On 09 Jul 2011, at 09:10, Russell Standish wrote:

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

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,

Well, carefull. It is unidversal in some sense, but is not Turing universal.

since the discovery of the
zero, but ancient Greek & Roman systems were not.

But they are universal in some other sense.

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

But they were way far from Turing universality.

Similarly, Babbage and Lovelace came very close to the Turing
universality concept, but again mysteriously shied away from

Here I disagree. I have made research, and I am convinced that babbage has been aware of the Turing universality, of, its notation system to describe its machine. He said that this was his real big discovery, but none understand it.

Then Emil Post is the second one, but nobody will listen (nor will Post really insist). Only with Church and Turing will the notion be admitted by the many. But still very badly understood, despite the concrete computers, which when programmed, hides their universality.

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.

I think it would have taken some more centuries. They might have discovered it in the 12 or 13th century. They would not have been able to miss it, especially with the development of math and calculus, which they would have developed much faster than Newton and Leibniz. OK, that is just my current opinion. We can't change history.



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