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 mc gee] THE BEGINNING OF MA THEM A TICS 653

totemic face-paint or tattoo-mark of the matron, or with the autobiographic calendar of the shaman ; while the industrial devices of early culture are held to absorb and retain a part of the personality of, and indeed to become subjective appendages to, their makers and users. So self-centered thinking is

crystallized by custom, and the thought and custom interact with cumulative effect in dominating the primitive mind well into the upper strata of prescriptorial life ; and numberless ves- tiges of egocentric cosmology cling even unto the higher phases of Aryan culture.

It cannot be too strongly emphasized that primitive thought is unlike the finer product of contemporary intellectuality: The most conspicuous differences are connected with the pervading mysticism and 'prevailing egoism of primitive thinkers, which are magnified in their influence by the fewness of concurrent intel- lectual motives; so that prescriptorial culture may justly be regarded as the outgrowth and outshowing of that mysticism- egoism which began to decline with the birth of writing yet still retains some hold on the minds of men.

Ill

Simple counting is an accomplishment common to men and many lower animals. The special appreciation of numbers some- times displayed by horses, dogs, and pigs may be due to human association, while the geometric sense of the bee may be con- sidered mechanical merely ; yet the well-known ability of the crow to count (or at least to discriminate units) up to six or seven, the similar faculty of the fox, and the habits of wasps in providing fixed numbers of spiders for their unborn progeny, as well as various other examples, demonstrate a native capacity for numerical concepts on the part of birds and mammals and insects. Apparently similar is the numerical capacity of various lowly tribes of different continents : Numerous Australian tribes are described as counting laboriously up to two, three, four, or

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