, Igbo year calendar cycle, Time

Measurement and finally Space-Time Continuum in Igbo Thought. It is our goal to unearth the

Igbo that lies suppressed and hidden since colonial times in order to falsify the claim that prior to

the coming of the Europeans the Igbo were a primitive, uncivilized people with no high cultures

and a system of thought but far beyond this, it is also our goal to push through these discoveries

into our modern lives for the sake of posterity and our invaluable identity.

Igbo Philosophy of Mathematics

Egbe bere Ugo bere or the law of Igwebuike is the most fundamental law of Igbo

thought which could be broken into two; (a) Nmekka (complementarity) Aka nri kw aka

2See Phenomenology of Spirits


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ekpe, aka ekpe akw aka nri and (b) Njikka (integrativity) ihe kwr, ihe akwdobe ya3

together with the law of nna-etiti undergird the basic parameters of thought in Igbo world

view. In Igbo mathematical concerns, by evoking the law of igwebike we come by two views

in treating mathematical objects namely; (a) different mathematical objects as points, lines

numbers etc., exist only in groups. For example, we do not talk of point or line or number if not

in reference to other points or lines or numbers. A thing cannot just exist on itself alone. Every

reality exists in a network where it serves as a missing link or necessary link connecting others

and others connecting it4. This is why in African number system, the first complementary or

integrativist whole number is two, one remains fractional until it is added to another one or any

other number5

(b) both mathematical objects and objective realities are meaningless on their

own until they conglomerate or form an amalgam; the former numbering, measuring and

grouping or classifying the latter and the latter giving the former a pseudo-objective existence by

receiving its predication6.

It is because of this mathematical orientation which often treats the number 2 as the first

whole number and the number 1 as somewhat fractional that the Igbo metric system generally

observes the number 2 as very important in metric arrangements. As the number 1 is somewhat

fractional, it is hardly an integrativist or complementary number. For example, among the Igbo, a

3 Jonathan Okeke Chimakonam, Introducing African Logic and Numeric System: Formalist and Axiomatic

Approach, Forthcoming; Also, in Integrative Humanism: Extensions and Clarifications Integrative Humanism

Journal, 3.1 forthcoming.

4Innocent Asouzu, Ibuanyidanda and the Philosophy of Essence, (Calabar: University of Calabar Press, 2011), p.41,

for a complementarist usage it is missing link; Jonathan Okeke Chimakonam, Introducing African Science:

Systematic and Philosophical Approach, (Indiana: Authorhouse, 2012), p. 106. Jonathan Okeke Chimakonam and

Sunny Agu, G. O. Ozumbas Integrative Humanism Project as a Model of Explanation in Science, for an

integrativist usage it is necessary link. Conference Proceeding (8.3, 2012), p.21.

5 Jonathan Okeke Chimakonam, Toward Integrative and Eliminative Epistemologies: From Facts to Fancies

Integrative Humanism Journal (2.1) p.164.

6In colonial times Igbo pupils found it difficult to follow the logic of number abstraction not because they do not

understand what say number 5 means but because the Igbo linguistic culture presents number in predicative form.

Thus the two ways present confusion which derail progress in mathematical studies. The first set of Igbo trained

teachers understood this having faced the challenge themselves hence they adopted the highly successful predicative

format. For example; otu otu oloma, abua oloma abua, ato oloma ato, etc.


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man is not regarded as complete until he marries a woman. This also explains why in making

petty gifts, it is abnormal to present one item. A woman generally would say I have two breasts

why give me one item?

There is another sense to which the number 2 could be interpreted but which is against

the understanding Igbo people give to it in normal epistemic contexts. As a result, the Igbo try to

draw a line even symbolically. The number 2 could be understood as contradiction where two

variables stand opposed to each other. Symbolically, when the kola has only two parts, it is taken

to signify contradiction and as a result rejected. If such kola was broken in any gathering, it

meant that some malignant spirits planned to bring division among the gathered kindred

members, village, friends, in-laws or family members. Measures are quickly taken to avert this

tragedy. The expression given to any kola with only two lobes is : ja kraka which means

that the kola clapped. This signifies contradiction, crises, clash, opposition or absence of

harmony. Therefore, contradiction is actually a tragedy in Igbo thought. This is not the sense in

which the Igbo employ the number 2 in normal epistemic and logical contexts.

