The Number Concept: Its Origin and Development Part 14

BARI

5. kanat 10. puok = 5 + 5?

KANURI

5. ugu.

10. megu = 2 5.

RIO NORTE AND SAN ANTONIO.[231]

5. juyopamauj.

10. juyopamauj ajte = 5 2.

API.[232]

5. lima.

10. lua-lima = 2 5.

ERROMANGO

5. suku-rim.

10. nduru-lim = 2 5.

TLINGIT, BRITISH COLUMBIA.[233]

5. kedjin (from djin = hand).

10. djinkat = both hands?

Thus far the quinary formation is simple and regular; and in view of the evidence with which these and similar ill.u.s.trations furnish us, it is most surprising to find an eminent authority making the unequivocal statement that the number 10 is nowhere expressed by 2 fives[234]--that all tribes which begin their count on a quinary base express 10 by a simple word. It is a fact, as will be fully ill.u.s.trated in the following pages, that quinary number systems, when extended, usually merge into either the decimal or the vigesimal. The result is, of course, a compound of two, and sometimes of three, systems in one scale. A pure quinary or vigesimal number system is exceedingly rare; but quinary scales certainly do exist in which, as far as we possess the numerals, no trace of any other influence appears. It is also to be noticed that some tribes, like the Eskimos of Point Barrow, though their systems may properly be cla.s.sed as mixed systems, exhibit a decided preference for 5 as a base, and in counting objects, divided into groups of 5, obtaining the sum in this way.[235]

But the savage, after counting up to 10, often finds himself unconsciously impelled to depart from his strict reckoning by fives, and to a.s.sume a new basis of reference. Take, for example, the Zuni system, in which the first 2 fives are:

5. opte = the notched off.

10. astem'thla = all the fingers.

It will be noticed that the Zuni does not say "two hands," or "the fingers of both hands," but simply "all the fingers." The 5 is no longer prominent, but instead the mere notion of one entire count of the fingers has taken its place. The division of the fingers into two sets of five each is still in his mind, but it is no longer the leading idea. As the count proceeds further, the quinary base may be retained, or it may be supplanted by a decimal or a vigesimal base. How readily the one or the other may predominate is seen by a glance at the following numerals:

GALIBI.[236]

5. atoneigne oietona = 1 hand.

10. oia batoue = the other hand.

20. poupoupatoret oupoume = feet and hands.

40. opoupoume = twice the feet and hands.

GUARANI.[237]

5. ace popetei = 1 hand.

10. ace pomocoi = 2 hands.

20. acepo acepiabe = hands and feet.

FATE.[238]

5. lima = hand.

10. relima = 2 hands.

20. relima rua = (2 5) 2.

KIRIRI

5. mibika misa = 1 hand.

10. mikriba misa sai = both hands.

20. mikriba nusa ideko ibi sai = both hands together with the feet.

ZAMUCO

5. tsuena yimana-ite = ended 1 hand.

10. tsuena yimana-die = ended both hands.

20. tsuena yiri-die = ended both feet.

PIk.u.mBUL

5. mulanbu.

10. bularin murra = belonging to the two hands.

15. mulanba dinna = 5 toes added on (to the 10 fingers).

20. bularin dinna = belonging to the 2 feet.

YARUROS.[239]

5. kani-iktsi-mo = 1 hand alone.

10. yowa-iktsi-bo = all the hands.

15. kani-tao-mo = 1 foot alone.

20. kani-pume = 1 man.

By the time 20 is reached the savage has probably allowed his conception of any aggregate to be so far modified that this number does not present itself to his mind as 4 fives. It may find expression in some phraseology such as the Kiriris employ--"both hands together with the feet"--or in the shorter "ended both feet" of the Zamucos, in which case we may presume that he is conscious that his count has been completed by means of the four sets of fives which are furnished by his hands and feet. But it is at least equally probable that he instinctively divides his total into 2 tens, and thus pa.s.ses unconsciously from the quinary into the decimal scale. Again, the summing up of the 10 fingers and 10 toes often results in the concept of a single whole, a lump sum, so to speak, and the savage then says "one man," or something that gives utterance to this thought of a new unit. This leads the quinary into the vigesimal scale, and produces the combination so often found in certain parts of the world. Thus the inevitable tendency of any number system of quinary origin is toward the establishment of another and larger base, and the formation of a number system in which both are used. Wherever this is done, the greater of the two bases is always to be regarded as the princ.i.p.al number base of the language, and the 5 as entirely subordinate to it. It is hardly correct to say that, as a number system is extended, the quinary element disappears and gives place to the decimal or vigesimal, but rather that it becomes a factor of quite secondary importance in the development of the scale. If, for example, 8 is expressed by 5-3 in a quinary decimal system, 98 will be 9 10 + 5-3. The quinary element does not disappear, but merely sinks into a relatively unimportant position.

One of the purest examples of quinary numeration is that furnished by the Betoya scale, already given in full in Chapter III., and briefly mentioned at the beginning of this chapter. In the simplicity and regularity of its construction it is so noteworthy that it is worth repeating, as the first of the long list of quinary systems given in the following pages. No further comment is needed on it than that already made in connection with its digital significance. As far as given by Dr. Brinton the scale is:

1. tey.