We have seen that speech at its origin was so humble as to need gesture to complete and to elucidate it. During its concrete-abstract period, numeration is in an analogous position. At first its extension is very limited: it progresses slowly and painfully from unity. Further, it can operate only when sustained by the concrete; it must have a material accompaniment. Counting is accomplished by the enunciation of words, with the aid of enumerated objects, as perceived at the same time, or with that of the fingers: which, let it be remarked, is the first essay in substitution. There is simultaneously concrete or digital, and verbal numeration.[74] We know that many Australian and South American tribes can count verbally to two only; some say two-one = three; two-two = four; others by the same process arrive at six (two-three = five, three-three = six): everything else is “much.” For the most part they count without words, with the aid of fingers or of articulation; even when they employ words, the two numerations—digital and verbal—are performed simultaneously.[75] This manner of counting is in first degree concrete; the concrete-abstract form is only there in embryo. A great advance, made early enough in many tribes, consisted in counting by five, taking the hand (five fingers) as a new unit, superior to the simple unit. Then: one hand = 5; two hands or half a man = 10; two hands, one foot = 15; two hands, two feet, or a man = 20. Such is the evident origin of the quinary, decimal, and vigesimal numerations. Sometimes fingers, as instruments of numeration, have been replaced by objects of a typical number. Ex.: 1 = moon or sun; 2 = the eyes or legs, etc. However varied these processes (of which only a few have been mentioned) in different races and periods, they are fundamentally identical to the psychologist. They may be reduced to this; numeration is performed more particularly with the aids of sensible perceptions; words are but an insignificant accompaniment, a superfluity—existing only as a proliferation—of so little utility that they are for the most part neglected.