The Igbo employ the number 2 in ways that signify coming together, harmonious

integration and complementarity. This agrees with the theme of this conference which is,

Ohaka: The Community is Supreme which can be variously interpreted as integration is better

than disintegration or coming together is better than standing apart. Mathematically, 1+1=2

because the fractional variables 1 and 1 are contraries in Igbo logical thought and not

contradictories which means they can achieve bonding. If they are lines, the Igbo conception

does not see them as parallel. Geometrically, it can be adduced that any two lines in Igbo thought

meets somewhere even the seemingly parallel must have a meeting point somewhere else, such

would be an anathema. For example an unmarried man is considered incomplete until he takes a

wife; it is not understandable for a ripe lady to remain in her fathers house unmarried, etc. The

two lines below have a point of complementation and can even form a triangle if we put the

dotted lines at its base.


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Fig. 1: showing complementary lines

Meeting point

Line 1 .. line 2

This gives us the three values in Igbo logic where the third value is obtained through the

complementation of two standard fractional values7

. This also explains why jugo, a kola with

three lobes is priced above all else in Igbo world view because it signifies the perfection of the

synergy of the fractional two. The third lobe is actually the physical proof that the other two are

not contradictories or did not clap. The three-valued thought model of the Igbo may be

diagrammed as below.

Fig. 2: showing the Igbo three-valued thought model

C

T F

The discussions and the diagrammes above simply show the interpretation of the number 2 in

Igbo thought which is also present in Igbo metric system. The number 2 logically represents two

fractional values of truth and falsehood labeled conventionally as T and F above which

necessarily integrate or complement each other in the third value labeled C above. The arrows in

the boxes show the movement of the values or variables as the case may be from a platform

where they are fragmented to a central platform where they achieve unity. This is against the

principle of bivalence which entrenches the place of contradiction in classical logic. What this

means however is that the reasoning pattern of the Igbo is non-bivalent or trivalent. The laws of

thought in Western logic (identity, contradiction and excluded-middle) for example are

demobilized in Igbo-African thought system and in their place are the Igbo laws of thought

namely; Njikka, Nmekka and nna-etiti.

7Jonathan, Introducing African Science,p.19-22. Chris Ijiomah, An Excavation of Logic in African World View,

African Journal of Religion, Culture and Society (1. 1. August, 2006): 29-35; Ikemesit Nkanta, Three-valued Logic

as an Explanatory Tool for some African Experiences, M.A Thesis, (Calabar: University of Calabar, 2012)

Unpublished, P. 1-10


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The Idea of Metric System in Igbo Thought

Thought system is the collection of standard beliefs in any culture which shape the

peoples thinking about reality. According to J. O. Chimakonam:

Let us roughly define a thought system as the aggregate of a peoples basic beliefs

which determine their norms, laws and judgments on what is acceptable and

unacceptable in accordance with established consensus. It determines the rules

within which a people's reflection on realities is organized. In other words, a

thought system consists of (but not only) the perspectives through which a people

rationally look at reality, i.e. it is the aggregate of beliefs, assumptions, norms

which have become basic in a given society and which define a peoples thinking

and understanding of realities around them8.

From the above we acknowledge the existence of Igbo thought system which shape the Igbo

peoples thinking and understanding of realities in their world-view. One of such is the idea of

metric system among the Igbo. It is easy to see with the study of Western education that the main

problem it has with African thought system is that it regards it as non-existent or at best a

collection of mystical and pre-logical traditions lacking in rationality. When he asks What is

meant by African culture as pre-logical and how was such a conclusion arrived at? (Hunnings

4) Gordon Hunnings replies:

One quite specific reason is because Aristotles Laws of Thought are not

formulated and do not appear to be observed in Africa languages. According to

classical logic, these laws are the supreme principles of logical truth and any

system of ideas expressed in a language in which these principles are not

observed can only be described as pre-logical. Furthermore, as these logical

principles represent the Laws of Thought their absence is not only a defect of

language but of the mentality of the users of the language. It was by reasoning

along these lines that Levy Bruhl felt entitled to draw far-reaching conclusions

about the mind and even the soul of African peoples. It has often been observed

8Jonathan, Introducing African Science,p.17.


