Excerpt: ...The next unit, mano, has in a similar manner been twisted out of its original sense, and in counting breadfruit is made to serve for 8000. In the northern, or Nukuhivan Islands, the decimal-quaternary system is more regular. It is in the counting of breadfruit only,202 4 breadfruits= 1 pona= 4. 10 pona= 1 toha= 40. 10 toha= 1 au= 400. 10 au= 1 mano= 4000. 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 ...
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Excerpt: ...The next unit, mano, has in a similar manner been twisted out of its original sense, and in counting breadfruit is made to serve for 8000. In the northern, or Nukuhivan Islands, the decimal-quaternary system is more regular. It is in the counting of breadfruit only,202 4 breadfruits= 1 pona= 4. 10 pona= 1 toha= 40. 10 toha= 1 au= 400. 10 au= 1 mano= 4000. 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, is203 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 x 40 + 10; 200 is lima tanaha, 5 x 40; and 864,895 is 2 x 400,000 + 40,000 + 6 x 4000 + 2 x 400 + 2 x 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 x 4, 100 x 4, 1000 x 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...
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