http://www.youtube.com/watch?v=pTbCNycm0nQ

Don't fight forces, use them R. Buckminster Fuller.

Complex systems live by feeding off (given) energy flows, but while dissipation is a necessary feature of complex systems, it is not just a measure of how wasteful complex states are in relation to simple ones. The given energy flows are from low-entropy to high-entropy states and a simple undisturbed flow wastes all that high-quality energy in the form of dissipated heat, so in terms of the ratio of useful work to wasted dissipation, simple states do worse.

I have difficult questions for Migeru.

Firstly, I am wondering, how necessary is dissipation waste given a constant energy source? Could a system, in principle, recycle anything it produces within finite time, without local entropy increase, so that overall entropy increase would be accounted at the energy source alone? Or does any 'work' requires local dissipation?

I agree that energy flow could be wasted without any work. Are there any theorems how much work (or complexity, or information) can be maximally created from a given energy and waste budget?

On the other hand, is waste necessarily synonymous to entropy increase? In the simple head conduction example, energy flow could be potentially useful if organized in some way, but that waste is not harmful either, since there is not much organization to break. Are we wasting Sun's energy by letting it escape to the space?  

In some sense, the 'real' waste is some output impending the system itself or 'someone' else. How much waste of this kind does a growing system has to produce?

I did not find much on 'period three' googling, except the theorem of Li & Yorke that any one-dimensional system which exhibits a regular cycle of period three will also display regular cycles of every other length as well as completely chaotic cycles. Though I am a bit confused how this theorem applies to this example.

I was making a point recently that while physical causality and models are interesting, some Darwinian or cybernetic dynamics might be more important for complex systems:

Generally, to have interesting developments, you need cyclic chains of events, or possibility to return to previous states. Classical thermodynamics kind of forbids cycles in equilibrium regimes; to have dynamics back to higher entropy states you need energy input. Once cycles of events are possible, they may organize and evolve themselves in some vaguely Darwinian fashion.

It is probably more instructive to look at the modern economy not from the bottom thermodynamics, but from a deep Darwinian point of view. Surely, Darwinian methaphors are prevalent enough in economic and social settings. Once you start talking about Darwinism, a whole train of images and recognizable comprehension kicks in - most of it rather irrelevant to a particular discussion.

What I mean by deep Darwinism here is manners in which repetitive events can organize themselves. It is an alternative to stochastic and deterministic chaos understanding of complex phenomena. Instead of wondering at fractals and "butterfly effects", the logic of self-enforcement and impulsive reaction should be appreciated. The physical models (be it stochastic or deterministic) are fine, and they do provide basic cause-effect pieces. But when it comes to pondering about unstable sensitivity to initial state parameters, or stochastic thresholds, limitations of those models should be recognized. That unstable sensitivity can actually be resolved by something outside the limited model! Particular events or causal effects can appear more numerously not by physical inevitabilities but by pieces of the natural selection logic: some events allow themselves to repeat successively, some events are 'suicidal'. Could repates - "repetitive event patterns" be considered as a new kind of replicators, along with genes and memes? (Cybernetic models are quite appropriate to this understanding. )

I agree but we're stuck with it.  

 

Have epistemological model of Complex Information environments. Will Travel.

Google "daisyworld" for the simplest and perhaps earliest example of a crude model of a planetary stability mechanism. Nobody here is suggesting that Gaia is God-- just that there is an incredible amount of good work that shows the evidence for stabilizing mechanisms, or self-organization in complex systems is overwhelming, and their study has come to form the basis of modern ecology.
There are several good theories of self-organization (no Gods in there either), and they evolve, and are in fact a fundamental ingredient in climate modelling as well, now.

Basic reading (my bookshelf, or part of it):

Bertalanffy, "General Systems Theory"

Bogdanof, "Tektology"

Early: Jantsch, "The Self-organizing universe", written before the math of complexity burst on the scene, then

Ilya Prigogine in Belgium and systems far from equilibrium, and the necessary non-linear equations,
which he deduced and called "Non-linear Thermodynamics (his Nobel Prize began here), (Migel, dissipation as a source of order? Yup.), producing his Nobel symposium on Dissipative structures, to:

Varela and Maturana in Chile, and their still-central work based on two works (so far) "Autopoiesis: The Organization of the Living", and"Autopoiesis and Cognition", which begat:

Stuart Kauffman, the grand Guru of life modelling and binary systems, cellular automata, who likes to hang his hat at the boundary region near the edge of "chaos". He would agree with you that we CAN fuck it up-

Networks on the boundary between order and chaos may have th flexibility to adapt rapidly and successfully through the accumulation of useful variations. In such poised systems, most mutations have small consequences becqause of the system's homeostatic nature.  A few mutations however, cause larger cascades of change. Poised systems will therefore typically adapt to a changing environment gradually, but if necessary they can occasionally change rapidly."

--but it's not a necessary outcome, and the system can also pitch us off it's (non-sentient?)back.
No theological dogma, no system of incredible power. just good, peer-reviewed, prize-winning research.
The earth responds. It adapts. Like a thing alive.

LIKE.

Chew through the above massive dose of cellulose, as I have. Or save the three years, and skip all the above books, and just read Capra, "The Web of Life".
Then tell me I'm wrong, because then you too will have done your homework.
If you have done, I apologize in advance.

Useful talking follows experience, the more experience the better. Talking that precedes experience is known as bullshit.

SIAM: The Power Grid as Complex System (December 1, 2003)

It's not hard to see the parallels between forest fires and sand piles and the electric power grid, and indeed, this is the focus of a series of papers by Dobson and his co-authors---Benjamin Carreras, David E. Newman, and others. (The papers can be found on Dobson's Web site, http://eceserv0.ece.wisc.edu/~dobson/home.html.) With data provided by NERC, the North American Electric Reliability Council, the researchers analyzed a 15-year time series of transmission system blackouts. Using three measures of blackout size, they demonstrated that the distribution of blackout sizes follows a power law, indicating, they say, that the power grid may be a self-organized critical system hovering at or near the critical point. As further evidence, they showed that the power data is, by several measures, similar to data from a sand pile model.

For the sand pile model, the counteraction of two processes---the localized addition of sand and the pull of gravity---is what keeps the system hovering at a dynamic equilibrium near the critical point. The researchers suggest that a corresponding pair of forces work to keep the electric power system in a near-critical balance. One is the yearly growth of about 2% in the amount of power coursing through the grid; the opposing force is the human response to blackouts. Each blackout, Dobson says, exposes bottlenecks in the grid, which the power companies address when they add capacity to the grid. That process, in turn, allows the grid to handle greater power loads, which exposes the system to new blackout threats.

Viewed another way, the power grid operates within margins: Each power line and each generator have a region of safe operation. When the power load exceeds the margin for a line, the line trips out and the power redistributes itself throughout the network according to the impedances of the surrounding lines. When the grid is run with low loading of power (which is economically impractical), a single event, such as a line tripping out, is unlikely to cause others; events are independent, and the distribution of event sizes has an exponential tail. Once loading is high, however, small events have a high probability of cascading and spreading into large outages. Extremely high loading is thus impractical as well.