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Show 464 DARWINISM CHAP. required to account for them. If this can be clearly shown for any one or more of the special faculties of intellectual man, we shall be justified in assuming that the same unknown cause or power may have had a much wider influence, and may have profoundly influenced the whole course of his development. The Origin of the Mathematical Faculty. We have ample evidence that, in all the lower races of man, what may be termed the mathematical faculty is, either absent, or, if present, quite unexercised. The Bushmen and the Brazilian Wood-Indians are said not to count beyond two. Many Australian tribes only have words for one and two, which are combined to make three, four, five, or six, beyond which they do not count. The Damaras of South Africa only count to three; and Mr. Galton gives a curious description of how one of them was hopelessly puzzled when he had sold two sheep for two sticks of tobacco each, and received four sticks in payment. He could only :find out that he was correctly paid by taking two sticks and then giving one sheep, then receiving two sticks more and giving the other sheep. Even the comparatively intellectual Zulus can only count up to ten by using the hands and fingers. The Ahts of N orth-vVest America count in nearly the same manner, and most of the tribes of South America are no further ad vanced.1 The Ka:ffirs have great herds of cattle, and if one is lost they miss it immediately, but this is not by counting, but by noticing the absence of one they know ; just as in a large family or a school a boy is missed without going through the process of counting. Somewhat higher races, as the Esquimaux, can count up to twenty by using the hands and the feet; and other races get even further than this by saying " one man " for twenty, "two men" for forty, and so on, equivalent to our rural mode of reckoning by scores. From the fact that so many of the existing savage races can only count to four or five, Sir John Lubbock thinks it improbable that our earliest ancestors could have counted as high as ten. 2 l Lubbock's Origin uf Civilisation, fourth edition, pp. 434-440 ; Tylor's Primitive Culture, chap. vii. 2 It has been recently stated that some of these facts are erroneous, and that some Australians can keep accurate reckoning up to 100, or more, when XV DARWINISM APPLIED TO MAN 465 When we turn to the more civilised races we find the ~se of numbers and the art of countinO' greatly extended lj ven the Tongas of the South Sea isla~ds are said to hav~ _1een able to count as high as l 00,000. But mere countIn~ does not imply either the possession or the u~e of anythmg. that can. be really called the mathematical faculty, the e_x:ercise o~ which ~n any broad sense ha only been possible smce the mtroductwn of the decimal notation. The Greeks the Romans, the Egyptians, the Jews, and the Chinese had al~ such . cumbrous systems, that anything like a science of anthmetJC, beyond very simple operations, was irnpo::siblc ; ~d the Roman system, by-whi<.;h the year 1888 would be written DCCCLXXXVIII, was that in common use in Europe down to the fourteenth or fifteenth centuries, and even much later in some places. Algebra, which was invented by the Hindoos from whom al~o came .the decimal notation, was not introduced into Euro~e till the ~hir~eenth century, although the Greeks had some acqu~mtance. wtth It; and it reached \Y estern Europe from Italy only m the sixteenth century.1 It was, no doubt, owing to the absence of a sound system of numeration that the mathematical ta~ent of tho. Greeks .was directed chiefly to geometry, in which scien~e Euch?, Archimedes, and others made "Uch brilliant discover~ e~ .. It Is, however, during the last three centuries only that the civ.Ihsed world appears to have become con cious of tl:c possesswn of a mar;ellous faculty which, when supplied with the necessary tools m the decimal notation, the elements of al.gebra ~nd geot?etry, and the power of rapidly communicating d1scovenes and Ideas by the art of. printing, has developed to an extent, the full grandeur of whiCh can be appreciated only by those who have devoted some time (even if unsuccessfully) to the study. The facts now set forth as to the almo t total ah once of ~ath~matical fa?ulty in savages and its wonderful development m qmte recent t1mes, are exceedingly suggestive, and in regard ~equir~cl. But this ~oes not alter the general fact that many low races, mclud1ng tl1e Austrahans, have no words for high !lUmbers and never require t~ use th~m: !f they are now, with a little practice, able to count much higher, th1s mchcates the possession of a facnlty which could not have been d?veloped under the law of utility only, since the absence of words for such h1gf nu~1bers s~ows t.ha~ they were neither used nor required. Art1cle Antbmetlc m Eng. Cyc. of Arts and Science$, 2H |