CHAPTER II

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NUMBER SYSTEM LIMITS.

With respect to the limits to which the number systems of the various uncivilized races of the earth extend, recent anthropological research has developed many interesting facts. In the case of the Chiquitos and a few other native races of Bolivia we found no distinct number sense at all, as far as could be judged from the absence, in their language, of numerals in the proper sense of the word. How they indicated any number greater than _one_ is a point still requiring investigation. In all other known instances we find actual number systems, or what may for the sake of uniformity be dignified by that name. In many cases, however, the numerals existing are so few, and the ability to count is so limited, that the term _number system_ is really an entire misnomer.

Among the rudest tribes, those whose mode of living approaches most nearly to utter savagery, we find a certain uniformity of method. The entire number system may consist of but two words, _one_ and _many_; or of three words, _one_, _two_, _many_. Or, the count may proceed to 3, 4, 5, 10, 20, or 100; passing always, or almost always, from the distinct numeral limit to the indefinite _many_ or several, which serves for the expression of any number not readily grasped by the mind. As a matter of fact, most races count as high as 10; but to this statement the exceptions are so numerous that they deserve examination in some detail. In certain parts of the world, notably among the native races of South America, Australia, and many of the islands of Polynesia and Melanesia, a surprising paucity of numeral words has been observed. The Encabellada of the Rio Napo have but two distinct numerals; _tey_, 1, and _cayapa_, 2.[20] The Chaco languages[21] of the Guaycuru stock are also notably poor in this respect. In the Mbocobi dialect of this language the only native numerals are _yña tvak_, 1, and _yfioaca_, 2. The Puris[22] count _omi_, 1, _curiri_, 2, _prica_, many; and the Botocudos[23] _mokenam_, 1, _uruhu_, many. The Fuegans,[24] supposed to have been able at one time to count to 10, have but three numerals,--_kaoueli_, 1, _compaipi_, 2, _maten_, 3. The Campas of Peru[25] possess only three separate words for the expression of number,--_patrio_, 1, _pitteni_, 2, _mahuani_, 3. Above 3 they proceed by combinations, as 1 and 3 for 4, 1 and 1 and 3 for 5. Counting above 10 is, however, entirely inconceivable to them, and any number beyond that limit they indicate by _tohaine_, many. The Conibos,[26] of the same region, had, before their contact with the Spanish, only _atchoupre_, 1, and _rrabui_, 2; though they made some slight progress above 2 by means of reduplication. The Orejones, one of the low, degraded tribes of the Upper Amazon,[27] have no names for number except _nayhay_, 1, _nenacome_, 2, _feninichacome_, 3, _ononoeomere_, 4. In the extensive vocabularies given by Von Martins,[28] many similar examples are found. For the Bororos he gives only _couai_, 1, _maeouai_, 2, _ouai_, 3. The last word, with the proper finger pantomime, serves also for any higher number which falls within the grasp of their comprehension. The Guachi manage to reach 5, but their numeration is of the rudest kind, as the following scale shows: _tamak_, 1, _eu-echo,_ 2, _eu-echo-kailau,_ 3, _eu-echo-way,_ 4, _localau_, 5. The Carajas counted by a scale equally rude, and their conception of number seemed equally vague, until contact with the neighbouring tribes furnished them with the means of going beyond their original limit. Their scale shows clearly the uncertain, feeble number sense which is so marked in the interior of South America. It contains _wadewo_, 1, _wadebothoa_, 2, _wadeboaheodo_, 3, _wadebojeodo_, 4, _wadewajouclay_, 5, _wadewasori_, 6, or many.

