On Mon, May 29, 2017 at 8:28 AM, Marcus Daniels <mar...@snoutfarm.com> wrote:
> Hurricanes are an instances of multiscale fluid dynamics, or set of > problems (cyclogenesis, heat engine, cyclolysis). They are all > complicated coupled systems, but it is not clear to me what extra insight > is gained by calling them complex systems. > Great question, Marcus. I think this helps reinforce my point more clearly. Depending on how you *model* cyclogenesis, there may not be any benefit using the language of complex systems. Just because it's a complicated coupled system, does not mean it's a complex system (in my definition). I'm not an expert on cyclogenesis, but a quick wiki lookup <https://en.wikipedia.org/wiki/Cyclogenesis> led me to one model description being around a coupled differential equation model using Q-Vectors: [image: Inline image 2] And here's more on Q-Vectors <https://en.wikipedia.org/wiki/Q-Vectors>. To me, this class of model is closer to my second model of a hurricane (random walker with specific terms of curl for Coriolis and and a global wind vector) than the first (dissipative structure formation where vorticity would be a symmetry breaking dynamic). And the second one, I offered was not a complex system. To me, the Q-Vectors model of cyclogenesis is missing micro and macro frames and probably would be a stretch to classify it as a complex systems model. Further, terms like vorticity is a prescribed time-based derivative and not emergent in the model. In alternative models, by contrast, vorticity would result from symmetry breaking in the critical regime and would be a candidate order parameter. I would be more likely to classify that type of model as a Complex Systems model. That said, I would more likely classify the Q-Vectors model as Dynamical System <https://en.wikipedia.org/wiki/Dynamical_system> model instead of a Complex System. I would argue knowing it's a *Dynamical System* you get the benefit to automatically know: - it can be characterized with phase spaces with attractors and repellors. - it has phase space will have basins of attraction and related separatices - it may have chaotic regimes in phase space While all complex systems models are dynamic they may not necessarily qualify as Dynamical Systems where time is modeled explicitly. And it is usually the case that a Dynamical Systems model is not a Complex System Model. Some researchers would disagree with me on this point. Dynamical Systems and Complex Systems language are often used interchangeably by different complexity researchers and the boundaries are fuzzy in practice. If we were able to classify it as a Complex Systems model, it allows one to import what's known to universally to apply to complex systems. eg: - the model will have narrow critical regimes which will have: - fractal pattern formation with powerlaw statistics - long range correlation in microlevel agents/entities - critical slowing down - critical fluctuations - high variation between runs (unpredictable) and sensitivity to initial conditions (chaotic) - symmetry breaking of macroscopic properties - rapid increase on constraints on degrees of freedom on microlevel components - highly predictable macroscopic patterns on either side of the critical regime - potential for self-tuning - It will have a universal order parameter of symmetry breaking at the macro scale. What breaks symmetry will be model dependent - I assert (I can't yet prove) that it will have a universal control parameter which can be characterized by the asymmetries of the micro-level interactions. eg: - the asymmetry of deceleration in deceleration and acceleration in a traffic model is a control parameter that can move the order parameter of the macroscopic symmetry breaking of a backward shockwave of a traffic jam through a phase transition. - the asymmetry of attraction and repulsion in a flocking model can move the macroscopic symmetry-breaking of linear momentum of a flock through a phase transition Another benefit of classifying it as a Complex Systems model is that it allows one to identify subclasses within complex systems models and find homologies which I think Nick would agree is the real power of metaphor in science. For example, a subclass of models in complex systems is a percolation model which exhibits all the characteristics above. But further, if I say a particular forest fire model, particular rumor model and a particular voter model are all of class percolation models, I can make many creative leaps back and forth between the three. And like all uses of metaphors it would be instructive when the metaphors break down between the systems. However, if the models are equivalent, it allows communication between disciplines. Another example is a particular ant food foraging model and a particular lightning model of dialectic breakdown which are equivalent in their implementation. This allows a Plasma Physicist to now have a fruitful interaction with an Entomologist and do some joint research. One last important point as I try to close myself out from this thread: I recognize that Complexity Research taken as a whole is a big tent and Complexity covers many loosely-related areas: - Network Dynamics / Graph Theory - Self-Organization - Evolutionary Dynamics and Evolutionary Computation - Dynamical Systems - Iterative Game Theory - Computational Complexity - Ecological Dynamics - Adaptation, Robustness and Resilience - Chaos Theory - Catastrophe Theory - Nonlinear Dynamics - Non-Equilibrium Thermodynamics - Non-Extensive Statistical Mechanics - etc It's gotten to the point where SFI describes itself more as a trans-disciplinary research institute than an institute focused on Complexity. The closest you get to agreement on a definition of Complexity which you'll see in the Complexiy Explore Video that Owen linked to is something like: "A system of multiple interacting components that have the capacity for emergent behavior." I'm good with that and recognize there's fuzzy terms lurking. In the list of areas above, my definitions of Complex Systems is very biased toward Self-Organization an Non-Equilibrium Thermodynamics as it's a handle on which I can make sense of the world and feel I can make some progress. When I use a definition of Complex Systems on this thread, I recognize it's particular to my understanding and many researchers have their own definitions. As you start to look at models in other spaces in Complex Systems research, my definitions will be strained to apply. It is not my intent to restrict other researchers from using the term Complex Systems based on my narrow definitions. If Russ and Glenn want to define Complex Systems in their way, there's plenty of precedent. I will just point out where there definitions are different than mine or push back if they assert my models don't qualify as Complex Systems.
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