CHAPTER IV._The Number Concept: Its Origin and Development

THE ORIGIN OF NUMBER WORDS.

(_CONTINUED_.)

By the slow, and often painful, process incident to the extension and

development of any mental conception in a mind wholly unused to

abstractions, the savage gropes his way onward in his counting from 1, or

more probably from 2, to the various higher numbers required to form his

scale. The perception of unity offers no difficulty to his mind, though he

is conscious at first of the object itself rather than of any idea of

number associated with it. The concept of duality, also, is grasped with

perfect readiness. This concept is, in its simplest form, presented to the

mind as soon as the individual distinguishes himself from another person,

though the idea is still essentially concrete. Perhaps the first glimmering

of any real number thought in connection with 2 comes when the savage

contrasts one single object with another--or, in other words, when he first

recognizes the _pair_. At first the individuals composing the pair are

simply "this one," and "that one," or "this and that"; and his number

system now halts for a time at the stage when he can, rudely enough it may

be, count 1, 2, many. There are certain cases where the forms of 1 and 2

are so similar than one may readily imagine that these numbers really were

"this" and "that" in the savage's original conception of them; and the same

likeness also occurs in the words for 3 and 4, which may readily enough

have been a second "this" and a second "that." In the Lushu tongue the

words for 1 and 2 are _tizi_ and _tazi_ respectively. In Koriak we find

_ngroka_, 3, and _ngraka_, 4; in Kolyma, _niyokh_, 3, and _niyakh_, 4; and

in Kamtschatkan, _tsuk_, 3, and _tsaak_, 4.[108] Sometimes, as in the case

of the Australian races, the entire extent of the count is carried through

by means of pairs. But the natural theory one would form is, that 2 is the

halting place for a very long time; that up to this point the fingers may

or may not have been used--probably not; and that when the next start is

made, and 3, 4, 5, and so on are counted, the fingers first come into

requisition. If the grammatical structure of the earlier languages of the

world's history is examined, the student is struck with the prevalence of

the dual number in them--something which tends to disappear as language

undergoes extended development. The dual number points unequivocally to the

time when 1 and 2 were _the_ numbers at mankind's disposal; to the time

when his three numeral concepts, 1, 2, many, each demanded distinct

expression. With increasing knowledge the necessity for this

differentiatuin would pass away, and but two numbers, singular and plural,

would remain. Incidentally it is to be noticed that the Indo-European words

for 3--_three_, _trois_, _drei_, _tres_, _tri,_ etc., have the same root as

the Latin _trans_, beyond, and give us a hint of the time when our Aryan

ancestors counted in the manner I have just described.

