The process just indicated may be gone through with at 5, or at 20, thus giving us a quinary or a vigesimal, or, more probably, a mixed system; and, in rare instances, some other number may serve as the point of departure from simple into compound numeral terms.

But the general idea is always the same, and only the details of formation are found to differ.
Without the establishment of some base any _system_ of numbers is impossible.

The savage has no means of keeping track of his count unless he can at each step refer himself to some well-defined milestone in his course.

If, as has been pointed out in the foregoing chapters, confusion results whenever an attempt is made to count any number which carries him above 10, it must at once appear that progress beyond that point would be rendered many times more difficult if it were not for the fact that, at each new step, he has only to indicate the distance he has progressed beyond his base, and not the distance from his original starting-point.
Some idea may, perhaps, be gained of the nature of this difficulty by imagining the numbers of our ordinary scale to be represented, each one by a single symbol different from that used to denote any other number.

How long would it take the average intellect to master the first 50 even, so that each number could without hesitation be indicated by its appropriate symbol?
After the first 50 were once mastered, what of the next 50?
and the next?
and the next?
and so on.