keeping the other two hidden.'[1] Throughout the world, the general relation between finger-counting and word-counting may be stated as follows. For readiness and for ease and apprehension of numbers, a palpable arithmetic, such as is worked on finger-joints or fingers,[2] or heaps of pebbles or beans, or the more artificial contrivances of the rosary or the abacus, has so great an advantage over reckoning in words as almost necessarily to precede it. Thus not only do we find finger-counting among savages and uneducated men, carrying on a part of their mental operations where language is only partly able to follow it, but it also retains a place and an undoubted use among the most cultured nations, as a preparation for and means of acquiring higher arithmetical methods.
Now there exists valid evidence to prove that a child learning to count upon its fingers does in a way reproduce a process of the mental history of the human race; that in fact men counted upon their fingers before they found words for the numbers they thus expressed; that in this department of culture, Word-language not only followed Gesture-language, but actually grew out of it. The evidence in question is principally that of language itself, which shows that, among many and distant tribes, men wanting to express 5 in words called it simply by their name for the hand which they held up to denote it, that in like manner they said two hands or half a man to denote 10, that the word foot carried on the reckoning up to 15,
- ↑ Gumilla, 'Historia del Orenoco,' vol. iii. ch. xlv.; Pott, 'Zählmethode,' p. 16.
- ↑ The Eastern brokers have used for ages, and still use, the method of secretly indicating numbers to one another in bargaining, 'by snipping fingers under a cloth.' 'Every joynt and every finger hath his signification,' as an old traveller says, and the system seems a more or less artificial development of ordinary finger-counting, the thumb and little finger stretched out, and the other fingers closed, standing for 6 or 60, the addition of the fourth finger making 7 or 70, and so on. It is said that between two brokers settling a price by thus snipping with the fingers, cleverness in bargaining, offering a little more, hesitating, expressing an obstinate refusal to go farther, &c., comes out just as in chaffering in words.
