Subject: Re: PLOT: A non-parenthesized, infix Lisp!
From: (Rob Warnock)
Date: Fri, 08 May 2009 19:59:33 -0500
Newsgroups: comp.lang.lisp,comp.lang.misc,comp.lang.scheme
Message-ID: <>
Matthias Blume  <> wrote:
| "John Thingstad" <> writes:
| > Well all irrational numbers and particularly all transcendental numbers.
| False. sqrt(2) is irrational -- and I just represented it. Many
| transcendentals are similarly representable as solutions to certain
| equations (just not algebraic ones). Any number you can describe to me
| unambiguously is representable. And -- by that definition -- you cannot
| unambiguously describe to me a particular number that is not
| representable.

Hah! What about numbers you can describe unambiguously but not
compute more than a tiny fraction of their leading bits?!?
[ least, not to better precision than the length of the
program that's doing the computation.] I refer, of course, to
Chaitin's "Omega" <>,
which is a real number between 0 & 1 but is algorithmically random.
[That is, the shortest program to output the first N bits of Omega
must be of size at least N-O(1).] It is not a computable number;
there is no computable function that enumerates its binary expansion.
[See the URL.]


Rob Warnock			<>
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