On Fri, Jul 08, 2011 at 11:04:56PM +0200, Bruno Marchal wrote:
> On 08 Jul 2011, at 03:39, B Soroud wrote:
> >I mean if you went back to classical greece... or classical
> >india.... could it have been predicted or shown to deduced?
> Excellent question. China was close. Reading the treatise "number"
> by Plotinus, and having a bit study Diophantus, I am not sure that
> in the world were Plato academia lasted longer they could have find
> it.  Nature found it before (quantum vaccum, DNA, Brain, humans,
> Human thought, computers, ...).
> It is the little God. The one you can named (Like FORTRAN, Java,
> c++, LISP, game of life, etc.) but when you name it, its names
> multiplies.

David Deutsch has an interesting discussion about this in his
"Beginning of Infinity". He actually introduces several notions of
universality, one of which is universality of the numbering
system. Our numbering system is universal, since the discovery of the
zero, but ancient Greek & Roman systems were not. Archimedes came
close to a universal numbering system in the "Sand Reckoner", but
mysteriously shied away from true universality (his system included
some rather arbitrary restrictions preventing it from true
universality). Similarly, Babbage and Lovelace came very close to the Turing
universality concept, but again mysteriously shied away from
it. Deutsch remarks that we as a species seem to have a reluctance to
making systems universal, which is quite curious.

So in answer to this question, even if Plato's academy had continued,
it probably still would not have discovered Turing universality.


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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