The Number Concept: Its Origin and Development Part 2

10. kodlin = the upper part--_i.e._ the fingers.

14. akimiaxotaityuna = I have not 15.

15. akimia. [This seems to be a real numeral word.]

20. inyuina = a man come to an end.

25. inyuina tudlimunin akbinidigin = a man come to an end and 5 on the next.

30. inyuina kodlinin akbinidigin = a man come to an end and 10 on the next.

35. inyuina akimiamin aipalin = a man come to an end accompanied by 1 fifteen times.

40. madro inyuina = 2 men come to an end.

In this scale we find the finger origin appearing so clearly and so repeatedly that one feels some degree of surprise at finding 5 expressed by a pure numeral instead of by some word meaning _hand_ or _fingers of one hand_. In this respect the Eskimo dialects are somewhat exceptional among scales built up of digital words. The system of the Greenland Eskimos, though differing slightly from that of their Point Barrow cousins, shows the same peculiarity. The first ten numerals of this scale are:[71]

1. atausek.

2. mardluk.

3. pingasut.

4. sisamat.

5. tatdlimat.

6. arfinek-atausek = to the other hand 1.

7. arfinek-mardluk = to the other hand 2.

8. arfinek-pingasut = to the other hand 3.

9. arfinek-sisamat = to the other hand 4.

10. kulit.

The same process is now repeated, only the feet instead of the hands are used; and the completion of the second 10 is marked by the word _innuk_, man. It may be that the Eskimo word for 5 is, originally, a digital word, but if so, the fact has not yet been detected. From the a.n.a.logy furnished by other languages we are justified in suspecting that this may be the case; for whenever a number system contains digital words, we expect them to begin with _five_, as, for example, in the Arawak scale,[72] which runs:

1. abba.

2. biama.

3. kabbuhin.

4. bibiti.

5. abbatekkabe = 1 hand.

6. abbatiman = 1 of the other.

7. biamattiman = 2 of the other.

8. kabbuhintiman = 3 of the other.

9. bibitiman = 4 of the other.

10. biamantekabbe = 2 hands.

11. abba kutihibena = 1 from the feet.

20. abba lukku = hands feet.

The four sets of numerals just given may be regarded as typifying one of the most common forms of primitive counting; and the words they contain serve as ill.u.s.trations of the means which go to make up the number scales of savage races. Frequently the finger and toe origin of numerals is perfectly apparent, as in the Arawak system just given, which exhibits the simplest and clearest possible method of formation. Another even more interesting system is that of the Montagnais of northern Canada.[73] Here, as in the Zuni scale, the words are digital from the outset.

1. inl'are = the end is bent.

2. nak'e = another is bent.

3. t'are = the middle is bent.

4. dinri = there are no more except this.

5. se-sunla-re = the row on the hand.

6. elkke-t'are = 3 from each side.

7.{ t'a-ye-oyertan = there are still 3 of them.

{ inl'as dinri = on one side there are 4 of them.

8. elkke-dinri = 4 on each side.

9. inl'a-ye-oyert'an = there is still 1 more.

10. onernan = finished on each side.

11. onernan inl'are ttcharidhel = 1 complete and 1.

12. onernan nak'e ttcharidhel = 1 complete and 2, etc.

The formation of 6, 7, and 8 of this scale is somewhat different from that ordinarily found. To express 6, the Montagnais separates the thumb and forefinger from the three remaining fingers of the left hand, and bringing the thumb of the right hand close to them, says: "3 from each side." For 7 he either subtracts from 10, saying: "there are still 3 of them," or he brings the thumb and forefinger of the right hand up to the thumb of the left, and says: "on one side there are 4 of them." He calls 8 by the same name as many of the other Canadian tribes, that is, two 4's; and to show the proper number of fingers, he closes the thumb and little finger of the right hand, and then puts the three remaining fingers beside the thumb of the left hand. This method is, in some of these particulars, different from any other I have ever examined.

It often happens that the composition of numeral words is less easily understood, and the original meanings more difficult to recover, than in the examples already given. But in searching for number systems which show in the formation of their words the influence of finger counting, it is not unusual to find those in which the derivation from native words signifying _finger, hand, toe, foot_, and _man_, is just as frankly obvious as in the case of the Zuni, the Arawak, the Eskimo, or the Montagnais scale. Among the Tamanacs,[74] one of the numerous Indian tribes of the Orinoco, the numerals are as strictly digital as in any of the systems already examined.

The general structure of the Tamanac scale is shown by the following numerals:

5. amgnaitone = 1 hand complete.

6. itacono amgna pona tevinitpe = 1 on the other hand.

10. amgna aceponare = all of the 2 hands.

11. puitta pona tevinitpe = 1 on the foot.

16. itacono puitta pona tevinitpe = 1 on the other foot.

20. tevin itoto = 1 man.

21. itacono itoto jamgnar bona tevinitpe = 1 on the hands of another man.

In the Guarani[75] language of Paraguay the same method is found, with a different form of expression for 20. Here the numerals in question are

5. asepopetei = one hand.

10. asepomokoi = two hands.

20. asepo asepi abe = hands and feet.

Another slight variation is furnished by the Kiriri language,[76] which is also one of the numerous South American Indian forms of speech, where we find the words to be

5. mi biche misa = one hand.

10. mikriba misa sai = both hands.

20. mikriba misa idecho ibi sai = both hands together with the feet.

Ill.u.s.trations of this kind might be multiplied almost indefinitely; and it is well to note that they may be drawn from all parts of the world. South America is peculiarly rich in native numeral words of this kind; and, as the examples above cited show, it is the field to which one instinctively turns when this subject is under discussion. The Zamuco numerals are, among others, exceedingly interesting, giving us still a new variation in method.

They are[77]

1. tsomara.

2. gar.

3. gadiok.

4. gahagani.

5. tsuena yimana-ite = ended 1 hand.

6. tsomara-hi = 1 on the other.

7. gari-hi = 2 on the other.

8. gadiog-ihi = 3 on the other.

9. gahagani-hi = 4 on the other.

10. tsuena yimana-die = ended both hands.

11. tsomara yiri-tie = 1 on the foot.

12. gar yiritie = 2 on the foot.

20. tsuena yiri-die = ended both feet.

As is here indicated, the form of progression from 5 to 10, which we should expect to be "hand-1," or "hand-and-1," or some kindred expression, signifying that one hand had been completed, is simply "1 on the other."

Again, the expressions for 11, 12, etc., are merely "1 on the foot," "2 on the foot," etc., while 20 is "both feet ended."

An equally interesting scale is furnished by the language of the Maipures[78] of the Orinoco, who count