Wei Dai wrote:
Jason wrote: >I assumed bounded memory due to the limited amount of matter and energy > available to build the computer. For instance I've seen it said that the > total information content of this universe is about 10^90 bits. If a > civilization gathered all the mass and energy available in their universe > to > build a computer, they could only accurately simulate universes with an > information content less than or equal to that of their host universe. But as I said, limited amount of matter and energy only implies limited memory if space is also bounded. See http://en.wikipedia.org/wiki/Bekenstein_bound. By spreading the energy over an ever increasing volume of space, we can obtain unbounded memory. This is essentially the same principle as get an unlimited number of computational steps from finite energy by continually slowing down the rate of computation. So again I don't know why you assume one thing but not the other.
Before you mentioned it in this thread, I was not aware that infinite memory could be obtained through spreading energy over an infinite amount of space. That is a very interesting result, and has forced me to reconsider my original hypothesis. One of my motivations for posting this was to see if anyone on this list could poke holes in or otherwise find problems with my speculation. I thank everyone who responded for their input.
An alternative explanation that I favor for the presence of computational limits is that they are necessary for the evolution of sentience. Without computational limits, an organism can respond to its environment in an apparently intelligent manner by using brute force algorithms, therefore sentience would have little evolutionary advantage.
I see your point. Enegry for metabolism needs to be a limited resource to spur competition and drive evolution. This has the consequence that energy is also limited for other purposes, such as computation.
Therefore it doesn't make sense to place more consideration on the simulated universes when we reason or make choices.
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