Decimal vs. Duodecimal in Africa:

An interaction between two systems of numeration

MATSUSHITA, Shuji

Background

Though the quinary system of numeration dominates among the languages of West Africa, decimal counting is found all over the area. Also, a small but sizeable number of languages in Nigerian Middle Belt have possessed, and still possess, a peculiar duodecimal system of numeration.

A few languages, actually, drifted from one system to the other in the short timespan under the scrutiny of various observers. Presently, the trend is changing from duodecimal into decimal. But somewhere in the past, a dialect had moved the other direction too, from decimal system to duodecimal.

1. Duodecimal Area in Nigeria

Meek reported several languages with duodecimal numeration. Most of them belong to Plateau Group of Niger-Kordofanian languages.

Janji (Jera Group, Plateau State, Bassa LGA) still retained the duodecimal counting when Meek compiled its vocabulary. Also mentioned were Kahugu (or Gbiri-Niragu, Kaduna State; Saminaka LGA), Gure (a.k.a. Gbiri-Niragu, Saminaka LGA), Piti (Kaduna State, Saminaka LGA). A lone Adamawa-Eastern language, Mumuye of Yendang had a trace of duodecimal system. But this language is located far east in Taraba State, completely isolated from the Plateau duodecimal groups.

Table 1: Duodecimal Numbers of Janji, Kahugu and Gure

	1	2	3	4	5	6	7	8	9	T	E	10
Janji	-nde/dingke	-re	-taro	-naze	-chibi	-tase	-sunare	-uro	-toroai	-turo	-belum	-kurno/kirau
Kahugu	inu	bao	taro	nazo	ishiko	tashi	sunduri	nanas	kishanoas	akernaba	kitishui	ripiri
Gure	-in	-ba	-tar	-nas	-shi	-tashe	-sunderi	konas	-torore	-ikeranaba	-lyem	-ikpiri

All these languages were in the process of transition to decimal system of numeration according to Meek. It is interesting because at the time of Meek's observaton, the all powerful British colonical regime brought the pervasive duodecimal currency, i.e. one shilling equals 12 pence.

Why had these languages adopted the duodecimal system beforehand? It is an enigma, because all other languages in the same Plateau group employed decimal or quinary system.

2. Moving from Duodecimal to Decimal

The transition of this direction is rather painless. Simply, duodecimal T and E are ignored, and duodecimal ten is used in situ as decimal ten. Thus, duodecimal 11 (decimal 13) becomes to mean decimal 11.

Table2: Duodecimal/Decimal Conversion of Gure

duodecimal	9	T	E	10	11
	-torore	-ikeranaba	-lyem	-ikpiri	-ikpiri abo -in
decimal	9	10	11	12	13
	-torore	-ikpiri	-ikpiri abo -in	-ikpiri abo -ba	-ikpiri abo -tar

3. Chadic Languages and Numerals

Chadic languages, generally, have decimal numeration with a liberal infusion of quinary trace. Some languages in this group show a peculiar formation for certain numbers. Eight is expressed by 4 + 4, and nine by 10 - 1. Bachama shows both of these tendancies.

Table 3: Bachama Decimal/Quinary Hybrid Numerals

Decimal	1	2	3	4	5	6	7	8	9	10
Bachama	hido	kpe	mwakin	fwot	tuf	tukoltaka	tukolukpe	fwofwot	dombi hido	bau

Only one Chadic language, Nimbia dialect of Gwandara, has the duodecimal system, while all other Gwandara dialects keep the strict decimal system.

Table 4: Duodecimal Nimbia Dialect and Decimal Karshi Dialect

Duodecimal	1	2	3	4	5	6	7	8	9	T	E	10
Nimbia	da	bi	ugu	furu	biyar	shide	bo'o	tager	tanran	gwom	kwada	tuni
Decimal	1	2	3	4	5	6	7	8	9	10	11	12
Karshi	da	bi	uku	huru	biyari	shida	bakwe	takushi	tara	gom	gom sha da	gom sha bi

Further Nimbia numbers over duodecimal 10 are:

	tuni mbe da	11 (decimal 13)
	gume bi	20 (decimal 24)
	gume bi ni da	21 (decimal 25)
	gume kwada ni kwada	EE (decimal 143)
	wo	100 (decimal 144)

4. Moving from Decimal to Duodecimal

Not a single Chadic languages but Nimbia Gwandara has the slightest trace of duodecimal system. Also, the location of this dialect lies far east detached from the main Gwandara area. Therefore, it is safe to conclude that the Nimbia dialect acquired its duodecimal system at a certain past stage, due to the contact with adjacent duodecimal patch of Plateau languages.

The strategy of changing over was to introduce two glosses, kwada, for duodecimal E, and tuni for duodecimal ten. Kwada obviously had an etymological "continue one more" value whereas origin of tuni remained uncertain. Decimal 10, gwom, a throughbred gloss since the Proto-Chadic stage, were kept intact. It is not unlike building a superstructure on the top of existing decimal numbers. All the decimal numbers stayed intact in the new system.

5. Moving Back to Decimal Again

The Nimbia dialect, too, is presently in the process of changin back to decimal system. The strategy is a little different the method taken by Plateau duodecimal languages.

Nimbia simply bypassed duodecimal E and 10 which were an additional "superstructure". In other words, the original decimal system has been restored. Presently, Nimbia people utilize decimal system which are the same as of the other Gwandara dialects and the dominant lingua franca, Hausa, in their daily life.

The memory of duodecimal system is still vivid. But it will fade away soon, leaving no noticable trace.

6. Conclusions

Moving from one numeration system to another does not seem to be a "big deal". It can be done within a short timespan, with the slightest push from the socio-economial factor.

In this respect, the numerals behave as if they were a part of extra-linguistic institution, like unit of measure, colonial law or some fancy goods in the market. The speakers, also, do not show any real resistance or animosity towards the numeric alteration. Many informants describe, matter-of-fact-ly;

"We used to count in old numbers. But now, we count in new numbers."

Bibliography

Ethnologue, SIL Database for World Languages, Africa, Nigeria.
Matsushita, S.: A Comparative Vocabulary of Gwandara Dialects, AA-ken (1974)
Meek, C. K.: Tribal Studies in Northern Nigeria, Volume I & II., Kegan Paul, London (1931)

NB: T (ten) and E (eleven) have been substituted for the A and B of the original.