Well, here's why it's not that simple....I can make any number N have a kolmogorov complexity number equal to 1--if the Turing machine has N+1 symbols :-) I ju

Well, here's why it's not that simple....I can make any number N have a kolmogorov complexity number equal to 1--if the Turing machine has N+1 symbols :-) I just express the number in base N. (which will bet "10" for any base :-) It true that we typically limit ourselves to binary when we are proving theorems, etc in Kolmogorov complexity. You can prove that for any two turing machines U and V, KU(X) <= KV(X) + O(1).....but this relies on the fact that there is an O(1)-sized program which lets U emulate V, and V emulate U. And that is only true if U and V share the same symbol set. If they don't, then the kolmogorov complexity of the two machines can be made arbitrarily different from each other, just by changing the symbol set.