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that whereas the truths of philosophy turn out to be trivial tautologies, it is the

errors of philosophy that are intrusive. This particular thesis seems to me not only

to be an error, but a particularly intrusive one. Most of Levy Bruhls critics have

contented themselves with a general refutation of his thesis on the ground that he

exaggerated the difference between African and Western cultures. This is

certainly true, but the philosophical errors involved in Levy Bruhls thesis are far

more subtle than that.9

The above observation is corroborated by Joseph Omoregbe when he says that Africans of old

may not have put their reasoning in the form of Aristotles syllogism or Russells logical form

but they sure had their reasoning pattern (6). Meinrad Hebga powerfully projected similar

argument when he echoes the following golden words:

The dogma of one standard and of one all-embracing prototype for civilization

and culture is losing its backers right along. If the fact of having arrived at the

atom, of having probed nature in its depth and furthermost reaches gives

legitimate pride to the discoveries and consecrates the civilizations which have

produced them, all this still leaves an important place to the other cultures,

embryonic though they may be called, a place which they occupy humbly, but at

the same time to the advantage of all. A fortiori, it is necessary to admit the

existence of opposed logics, structures of thoughts, methods of research,

contradictory in their methods or their conclusions.10

We therefore find assurance in the thoughts above which demonstrate that African culture need

not appeal to Western thought structure to become legitimately rational. And against the thesis of

Levy Bruhl, African culture is rational by the native internal logic which undergirds the systemto which the Western critics are ignorant of. It is upon this native thought structure of Africa that

we here systematize and interpret Igbo metric system.

9Hunnings, Gordon. Logic, Language and Culture. Second Order, p. 4

10Hebga, Meinrad. Logic in Africa. Philosophy Today, Vol. 11. No. 4/4 1958. Pp. 222-23


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In this work, we focused on identifying and systematizing the Igbo metric system and

where appropriate we did some mathematical conversions. Every thought system has its own

laws which guide the reasoning of the people on reality issues. The same is true of the Igbo

thought system. Two of such laws which we shall find handy in this work include: Njikka

(integrativity) and Nmekka (complementarity).

According to J. O. Chimakonam11 integration is a near equivalence of the Igbo term

Njikka which means truth, value or meaning is derived from variables when they are brought

together, whereas the term complementarity comes nearest to explaining the concept of

Nmekka. Literarily, Nmekka means that strength or power is found in the group or achieved in

coming together. The focus of the law of complementarity is on group strength or power. The

difference between the law of complementarity and that of integrativity is at two levels, while the

former centers on group power the latter focuses on group identity; again, while in the latter, the

individual finds its identity in the group, in the former, the individual must join or team up with

others to generate group power. Hence, in complementarity, the individual loses itself in the

group whereas, in integrativity, the individual finds or discovers itself in the group.

From ages past, the Igbo have a sense of arithmetical measurement. This of course, is

based on the idea of group identity although each group is made up of individuals. The Igbo

societies are more gregarious, the individual does not exist in isolation, he exists in a group. It is

the group that gives identity, hence the ideas of integrativity Njikka and complementarity-

Nmekka as laws of thought in Igbo thought system! Among the Igbo, people are identified in

the group i.e. their villages, kindred or families. Anyone who does not belong to these groups

does not actually exist. The individuals in a group going by the laws of integrativity and

complementarity are not unique but similar or related.

If we recall that for the Igbo numbering conveys idea of things then we would understandwhy the Igbo numeric sense is that of group identity and not individual identity. Following the

principle of integrativity in Igbo philosophy of mathematics, the number one is isolated because

its idea cannot be completely formed. One would seemingly mean one thing in Igbo numeric

11Jonathan, Introducing African Logic and Numeric System,Forthcoming


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sense but one thing cannot be predicated or placed in a logical relation. Colloquially, it takes two

to tango. Thus we may have one Nda (closer to gramme in standard western scale) but until

another one is added to it to make it two, the previous one is isolated. Hence, by the integrativist

and complementarist principles actual numbering starts from two. This is evident in all forms of

measurement as counting set, area, capacity, linear, temperature and mass and weight where the

number 2 is a base.

Counting set

The counting set comprises of range of even numbers which characterizes the grouping

of things. It serves in packaging of things or the arrangement of articles in business from the

olden times and it also characterizes currency denominations. The counting set therefore

represents standard range of arranging items or denominating currency among the Igbo. One

significant factor in this system is that by the correspondence of its elliptical progression, the

mind easily follows up on its increase. This remains the basic justification for the use of the idea

in business and in currency related issues. The table below shows some of the sets and their

interpretations.

