On Sat, Sep 15, 2012 at 02:55:17AM -0400, Stephen P. King wrote:
> >> Dear Bruno,
> >>
> >>    Could you elaborate on what your definition of "a digital
> >>machine" is?
> >
> >Anything Turing emulable.
> Dear Bruno,
>     OK. But you do understand that this assumes an unnecessary
> restrictive definition of computation. I define computation as "any
> transformation of information" and Information is defined as "the
> difference between a pair that makes a difference to a third".

That is far too inclusive a definition of computation. A map from i in
N to the ith decimal place of Chaitin's number Omega would satisfy you
definition of transformation of information, yet the posession of such
an "algorithm" would render oneself omniscient. You can answer any
question posable in a formal language by means of running this
algorithm for the correct decimal place. See Li and Vitanyi, page 218
for a discussion, or the reference they give:

Bennett & Gardiner, (1979) Scientific American, 241, 20-34.


Prof Russell Standish                  Phone 0425 253119 (mobile)
Principal, High Performance Coders
Visiting Professor of Mathematics      hpco...@hpcoders.com.au
University of New South Wales          http://www.hpcoders.com.au

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