**From:** Marc Geddes (*marc_geddes@yahoo.co.nz*)

**Date:** Tue Aug 17 2004 - 00:58:42 MDT

**Next message:**Eliezer Yudkowsky: "Re: Final draft of my philosophical platform now on line"**Previous message:**Tomaz Kristan: "Re: All is information (was: All is number)"**In reply to:**Christian Szegedy: "Re: Final draft of my philosophical platform now on line"**Next in thread:**Marc Geddes: "Re: Final draft of my philosophical platform now on line"**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ] [ attachment ]

--- Christian Szegedy <szegedy@or.uni-bonn.de> wrote:

*> >
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*> There are methamatically definable functions that
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*> are
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*> not Turing computable. For example the function
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*> defined by the halting problem is a well-known
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*> example
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*> for that:
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*> Let T be a fixed universal Turing machine. For a
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*> sequence
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*> s of bits let f(s)=true if T stops on input s, false
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*> otherwise.
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*> Function f is clearly well-defined, and it is simple
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*> to see that
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*> it is not Turing computable.
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*>
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*Sigh* Yes I am very well aware of this very basic

fact. Read what I said again. Note my use of the

word 'FINITE' in my paragraph.

Those so-called 'uncomputable' functions are totally

misinterpreted by ameuter science writers and

arm-chair philosophers.

All the word 'uncomputable' really means in the

technical sense is that the mathematical function in

question has infinite (or trans-finite) complexity.

This is purely an artifact of human defintions - an

infinite array of what are actually *finite* entirely

computable functions have simply all been lumped

together and misinterpreted by humans as a 'single'

function.

Any finite section of those so-called 'uncomputable'

functions are in fact totally computable. So we can

in fact compute the function to any desired degree of

accuracy. That is all we need.

=====

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- Gen. John Stark

"The Universe...or nothing!"

-H.G.Wells

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