The Number Concept: Its Origin and Development Part 4

7. tannituna = index finger.

8. tannituna cabiasu = the finger next the index finger.

9. bitin otegla cabiasu = hand next to complete.

10. catogladu = 2 hands.

As if to emphasize the rarity of this method of forming numerals, the Jiviros afterward discarded the last five of the above scale, replacing them by words borrowed from the Quichuas, or ancient Peruvians. The same process may have been followed by other tribes, and in this way numerals which were originally digital may have disappeared. But we have no evidence that this has ever happened in any extensive manner. We are, rather, impelled to accept the occasional numerals of this cla.s.s as exceptions to the general rule, until we have at our disposal further evidence of an exact and critical nature, which would cause us to modify this opinion. An elaborate philological study by Dr. J.H. Trumbull[86] of the numerals used by many of the North American Indian tribes reveals the presence in the languages of these tribes of a few, but only a few, finger names which are used without change as numeral expressions also. Sometimes the finger gives a name not its own to the numeral with which it is a.s.sociated in counting--as in the Chippeway dialect, which has _nawi-nindj_, middle of the hand, and _nisswi_, 3; and the Cheyenne, where _notoyos_, middle finger, and _na-nohhtu_, 8, are closely related. In other parts of the world isolated examples of the transference of finger names to numerals are also found. Of these a well-known example is furnished by the Zulu numerals, where "_tatisitupa_, taking the thumb, becomes a numeral for six.

Then the verb _komba_, to point, indicating the forefinger, or 'pointer,'

makes the next numeral, seven. Thus, answering the question, 'How much did your master give you?' a Zulu would say, '_U kombile_,' 'He pointed with his forefinger,' _i.e._ 'He gave me seven'; and this curious way of using the numeral verb is also shown in such an example as '_amahasi akombile_,'

'the horses have pointed,' _i.e._ 'there were seven of them.' In like manner, _Kijangalobili_, 'keep back two fingers,' _i.e._ eight, and _Kijangalolunje_, 'keep back one finger,' _i.e._ nine, lead on to _k.u.mi_, ten."[87]

Returning for a moment to the consideration of number systems in the formation of which the influence of the hand has been paramount, we find still further variations of the method already noticed of constructing names for the fives, tens, and twenties, as well as for the intermediate numbers. Instead of the simple words "hand," "foot," etc., we not infrequently meet with some paraphrase for one or for all these terms, the derivation of which is unmistakable. The Nengones,[88] an island tribe of the Indian Ocean, though using the word "man" for 20, do not employ explicit hand or foot words, but count

1. sa.

2. rewe.

3. tini.

4. etse.

5. se dono = the end (of the first hand).

6. dono ne sa = end and 1.

7. dono ne rewe = end and 2.

8. dono ne tini = end and 3.

9. dono ne etse = end and 4.

10. rewe tubenine = 2 series (of fingers).

11. rewe tubenine ne sa re ts.e.m.e.ne = 2 series and 1 on the next?

20. sa re nome = 1 man.

30. sa re nome ne rewe tubenine = 1 man and 2 series.

40. rewe ne nome = 2 men.

Examples like the above are not infrequent. The Aztecs used for 10 the word _matlactli_, hand-half, _i.e._ the hand half of a man, and for 20 _cempoalli_, one counting.[89] The Point Barrow Eskimos call 10 _kodlin_, the upper part, _i.e._ of a man. One of the Ewe dialects of Western Africa[90] has _ewo_, done, for 10; while, curiously enough, 9, _asieke_, is a digital word, meaning "to part (from) the hand."

In numerous instances also some characteristic word not of hand derivation is found, like the Yoruba _oG.o.dzi_, string, which becomes a numeral for 40, because 40 cowries made a "string"; and the Maori _tekau_, bunch, which signifies 10. The origin of this seems to have been the custom of counting yams and fish by "bunches" of ten each.[91]

Another method of forming numeral words above 5 or 10 is found in the presence of such expressions as second 1, second 2, etc. In languages of rude construction and incomplete development the simple numeral scale is often found to end with 5, and all succeeding numerals to be formed from the first 5. The progression from that point may be 5-1, 5-2, etc., as in the numerous quinary scales to be noticed later, or it may be second 1, second 2, etc., as in the Niam Niam dialect of Central Africa, where the scale is[92]

1. sa.

