Quoting mcintosh@servidor.unam.mx:
Quoting asimovd@aol.com:
I forget who mentioned that e was found to be the "best" number base. I would like to know in what sense it is best -- or is this just some kind of offhand, non-rigorous comment?
My memory is very hazy about this, but doesn't the result go back to Shannon and have something to do with entropy?
I didn't find Petersen's book on coding theory but my memory has improved somewhat. Entropy is p ln(p) summed over alternatives. It vanishes for p = 0 and p = 1, with a maximum somewhere inbetween, say at p = 1/e. That isn't integral, but it lies close to either 1/2 or 1/3; being that it is a fairly round maximum, either will work pretty well and better than some other approximation. The former leads to binary coding, where the best choice is to split things in half even though it can lead to lots of bits in a numerical value. Folklore holds that von Neumann used this optimization to justify using binary hardware for computing directly without passing through decade counters and interconversion from binary flipflops to decimal finger based tradition. Folklore also holds that CMOS can be a good thing with three levels: +, 0, - because it is still near the optimum even if on the other side. - hvm ------------------------------------------------- Obtén tu correo en www.correo.unam.mx UNAMonos Comunicándonos