From: Marc Geddes (email@example.com)
Date: Tue Aug 17 2004 - 00:58:42 MDT
--- Christian Szegedy <firstname.lastname@example.org> wrote:
> There are methamatically definable functions that
> not Turing computable. For example the function
> defined by the halting problem is a well-known
> for that:
> Let T be a fixed universal Turing machine. For a
> s of bits let f(s)=true if T stops on input s, false
> Function f is clearly well-defined, and it is simple
> to see that
> it is not Turing computable.
*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
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'
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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