2. uwi.

3. biata.

4. biama.

5. biswi.

6. batissa = 2d 1.

7. batiwwi = 2d 2.

8. batti-biata = 2d 3.

9. batti-biama = 2d 4.

10. bauwe = 2d 5.

That this method of progression is not confined to the least developed languages, however, is shown by a most cursory examination of the numerals of our American Indian tribes, where numeral formation like that exhibited above is exceedingly common. In the Kootenay dialect,[93] of British Columbia, _qaetsa_, 4, and _wo-qaetsa,_ 8, are obviously related, the latter word probably meaning a second 4. Most of the native languages of British Columbia form their words for 7 and 8 from those which signify 2 and 3; as, for example, the Heiltsuk,[94] which shows in the following words a most obvious correspondence:

2. matl. 7. matlaaus.

3. yutq. 8. yutquaus.

In the Choctaw language[95] the relation between 2 and 7, and 3 and 8, is no less clear. Here the words are:

2. tuklo. 7. untuklo.

3. tuchina. 8. untuchina.

The Nez Perces[96] repeat the first three words of their scale in their 6, 7, and 8 respectively, as a comparison of these numerals will show.

1. naks. 6. oilaks.

2. lapit. 7. oinapt.

3. mitat. 8. oimatat.

In all these cases the essential point of the method is contained in the repet.i.tion, in one way or another, of the numerals of the second quinate, without the use with each one of the word for 5. This may make 6, 7, 8, and 9 appear as second 1, second 2, etc., or another 1, another 2, etc.; or, more simply still, as 1 more, 2 more, etc. It is the method which was briefly discussed in the early part of the present chapter, and is by no means uncommon. In a decimal scale this repet.i.tion would begin with 11 instead of 6; as in the system found in use in Tagala and Pampanaga, two of the Philippine Islands, where, for example, 11, 12, and 13 are:[97]

11. labi-n-isa = over 1.

12. labi-n-dalaua = over 2.

13. labi-n-tatlo = over 3.

A precisely similar method of numeral building is used by some of our Western Indian tribes. Selecting a few of the a.s.siniboine numerals[98] as an ill.u.s.tration, we have

11. ak kai washe = more 1.

12. ak kai noom pah = more 2.

13. ak kai yam me nee = more 3.

14. ak kai to pah = more 4.

15. ak kai zap tah = more 5.

16. ak kai shak pah = more 6, etc.

A still more primitive structure is shown in the numerals of the Mboushas[99] of Equatorial Africa. Instead of using 5-1, 5-2, 5-3, 5-4, or 2d 1, 2d 2, 2d 3, 2d 4, in forming their numerals from 6 to 9, they proceed in the following remarkable and, at first thought, inexplicable manner to form their compound numerals:

1. ivoco.

2. beba.

3. belalo.

4. benai.

5. betano.

6. ivoco beba = 1-2.

7. ivoco belalo = 1-3.

8. ivoco benai = 1-4.

9. ivoco betano = 1-5.

10. dioum.

No explanation is given by Mr. du Chaillu for such an apparently incomprehensible form of expression as, for example, 1-3, for 7. Some peculiar finger pantomime may accompany the counting, which, were it known, would enlighten us on the Mbousha's method of arriving at so anomalous a scale. Mere repet.i.tion in the second quinate of the words used in the first might readily be explained by supposing the use of fingers absolutely indispensable as an aid to counting, and that a certain word would have one meaning when a.s.sociated with a certain finger of the left hand, and another meaning when a.s.sociated with one of the fingers of the right. Such scales are, if the following are correct, actually in existence among the islands of the Pacific.

BALAD.[100] UEA.[100]

1. parai. 1. tahi.

2. paroo. 2. lua.

3. pargen. 3. tolu.

4. parbai. 4. fa.

5. panim. 5. lima.

6. parai. 6. tahi.

7. paroo. 7. lua.