On Fri, Oct 13, 2000 at 08:25:39PM -0700, [EMAIL PROTECTED] wrote: > I'm not sure it would be zero. The program for the CSO is not > particularly complex compared to other observer programs. If you have the > program for a constant-speed observer then you only need to simulate the > program, inserting ever increasing delays between simulated clock cycles. > > Now all you have to do is wait infinity+1 ticks of the UTM and you will > have your CSO at subjective time 1, and the program to create him was > not particularly long or unlikely.

Did you really have in mind something like the following? for (i=0; i<infinity+1; i++) ComputeNextStepOfUniverse(); OutputObserverMoment(); I'm not sure how you can define a model of computation that involves transfinite time (i.e., one where the above program would have a well-defined output). If it is possible, I have a feeling that the model might be equivalent to an UTM that has access to an oracle for the halting problem. > This sounds correct; it's hard to imagine a problem which takes an > infinite amount of computation to solve, but whose solutions could be > tested in finite time. Is this a theorem of computational theory? If the solutions can be tested in finite time, then you can solve the problem by testing all possible solutions, and this process would halt in a finite amount of time. (I'm assuming that "no solution" counts as a solution.) > On the other hand there might be theoretical reasons to believe in the > RAC; for example, if the laws of physics appear to be such as to allow > for infinitely fast computation, then it might be that we believe in > the RAC due to our understanding of the details of its construction. > It's like our belief today in the correctness of large proofs that can > only be verified by computer. It boils down to how to define the measure of observer moments. If you define it with a standard UTM, then nothing can convince you that RACs exist. If the laws of physics appear to allow infinitely fast computation, you'll just assume that you don't have a complete understanding of those laws.