Part 11 (2/2)

10 mano = 1 tini = 40,000.

10 tini = 1 tufa = 400,000.

10 tufa = 1 pohi = 4,000,000.

In the Hawaiian dialect this scale is, with slight modification, the universal scale, used not only in counting breadfruit, but any other objects as well. The result is a complete decimal-quaternary system, such as is found nowhere else in the world except in this and a few of the neighbouring dialects of the Pacific. This scale, which is almost identical with the Nukuhivan, is[203]

4 units = 1 ha or tauna = 4.

10 tauna = 1 tanaha = 40.

10 tanaha = 1 lau = 400.

10 lau = 1 mano = 4000.

10 mano = 1 tini = 40,000.

10 tini = 1 lehu = 400,000.

The quaternary element thus introduced has modified the entire structure of the Hawaiian number system. Fifty is _tanaha me ta umi_, 40 + 10; 76 is 40 + 20 + 10 + 6; 100 is _ua tanaha ma tekau_, 2 40 + 10; 200 is _lima tanaha_, 5 40; and 864,895 is 2 400,000 + 40,000 + 6 4000 + 2 400 + 2 40 + 10 + 5.[204] Such examples show that this secondary influence, entering and incorporating itself as a part of a well-developed decimal system, has radically changed it by the establishment of 4 as the primary number base. The role which 10 now plays is peculiar. In the natural formation of a quaternary scale new units would be introduced at 16, 64, 256, etc.; that is, at the square, the cube, and each successive power of the base. But, instead of this, the new units are introduced at 10 4, 100 4, 1000 4, etc.; that is, at the products of 4 by each successive power of the old base. This leaves the scale a decimal scale still, even while it may justly be called quaternary; and produces one of the most singular and interesting instances of number-system formation that has ever been observed. In this connection it is worth noting that these Pacific island number scales have been developed to very high limits--in some cases into the millions. The numerals for these large numbers do not seem in any way indefinite, but rather to convey to the mind of the native an idea as clear as can well be conveyed by numbers of such magnitude. Beyond the limits given, the islanders have indefinite expressions, but as far as can be ascertained these are only used when the limits given above have actually been pa.s.sed. To quote one more example, the Hervey Islanders, who have a binary-decimal scale, count as follows:

5 kaviri (bunches of cocoanuts) = 1 takau = 20.

10 takau = 1 rau = 200.

10 rau = 1 mano = 2000.

10 mano = 1 kiu = 20,000.

10 kiu = 1 tini = 200,000.

Anything above this they speak of in an uncertain way, as _mano mano_ or _tini tini_, which may, perhaps, be paralleled by our English phrases ”myriads upon myriads,” and ”millions of millions.”[205] It is most remarkable that the same quarter of the globe should present us with the stunted number sense of the Australians, and, side by side with it, so extended and intelligent an appreciation of numerical values as that possessed by many of the lesser tribes of Polynesia.

The Luli of Paraguay[206] show a decided preference for the base 4. This preference gives way only when they reach the number 10, which is an ordinary digit numeral. All numbers above that point belong rather to decimal than to quaternary numeration. Their numerals are:

1. alapea.

2. tamop.

3. tamlip.

4. lokep.

5. lokep moile alapea = 4 with 1, or is-alapea = hand 1.

6. lokep moile tamop = 4 with 2.

7. lokep moile tamlip = 4 with 3.

8. lokep moile lokep = 4 with 4.

9. lokep moile lokep alapea = 4 with 4-1.

10. is yaoum = all the fingers of hand.

11. is yaoum moile alapea = all the fingers of hand with 1.

20. is elu yaoum = all the fingers of hand and foot.

30. is elu yaoum moile is-yaoum = all the fingers of hand and foot with all the fingers of hand.

Still another instance of quaternary counting, this time carrying with it a suggestion of binary influence, is furnished by the Mocobi[207] of the Parana region. Their scale is exceedingly rude, and they use the fingers and toes almost exclusively in counting; only using their spoken numerals when, for any reason, they wish to dispense with the aid of their hands and feet. Their first eight numerals are:

1. iniateda.

2. inabaca.

3. inabacao caini = 2 above.

4. inabacao cainiba = 2 above 2; or natolatata.

5. inibacao cainiba iniateda = 2 above 2-1; or natolatata iniateda = 4-1.

6. natolatatata inibaca = 4-2.

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