From: Peter Kirk (email@example.com)
Date: Thu Oct 16 2003 - 15:31:55 CST
On 16/10/2003 13:12, John Cowan wrote:
>Asmus Freytag scripsit:
>>PS: private answer to Jill: make sure that your characters are always
>>represented internally by infinite precision integers.
>Actually, the intractability of the transfinite ordinals shows us that
>there can be no such thing. Ordinary "infinite precision" integers
>begin with a fixed-size length word saying how many words (for whatever
>definition of "word") follow. But eventually the fixed-size length
>word will overflow, and must be replaced by a variable-sized length
>word, itself prefixed by a length^2 word. But eventually the length^2
>word will overflow, and must be replaced .... But eventually the number
>of length words will become too large, and the length-length word will
>overflow, requiring ... But then ...
>You can't win.
But what if you use a null terminated string, and precede it with
decimal digits (what's a bit of inefficiency when you are talking about
infinity?) or any encoding in which null is not a valid part of the
number? Then the precision is truly infinite, surely (at least to the
first transfinite number), except that if the universe is finite there
is an ultimate limit on storage capacity.
It all reminds me of a book I read, not intended as science fiction but
as a real contribution to science and philosophy, which predicted that
the universe would collapse but as it collapses be converted into a
giant computer whose speed would increase exponentially (or something)
as it collapsed in such a way that in the finite time before the
collapse it could perform an infinite number of calculations. Which had
some rather interesting consequences, but they go well off topic!
-- Peter Kirk firstname.lastname@example.org (personal) email@example.com (work) http://www.qaya.org/
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