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 dialect29 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 Yuckaburra33 natives can go no further than wigsin, 1, bullaroo, 2, goolbora, 3. Above here all is referred to as moorgha, many. The Marachowies34 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 dialect35 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 rivers36 the scale appears as yaburu, 1, boolaroo, 2, boolaroo yaburu, 3, and gurul for 4 or anything beyond. The Wiraduroi37 have numbai, 1, bula, 2, bula numbai, 3, bungu, 4, or many, and bungu galan or bian galan, 5, or very many. The Kamilaroi38 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 Chapter V. may be consulted.
Taken as a whole, the Australian and Tasmanian tribes seem to have been distinctly inferior to those of South America in their ability to use and to comprehend numerals. In all but two or three cases the Tasmanians39 were found to be unable to proceed beyond 2; and as the foregoing examples have indicated, their Australian neighbours were but little better off. In one or two instances we do find Australian numeral scales which reach 10, and perhaps we may safely say 20. One of these is given in full in a subsequent chapter, and its structure gives rise to the suspicion that it was originally as limited as those of kindred tribes, and that it underwent a considerable development after the natives had come in contact with the Europeans. There is good reason to believe that no Australian in his wild state could ever count intelligently to 7.40
In certain portions of Asia, Africa, Melanesia, Polynesia, and North America, are to be found races whose number systems are almost and sometimes quite as limited as are those of the South. American and Australian tribes already cited, but nowhere else do we find these so abundant as in the two continents just mentioned, where example after example might be cited of tribes whose ability to count is circumscribed within the narrowest limits. The Veddas41 of Ceylon have but two numerals, ekkameī, 1, dekkameï, 2. Beyond this they count otameekaï, otameekaï, otameekaï, etc.; i.e. “and one more, and one more, and one more,” and so on indefinitely. The Andamans,42 inhabitants of a group of islands in the Bay of Bengal, are equally limited in their power of counting. They have ubatulda, 1, and ikporda, 2; but they can go no further, except in a manner similar to that of the Veddas. Above two they proceed wholly by means of the fingers, saying as they tap the nose with each successive finger, anka, “and this.” Only the more intelligent of the Andamans can count at all, many of them seeming to be as nearly destitute of the number sense as it is possible for a human being to be. The Bushmen43 of South Africa have but two numerals, the pronunciation of which can hardly be indicated without other resources than those of the English alphabet. Their word for 3 means, simply, many, as in the case of some of the Australian tribes. The Watchandies44 have but two simple numerals, and their entire number system is cooteon, 1, utaura, 2, utarra cooteoo, 3, atarra utarra, 4. Beyond this they can only say, booltha, many, and booltha bat, very many. Although they have the expressions here given for 3 and 4, they are reluctant to use them, and only do so when absolutely required. The natives of Lower California45 cannot count above 5. A few of the more intelligent among them understand the meaning of 2 fives, but this number seems entirely beyond the comprehension of the ordinary native. The Comanches, curiously enough, are so reluctant to employ their number words that they appear to prefer finger pantomime instead, thus giving rise to the impression which at one time became current, that they had no numerals at all for ordinary counting.
Aside from the specific examples already