[Is anybody tying the bits together?] - A New Kind of Science: The NKS Forum
A New Kind of Science: The NKS Forum
Is anybody tying the bits together?(Click here to view the original thread with full colors/images)
Posted by: Tony Smith
I recently tried to address somebody's skepticism about seeing chaos (extreme sensitivity to initial conditions) as the source of the variation that Darwin freely admitted implying as random as cover for being unknowable in his time.
An idea invoking effective mathematical independence suddenly fell into place that seems to say something useful about the often challenging relationship between our fancy models and real world systems, analogous to the map-territory dichotomy.
In the real world (and most of the human constructed world) true independence is clearly relative. Whatever the rule is for determining the next local state from the previous local neighbourhood state, every system at every scale ultimately emerges from its collective effect.
Everything that persists, aka emergent organisation (order), is necessarily found in its particular attractor basin. Yet because it is in the same universe it remains open to disturbance by effects operating at other scales of space and time, effects which math can only treat as independent, at least in the general case.
While Rosen has said a lot about the modeling relationship and there is no shortage of work on each of the parts mentioned above, I'm coming up completely empty on searches to try to find anybody who has started to put these bits together into a strong account of the origins of variation in real world systems far beyond the narrow scope of biological evolution (where some clever enhancements have also evolved).
I've raised this idea with a couple of competent audiences in recent days, but nobody has come back with suggestions of prior work, so I figured I should also try with whoever is still reading here.
Posted by: David Brown
"... find anybody who has started to put these bits together into a strong account of the origins of variation in real world systems ..."
The work of Feigenbaum might be relevant.
The work of some of the other winners of the Heineman prize might be relevant.
http://en.wikipedia.org/wiki/Dannie...matical_Physics Heineman prize
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