No one has yet explained why, when counting to 1023 is possible, we get through most of our lives only getting to 10 and never get any feeling of "waste". So then... why?
It's all due to redundancy. How many ways are there of representing 1 in the usual system? Ten. And two? Forty-five. Five can be made in no less than 15120 ways.
The ideal system would have only one way of representing each number, to make best use of the possible combinations. The "finger up, finger down" system meets this criterion, since it is effectively a model of binary which we know gives any integer a unique representation.
However, representing the number n in the preschool way is possible in 10Cn different ways; this also shows why 10 is the highest number we can possibly make with this system.
Hence, the preschool system has very high redundancy by duplicity, whereas the previously suggested binary system has none.