Colin Hales wrote:
> 
> Hi Folks,
> 
> I have chewed this thread with great interest.
> 
> Our main gripe is the issue of emergent behaviour and the mathematical
> treatment thereof? Yes? This is the area in which Wolfram claims to have
> made progress. (I am still wading my way through his tome).
> 
> ***Isnít the 'algorithmic revolution' really a final acceptance that there
> are behaviours in numbers that are simply inaccessible to "closed form"
> mathematical formulae?  - That closed-form mathematics cannot traverse the
> complete landscape of the solution space in all contexts?
> 

If this were the case, the 'algorithmic revolution' is at least 200
years old, as people have known at least this long that most
integrals cannot be written in "closed form".

Of course, from a practical point of view, it was so expesnive to
solve mathematical problems numerically, that hardly anyone bothered
until the advent of the electronic computer. Since then, of course
computational science has taken off like a rocket, and keeps the likes
of me employed. But this is hardly new news, or philosophically
interesting.

                                                Cheers

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