Table. 1 : table of sets and interpretation

Set

Interpretation Translation

2 g Set

4 g-ab Two-sets

6 g-at Three-sets

8 g-an Four-sets


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10

g-ise Five-sets

20 g-iri Ten-sets

40 Nn Many-sets

100 kala-akpa Half-bag

200 Otu-akpa One-bag

1000

Akpa-ise Five-bags

This arrangement continues ad infinitum. The numeric representation of the counting set

is shown in the table below:

Table. 2 : numeric representation of counting set

Nt-

an

(unit

)

Iri

(ten

)

Naar

(hundre

d)

Puku

(thousand)

Nde

(million)

Ijeri

(billion) etc.

1+1

10 100 1000 1,000,000 1,000,000,000

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.


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9 90 900 900,000 900,000,000 900,000,000,000

This same exercise could be continued to Nzeri12(trillion).

Set correspondences

1+1 = nt-an/Standard unit

25 = Iri/ten (g-ise)

102 = Iri-ab/twenty (g-iri)

202 = Iri-an/forty (nn)

402 = Iri-asat/eighty (nn-ab)

205 = Otu-naar/one hundred (kala-akpa)

1002 = Naar-ab/two hundred (otu-akpa)

2005 = Otu-puku/one thousand (akpa-ise) etc.

The above tables and permutations offer various explanations to the counting set in Igbo numericsystem and metric system.

Linear measurement

Africans have idea of distance and they characterize it differently with body parts and

sometimes with objects or farm tools. The length of the middle part of an average persons index

finger is called Ntaji and is equivalent to twenty millimeters in western measurement standard.

One tenth of it is called Ntji and is equivalent to two millimeters. Two, we recall, is the first

integer in Igbo-African number system according to the integrativist thesis. Some traditions in

Igbo-Africa use the thumb nail, the finger length, palm length, arm length, foot length, and

distance between two steps, machete length, and palm frond stem; for radius some use hoe

tongue and mortar, etc. What we reproduce here is the consensus from various traditions. The

12Our choice of word nzeri for trillion is phonetic. Some prefer mbieri, others mbari, but nzeri commands and

presents clearer imagery of the magnitude of trillion.


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table below shows the idea of linear measurement in Igbo-African thought with its western

equivalents.

Table. 3: table of linear measurement

Name Unit Western Conversions where one Ntji-nchi corresponds to one out

of the conversions

Ntji-nchi 1

n/n

2 m/m Ntaji-nchi

nt/n

110

Nkeji-nchi

nk/n

1200

Nchi n/c

11000

Omulu-nchi o/n

12,000,000

From the above we can construct a complete linear measurement table as follows:

10 ntji-nchi 1 ntaji-nchi (nt/n)

10 ntaji-nchi 1 nkeji-nchi (nk/n)

10 nkeji-nchi 1 nchi (n/c)

1000 nchi 1 ml-nchi (m/n)

In the above we adopt the Igbo standard nchi13

meaning literally an uncertain distance not farther

than two full steps. In Western standard it would be equivalent to about two meters.

Capacity Measurement (fluid volume)

We shall adopt iko as our basic standard. The term iko14

literally translates to cup. But in the

traditional Igbo sense we are employing it, it is a standard for measuring quantities of grain, dust

and liquid. In Western standard it is equivalent to two liters.

10 ntji-iko (n/i) 1 ntaji-iko (na/i)

10 ntaji-iko 1 nkeji-iko (ne/i)

13The term obviously is a primeval term in the dialect of people of old idemili area.

14It should be noted that iko could also mean drinking cup which is far smaller than iko as a standard for measuring

grains, dust and liquid. An alternative standard is akpa which translates to bag. However, we prefer iko because in

the modern mathematically-oriented world, it is easier to achieve precision with iko than with akpa.


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10 nkeji-iko 1 iko (ik)

Area measurement

Here we shall adopt g as area measurement standard. g figuratively means a given areawhich could be in radius, square, perimeter, circumference etc. for example, the tongue of a hoe

which could take any shape. In Western standard one g-nchi would be equivalent to two

square meters or two meter radius or diameter or circumference.