The first real difficulty which the savage experiences in counting, the

difficulty which comes when he attempts to pass beyond 2, and to count 3,

4, and 5, is of course but slight; and these numbers are commonly used and

readily understood by almost all tribes, no matter how deeply sunk in

barbarism we find them. But the instances that have already been cited must

not be forgotten. The Chiquitos do not, in their primitive state, properly

count at all; the Andamans, the Veddas, and many of the Australian tribes

have no numerals higher than 2; others of the Australians and many of the

South Americans stop with 3 or 4; and tribes which make 5 their limit are

still more numerous. Hence it is safe to assert that even this

insignificant number is not always reached with perfect ease. Beyond 5

primitive man often proceeds with the greatest difficulty. Most savages,

even those of the tribes just mentioned, can really count above here, even

though they have no words with which to express their thought. But they do

it with reluctance, and as they go on they quickly lose all sense of

accuracy. This has already been commented on, but to emphasize it afresh

the well-known example given by Mr. Oldfield from his own experience among

the Watchandies may be quoted.[109] "I once wished to ascertain the exact

number of natives who had been slain on a certain occasion. The individual

of whom I made the inquiry began to think over the names ... assigning one

of his fingers to each, and it was not until after many failures, and

consequent fresh starts, that he was able to express so high a number,

which he at length did by holding up his hand three times, thus giving me

to understand that fifteen was the answer to this most difficult

arithmetical question." This meagreness of knowledge in all things

pertaining to numbers is often found to be sharply emphasized in the names

adopted by savages for their numeral words. While discussing in a previous

chapter the limits of number systems, we found many instances where

anything above 2 or 3 was designated by some one of the comprehensive terms

_much_, _many_, _very many_; these words, or such equivalents as _lot_,

_heap_, or _plenty_, serving as an aid to the finger pantomime necessary to

indicate numbers for which they have no real names. The low degree of

intelligence and civilization revealed by such words is brought quite as

sharply into prominence by the word occasionally found for 5. Whenever the

fingers and hands are used at all, it would seem natural to expect for 5

some general expression signifying _hand_, for 10 _both hands_, and for 20

_man_. Such is, as we have already seen, the ordinary method of

progression, but it is not universal. A drop in the scale of civilization

takes us to a point where 10, instead of 20, becomes the whole man. The

Kusaies,[110] of Strong's Island, call 10 _sie-nul_, 1 man, 30 _tol-nul_, 3

men, 40 _a naul_, 4 men, etc.; and the Ku-Mbutti[111] of central Africa

have _mukko_, 10, and _moku_, man. If 10 is to be expressed by reference to

the man, instead of his hands, it might appear more natural to employ some

such expression as that adopted by the African Pigmies,[112] who call 10

_mabo_, and man _mabo-mabo_. With them, then, 10 is perhaps "half a man,"

as it actually is among the Towkas of South America; and we have already

seen that with the Aztecs it was _matlactli_, the "hand half" of a

man.[113] The same idea crops out in the expression used by the Nicobar

Islanders for 30--_heam-umdjome ruktei_, 1 man (and a) half.[114] Such

nomenclature is entirely natural, and it accords with the analogy offered

by other words of frequent occurrence in the numeral scales of savage

races. Still, to find 10 expressed by the term _man_ always conveys an

impression of mental poverty; though it may, of course, be urged that this

might arise from the fact that some races never use the toes in counting,

but go over the fingers again, or perhaps bring into requisition the

fingers of a second man to express the second 10. It is not safe to

postulate an extremely low degree of civilization from the presence of

certain peculiarities of numeral formation. Only the most general

statements can be ventured on, and these are always subject to modification

through some circumstance connected with environment, mode of living, or

intercourse with other tribes. Two South American races may be cited, which

seem in this respect to give unmistakable evidence of being sunk in deepest

barbarism. These are the Juri and the Cayriri, who use the same word for

man and for 5. The former express 5 by _ghomen apa_, 1 man,[115] and the

latter by _ibicho_, person.[116] The Tasmanians of Oyster Bay use the

native word of similar meaning, _puggana_, man,[117] for 5.

Wherever the numeral 20 is expressed by the term _man_, it may be expected

that 40 will be 2 men, 60, 3 men, etc. This form of numeration is usually,

though not always, carried as far as the system extends; and it sometimes

leads to curious terms, of which a single illustration will suffice. The

San Blas Indians, like almost all the other Central and South American

tribes, count by digit numerals, and form their twenties as follows:[118]

20. tula guena = man 1.

40. tula pogua = man 2.

100. tula atala = man 5.

120. tula nergua = man 6.

1000. tula wala guena = great 1 man.

The last expression may, perhaps, be translated "great hundred," though the

literal meaning is the one given. If 10, instead of 20, is expressed by the

word "man," the multiples of 10 follow the law just given for multiples of

20. This is sufficiently indicated by the Kusaie scale; or equally well by

the Api words for 100 and 200, which are[119]

_duulimo toromomo_ = 10 times the whole man.

_duulimo toromomo va juo_ = 10 times the whole man taken 2 times.

As an illustration of the legitimate result which is produced by the

attempt to express high numbers in this manner the term applied by educated

native Greenlanders[120] for a thousand may be cited. This numeral, which

is, of course, not in common use, is

_inuit kulit tatdlima nik kuleriartut navdlugit_ = 10 men 5 times 10

times come to an end.

It is worth noting that the word "great," which appears in the scale of the

San Blas Indians, is not infrequently made use of in the formation of

higher numeral words. The African Mabas[121] call 10 _atuk_, great 1; the

Hottentots[122] and the Hidatsa Indians call 100 great 10, their words

being _gei disi_ and _pitikitstia_ respectively.

The Nicaraguans[123] express 100 by _guhamba_, great 10, and 400 by

_dinoamba_, great 20; and our own familiar word "million," which so many

modern languages have borrowed from the Italian, is nothing more nor less

than a derivative of the Latin _mille_, and really means "great thousand."

