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From: Wei Dai <weidai.domain.name.hidden>

Date: Tue, 17 Oct 2000 02:59:39 -0700

On Fri, Oct 13, 2000 at 08:25:39PM -0700, hal.domain.name.hidden wrote:

*> I'm not sure it would be zero. The program for the CSO is not
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*> particularly complex compared to other observer programs. If you have the
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*> program for a constant-speed observer then you only need to simulate the
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*> program, inserting ever increasing delays between simulated clock cycles.
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*>
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*> Now all you have to do is wait infinity+1 ticks of the UTM and you will
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*> have your CSO at subjective time 1, and the program to create him was
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*> not particularly long or unlikely.
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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
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*> infinite amount of computation to solve, but whose solutions could be
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*> tested in finite time. Is this a theorem of computational theory?
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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
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*> RAC; for example, if the laws of physics appear to be such as to allow
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*> for infinitely fast computation, then it might be that we believe in
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*> the RAC due to our understanding of the details of its construction.
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*> It's like our belief today in the correctness of large proofs that can
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*> only be verified by computer.
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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.

Received on Tue Oct 17 2000 - 03:04:40 PDT

Date: Tue, 17 Oct 2000 02:59:39 -0700

On Fri, Oct 13, 2000 at 08:25:39PM -0700, hal.domain.name.hidden wrote:

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.

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.)

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.

Received on Tue Oct 17 2000 - 03:04:40 PDT

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