Juergen: > I think we may not ignore infinities for quite pragmatic, > non-esoteric reasons. Many believe the history of our own universe > will be infinite - certainly there is no evidence against this > possibility. Also, any finite never-halting program for a virtual > reality corresponds to an infinite history. TOEs ignoring this seem > unnecessarily restrictive.
Yes, I agree. I think my objection was to those infinite representations... > What you cannot construct in finite time is just a particular > representation of Pi, namely, the one consisting of infinitely many > digits. But this is not a problem of Pi, it is a problem of this > particular representation. There are better, finite, unambiguous > representations of Pi: its programs. You can manipulate them, copy > them, insert into other finite programs and theorem provers, etc. > Proofs of Pi's properties are essentially proofs of properties of > Pi's programs. Yes, ok, I see the distinction now. I think I was arguing against the use of "Pi as a process" as a fundamental building block of a Theory of Everything. i.e. We cannot reasonably expect the function Pi() to return a value that we will use during some step in a series to perform some calculation. >> Juergen, what do you think about the minimal cellular automaton? Is >> it a good candidate ATOE (algorithmic theory of everything)? > > it depends - minimal for what purpose? Minimal in the sense that the computational process that these automata represent cannot be simplified. Since there are no unreachable configurations for a minimal cellular automaton, no part of the computation can be thrown out. In contrast, non-minimal automata (most CA) have certain configurations that are never reached, and thus, we can rewrite them as a new automaton using fewer states per cell. Joel