The Dakota[124] language shows the same origin for its expression of

1,000,000, which is _kick ta opong wa tunkah_, great 1000. The origin of

such terms can hardly be ascribed to poverty of language. It is found,

rather, in the mental association of the larger with the smaller unit, and

the consequent repetition of the name of the smaller. Any unit, whether it

be a single thing, a dozen, a score, a hundred, a thousand, or any other

unit, is, whenever used, a single and complete group; and where the

relation between them is sufficiently close, as in our "gross" and "great

gross," this form of nomenclature is natural enough to render it a matter

of some surprise that it has not been employed more frequently. An old

English nursery rhyme makes use of this association, only in a manner

precisely the reverse of that which appears now and then in numeral terms.

In the latter case the process is always one of enlargement, and the

associative word is "great." In the following rhyme, constructed by the

mature for the amusement of the childish mind, the process is one of

diminution, and the associative word is "little":

One's none,

Two's some,

Three's a many,

Four's a penny,

Five's a little hundred.[125]

Any real numeral formation by the use of "little," with the name of some

higher unit, would, of course, be impossible. The numeral scale must be

complete before the nursery rhyme can be manufactured.

It is not to be supposed from the observations that have been made on the

formation of savage numeral scales that all, or even the majority of

tribes, proceed in the awkward and faltering manner indicated by many of

the examples quoted. Some of the North American Indian tribes have numeral

scales which are, as far as they go, as regular and almost as simple as our

own. But where digital numeration is extensively resorted to, the

expressions for higher numbers are likely to become complex, and to act as

a real bar to the extension of the system. The same thing is true, to an

even greater degree, of tribes whose number sense is so defective that they

begin almost from the outset to use combinations. If a savage expresses the

number 3 by the combination 2-1, it will at once be suspected that his

numerals will, by the time he reaches 10 or 20, become so complex and

confused that numbers as high as these will be expressed by finger

pantomime rather than by words. Such is often the case; and the comment is

frequently made by explorers that the tribes they have visited have no

words for numbers higher than 3, 4, 5, 10, or 20, but that counting is

carried beyond that point by the aid of fingers or other objects. So

reluctant, in many cases, are savages to count by words, that limits have

been assigned for spoken numerals, which subsequent investigation proved to

fall far short of the real extent of the number systems to which they

belonged. One of the south-western Indian tribes of the United States, the

Comanches, was for a time supposed to have no numeral words below 10, but

to count solely by the use of fingers. But the entire scale of this

taciturn tribe was afterward discovered and published.

To illustrate the awkward and inconvenient forms of expression which

abound in primitive numeral nomenclature, one has only to draw from such

scales as those of the Zuñi, or the Point Barrow Eskimos, given in the

last chapter. Terms such as are found there may readily be duplicated

from almost any quarter of the globe. The Soussous of Sierra Leone[126]

call 99 _tongo solo manani nun solo manani_, _i.e._ to take (10

understood) 5 + 4 times and 5 + 4. The Malagasy expression for 1832

is[127] _roambistelo polo amby valonjato amby arivo_, 2 + 30 + 800 + 1000.