Turning to the languages of the extinct, or fast vanishing, tribes of Australia, we find a still more noteworthy absence of numeral expressions. In the Gudang dialect[29] but two numerals are found--_pirman_, 1, and _ilabiu_, 2; in the Weedookarry, _ekkamurda_, 1, and _kootera_, 2; and in the Queanbeyan, _midjemban_, 1, and _bollan_, 2. In a score or more of instances the numerals stop at 3. The natives of Keppel Bay count _webben_, 1, _booli_, 2, _koorel_, 3; of the Boyne River, _karroon_, 1, _boodla_, 2, _numma_, 3; of the Flinders River, _kooroin_, 1, _kurto_, 2, _kurto kooroin_, 3; at the mouth of the Norman River, _lum_, 1, _buggar_, 2, _orinch_, 3; the Eaw tribe, _koothea_, 1, _woother_, 2, _marronoo_, 3; the Moree, _mal_, 1, _boolar_, 2, _kooliba_, 3; the Port Essington,[30] _erad_, 1, _nargarick_, 2, _nargarickelerad_, 3; the Darnly Islanders,[31] _netat_, 1, _naes_, 2, _naesa netat_, 3; and so on through a long list of tribes whose numeral scales are equally scanty. A still larger number of tribes show an ability to count one step further, to 4; but beyond this limit the majority of Australian and Tasmanian tribes do not go. It seems most remarkable that any human being should possess the ability to count to 4, and not to 5. The number of fingers on one hand furnishes so obvious a limit to any of these rudimentary systems, that positive evidence is needed before one can accept the statement. A careful examination of the numerals in upwards of a hundred Australian dialects leaves no doubt, however, that such is the fact. The Australians in almost all cases count by pairs; and so pronounced is this tendency that they pay but little attention to the fingers. Some tribes do not appear ever to count beyond 2--a single pair. Many more go one step further; but if they do, they are as likely as not to designate their next numeral as two-one, or possibly, one-two. If this step is taken, we may or may not find one more added to it, thus completing the second pair. Still, the Australian's capacity for understanding anything which pertains to number is so painfully limited that even here there is sometimes an indefinite expression formed, as many, heap, or plenty, instead of any distinct numeral; and it is probably true that no Australian language contains a pure, simple numeral for 4. Curr, the best authority on this subject, believes that, where a distinct word for 4 is given, investigators have been deceived in every case.[32] If counting is carried beyond 4, it is always by means of reduplication. A few tribes gave expressions for 5, fewer still for 6, and a very small number appeared able to reach 7. Possibly the ability to count extended still further; but if so, it consisted undoubtedly in reckoning one pair after another, without any consciousness whatever of the sum total save as a larger number.

The numerals of a few additional tribes will show clearly that all distinct perception of number is lost as soon as these races attempt to count above 3, or at most, 4. The Yuckaburra[33] natives can go no further than _wigsin_, 1, _bullaroo_, 2, _goolbora_, 3. Above here all is referred to as _moorgha_, many. The Marachowies[34] have but three distinct numerals,--_cooma_, 1, _cootera_, 2, _murra_, 3. For 4 they say _minna_, many. At Streaky Bay we find a similar list, with the same words, _kooma_ and _kootera_, for 1 and 2, but entirely different terms, _karboo_ and _yalkata_ for 3 and many. The same method obtains in the Minnal Yungar tribe, where the only numerals are _kain_, 1, _kujal_, 2, _moa_, 3, and _bulla_, plenty. In the Pinjarra dialect we find _doombart_, 1, _gugal_, 2, _murdine_, 3, _boola_, plenty; and in the dialect described as belonging to "Eyre's Sand Patch," three definite terms are given--_kean_, 1, _koojal_, 2, _yalgatta_, 3, while a fourth, _murna_, served to describe anything greater. In all these examples the fourth numeral is indefinite; and the same statement is true of many other Australian languages. But more commonly still we find 4, and perhaps 3 also, expressed by reduplication. In the Port Mackay dialect[35] the latter numeral is compound, the count being _warpur_, 1, _boolera_, 2, _boolera warpur_, 3. For 4 the term is not given. In the dialect which prevailed between the Albert and Tweed rivers[36] the scale appears as _yaburu_, 1, _boolaroo_, 2, _boolaroo yaburu_, 3, and _gurul_ for 4 or anything beyond. The Wiraduroi[37] have _numbai_, 1, _bula_, 2, _bula numbai_, 3, _bungu_, 4, or many, and _bungu galan_ or _bian galan_, 5, or very many. The Kamilaroi[38] scale is still more irregular, compounding above 4 with little apparent method. The numerals are _mal_, 1, _bular_, 2, _guliba_, 3, _bular bular_, 4, _bular guliba_, 5, _guliba guliba_, 6. The last two numerals show that 5 is to these natives simply 2-3, and 6 is 3-3. For additional examples of a similar nature the extended list of Australian scales given in