The Number Concept: Its Origin and Development Part 3

1. papita.

2. avanume.

3. apekiva.

4. apekipaki.

5. papitaerri capiti = 1 only hand.

6. papita yana pauria capiti purena = 1 of the other hand we take.

10. apanumerri capiti = 2 hands.

11. papita yana kiti purena = 1 of the toes we take.

20. papita camonee = 1 man.

40. avanume camonee = 2 men.

60. apekiva camonee = 3 men, etc.

In all the examples thus far given, 20 is expressed either by the equivalent of "man" or by some formula introducing the word "feet." Both these modes of expressing what our own ancestors termed a "score," are so common that one hesitates to say which is of the more frequent use. The following scale, from one of the Betoya dialects[79] of South America, is quite remarkable among digital scales, making no use of either "man" or "foot," but reckoning solely by fives, or hands, as the numerals indicate.

1. tey.

2. cayapa.

3. toazumba.

4. cajezea = 2 with plural termination.

5. teente = hand.

6. teyentetey = hand + 1.

7. teyente cayapa = hand + 2.

8. teyente toazumba = hand + 3.

9. teyente caesea = hand + 4.

10. caya ente, or caya huena = 2 hands.

11. caya ente-tey = 2 hands + 1.

15. toazumba-ente = 3 hands.

16. toazumba-ente-tey = 3 hands + 1.

20. caesea ente = 4 hands.

In the last chapter mention was made of the scanty numeral systems of the Australian tribes, but a single scale was alluded to as reaching the comparatively high limit of 20. This system is that belonging to the Pik.u.mbuls,[80] and the count runs thus:

1. mal.

2. bular.

3. guliba.

4. bularbular = 2-2.

5. mulanbu.

6. malmulanbu mummi = 1 and 5 added on.

7. bularmulanbu mummi = 2 and 5 added on.

8. gulibamulanbu mummi = 3 and 5 added on.

9. bularbularmulanbu mummi = 4 and 5 added on.

10. bularin murra = belonging to the 2 hands.

11. maldinna mummi = 1 of the toes added on (to the 10 fingers).

12. bular dinna mummi = 2 of the toes added on.

13. guliba dinna mummi = 3 of the toes added on.

14. bular bular dinna mummi = 4 of the toes added on.

15. mulanba dinna = 5 of the toes added on.

16. mal dinna mulanbu = 1 and 5 toes.

17. bular dinna mulanbu = 2 and 5 toes.

18. guliba dinna mulanbu = 3 and 5 toes.

19. bular bular dinna mulanbu = 4 and 5 toes.

20. bularin dinna = belonging to the 2 feet.

As has already been stated, there is good ground for believing that this system was originally as limited as those obtained from other Australian tribes, and that its extension from 4, or perhaps from 5 onward, is of comparatively recent date.

A somewhat peculiar numeral nomenclature is found in the language of the Klamath Indians of Oregon. The first ten words in the Klamath scale are:[81]

1. nash, or nas.

2. lap = hand.

3. ndan.

4. vunep = hand up.

5. tunep = hand away.

6. nadshkshapta = 1 I have bent over.

7. lapkshapta = 2 I have bent over.

8. ndankshapta = 3 I have bent over.

9. nadshskeksh = 1 left over.

10. taunep = hand hand?

In describing this system Mr. Gatschet says: "If the origin of the Klamath numerals is thus correctly traced, their inventors must have counted only the four long fingers without the thumb, and 5 was counted while saying _hand away! hand off!_ The 'four,' or _hand high! hand up!_ intimates that the hand was held up high after counting its four digits; and some term expressing this gesture was, in the case of _nine_, subst.i.tuted by 'one left over' ... which means to say, 'only one is left until all the fingers are counted.'" It will be observed that the Klamath introduces not only the ordinary finger manipulation, but a gesture of the entire hand as well. It is a common thing to find something of the kind to indicate the completion of 5 or 10, and in one or two instances it has already been alluded to.

Sometimes one or both of the closed fists are held up; sometimes the open hand, with all the fingers extended, is used; and sometimes an entirely independent gesture is introduced. These are, in general, of no special importance; but one custom in vogue among some of the prairie tribes of Indians, to which my attention was called by Dr. J. Owen Dorsey,[82] should be mentioned. It is a gesture which signifies multiplication, and is performed by throwing the hand to the left. Thus, after counting 5, a wave of the hand to the left means 50. As multiplication is rather unusual among savage tribes, this is noteworthy, and would seem to indicate on the part of the Indian a higher degree of intelligence than is ordinarily possessed by uncivilized races.

In the numeral scale as we possess it in English, we find it necessary to retain the name of the last unit of each kind used, in order to describe definitely any numeral employed. Thus, fifteen, one hundred forty-two, six thousand seven hundred twenty-seven, give in full detail the numbers they are intended to describe. In primitive scales this is not always considered necessary; thus, the Zamucos express their teens without using their word for 10 at all. They say simply, 1 on the foot, 2 on the foot, etc.

Corresponding abbreviations are often met; so often, indeed, that no further mention of them is needed. They mark one extreme, the extreme of brevity, found in the savage method of building up hand, foot, and finger names for numerals; while the Zuni scale marks the extreme of prolixity in the formation of such words. A somewhat ruder composition than any yet noticed is shown in the numerals of the Vilelo scale,[83] which are:

1. agit, or yaagit.

2. uke.

3. nipetuei.

4. yepkatalet.

5. isig-nisle-yaagit = hand fingers 1.

6. isig-teet-yaagit = hand with 1.

7. isig-teet-uke = hand with 2.

8. isig-teet-nipetuei = hand with 3.

9. isig-teet-yepkatalet = hand with 4.

10. isig-uke-nisle = second hand fingers (lit. hand-two-fingers).

11. isig-uke-nisle-teet-yaagit = second hand fingers with 1.

20. isig-ape-nisle-lauel = hand foot fingers all.

In the examples thus far given, it will be noticed that the actual names of individual fingers do not appear. In general, such words as thumb, forefinger, little finger, are not found, but rather the hand-1, 1 on the next, or 1 over and above, which we have already seen, are the type forms for which we are to look. Individual finger names do occur, however, as in the scale of the Hudson's Bay Eskimos,[84] where the three following words are used both as numerals and as finger names:

8. kittukleemoot = middle finger.

9. mikkeelukkamoot = fourth finger.

10. eerkitkoka = little finger.

Words of similar origin are found in the original Jiviro scale,[85] where the native numerals are:

1. ala.

2. catu.

3. cala.

4. encatu.

5. alacotegladu = 1 hand.

6. intimutu = thumb (of second hand).