The Aztec equivalent for 399 is[128] _caxtolli onnauh poalli ipan caxtolli

onnaui_, (15 + 4) × 20 + 15 + 4; and the Sioux require for 29 the

ponderous combination[129] _wick a chimen ne nompah sam pah nep e chu wink

a._ These terms, long and awkward as they seem, are only the legitimate

results which arise from combining the names of the higher and lower

numbers, according to the peculiar genius of each language. From some of

the Australian tribes are derived expressions still more complex, as for

6, _marh-jin-bang-ga-gudjir-gyn_, half the hands and 1; and for 15,

_marh-jin-belli-belli-gudjir-jina-bang-ga_, the hand on either side and

half the feet.[130] The Maré tribe, one of the numerous island tribes of

Melanesia,[131] required for a translation of the numeral 38, which occurs

in John v. 5, "had an infirmity thirty and eight years," the

circumlocution, "one man and both sides five and three." Such expressions,

curious as they seem at first thought, are no more than the natural

outgrowth of systems built up by the slow and tedious process which so

often obtains among primitive races, where digit numerals are combined in

an almost endless variety of ways, and where mere reduplication often

serves in place of any independent names for higher units. To what extent

this may be carried is shown by the language of the Cayubabi,[132] who have

for 10 the word _tunca_, and for 100 and 1000 the compounds _tunca tunca_,

and _tunca tunca tunca_ respectively; or of the Sapibocones, who call 10

_bururuche_, hand hand, and 100 _buruche buruche_, hand hand hand

hand.[133] More remarkable still is the Ojibwa language, which continues

its numeral scale without limit, furnishing combinations which are really

remarkable; as, _e.g._, that for 1,000,000,000, which is _me das wac me das

wac as he me das wac_,[134] 1000 × 1000 × 1000. The Winnebago expression

for the same number,[135] _ho ke he hhuta hhu chen a ho ke he ka ra pa ne

za_ is no less formidable, but it has every appearance of being an honest,

native combination. All such primitive terms for larger numbers must,

however, be received with caution. Savages are sometimes eager to display a

knowledge they do not possess, and have been known to invent numeral words

on the spot for the sake of carrying their scales to as high a limit as

possible. The Choctaw words for million and billion are obvious attempts to

incorporate the corresponding English terms into their own language.[136]

For million they gave the vocabulary-hunter the phrase _mil yan chuffa_,

and for billion, _bil yan chuffa_. The word _chuffa_ signifies 1, hence

these expressions are seen at a glance to be coined solely for the purpose

of gratifying a little harmless Choctaw vanity. But this is innocence

itself compared with the fraud perpetrated on Labillardière by the Tonga

Islanders, who supplied the astonished and delighted investigator with a

numeral vocabulary up to quadrillions. Their real limit was afterward found

to be 100,000, and above that point they had palmed off as numerals a

tolerably complete list of the obscene words of their language, together

with a few nonsense terms. These were all accepted and printed in good

faith, and the humiliating truth was not discovered until years

afterward.[137]

One noteworthy and interesting fact relating to numeral nomenclature is the

variation in form which words of this class undergo when applied to

different classes of objects. To one accustomed as we are to absolute and

unvarying forms for numerals, this seems at first a novel and almost

unaccountable linguistic freak. But it is not uncommon among uncivilized

races, and is extensively employed by so highly enlightened a people, even,

as the Japanese. This variation in form is in no way analogous to that

produced by inflectional changes, such as occur in Hebrew, Greek, Latin,

etc. It is sufficient in many cases to produce almost an entire change in

the form of the word; or to result in compounds which require close

scrutiny for the detection of the original root. For example, in the

Carrier, one of the Déné dialects of western Canada, the word _tha_ means 3

things; _thane_, 3 persons; _that_, 3 times; _thatoen_, in 3 places;

_thauh_, in 3 ways; _thailtoh_, all of the 3 things; _thahoeltoh_, all of

the 3 persons; and _thahultoh_, all of the 3 times.[138] In the Tsimshian

language of British Columbia we find seven distinct sets of numerals "which

are used for various classes of objects that are counted. The first set is

used in counting where there is no definite object referred to; the second

class is used for counting flat objects and animals; the third for counting

round objects and divisions of time; the fourth for counting men; the fifth

for counting long objects, the numerals being composed with _kan_, tree;

the sixth for counting canoes; and the seventh for measures. The last seem

to be composed with _anon_, hand."[139] The first ten numerals of each of

these classes is given in the following table:

+----+---------+---------+---------+----------+------------+-------------+-------------+

+----+---------+---------+---------+----------+------------+-------------+-------------+

| 1 |gyak gak |g'erel |k'al |k'awutskan|k'amaet |k'al | |

+----+---------+---------+---------+----------+------------+-------------+-------------+

Remarkable as this list may appear, it is by no means as extensive as that

derived from many of the other British Columbian tribes. The numerals of

the Shushwap, Stlatlumh, Okanaken, and other languages of this region exist

in several different forms, and can also be modified by any of the

innumerable suffixes of these tongues.[140] To illustrate the almost

illimitable number of sets that may be formed, a table is given of "a few

classes, taken from the Heiltsuk dialect.[141] It appears from these

examples that the number of classes is unlimited."