100 g-ntji (/n) 1 g-ntaji (/t)

100 g-ntaji 1 g-nkeji (/k)

100 g-nkeji 1 g-nchi (/nc)

1000 g-nchi 1 g-mlnchi (/mn)

Mass and weight

Here we shall adopt nda15 as mass and weight measurement standard. Nda as an Igbo word

means weigh. Literally, it means how weighty or how much or how big. In Western standard,

one nda would be equivalent to two grammes.

10 ntji-nda (nd) 1 ntaji-nda (na/d)

10 ntaji-nda 1 nkeji-nda (ne/d)

10 nkeji-nda 1 nda (nd)

1000 nda 1 ml-nda (m/d)

1000 ml-nda 1 ogwe (og)

The difference shown in the first table above between ntji-nchi and ntaji-nchi and the

western millimeters applies throughout the rest of the Igbo-African standards treated thereafter.

So it is not to be taken for example that ten ntji-nda is equivalent to ten milligrams. On the

contrary, ten ntji-nda corresponds to almost twenty milligrams of the western metric system.

Temperature Measurement

One striking difference in temperature measure between the standard western metric

system and that of the Igbo people as we found in this research is that whereas the west measure

15The term is n !g"o #or$ for %#eigh& s in #hen the !g"o s'( ole ' $r) *ht $oes it #eigh)


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in degrees Igbo people from time immemorial measure in stages or what is called Agba16 in

Igbo. Let us take for example the measurement of heat, Igbo people say for a body that:

Table 4: showing stages of temperature measurement in Igbo thought

Agba (Stages) Temperature

dghk Body is not hot

dobere k Body is warm or a little hot

dk Body is hot

dnnukwu k Body is very hot

One notices the obvious limitation of this standard (Agba) of measurement in that it does not

readily provide mathematical precision which is why the west measure in degrees. The reason

for this is because in Igbo philosophy of mathematics the overview of mathematics is not strictly

that of precision and individual conception of numbers as it is in the west but essentially that of

relativity and group conception of numbers. A number is a number because it is capable of group

conception. The value of number one is not appreciated until it is integrated which is why going

by the laws of Njikka and Nmekka, the number 2 represents the foundational number in Igbo

philosophy of mathematics- the first integrativist number. Notice that in the temperature

measurement diagramme bellow the Igbo thermometer started with the number 2 as a

complement of the number 1 from each side.

Fig. 3: Igbo thermometer

Point of integration or complementation (both hot and cold)

Agba-oyi (cold) Agba-k(hot)

16+g" is n !g"o #or$ tht literlly mens stge or perio$, -or e.mple/ g" n'e m"fisrt stge or g" h

mo$ern perio$, *e employ it here in the sense of stge,

20 10 5 2 5 10 20


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When you multiply 2 by 5 it gives you 10 and 10 by 2 gives you 20 and so on (see also the above

discussion on counting set to understand the Igbo idea of base 10 and the standard unit 2). This

represents the Agba or stages of heat or coldness in Igbo thermometer. Notice that on each side

the reading of the thermometer started between 2 and 5. The sum of the two sides gives you 10

as well. This also explains why the unit of Igbo temperature measurement is not unified as it is in

western standard which measures both hot and cold in degrees. In Igbo standard we do not unify,

we measure both hot and cold differently i.e. agba-oyi (stages of coldness) and agba-k(stages

of hotness).

We admitted earlier that lack of precision in Igbo conception of number was a weakness

but there are some senses to which it could be advantageous. A lab scientist would probably

prefer knowing the exact temperature of the body he is working on but outside the controlled

environment such precision is doomed to continuous change from moment to moment either in

excess or in deficit. It is at such circumstances that the Igbo stage measurement becomes

relevant. Again, it promotes relativity and discourages absoluteness in science. Hence the axiom,

wa dka akpkpogwumagana, reality changes like chameleon!

Also, a close look at the Igbo thermometer reveals the presence of Igbo three-valued

logic. Agba-oyi and agba-k represents the two standard values whereas their point of

integration or complementation represents the third value. In the diagramme above, we notice

that the Igbo thermometer read the point of complementation as both hot and cold. This is in line

with the logical interpretation of the third value as both true and false (truth-value glut). So we

have in Igbo metric system a point of both hot and cold (relative to individuals and contexts)

before the stages of not hot and not cold.

