Phil, > Not sure if it fits, but the type of complex systems I first > carefully studied were natural air currents.
Yes, the emergence of convective cells, esp Rayleigh-Bénard convection, is an oft-cited example in Complexity: http://en.wikipedia.org/wiki/Convection > 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. You can look at the degrees of freedom of the elements/agents in the system. In this case, it would be the air molecules. Given a small gradient below a critical value, the molecules are able to randomly collide with one another and transfer the energy along the gradient. In the absence of a gradient, the air molecules are unorganized and have maximum degrees of freedom. The system is symmetric and at maximum entropy. ie, given the position of one air molecule, an observer has no information about the position of another air particle and no work can be extracted from the system. As you move the system away from equilibrium by applying an energy gradient, the air particles will initially dissipate the potential primarily via conduction (a heat process). Heat can be defined as the unconstrained transfer of energy. Here, i would interpret unconstrained as the air particle randomly transfering into their six degrees of freedom the energy from the gradient. Random collisions obeying conservation of momentum will propagate the energy along the gradient setting up a flow process. As the systems is moved further from equilibrium, it will cross a critical threshold where the ability of the system to dissipate the potential via a purely heat process will be insufficient. The motion of the air particles will become coordinated into convective cells and the majority of the dissipation will happen via mass transfer instead of conduction. Coordination implies that the state of one air molecule is constrained by the state of another air molecule. Emergence of constraint is the loss of degrees of freedom at the micro level. Air molecules lose degrees of freedom as the system becomes organized via convection. In our language, conduction is a heat process (the unconstrained transfer of energy). Convection is a work process (the constrained transfer of energy). In other systems like the ant foraging ABM model, we're trying to generalize the notions of "work" and "heat" beyond traditional mechanical processes. we've said that work is performed on the agents at the micro level as the system becomes complex and moves toward an organized state. For example, ants are informed by the pheromone field; work is peformed on them as they lose degrees of freedom in their movement and follow the gradient. Ultimately, I'm claiming, unformally at this point, that complex systems are a method for converting heat to work. -Stephen > -----Original Message----- > From: Phil Henshaw [mailto:[EMAIL PROTECTED] > Sent: Saturday, July 22, 2006 2:29 PM > To: 'The Friday Morning Applied Complexity Coffee Group' > Subject: Re: [FRIAM] formalization of Complexity (was > Dynamics of ComplexSystems by Yaneer Bar-Yam) > > 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 > > ============================================================ 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