+-----------------------+-------------+--------------+--------------+

| | One. | Two. | Three. |

+-----------------------+-------------+--------------+--------------+

|Together on beach. |---- |maalis |---- |

|Together in house, etc.|---- |maalitl |---- |

+-----------------------+-------------+--------------+--------------+

Variation in numeral forms such as is exhibited in the above tables is not

confined to any one quarter of the globe; but it is more universal among

the British Columbian Indians than among any other race, and it is a more

characteristic linguistic peculiarity of this than of any other region,

either in the Old World or in the New. It was to some extent employed by

the Aztecs,[142] and its use is current among the Japanese; in whose

language Crawfurd finds fourteen different classes of numerals "without

exhausting the list."[143]

In examining the numerals of different languages it will be found that the

tens of any ordinary decimal scale are formed in the same manner as in

English. Twenty is simply 2 times 10; 30 is 3 times 10, and so on. The word

"times" is, of course, not expressed, any more than in English; but the

expressions briefly are, 2 tens, 3 tens, etc. But a singular exception to

this method is presented by the Hebrew, and other of the Semitic languages.

In Hebrew the word for 20 is the plural of the word for 10; and 30, 40, 50,

etc. to 90 are plurals of 3, 4, 5, 6, 7, 8, 9. These numerals are as

follows:[144]

10, eser, 20, eserim,

3, shalosh, 30, shaloshim,

4, arba, 40, arbaim,

5, chamesh, 50, chamishshim,

6, shesh, 60, sheshshim,

7, sheba, 70, shibim,

8, shemoneh 80, shemonim,

9, tesha, 90, tishim.

The same formation appears in the numerals of the ancient Phoenicians,[145]

and seems, indeed, to be a well-marked characteristic of the various

branches of this division of the Caucasian race. An analogous method

appears in the formation of the tens in the Bisayan,[146] one of the Malay

numeral scales, where 30, 40, ... 90, are constructed from 3, 4, ... 9, by

adding the termination _-an_.

No more interesting contribution has ever been made to the literature of

numeral nomenclature than that in which Dr. Trumbull embodies the results

of his scholarly research among the languages of the native Indian tribes

of this country.[147] As might be expected, we are everywhere confronted

with a digital origin, direct or indirect, in the great body of the words

examined. But it is clearly shown that such a derivation cannot be

established for all numerals; and evidence collected by the most recent

research fully substantiates the position taken by Dr. Trumbull. Nearly all

the derivations established are such as to remind us of the meanings we

have already seen recurring in one form or another in language after

language. Five is the end of the finger count on one hand--as, the Micmac

_nan_, and Mohegan _nunon_, gone, or spent; the Pawnee _sihuks_, hands

half; the Dakota _zaptan_, hand turned down; and the Massachusetts

_napanna_, on one side. Ten is the end of the finger count, but is not

always expressed by the "both hands" formula so commonly met with. The Cree

term for this number is _mitatat_, no further; and the corresponding word

in Delaware is _m'tellen_, no more. The Dakota 10 is, like its 5, a

straightening out of the fingers which have been turned over in counting,

or _wickchemna_, spread out unbent. The same is true of the Hidatsa

_pitika_, which signifies a smoothing out, or straightening. The Pawnee 4,

_skitiks_, is unusual, signifying as it does "all the fingers," or more

properly, "the fingers of the hand." The same meaning attaches to this

numeral in a few other languages also, and reminds one of the habit some

people have of beginning to count on the forefinger and proceeding from

there to the little finger. Can this have been the habit of the tribes in

question? A suggestion of the same nature is made by the Illinois and Miami

words for 8, _parare_ and _polane_, which signify "nearly ended." Six is

almost always digital in origin, though the derivation may be indirect, as

in the Illinois _kakatchui_, passing beyond the middle; and the Dakota

_shakpe_, 1 in addition. Some of these significations are well matched by

numerals from the Ewe scales of western Africa, where we find the

following:[148]

1. de = a going, _i.e._ a beginning. (Cf. the Zuñi _töpinte_, taken to

start with.)

3. eto = the father (from the middle, or longest finger).

6. ade = the other going.

9. asieke = parting with the hands.

10. ewo = done.