You may have also noticed that the Igbo thermometer does not read in negative numbers

e.g. -5,-10, -20 etc., this is because such integers do not form standard mathematical expressionsin Igbo thought system. We do not say by implication that the mathematical sign of subtraction

does not exist in Igbo thought, what we wish to emphasize is the image created when we make

such expressions. -5 in Igbo thought does not make reference to 5 objects that do not exist but to

5 objects that existed, so it becomes trivial and sometimes misleading to add the minus sign -.

The important difference marker here is time such that when we talk of 5 objects that existed

we do not look out for the sign - but to the time indicator which conveys the accurate image.


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Thus if a bodys temperature is measured at 20(agba-k), its opposite would be 20 (agba-oyi).

Note the positioning of the Igbo temperature indicator (the little hanging a) in the cold and

hot temperature measure.

Plane angle measure

The Igbo word for angle is aka which literally means arm but derived from aka-mgbag

or bent arm as in when the arm is bent to obtain angle 84 or 90 in western standard. Basically,

there are four cardinal angles in Igbo plane angle measurement called Izu and comprising of 84

(agba) or 84 each.

Fig. 4:Four Igbo cardinal angles (Izu)

This is also equivalent to western 90. These angels have names example angle 252

which is called Ekeukwu, 336 called Oyeukwu, 84 called Afukwu and 168 called

Nkwukwu. Whereas 252 and 336 are aka-ekpe (left angles), 84 and 168 are aka-nri (right

angles). Also, while 336 and 84 are aka-enu (up angles), 168 and 252 are aka-an (down

angles). Each angle can be further divided into three smaller angles yielding 12 angles in all with

peculiar names. Also, each of the four is called aha; two put together is called ahanab; three is

called ahanatwhile four of the angles put together is called ahanan or izu measuring 336.

See the diagramme below:

+fo'#336

ye'#

252

'e'#

84

'#o'#

168


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Fig. 5: The twelve in four Igbo angles

84Nkwoukwu

In the above diagramme we see how the four cardinal angles make up the Izu and yield further

twelve angles each with peculiar name. Let us therefore point out here that this diagramme is

also a chart interpretation of the Igbo calendar year to which we presently turn to.

Igbo Calendar Year

The Igbo people long had a calendar year chart probably before the preparation of the Gregorian

calendar introduced and signed into law on 24thFebruary 1582 by Pope Gregory XIII. Alexander

Animalu in his 1990 Ahiajoku Lecture17

showed a 1590 AD map of Africa showing the thriving

civilization of the Igbo and it is believed the Igbo calendar was long in use before this period. As

Animalu puts it:One of the oldest map of Africa I have come across is Africa in 1590 ADThe

significant feature of the mapis the appearance on the map of 16thcentury Igbo

culture area under the legendary name, Biafra [written Biafar on the map]. This

17Alexander Animalu, Ucheakonam:A Way of Life in the Modern Scientific Age, 1990 Ahiajoku Lecture, (Owerri.

Printed in 2001 Igbo Day Lecture. Snaap Press, 2001), p. 45.

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Fig. 6: Picture of twelve in four Igbo calendar chart located at Isseke ancient monument

Let us reproduce the carving that looks more like an x on a square for clarity.

Fig. 7: a reproduction of the wall carving

In this carving you notice four squares inside representing the four cardinal months or onwa as it

is called in Igbo. In the Igbo and Gregorian calendars they would be Ekeukwu/January,

Oyeukwu/April, Afukwu/July and Nkwukwu/October. Also you see eight half squares outside

representing the two other months under each cardinal month. You could see how two half

squares flank each cardinal square should you observe the picture or figure from the periphery.

Put together it gives us the twelve nwa/months in Igbo calendar. Below is a breakdown of year

cycle in Igbo calendar:

Igbo year calendar cycle

1 aban(night) + 1 echi (day) = 1 bch(full day)

4 bch= 1 izu

7 izu = 1 nwa (month)

28 bch= 1 nwa12 nwa = 1 ar(year)

84 izu = 1 ar

336 bch= 1 ar

Note that the integration of 1+ 1 forms the standard unit 2 in Igbo philosophy or idea of

mathematics.

Below are the names of the days and months in Igbo calendar:


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cyclic. A. Animalu 1990 as well as A. O. Anya 1981 variously attests to this claim20 . Below is a

figure showing the stages and cyclical nature of time in Igbo thought system.

