Which base?
If the choice of a base were left to a group of experts, we should probably witness a conflict between who would adopt a composite base and and who would want a prime number for a base.
As Dantzig states, a practical man, would insist on a base with the greatest number of divisors, such as twelve, while the mathematician would want a prime number, such as seven or eleven.
Dantzig also reports an example: the great mathematician Lagrange claimed that a prime base is far more advantageous. He pointed to the fact that with a prime base every systematic fraction would be irreducible and would therefore represent the number in a unique way. In our present numeration, for instance, the decimal fraction 0.36 stands really for many fractions: 36⁄100, 18⁄50, and 9⁄25 ….
Such an ambiguity would be considered lessened if a prime base, such as eleven, were adopted.
The base that the most of us uses every day is ten which is neither prime nor has it a sufficient number of divisors. In an age, when calculating devices have largely supplanted mental arithmetic, probably we would choose a different number for base. But the tradition of counting by tens is so firm, that the challenge seems impossible. As long as man counts by tens, his ten fingers will remind him of the human origin of this important phase of his mental life.