In studying the names for 2 we are at once led away from a strictly digital

origin for the terms by which this number is expressed. These names seem to

come from four different sources: (1) roots denoting separation or

distinction; (2) likeness, equality, or opposition; (3) addition, _i.e._

putting to, or putting with; (4) coupling, pairing, or matching. They are

often related to, and perhaps derived from, names of natural pairs, as

feet, hands, eyes, arms, or wings. In the Dakota and Algonkin dialects 2 is

almost always related to "arms" or "hands," and in the Athapaskan to

"feet." But the relationship is that of common origin, rather than of

derivation from these pair-names. In the Puri and Hottentot languages, 2

and "hand" are closely allied; while in Sanskrit, 2 may be expressed by any

one of the words _kara_, hand, _bahu_, arm, _paksha_, wing, or _netra,_

eye.[149] Still more remote from anything digital in their derivation are

the following, taken at random from a very great number of examples that

might be cited to illustrate this point. The Assiniboines call 7, _shak ko

we_, or _u she nah_, the odd number.[150] The Crow 1, _hamat,_ signifies

"the least";[151] the Mississaga 1, _pecik_, a very small thing.[152] In

Javanese, Malay, and Manadu, the words for 1, which are respectively

_siji_, _satu_, and _sabuah_, signify 1 seed, 1 pebble, and 1 fruit

respectively[153]--words as natural and as much to be expected at the

beginning of a number scale as any finger name could possibly be. Among

almost all savage races one form or another of palpable arithmetic is

found, such as counting by seeds, pebbles, shells, notches, or knots; and

the derivation of number words from these sources can constitute no ground

for surprise. The Marquesan word for 4 is _pona_, knot, from the practice

of tying breadfruit in knots of 4. The Maori 10 is _tekau_, bunch, or

parcel, from the counting of yams and fish by parcels of 10.[154] The

Javanese call 25, _lawe_, a thread, or string; 50, _ekat_, a skein of

thread; 400, _samas_, a bit of gold; 800, _domas_, 2 bits of gold.[155] The

Macassar and Butong term for 100 is _bilangan_, 1 tale or reckoning.[156]

The Aztec 20 is _cem pohualli_, 1 count; 400 is _centzontli_, 1 hair of the

head; and 8000 is _xiquipilli_, sack.[157] This sack was of such a size as

to contain 8000 cacao nibs, or grains, hence the derivation of the word in

its numeral sense is perfectly natural. In Japanese we find a large number

of terms which, as applied to the different units of the number scale, seem

almost purely fanciful. These words, with their meanings as given by a

Japanese lexicon, are as follows:

10,000, or 10^4, män = enormous number.

10^8, oku = a compound of the words "man" and "mind."

10^12, chio = indication, or symptom.

10^16, kei = capital city.

10^20, si = a term referring to grains.

10^24, owi = ----

10^28, jio = extent of land.

10^32, ko = canal.

10^36, kan = some kind of a body of water.

10^40, sai = justice.

10^44, s[=a] = support.

10^48, kioku = limit, or more strictly, ultimate.

.01^2, rin = ----

.01^3, mo = hair (of some animal).

.01^4, shi = thread.

In addition to these, some of the lower fractional values are described by

words meaning "very small," "very fine thread," "sand grain," "dust," and

"very vague." Taken altogether, the Japanese number system is the most

remarkable I have ever examined, in the extent and variety of the higher

numerals with well-defined descriptive names. Most of the terms employed

are such as to defy any attempt to trace the process of reasoning which led

to their adoption. It is not improbable that the choice was, in some of

these cases at least, either accidental or arbitrary; but still, the

changes in word meanings which occur with the lapse of time may have

differentiated significations originally alike, until no trace of kinship

would appear to the casual observer. Our numerals "score" and "gross" are

never thought of as having any original relation to what is conveyed by the

other meanings which attach to these words. But the origin of each, which

is easily traced, shows that, in the beginning, there existed a

well-defined reason for the selection of these, rather than other terms,

for the numbers they now describe. Possibly these remarkable Japanese terms

may be accounted for in the same way, though the supposition is, for some

reasons, quite improbable. The same may be said for the Malagasy 1000,

_alina_, which also means "night," and the Hebrew 6, _shesh_, which has the

additional signification "white marble," and the stray exceptions which now

and then come to the light in this or that language. Such terms as these

may admit of some logical explanation, but for the great mass of numerals

whose primitive meanings can be traced at all, no explanation whatever is

needed; the words are self-explanatory, as the examples already cited show.

A few additional examples of natural derivation may still further emphasize

the point just discussed. In Bambarese the word for 10, _tank_, is derived

directly from _adang_, to count.[158] In the language of Mota, one of the

islands of Melanesia, 100 is _mel nol_, used and done with, referring to

the leaves of the cycas tree, with which the count had been carried

on.[159] In many other Melanesian dialects[160] 100 is _rau_, a branch or

leaf. In the Torres Straits we find the same number expressed by _na won_,

the close; and in Eromanga it is _narolim narolim_ (2 × 5)(2 × 5).[161]

This combination deserves remark only because of the involved form which

seems to have been required for the expression of so small a number as 100.

