Nets: Edge of Chaos

[James Brody]

Minds, communities, and gasses often demonstrate three phases: chaos, order, and a phase transition between them. Such appears true in gasses, minds, and communities. This idea - one of the most powerful in developmental-physics, -biology, -psychology, or -politics - was conceived by Chris Langton and publicized by Stuart Kauffman. It is, however, ignored by psychologists who use it instinctively when they treat psychopathology. The abstract by Rohlf and Bornholdt is followed by several paragraphs from Rebellion.

JimB

"Self-organized criticality and adaptation in discrete dynamical networks
"Thimo Rohlf and Stefan Bornholdt
"Abstract It has been proposed that adaptation in complex systems is optimized at the critical boundary between ordered and disordered dynamical regimes. Here, we review models of evolving dynamical networks that lead to self-organization of network topology based on a local coupling between a dynamical order parameter and rewiring of network connectivity, with convergence towards criticality in the limit of large network size N. In particular, two adaptive schemes are discussed and compared in the context of Boolean Networks and Threshold Networks: 1) Active nodes loose links, frozen nodes aquire new links, 2) Nodes with correlated activity connect, de-correlated nodes disconnect. These simple local adaptive rules lead to co-evolution of network topology and -dynamics. Adaptive networks are strikingly different from random networks: They evolve inhomogeneous topologies and broad plateaus of homeostatic regulation, dynamical activity exhibits 1/ f noise and attractor periods obey a scale-free distribution. The proposed co-evolutionarymechanism of topological self-organization is robust against noise and does not depend on the details of dynamical transition rules. Using finite-size scaling, it is shown that networks converge to a self-organized critical state in the thermodynamic limit."

"Your Most Familiar Phase Transition: Floating on Your Back

"Life, as we usually think of it, follows water. Water takes three forms and gives a feel for phase transitions. That is, water can be very cold but still liquid until 0 degrees C: drop the temperature one more degree, however, and a block of ice forms. Raise the temperature a hair beyond 100 degrees C and water disappears into a vapor. Water is a very narrow phase, a transition between ones known as ice and vapor, each of which can exist in much greater temperature extremes. For example, the temperatures in the solar system range between a few degrees above absolute zero (0 degrees kelvin or 273.15 degrees below zero degrees, Centigrade) and the temperatures in micro black holes that approximate 57,800 degrees K (http://en.wikipedia.org/wiki/1_E6_K)."

"Water's 100 degrees is tiny in comparison with the 60,000 degree range that frames other states of matter.
You have other experiences of phase transitions. You have shaken oil and vinegar in a cruet and hurried to pour the cloudy mix onto a salad before the layers separate again. You also live in a phase transition that is about twelve inches thick when you float on your back in a swimming pool, too heavy to fly but too light to sink."

"There are psychological parallels to what you find in water. On the highway, you have a comfort range for a driving speed that varies with road surface, weather, and the density and speed of other traffic. You are bored if you move too slowly but anxious if you move too fast. Even when you are at work or home, you understand what it means to be overwhelmed, to be productively active, or to be bored out of your mind but you seldom relate those experiences to the swimming pool. Furthermore, you do not relate them to the human discomforts that psychologists call internalizing or externalizing disorders, to your confusions when taking on a partner or rearing children, nor to the persistence with which you sometimes defy boundaries or hug predictability."

References
Brody J (2008) Rebellion: Physics to Personal Will. Lincoln, NE: iUniverse.
Rohlf T & Bornholdt, S. Self-organized criticality and adaptation in discrete dynamical networks. arXiv:0811.0980v1 [nlin.AO] 6 Nov 2008.