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?

My own approach has been to regard emergence as the repositioning of the
observer of a system such that the mathematical descriptions you have been
using fall over/cease to be relevant. The idea that the math can seamlessly
transcend an observerís scope is, I concluded, simply meaningless as the
math is defined by the observerís scope. The prejudices of our position as
observers are therefore automatically destined to be embedded in our
descriptors of things.

If this is the case then one cannot overlook the use of computers or the AIT
approach if you need to study, understand and replicate real-world phenomena
(in particular, MIND) that transcend the boundaries of emergence.

Will the historians look back on our obsession with closed form math and see
it as the machinations of mathematical youth? Para *** above is the clincher
and I have been unable to distil a definitive stance from all the writings.
Clues anyone?


Colin Hales
* somewhat perplexed *

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