Have you ever wondered why we chose base 10 for our number system? E.g. 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 etc. and not 0, 1, 2, 10, 11, 12... (base 3).

Obviously, because we have 10 fingers. But that's kind of selfish of us - and should I also say not very mathematical. Tens do not occur often in nature anyways - it just so happens that we have 10 fingers.

Interestingly, before base 10 was universally used, base 11, 12, and 20 have been used. This is shown in our languages. E.g. eleven, twelve, as opposed to oneteen, twoteen; or vingt and quatre-vingt in french.

Base 2 is singled out as the one with the smallest possible base. Only digits 1 and 0 are used. Every other number could be represented by 1's and 0's. So that 1 + 1 = 10 and 1 * 1 = 1. The obvious disadvantage of this binary system is that long expressions are needed to represent even small numbers. E.g. 79 is expressed as 1001111, which is really 7*10^1 + 9*10^0 = 1*2^6 + 0*2^5 + 0*2^4 + 1*2^3 + 1*2^2 + 1*2^1 + 1*2^0. But multiplication is very easy. And other possible problems may also be easily solved with binary. Is this what God uses?

## Tuesday, March 20, 2007

Subscribe to:
Post Comments (Atom)

## No comments:

Post a Comment