--- John Thornton <jthorn65 at mchsi.com> wrote:
>
> >Btw, all
> >thinking, algorithmic or not, _can_ be represented
> as
> >the output of a Turing machine, but it turns out
> that
> >this is not a useful or illuminating fact beyond
> the
> >most abstract level of analysis. jks
>
> I don't think so. The definition of what is or isn't
> computational (i.e.
> algorithmic) is whether it can or can not be done
> with a Turing machine.
> The Church-Turing Thesis is that Turing machines are
> formal versions of
> algorithms. No computational procedure is an
> algorithm unless it can be
> presented as a Turing machine. Church's work shows
> that any computable
> (i.e. algorithmic) function can be transformed into
> an expression in the
> lambda-calculus. Church's work is equivalent to
> Turing's description of a
> LCM. What non-algorithmic function did you have in
> mind?
>
> John Thornton
>
>
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