On Sat, Jul 09, 2011 at 02:26:19PM +0200, Bruno Marchal wrote:
> >
> >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.

Of course. This is David's idea (not mine), expounded in Beginning of
Infinity, of various sorts of universality, leading up to the idea of
a universal knowledge creator. I haven't got to that part of the book
yet, but I've noticed a bit of controversy about it on the FOR list. 

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

Fair enough (as far as I am concerned). It is a historical matter,
in which I have no stake. But David Deutsch does make this claim on
BoI, and in particular refers to the "Lovelace objection".

> 
> 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.

Fair enough. BTW, in response to your follow-on message when you
mention Hypatia, don't take the movie "Agora" as the gospel truth -
certain matters were exaggerated to make it cinematically more
interesting. My son discovered this when he wrote a play based on
those events for a school assignment (for which he got top marks).

Nevertheless, it must be true that the European dark ages set us back
several centuries.

> 
> Bruno
> 
> 
> http://iridia.ulb.ac.be/~marchal/
> 
> 
> 
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