Dan Fabulich, <email@example.com>, writes:
> Tipler's argument leads me to hold that unless we actually have infinite
> computing power, life will not go on forever in any meaningful sense of
> the word. Infinite time is not infinite life.
Actually I am beginning to think that it is worse than this. We not only need infinite computing power, we may need infinite information, that is, we may require in effect an infinite amount of "noise".
Imagine an infinitely powerful but completely self contained computer. Start it with a seed program that has only a finite amount of information. (Imagine a Game of Life pattern surrounded by an infinite but empty plain.) Now, it can run forever, but ultimately the amount of information in the program cannot increase. Everything it ever does was determined by the initial allocation of information it got.
Consider in contrast an infinite computer with an infinite supply of information, for example, a Game of Life simulation on an infinite plain which is randomly populated. In this situation the future course of the program is completely unpredictable. It can evolve and display an infinite number of possible variations, incorporating an infinite amount of information into its structure by "observing" the universe around it.
I am not 100% sure whether this is really an issue, whether it is a true limitation on a program that its ultimate ramifications are completely determined by the fixed and finite initial allocation of information it receives. A conscious program could seemingly still evolve through an infinity of new states, never looping, never falling into a fixed pattern. It's not clear how significant it is that all of this evolution was in a sense illusory in that it does not generate new information.