Steven, Not sure if it fits, but the type of complex systems I first carefully studied were natural air currents.
There's a clear energy gradient involved when sunlight provides heat at the bottom of a column of air and buoyancy drives the development of intricate motions. What I noticed is that the paths of motion evolve individually by growth processes. Some small perturbation at an instability results in a positively reinforced development of movements, that gives the air a system of solving the problem of getting out of its own way, to release the gradient. From observation, it looks like there are some delays in the right disturbance occurring, perhaps. Individual currents rising from a floor can develop in what appears to be erratic and lazy fashion. I think this behavior probably fits your model somehow, but I don't see the degrees of freedom or capacities you refer to as the gateway to relieving any gradient. Make any sense? > > > > > Yet when I ask for a formal treatment, I get no answer. > > I very much like Hubler's deceptively simple definition of complexity: > "A complex systems is a system with large throughput of > Energy, Information, Force, .... through a well designed boundary." > > His notes from the SFI CSSS school with this definition are > here: http://www.how-why.com/ucs2002/tutorial/ > > > As a restatement of the same ideas that formalizes what > "large" means, I would > offer: > "complexity emerges when a gradient acting on a system > exceeds the capacity of the internal degrees of freedom of > the system to dissipate the gradient". > > > Is that formal enough? or, does the statement need to be mathematized? > > -Steve > > ________________________________________ > [EMAIL PROTECTED] > www.Redfish.com > 624 Agua Fria Street, Santa Fe, NM 87501 > mobile: (505)577-5828 > office: Santa Fe, NM (505)995-0206 / London, UK +44 (0) 20 7993 4769 > > > ============================================================ > FRIAM Applied Complexity Group listserv > Meets Fridays 9a-11:30 at cafe at St. John's College > lectures, archives, unsubscribe, maps at http://www.friam.org > > ============================================================ FRIAM Applied Complexity Group listserv Meets Fridays 9a-11:30 at cafe at St. John's College lectures, archives, unsubscribe, maps at http://www.friam.org
