Matt Gingell <mjg223@nyu.edu> Wrote:
>It seems to me that there must be some smallest unit of matter capable of doing
>computation, some sort of computational 'atom', in the ancient Greek sense of
>the word. This would impose an upper bound on the amount of number crunching you
>could possibly do with a finite amount of mass.
Size is as important as mass. If the Beckenstein bound is true ( it probably is but has never been rigorously proven) then the amount of information inside a sphere of radius R that contains energy E is less than or equal to 2*PI*E*R/(h *ln2), h is really h bar. For meters (R) and kilograms (M) that works out to 2.577 *10^43* M*R bits.
A proton has a radius of 10^-15 meters and a mass of 1.67 *10^-27 kilograms, plug that in and you get 44 bits. You'd do a lot better with a Hydrogen atom. The mass is almost the same but it's a lot bigger, about 10^-10 meters, so a hydrogen atom can store 4*10^6 bits.
> if we are being simulated by a computer built in a world whose
>physics match our own, and we are being simulated in real time, then the
>computer simulating us must be at least as big as our entire universe.