Wednesday, January 11, 2006
Additional reading:
Cory Casanave's paper on Data
Access
work on ontology for biological signal pathways
[126]
ß parallel discussion in
generative methodology bead thread
Discussion on informational invariance
[342], [343], [344], [345], [346], [347], [348], [348], [349]
Note from Paul Werbos
Hi, Paul (Prueitt)
Per your request, I have clicked on the definition of "complex system" from Judith.
I guess one of the earliest practical lessons in verbal reasoning is that it's usually silly to debate too hard over the "right definition," since definitions are all arbitrary in some sense.(There are good reasons why I have weasel-worded this... but let me not spend a lot of time on caveats...)
There are folks at NSF right now putting lots of energy into "complexity" and "complex systems. "Some of them are very excited by recent work by John Doyle of CalTech.
Crudely speaking... I have a feeling that Rosen's definition ... feels like "the left wing" to me, and Doyle's like the "right wing," and, as usual, I would be more comfortable with a position somewhere in the hyper plane halfway between the usual extremities.
In particular --
the Rosen definition clearly does NOT allow for emergent complexity. [1]
If one can start with simple underlying rules or axioms or dynamics (either in forwards time or symmetric time or hyper time), and generate all kinds of emergent complexity by applying these rules over a huge field of entities... I wouldn't want to rule that out a priori.
For example... one can specify (hypothetical) mathematical universes totally governed by simple PDE, in which planets and life and social organization do emerge, all as the result of processes of evolution. There are those who say that those models are not rich enough to capture everything going on in evolution on earth, but I would feel very uncomfortable with a definition of "complex system" which excludes all such research.
Of course, in logic, there is an analogy here to the kind of complexity which can emerge when one allows quantifiers over infinite fields of entities. Various orders of logic.
Best,
Paul W.