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 develop- 

 ment. 



The Origin of the MatJiematical 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 AYood-Indians are said not to count beyond two. 

 Many Australian tribes only have words for one and two, 

 Avhich 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 descrip- 

 tion of how one of them w^as 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 w^as 

 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 North-West 

 America count in nearly the same manner, and most of the 

 tribes of South America are no further advanced.^ The 

 Kaffirs 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 



' Lubbock's Origin of Civilisation, fourth edition, pp. 434-440 ; Tylor's 

 Primitive Ctdture, chap. vii. 



'^ It has beeu recently stated that some of these facts are erroneous, and 

 that .some Australians can keep accurate reckoning up to 100, or more, when 



