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? regards, Colin Hales * somewhat perplexed *