Re: The Rapidly-Accelerating Computer

From: <hal.domain.name.hidden>
Date: Fri, 13 Oct 2000 20:25:39 -0700

Wei writes:
> If you follow my suggestion that the measure of an
> observer moment is equal to its universal a priori probability (which is
> defined as the probability that a universal Turing machine with a
> uniformly random input tape will produce that output), then the measure
> of the CSO at subjective time 1 is zero (unless you count observers
> having hallucinations that they are the CSO at subjective time 1).

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.

The hard part here is to understand the behavior of a TM that can run
for a transfinite number of ticks. If such things are possible, then
the CSO at time 1 does not necessarily have a small measure.

> Suppose someone said he had access to a RAC. How could he prove it to
> you? The most he could do is show that he could solve any problem that
> you can verify the solution of, but unless you already had access to a
> RAC, all such problems can be solved in finite time on a regular Turing
> machine. For an observer that starts out with finite computing resources,
> there is no way to verify that anything purported to be a RAC actually is
> one, so there is no possible empirical reason for him not to believe that
> RACs don't exist.

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?

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.

Hal
Received on Fri Oct 13 2000 - 20:39:06 PDT