Fig. 9: stages of time or motion in Igbo thought

Time

Space

The above figure shows the 12 hourly cycle from morning to pre-noon to afternoon to evening

and then from night to pre-midnight to after midnight to early morning. The four apiece represent

the various stages of time. As already shown in the Igbo calendar year cycle somewhere above,

one day time 12 hourly cycle gives us one echi whereas one night time 12 hourly cycle gives us

one abani, put together they give us one 24 hourly full day or bch. This is also what

Alexander Animalu in the appendix to his 1990 Ahiajoku Lecture21 characterizes in such a way

as to draw a line between the 12 hourly daytime cycle and the 12 hourly night time cycle. The

former utilized by the Igbo for their life activities while the latter is utilized by the Olu (any

people, spirits, night marauders, people of distant lands etc.) for their own activities. Each of the

12 hourly cycle is made up of four basic stages as locations in both time and space. By his

characterization, if Eke, Oye, Af and Nkw are locations in time, Eke-Igbo, Oye-Igbo, Af-

Igbo, Nkw-Igbo, Eke-Olu, Oye-Olu, Af-Olu and Nkw-Olu would be locations in both time

and space (see also the discussions on Space-time continuum in Igbo thought below; and Figures

10 and 12 below). Figure 10 below shows a reversal of figure 9 above.

20Animalu, p. 51.

21Animalu, p. 90.

Stge1

Stge2

Stge3

Stge4

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Fig. 10: showing the space-time continuum

Location in time and space

In the above figure, we demonstrate space-time continuum in Igbo thought. (see the section on

space-time continuum below for detailed discussions).

Measurement of the Igbo ticking time

60 Ntaji =1 Nkeji

60 Nkeji = 1 Awa

3 Awa = Ahaukwu = 84

6 Awa = Ahanab= 1686 Awa /2 Awa = 84

9 Awa = Ahanat= 252

9 Awa/ 3Awa = 84

12 Awa x 2 = 24 Awa

24 Awa = Ahananor Izu = 336

12 Awa/ 4Awa = 84

24 Awa/ 8 Awa = 84

The Igbo ticking time runs in a 24 hourly cycle called bchbut divided up to 12 hours apiece

of echi and abanrespectively as already shown in the Igbo calendar year cycle.

Space-Time Continuum in Igbo Thought

Igbo people do not really see any serious polarity in ogwe or mbara/space and oge/time

or motion. Space is in motion and motion is a manifestation of space. For want of clarity, space

is conceived in a cyclical dimension whereas time is in itself a cyclical phenomenon. Many Igbo

scholars have described the Igbo idea of space as consisting of three cyclical dimension or

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stages22 namely Igwe/Sky where Chukwu and angels dwell, Ala/Earth where men and beasts

dwell and Alanm/Underworld where the ancestors and evil spirits etc., dwell. However, we

find in our own interpretation of Igbo worldview that as much as this is correct it is incomplete.

Ancestors are people who lived well and are rewarded with the bliss of ancestral world whereas

others who led a bad life are cast down to suffer in a world filled will evil forces. This shows that

there are two worlds beneath and not one, as the ancestors cannot be co-tenants with evil men

and forces. The ancestral world is the first world beneath while the dark world of evil and

suffering lies far below. It does appear that why popular scholarly opinions fail to make this

demarcation is due to error of assumption that the underworld is just one world with a huge red

earth wall separating the ancestors and evil forces.

We came to conclusion in this research that this conception must be wrong because the

Igbo conception of beings for example, is vertical and not horizontal. Thus the ancestors simply

cannot be on the same plane with evil men and malignant forces. This helps us to fix the puzzle

of four dimensional space in Igbo thought namely Ekeukwu, Oyeukwu, Afukwu and

Nkwukwu (see also figure 4 above). These correspond to the four spaces in Igbo world view

namely; Igwe, Ala/wa, Ala ndi ichie and Alanm.

