Thanks for that explanation Hal. I'd been wondering what Saibal was on
about!
Cheers
Hal Finney wrote:
>
> Saibal Mitra writes:
> > Shouldn't the probability go to zero faster than 1/2^n ? If you consider the
> > sequence of programs p_{k} were p_{k} will run k idintical copies of a
> > certain observer. The probability that the observer finds himself in p_{i}
> > should be i times the measure of P_{i}. I conclude that the measure of p{i}
> > should go to zero faster than 1/i. The length of the program is some
> > constant plus Log(i)/Log(2), therefore, if the measure depends only on
> > program length, it should go to zero faster than 1/2^n.
>
> It is true, adding a counter of length Log(k)/Log(2) would allow a program
> to create k duplicates. Increasing the program by this length (which is
> log to the base 2 of k) will reduce its measure by a factor of 2^length
> which is k. So these factors balance out.
>
> It is similar to extending the length of a program by n unused bits.
> This creates 2^n functionally identical programs corresponding to the
> 2^n possible values of the n unused bits. But it reduces the measure
> of each one by a factor of 2^n, which balances.
>
> These considerations are what lead to the factor of 2^n for comparing
> the measure of two programs whose length differs by n.
>
> Hal Finney
>
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Received on Wed Jun 19 2002 - 17:15:45 PDT