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SCIENCE AND AFRICA  CHAPMAN
to count the fingers and toes with the aid of marks in the sand with-out a system of numerals. A careful study of their social life will reveal why this is so; at any rate it is not a trait that is transmitted through the germ-plasm. 
abstract and concrete numbers
Abstraction, or the ability to abstract, does not imply superior intelligence. It implies that one people have had more a diverse social experience and cultural contact than another, and this is usually due to happy accident. Everyone knows what Cicero said about Anglo-Saxon slaves. But due to diverse social experiences which resulted from contact with alien cultures these "stupid people", as Cicero calls them, produced such men as Bacon, Newton, and Darwin. 
Amongst most primitive folk th eobject is all-important; it's one-rock, one-day, but never just one. As Bertrand Russel says, Man had to wait for thousands of years before entering upon the stage of abstraction; he had to wait until cultural progress created the need for his entry. We think of a number seven without any longer thinking of a particular object or group of objects; we think of a symbol which comes after "6" just before "8" in an arithmetical series. The Zulu, however, when he wishes to express the number six, says, "taking the thumb", (tatisitupa), which means he has counted all the figures on the left hand and is beginning with the thumb on the right. For seven he simply exclaims, "he pointed" (u kombile), which means he has reached his pointing finger. The Niues of the South Pacific say, "one-fruit, two-fruits, three-fruits"; another folk of the South says, "one-grain, two-grains, three-grains", and we frequently employ such usage as the foot, ell, and furlong (furrow long). All this belongs to the concrete stage of counting and in the course of human history these terms lose their concrete meaning and we think of them as abstract. 
Also we should like to remark in passing that men probably wondered about time and space and infinity far earlier than the average student is willing to admit. There is also much talk about a primitive type of "mind" and an advanced type of "mind". These conceptualists rarely pause to consider what it is in fact that they are talking about; they never stop to consider that this whole business about "mind" types is merely a collocation of convenient verbalizations; indeed the scientist's behavior is very similar to that of the primitive he is talking about when he verbalizes about "mind types." This stifling 
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---------- Reopened for Editing 2024-02-09 12:38:59