The Number Concept: Its Origin and Development

by Levi L. Conant

Tsimshian.[³⁶¹]

10.	gy'ap.
20.	kyedeel	= 1 man.
30.	gulewulgy'ap.
40.	t'epqadalgyitk, or tqalpqwulgyap.
50.	kctoncwulgyap.
100.	kcenecal.
200.	k'pal.
300.	k'pal te kcenecal	= 200 + 100.
400.	kyedal.
500.	kyedal te kcenecal	= 400 + 100.
600.	gulalegyitk.
700.	gulalegyitk te kcenecal	= 600 + 100.
800.	tqalpqtalegyitk.
900.	tqalpqtalegyitk te kcenecal	= 800 + 100.
1000.	k'pal.

To the unobservant eye this scale would certainly appear to contain no more than a trace of the vigesimal in its structure. But Dr. Boas, who is one of the most careful and accurate of investigators, says in his comment on this system: “It will be seen at once that this system is quinary-vigesimal.… In 20 we find the word gyat, man. The hundreds are identical with the numerals used in counting men (see [p. 87]), and then the quinary-vigesimal system is most evident.”

Rio Norte Indians.[³⁶²]

20.	taiguaco.
30.	taiguaco co juyopamauj ajte	= 20 + 2 × 5.
40.	taiguaco ajte	= 20 × 2.
50.	taiguaco ajte co juyopamauj ajte	= 20 × 2 + 5 × 2.

Caribs of Essiquibo, Guiana

10.	oween-abatoro.
20.	owee-carena	= 1 person.
40.	oko-carena	= 2 persons.
60.	oroowa-carena	= 3 persons.

Otomi

10.	ra-tta.
20.	na-te.
30.	na-te-m'a-ratta	= 20 + 10.
40.	yo-te	= 2 × 30.
50.	yote-m'a-ratta	= 2 × 20 + 10.
60.	hiu-te	= 3 × 20.
70.	hiute-m'a-ratta	= 3 × 20 + 10.
80.	gooho-rate	= 4 × 20.
90.	gooho-rate-m'a ratta	= 4 × 20 + 10.
100.	cytta-te	= 5 × 20,
	or nanthebe	= 1 × 100.

Maya, Yucatan.[³⁶³]

1.	hun.
10.	lahun	= it is finished.
20.	hunkal	= a measure, or more correctly, a fastening together.
30.	lahucakal	= 40 − 10?
40.	cakal	= 2 × 20.
50.	lahuyoxkal	= 60 − 10.
60.	oxkal	= 3 × 20.
70.	lahucankal	= 80 − 10.
80.	cankal	= 4 × 20.
90.	lahuyokal	= 100 − 10.
100.	hokal	= 5 × 20.
110.	lahu uackal	= 120 − 10.
120.	uackal	= 6 × 20.
130.	lahu uuckal	= 140 − 10.
140.	uuckal	= 7 × 20.
200.	lahuncal	= 10 × 20.
300.	holhukal	= 15 × 20.
400.	hunbak	= 1 tying around.
500.	hotubak.
600.	lahutubak
800.	calbak	= 2 × 400.
900.	hotu yoxbak.
1000.	lahuyoxbak.
1200.	oxbak	= 3 × 400.
2000.	capic (modern).
8000.	hunpic	= 1 sack.
16,000.	ca pic (ancient).
160,000.	calab	= a filling full
3,200,000.	kinchil.
64,000,000.	hunalau.

In the Maya scale we have one of the best and most extended examples of vigesimal numeration ever developed by any race. To show in a more striking and forcible manner the perfect regularity of the system, the following tabulation is made of the various Maya units, which will correspond to the “10 units make one ten, 10 tens make one hundred, 10 hundreds make one thousand,” etc., which old-fashioned arithmetic compelled us to learn in childhood. The scale is just as regular by twenties in Maya as by tens in English. It is[³⁶⁴]

20 hun	= 1 kal	= 20.
20 kal	= 1 bak	= 400.
20 bak	= 1 pic	= 8000.
20 pic	= 1 calab	= 160,000.
20 calab	= 1{ kinchil } tzotzceh	= 3,200,000.
20 kinchil	= 1 alau	= 64,000,000.

The original meaning of pic, given in the scale as “a sack,” was rather “a short petticoat, somtimes used as a sack.” The word tzotzceh signified “deerskin.” No reason can be given for the choice of this word as a numeral, though the appropriateness of the others is sufficiently manifest. No evidence of digital numeration appears in the first 10 units, but, judging from the almost universal practice of the Indian tribes of both North and South America, such may readily have been the origin of Maya counting. Whatever its origin, it certainly expanded and grew into a system whose perfection challenges our admiration. It was worthy of the splendid civilization of this unfortunate race, and, through its simplicity and regularity, bears ample testimony to the intellectual capacity which originated it.

The only example of vigesimal reckoning which is comparable with that of the Mayas is the system employed by their northern neighbours, the Nahuatl, or, as they are more commonly designated, the Aztecs of Mexico. This system is quite as pure and quite as simple as the Maya, but differs from it in some important particulars. In its first 20 numerals it is quinary (see [p. 141]), and as a system must be regarded as quinary-vigesimal. The Maya scale is decimal through its first 20 numerals, and, if it is to be regarded as a mixed scale, must be characterized as decimal-vigesimal. But in both these instances the vigesimal element preponderates so strongly that these, in common with their kindred number systems of Mexico, Yucatan, and Central America, are always thought of and alluded to as vigesimal scales. On account of its importance, the Nahuatl system[³⁶⁵] is given in fuller detail than most of the other systems I have made use of.