Re: every number has its own significance.....
From: Rob Warnock (rpw3_at_rpw3.org)
Date: 11/28/05
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Date: Mon, 28 Nov 2005 05:18:28 -0600
Unruh <unruh-spam@physics.ubc.ca> wrote:
+---------------
| run_signature_script_for_my_email@INVALID.com (laura fairhead) writes:
| >>As to the notion of measuring interest by the inverse of the
| >>minimal size of a descriptive formula, that's ground that
| >>Chaitin has addressed (check out his Web site).
|
| >His ? Or hers ?! I checked out Professor Chaitin-Chatelin's website
| >which has some extremely interesting papers but I couldn't find
| >anything like this; have I got the wrong Chaitin ?
|
| Probably. Definitely a "his".
+---------------
Try <http://www.cs.umaine.edu/~chaitin/>, and especially w.r.t. the notion
of "interesting numbers", <http://www.cs.umaine.edu/~chaitin/summer.html>,
which shows how the Berry Paradox ["The first positive integer that can't
be named in less than a billion bytes"] when combined with the notion of
complexity based on program size leads to simple alternative ways of
demonstrating such things as Gödel's Proof and Turing's Halting
Problem.
+---------------
| Chaitin/Kolmagorov developed a notion of the
| entropy of a string by defining it to be the shortest program in some
| language which will print out that string. There is always a program a
| little longer than the string ( Print <string>). This is a relational
| entropy since it depends on the language used.
+---------------
Though in <http://www.cs.umaine.edu/~chaitin/lisp.html> (and elsewhere)
Chaitin shows that the language used to implement the UTM "decompressor"
at most changes the result by a constant (~400 bits for the non-standard
dialect of Lisp he uses). So that while the absolute length of a
single "shortest program" in a single language does indeed depend
on the language, the results when comparing the shortest program to
generate String A versus String B when using language X will be the
same as when comparing String A versus String B when using language Y.
In this sense, then, his results *are* language-independent.[1]
-Rob
[1] Which is why I don't understand why he didn't use one of the
more standard Lisps such as Common Lisp or Scheme rather than
inventing his own stunted[2] hard-to-read version. It would
have only changed the results by a very small constant.
[2] E.g., his requires *only* fixed-arity functions: no &OPTIONAL,
&KEY, or &REST arguments [what are called "varargs" in C].
-----
Rob Warnock <rpw3@rpw3.org>
627 26th Avenue <URL:http://rpw3.org/>
San Mateo, CA 94403 (650)572-2607
- Previous message: Rev Turd Fredericks: "Re: Jos olet USAssa .. ala koskaan muuta takaisin Suomeen .... omat kokemukseni vuodesta 2002"
- In reply to: Unruh: "Re: every number has its own significance....."
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