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Welcome to my blog, which was once a mailing list of the same name and is still generated by mail. Please reply via the "comment" links.

Always interested in offers/projects/new ideas. Eclectic experience in fields like: numerical computing; Python web; Java enterprise; functional languages; GPGPU; SQL databases; etc. Based in Santiago, Chile; telecommute worldwide. CV; email.

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© 2006-2017 Andrew Cooke (site) / post authors (content).

On Computable Numbers, with an application to the Entscheidungsproblem

From: "andrew cooke" <andrew@...>

Date: Mon, 9 Jan 2006 05:56:04 -0300 (CLST) 

Working through this text by Chaitin -
http://www.cs.auckland.ac.nz/CDMTCS/chaitin/unm.html - I decided I needed
to read the original.  Eventually I found bibliography section of Andrew
Hodges's site (the author of the major Turing autobiography) -
http://www.turing.org.uk/sources/biblio4.html - which gives online links.

http://www.emula3.com/docs/OnComputableNumbers.pdf

"In §8 I examine certain arguments which would seem to prove the contrary.
By the correct application of one of these arguments, conclusions are
reached which are superficially similar to those of Gödel [1] . These
results {231} have valuable applications. In particular, it is shown (§11)
that the Hilbertian Entscheidungsproblem can have no solution."

Andrew

Fits 64 bits of Omega

From: "andrew cooke" <andrew@...>

Date: Mon, 9 Jan 2006 13:59:13 -0300 (CLST) 

Didn't seem worth a new post, but here's a link to someone calculating the
first 64 bits of Omega -
http://www.expmath.org/expmath/volumes/11/11.3/Calude361_370.pdf

And here they are:
0000001000000100000110001000011010001111110010111011101000010000

Andrew

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