Fig. 11: showing four dimensional spaces in Igbo worldview

Igwe

Ala/wa .. Ala ndi ichie

Alanm

The cycle of birth, death, regeneration and rebirth occurs around the hypocycloid in the middle;

an evil man rarely gets a chance to be reborn neither do men go beyond the earth plane into the

22 Udobata Onunwa, Humanism: The Bedrock of African Traditional Religion and Culture, Religious Humanism (Vol.

XXV, No. 2, Spring 1991), 66 71. ; Chris Ijiomah, Some Epistemological Tools with which Africans Relate to their

Realities, pp. 75 87; Ekwealor, C. C. The Igbo World-View: A General Survey. The Humanities and All of Us,

Emeka Oguegbu (ed) (Onitsha: Watchword, 1990) Pp. 29 33.


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heavens. The period of regeneration is a stage of ontological preparation for rebirth. When

descended in death and decay, it is assumed that one passes a stage of beingpurification in order

to get ready for the beginning of another cycle.

The point we wish to make here is that space and time intermingle in Igbo world view.

Alexander Animalu cites Anya as follows:

Most African societies, including the Nigerian society operate on a cosmological

framework in which time is cyclical and space organized in three compartments-

the heavens above, the earth below it and the underworld beneath the earth- all

conceived as contiguous and continuous, once more in a cyclical continuum23

We have already corrected the perception which limits the spaces to three dimensions only. The

rest of the quotation supports our thesis here that time and space in Igbo cosmology are jointly in

a cyclical continuum. The figure below shows the space-time continuum in Igbo thought.

Fig. 12: showing the joint cyclical space-time continuum in Igbo thought

The outer circle represents various stages of time just as the inner circle represents various

compartments of space, thus the outer circle = the inner circle. Abanis a stage in the 12 hourly

cycle of night as well as an angle space Ekeukwu, as it rolls over to ngabi-aban , Ekeukwu

23Animalu, p. 51.

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Time:spe

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ng"i8"ni

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Bibliography

Animalu, Alexander. Ucheakonam:A Way of Life in the Modern Scientific Age, 1990 Ahiajoku

Lecture, Owerri. Printed in 2001 Igbo Day Lecture. Snaap Press, 2001.

Asouzu, Innocent. Ibuanyidanda and the Philosophy of Essence, Calabar: University of Calabar

Press, 2011

Chimakonam, Okeke Jonathan. Introducing African Logic and Numeric System: Formalist and

Axiomatic Approach, Forthcoming

Chimakonam, Okeke Jonathan. Integrative Humanism: Extensions and Clarifications

Integrative Humanism Journal, 3.1 forthcoming.

Chimakonam, Okeke Jonathan. Introducing African Science: Systematic and Philosophical

Approach, Indiana: Authorhouse, 2012

Chimakonam, Okeke Jonathan and Sunny Agu, G. O. Ozumbas Integrative Humanism Project

as a Model of Explanation in Science, Conference Proceeding 8.3, (2012):17-24

Chimakonam, Okeke Jonathan. Integrative and Eliminative Epistemologies: From Facts to

Fancies Integrative Humanism Journal 2.1(2012):158-170

Ekwealor, C. C. The Igbo World-View: A General Survey. The Humanities and All of Us,Emeka Oguegbu (ed) Onitsha: Watchword, (1990): 29 33.

Hebga, Meinrad. Logic in Africa. Philosophy Today, Vol. 11. No. 4/4 1958. Pp. 222-23

Hunnings, Gordon. Logic, Language and Culture. Second Order: An African Journal of

Philosophy, Vol. 4, No. 1. p. 4

Ijiomah, Chris. An Excavation of Logic in African World View, African Journal of Religion,

Culture and Society 1. 1. (August, 2006): 29-35

Ijiomah, Chris. Some Epistemological Tools with which Africans Relate to their Realities,Ultimate Reality and Meaning. 28, No 1, (March, 2005): 75-87

Nkanta, Ikemesit. Three-valued Logic as an Explanatory Tool for some African Experiences,

M.A Thesis, Calabar: University of Calabar, Unpublished 2012

Omoregbe, Joseph. African Philosophy: Yesterday and Today. African Philosophy: An

Anthology. Emmanuel Eze (ed.), Massachusetts: Blackwell, 1998


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Onunwa, Udobata. Humanism: The Bedrock of African Traditional Religion and Culture,

Religious Humanism Vol. XXV, No. 2, (Spring 1991): 66 71.

i+'no#le$gement( ! #ish to ppreite Prof, +,, , +niml of ;ni

chimakonam-metric system in igbo thought final-libre

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