Negentropy Overrated?

Quoting from your linked post:

Anything you can compute using an infinite amount of negentropy, time T, and space S, can be computed using only about S negentropy if you are willing to spend a little bit of extra space and time (S log T and T^1.5, for example, or S and 2^S * T). So future universes may be constrained by available space and time rather than negentropy,

I don't understand the conclusion here. It sounds like the set of potential computations we can do is a (somewhat complicated) function of available time, space, and negentropy. Given a fix... (read more)

In general, a source of unlimited negentropy buys you only a small polynomial increase in the available time and space. So negentropy does matter, but the total amount of computation you can do is dominated by the available space and time rather than the available negentropy.

In the limit where you have exponentially more time than space (say, the universe turns out to be some arbitrary reversible bounded cellular automaton) then entropy does no good at all.

Negentropy Overrated?

by paulfchristiano 1 min read29th Dec 201132 comments


This post may be interesting to some LWers.

In summary: it looks like our universe can support reversible computers which don't create entropy. Reversible computers can simulate irreversible computers, with pretty mild time and space blowup. So if moral value comes from computation, negentropy probably won't be such an important resource for distant future folks, and if the universe lasts a long time we may be able to simulate astronomically long-lived civilizations (easily 10^(10^25) clock cycles, using current estimates and neglecting other obstructions). 

Has this been discussed before, and/or is there some reason that it doesn't work or isn't relevant? I suspect that this consideration won't matter in the long run, but it is at least interesting and seems to significantly deflate (long-run) concerns about entropy.