A compound instead of a simple term for any higher unit is never to be

wondered at, so rude are some of the savage methods of expressing number;

but "two fives (times) two fives" is certainly remarkable. Some form like

that employed by the Nusqually[162] of Puget Sound for 1000, i.e.

_paduts-subquätche_, ten hundred, is more in accordance with primitive

method. But we are equally likely to find such descriptive phrases for this

numeral as the _dor paka_, banyan roots, of the Torres Islands; _rau na

hai_, leaves of a tree, of Vaturana; or _udolu_, all, of the Fiji Islands.

And two curious phrases for 1000 are those of the Banks' Islands, _tar

mataqelaqela_, eye blind thousand, _i.e._ many beyond count; and of

Malanta, _warehune huto_, opossum's hairs, or _idumie one_, count the

sand.[163]

The native languages of India, Thibet, and portions of the Indian

archipelago furnish us with abundant instances of the formation of

secondary numeral scales, which were used only for special purposes, and

without in any way interfering with the use of the number words already in

use. "Thus the scholars of India, ages ago, selected a set of words for a

memoria technica, in order to record dates and numbers. These words they

chose for reasons which are still in great measure evident; thus 'moon' or

'earth' expressed 1, there being but one of each; 2 might be called 'eye,'

'wing,' 'arm,' 'jaw,' as going in pairs; for 3 they said 'Rama,' 'fire,' or

'quality,' there being considered to be three Ramas, three kinds of fire,

three qualities (guna); for 4 were used 'veda,' 'age,' or 'ocean,' there

being four of each recognized; 'season' for 6, because they reckoned six

seasons; 'sage' or 'vowel,' for 7, from the seven sages and the seven

vowels; and so on with higher numbers, 'sun' for 12, because of his twelve

annual denominations, or 'zodiac' from his twelve signs, and 'nail' for 20,

a word incidentally bringing in finger notation. As Sanskrit is very rich

in synonyms, and as even the numerals themselves might be used, it became

very easy to draw up phrases or nonsense verses to record series of numbers

by this system of artificial memory."[164]

More than enough has been said to show how baseless is the claim that all

numeral words are derived, either directly or indirectly, from the names of

fingers, hands, or feet. Connected with the origin of each number word

there may be some metaphor, which cannot always be distinctly traced; and

where the metaphor was born of the hand or of the foot, we inevitably

associate it with the practice of finger counting. But races as fond of

metaphor and of linguistic embellishment as are those of the East, or as

are our American Indians even, might readily resort to some other source

than that furnished by the members of the human body, when in want of a

term with which to describe the 5, 10, or any other number of the numeral

scale they were unconsciously forming. That the first numbers of a numeral

scale are usually derived from other sources, we have some reason to

believe; but that all above 2, 3, or at most 4, are almost universally of

digital origin we must admit. Exception should properly be made of higher

units, say 1000 or anything greater, which could not be expected to conform

to any law of derivation governing the first few units of a system.

Collecting together and comparing with one another the great mass of terms

by which we find any number expressed in different languages, and, while

admitting the great diversity of method practised by different tribes, we

observe certain resemblances which were not at first supposed to exist. The

various meanings of 1, where they can be traced at all, cluster into a

little group of significations with which at last we come to associate the

idea of unity. Similarly of 2, or 5, or 10, or any one of the little band

which does picket duty for the advance guard of the great host of number

words which are to follow. A careful examination of the first decade

warrants the assertion that the probable meaning of any one of the units

will be found in the list given below. The words selected are intended

merely to serve as indications of the thought underlying the savage's

choice, and not necessarily as the exact term by means of which he

describes his number. Only the commonest meanings are included in the

tabulation here given.

1 = existence, piece, group, beginning.

2 = repetition, division, natural pair.

3 = collection, many, two-one.

4 = two twos.

5 = hand, group, division,

6 = five-one, two threes, second one.

7 = five-two, second two, three from ten.

8 = five-three, second three, two fours, two from ten.

9 = five-four, three threes, one from ten.

10 = one (group), two fives (hands), half a man, one man.

15 = ten-five, one foot, three fives.

20 = two tens, one man, two feet.[165]