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 fixed amount of time and space, we can do more computations if we had more negentropy, right? So in what sense would we not be constrained by negentropy?
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.
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.
Ok, I see, but this assumes that once you’ve completed a computation, a second execution of it has no moral value, right? (Because more negentropy would allow you to drive the reversible computation forward faster and complete more executions in the same available time.)
Yes—if over the course of your computation you explore on a fraction X of all possible states of the computer, a supply of infinite negentropy would allow you to run the computation something like 1/X faster.
Quoting from your linked post:
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 fixed amount of time and space, we can do more computations if we had more negentropy, right? So in what sense would we not be constrained by negentropy?
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.
Ok, I see, but this assumes that once you’ve completed a computation, a second execution of it has no moral value, right? (Because more negentropy would allow you to drive the reversible computation forward faster and complete more executions in the same available time.)
Yes—if over the course of your computation you explore on a fraction X of all possible states of the computer, a supply of infinite negentropy would allow you to run the computation something like 1/X faster.