The Number Concept: Its Origin and Development Part 37

AINO.[353]

10. wambi.

20. choz.

30. wambi i-doehoz = 10 from 40.

40. tochoz = 2 20.

50. wambi i-richoz = 10 from 60.

60. rechoz = 3 20.

70. wambi [i?] inichoz = 10 from 80.

80. inichoz = 4 20.

90. wambi aschikinichoz = 10 from 100.

100. aschikinichoz = 5 20.

110. wambi juwanochoz = 10 from 120.

120. juwano choz = 6 20.

130. wambi aruwanochoz = 10 from 140.

140. aruwano choz = 7 20.

150. wambi tubischano choz = 10 from 160.

160. tubischano choz = 8 20.

170. wambi schnebischano choz = 10 from 180.

180. schnebischano choz = 9 20.

190. wambi schnewano choz = 10 from 200.

200. schnewano choz = 10 20.

300. aschikinichoz i gaschima chnewano choz = 5 20 + 10 20.

400. toschnewano choz = 2 (10 20).

500. aschikinichoz i gaschima toschnewano choz = 100 + 400.

600. reschiniwano choz = 3 200.

700. aschikinichoz i gaschima reschiniwano choz = 100 + 600.

800. inischiniwano choz = 4 200.

900. aschikinichoz i gaschima inischiniwano choz = 100 + 800.

1000. aschikini schinewano choz = 5 200.

2000. wanu schinewano choz = 10 (10 20).

This scale is in one sense wholly vigesimal, and in another way it is not to be regarded as pure, but as mixed. Below 20 it is quinary, and, however far it might be extended, this quinary element would remain, making the scale quinary-vigesimal. But in another sense, also, the Aino system is not pure. In any unmixed vigesimal scale the word for 400 must be a simple word, and that number must be taken as the vigesimal unit corresponding to 100 in the decimal scale. But the Ainos have no simple numeral word for any number above 20, forming all higher numbers by combinations through one or more of the processes of addition, subtraction, and multiplication. The only number above 20 which is used as a unit is 200, which is expressed merely as 10 twenties. Any even number of hundreds, or any number of thousands, is then indicated as being so many times 10 twenties; and the odd hundreds are so many times 10 twenties, plus 5 twenties more. This scale is an excellent example of the c.u.mbersome methods used by uncivilized races in extending their number systems beyond the ordinary needs of daily life.

In Central Asia a single vigesimal scale comes to light in the following fragment of the Leptscha scale, of the Himalaya region:[354]

10. kati.

40. kafali = 4 10, or kha nat = 2 20.

50. kafano = 5 10, or kha nat sa kati = 2 20 + 10.

100. gjo, or kat.

Further to the south, among the Dravidian races, the vigesimal element is also found. The following will suffice to ill.u.s.trate the number systems of these dialects, which, as far as the material at hand shows, are different from each other only in minor particulars:

MUNDARI.[355]

10. gelea.

20. mi hisi.

30. mi hisi gelea = 20 + 10.

40. bar hisi = 2 20.

60. api hisi = 3 20.

80. upun hisi = 4 20.

100. mone hisi = 5 20.

In the Nicobar Islands of the Indian Ocean a well-developed example of vigesimal numeration is found. The inhabitants of these islands are so low in the scale of civilization that a definite numeral system of any kind is a source of some surprise. Their neighbours, the Andaman Islanders, it will be remembered, have but two numerals at their command; their intelligence does not seem in any way inferior to that of the Nicobar tribes, and one is at a loss to account for the superior development of the number sense in the case of the latter. The intercourse of the coast tribes with traders might furnish an explanation of the difficulty were it not for the fact that the numeration of the inland tribes is quite as well developed as that of the coast tribes; and as the former never come in contact with traders and never engage in barter of any kind except in the most limited way, the conclusion seems inevitable that this is merely one of the phenomena of mental development among savage races for which we have at present no adequate explanation. The princ.i.p.al numerals of the inland and of the coast tribes are:[356]

INLAND TRIBES COAST TRIBES

10. teya. 10. sham.

20. heng-inai. 20. heang-inai.

30. heng-inai-tain 30. heang-inai-tanai = 20 + 5 (couples). = 20 + 5 (couples).

40. au-inai = 2 20. 40. an-inai = 2 20.

100. tain-inai = 5 20. 100. tanai-inai = 5 20.

200. teya-inai = 10 20. 200. sham-inai = 10 20.

300. teya-tain-inai 300. heang-tanai-inai = (10 + 5) 20. = (10 + 5) 20.

400. heng-teo. 400. heang-momchiama.

In no other part of the world is vigesimal counting found so perfectly developed, and, among native races, so generally preferred, as in North and South America. In the eastern portions of North America and in the extreme western portions of South America the decimal or the quinary decimal scale is in general use. But in the northern regions of North America, in western Canada and northwestern United States, in Mexico and Central America, and in the northern and western parts of South America, the unit of counting among the great majority of the native races was 20. The ethnological affinities of these races are not yet definitely ascertained; and it is no part of the scope of this work to enter into any discussion of that involved question. But either through contact or affinity, this form of numeration spread in prehistoric times over half or more than half of the western hemisphere. It was the method employed by the rude Eskimos of the north and their equally rude kinsmen of Paraguay and eastern Brazil; by the forest Indians of Oregon and British Columbia, and by their more southern kinsmen, the wild tribes of the Rio Grande and of the Orinoco. And, most striking and interesting of all, it was the method upon which were based the numeral systems of the highly civilized races of Mexico, Yucatan, and New Granada. Some of the systems obtained from the languages of these peoples are perfect, extended examples of vigesimal counting, not to be duplicated in any other quarter of the globe. The ordinary unit was, as would be expected, "one man," and in numerous languages the words for 20 and man are identical. But in other cases the original meaning of that numeral word has been lost; and in others still it has a signification quite remote from that given above. These meanings will be noticed in connection with the scales themselves, which are given, roughly speaking, in their geographical order, beginning with the Eskimo of the far north.

The systems of some of the tribes are as follows:

ALASKAN ESKIMOS.[357]

10. koleet.

20. enuenok.

30. enuenok kolinik = 20 + 10.

40. malho kepe ak = 2 20.

50. malho-kepe ak-kolmik che pah ak to = 2 20 + 10.

60. pingi shu-kepe ak = 3 20.

100. tale ma-kepe ak = 5 20.

400. enue nok ke pe ak = 20 20.

TCHIGLIT.[358]

10. krolit.

20. kroleti, or innun = man.

30. innok krolinik-tchikpalik = man + 2 hands.

40. innum mallerok = 2 men.

50. adjigaynarmitoat = as many times 10 as the fingers of the hand.

60. innumipit = 3 men.

70. innunmalloeronik arveneloerit = 7 men?

80. innun pinatcunik arveneloerit = 8 men?

90. innun tcitamanik arveneloerit = 9 men?

100. itchangnerkr.

1000. itchangner-park = great 100.