Re: Hey CANTORIANS!! HOW MANY DIGITS?

From: |-|erc (h_at_r.c)
Date: 01/09/05 

Date: Sun, 9 Jan 2005 10:55:42 +1000

"The Ghost In The Machine" <ewill@sirius.athghost7038suus.net> wrote in
> In sci.logic, |-|erc
> <h@r.c>
> wrote
> on Sat, 8 Jan 2005 17:59:06 +1000
> <349i5tF46q2ljU1@individual.net>:
> > (A)
> > SEQUENCE = <314159265..........................................................................>>
> >
> > <--- HOW MANY DIGITS???--->
> >
> >
> >
> > (B)
> > COMPUTABLES
> > 1 <398498498.................>
> > 2 <484849848.................>
> > 3 <383873838.................>
> > ..
> >
> > How many digits of (A) appear in correct sequence in (B), guaranteed?
>
> (a) presumably is pi, though you've not given an explicit computation
> therefor (however, that's a minor detail, as almost everyone,
> with the possible exception of S. Enterprize, has memorized
> at least 5, and probably more, digits thereof).
>
> (b) looks like FumbleFingered Typing(tm). Did you have an explicit
> construction method, or is this generated by, say, the
> number of muons falling through a certain region of a
> detector unit?
>
> (c) I should mention that the digit sequence of pi is computable
> using a Turing machine; the simplest method I can think of
> involves a modified Maclaurin sequence based on
> 16 * atan(1/5) - 4 * atan(1/239); since the tape is infinite
> the primary problems are technical ones, plus the issue
> that, when extending the accumulator, the entire computation
> may have to be redone over that accumulator. There are
> probably more elegant methods.
>
> Therefore, pi may be included in your computables list.
> But without (b) it's hard to say.
>

B is the output of a UTM(number, digit) mod 10

Yes pi appears on a UTM, but you have to *guarantee* <314159265.................>
is on there, (how many digits are guaranteed to be on the list)
Ambiguous but you can't assume it is pi, (here).

Herc

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