Part 39 (2/2)

100. macuilpoalli = 5 20.

120. chiquacempoalli = 6 20.

140. chicompoalli = 7 20.

160. chicuepoalli = 8 20.

180. chiconauhpoalli = 9 20.

200. matlacpoalli = 10 20.

220. matlactli oncempoalli = 11 20.

240. matlactli omompoalli = 12 20.

260. matlactli omeipoalli = 13 20.

280. matlactli onnauhpoalli = 14 20.

300. caxtolpoalli = 15 20.

320. caxtolli oncempoalli.

399. caxtolli onnauhpoalli ipan caxtolli onnaui = 19 20 + 19.

400. centzontli = 1 bunch of gra.s.s, or 1 tuft of hair.

800. ometzontli = 2 400.

1200. eitzontli = 3 400.

7600. caxtolli onnauhtzontli = 19 400.

8000. cenxiquipilli, or cexiquipilli.

160,000. cempoalxiquipilli = 20 8000.

3,200,000. centzonxiquipilli = 400 8000.

64,000,000. cempoaltzonxiquipilli = 20 400 8000.

Up to 160,000 the Nahuatl system is as simple and regular in its construction as the English. But at this point it fails in the formation of a new unit, or rather in the expression of its new unit by a simple word; and in the expression of all higher numbers it is forced to resort in some measure to compound terms, just as the English might have done had it not been able to borrow from the Italian. The higher numeral terms, under such conditions, rapidly become complex and c.u.mbersome, as the following a.n.a.lysis of the number 1,279,999,999 shows.[366] The a.n.a.lysis will be readily understood when it is remembered that _ipan_ signifies plus.

_Caxtolli onnauhpoaltzonxiquipilli ipan caxtolli onnauhtzonxiquipilli ipan caxtolli onnauhpoalxiquipilli ipan caxtolli onnauhxiquipilli ipan caxtolli onnauhtzontli ipan caxtolli onnauhpoalli ipan caxtolli onnaui;_ _i.e._ 1,216,000,000 + 60,800,000 + 3,040,000 + 152,000 + 7600 + 380 + 19. To show the compounding which takes place in the higher numerals, the a.n.a.lysis may be made more literally, thus: + (15 + 4) 400 800 + (15 + 4) 20 8000 + (15 + 4) 8000 + (15 + 4) 400 + (15 + 4) 20 + 15 + 4. Of course this resolution suffers from the fact that it is given in digits arranged in accordance with decimal notation, while the Nahuatl numerals express values by a base twice as great. This gives the effect of a complexity and awkwardness greater than really existed in the actual use of the scale. Except for the presence of the quinary element the number just given is really expressed with just as great simplicity as it could be in English words if our words ”million” and ”billion” were replaced by ”thousand thousand” and ”thousand thousand thousand.” If Mexico had remained undisturbed by Europeans, and science and commerce had been left to their natural growth and development, uncompounded words would undoubtedly have been found for the higher units, 160,000, 3,200,000, etc., and the system thus rendered as simple as it is possible for a quinary-vigesimal system to be.

Other number scales of this region are given as follows:

HUASTECA.[367]

10. laluh.

20. hum-inic = 1 man.

30. hum-inic-lahu = 1 man 10.

40. tzab-inic = 2 men.

50. tzab-inic-lahu = 2 men 10.

60. ox-inic = 3 men.

70. ox-inic-lahu = 3 men 10.

80. tze-tnic = 4 men.

90. tze-ynic-kal-laluh = 4 men and 10.

100. bo-inic = 5 men.

200. tzab-bo-inic = 2 5 men.

300. ox-bo-inic = 3 5 men.

400. tsa-bo-inic = 4 5 men.

600. acac-bo-inic = 6 5 men.

800. huaxic-bo-inic = 8 5 men.

1000. xi.

8000. huaxic-xi = 8-1000.

The essentially vigesimal character of this system changes in the formation of some of the higher numerals, and a suspicion of the decimal enters. One hundred is _boinic_, 5 men; but 200, instead of being simply _lahuh-inic_, 10 men, is _tsa-bo-inic_, 2 100, or more strictly, 2 times 5 men.

Similarly, 300 is 3 100, 400 is 4 100, etc. The word for 1000 is simple instead of compound, and the thousands appear to be formed wholly on the decimal base. A comparison of this scale with that of the Nahuatl shows how much inferior it is to the latter, both in simplicity and consistency.

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