The dual number points unequivocally to the time when 1 and 2 were _the_ numbers at mankind's disposal; to the time when his three numeral concepts, 1, 2, many, each demanded distinct expression.

With increasing knowledge the necessity for this differentiatuin would pass away, and but two numbers, singular and plural, would remain.

Incidentally it is to be noticed that the Indo-European words for 3--_three_, _trois_, _drei_, _tres_, _tri,_ etc., have the same root as the Latin _trans_, beyond, and give us a hint of the time when our Aryan ancestors counted in the manner I have just described.
The first real difficulty which the savage experiences in counting, the difficulty which comes when he attempts to pass beyond 2, and to count 3, 4, and 5, is of course but slight; and these numbers are commonly used and readily understood by almost all tribes, no matter how deeply sunk in barbarism we find them.

But the instances that have already been cited must not be forgotten.

The Chiquitos do not, in their primitive state, properly count at all; the Andamans, the Veddas, and many of the Australian tribes have no numerals higher than 2; others of the Australians and many of the South Americans stop with 3 or 4; and tribes which make 5 their limit are still more numerous.