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Week 5 Discussion Questions
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Departments of Geography & Civil and Environ Engineering, UC Berkeley
1. On p 622, Brown et al. state “In theory, a perfect fractal is self-similar at all scales; it can be scaled up and down to infinity. Of course this is not true of any real biological or ecological system. The self-similarity is confined to a finite domain.” But how across many scales must this finite domain operate in order to ‘prove’ that the organization of the phenomenon if interest is fractal-like? Does it depend on they type of system?
2. Given the problems the authors describe in determining whether, and at what scales, phenomena are fractal-like, do we need to use more caution in drawing conclusions from mechanistic models, which often rely on these empirical assumptions to identify underlying mechanisms?
3. Carlson and Doyle conclude that “If environmental systems are HOT states, then the burden of proof in the ecological debate must shift from a policy of ‘‘waiting for the science’’ to confirm negative effects such as ozone depletion or global warming, to a policy which re- quires substantial scientific investigation of whether the perturbed system is robust to proposed changes before they are introduced.” However, isn’t this policy approach also in line with the SOC perspective, if anthropogenic changes are seen as overarching constraints on the form of the system (e.g. drying out the wet sand in the sand experiment, thereby causing massive avalanches?).
4. If, as Frigg argues, most SOC models are so over-simplified as to be wrong most of the time, are they useful in addressing short timescale, real world problems? Or should they only be used when the goal is to ‘open doors’ into other modes or avenues of research?
Bak and Chen contend that the critical state–wherein events of all sizes are possible–is robust, and that the critical state is an attractor. It is not clear to me that this indicates that the absolute magnitudes of the events are the same in systems with different rules (wet sand vs. dry sand). Does a managed system delay catastrophic events with disastrous (higher magnitude) consequences (e.g. snow screens or levees)? Perhaps the ‘rule changes’ that Bak and Chen talk about are more like ‘design’ in HOT theory.
It is also not clear to me that there might not be more than one critical state (I’m thinking here about anthropogenic perturbation of climate into an alternate regime). Or do such catastrophic events more closely resemble a system collapse as in HOT theory?
Using the framework for SOC application types that Frigg lays out, what types of applications are exhibited by Brown et al. and what do we stand to learn from these types of analyses? There are serious limitations to the application of SOC analyses to the real world that are revealed in Bak and Chen and then taken up by Frigg. Nevertheless, Frigg contends that such analyses remain useful in certain ways. How/in what applications so you see SOC (or HOT) theory to be useful?
Self-Organized Criticality questions for 2/19/13
1. Bak & Chen (1991) posit that large interactive systems naturally evolved toward critical states in which minor events can start a chain reaction that can lead to catastrophe. The sand pile experiment with a 4 cm plate gives evidence for this, but the 8 cm plate does not produce small avalanches. Why would only small piles evolve to a critical state if the idea is that large interactive systems display these dynamics?
2. In search of more exotic examples of self-organized criticality, how would you research the flicker noise to justify a self-organized criticality hypothesis related to a social example like war? What signals would you examine?
3. Clarification question: Can you describe more about how power laws can emerge because of very general dimensional relationships among variables? Is this ever difficult to discover in specific applications of SOC?
4. How can one determine if power law distributions are a result of stochastic processes and do not have a mechanistic explanation?
5. The authors of the HOT paper (Carlson and Doyle 1999) contend SOC does not permit feedbacks in mechanisms that affect weights of different system configurations. Is this a semantic issue, about definitions of SOC versus HOT, or is it a real description of SOC applications?
6. In the case of environmental policy, there are fundamental distinctions between the implications of SOC and HOT and questions as to which models capture the essential features of real environmental systems. Do you agree that if ecosystems are in a state of SOC and internal dynamics drive extinctions, the implication is we don’t have any reason to address climate change in policy?
7. Frigg (2003) is interested in advancements in scientific understanding. When is a paradigm shift or new theory like SOC progressive?
In the niche theory every species have a specific niche (could be related as a function of one species in the ecosystem). Could be related with the normalizations constants (Brown et al. 2002) or the critical state (Bak and Chen 1991), where every specie have a attractor , and with this allow a variety of living organism in Earth?
In the same way, Could be analyzed the convergent evolution (where different taxas have a similar biological traits) as a pattern of SOC?
How can be explained that the Mediterranean ecosystems (California, South Africa, Chile, Australia, and Mediterranean Basin) have a high number of endemic species? Is this a pattern of a power law of organism under similar climatic conditions?
Could be saw the social revolutions as a pattern of a fractal historic system? Why the idea of develop an unified theory in sciences has been seen so attractive in human history, is this a pattern of human behavior?
1. Bak and Chen 1991. With self-organized criticality theory — I’m trying to image how this theory could be applied to alluvial fan construction? The fan reaches a critical state and then locally changes while maintaining a global stability (slope, extent/radius).
Would this theory suggest a globally consistent average slope? Would the slope exhibit a power law relationship (rise:run)? Or would you look at the energetics of the system to define the power law relation (as in earthquakes)? What would fractal (spatial — extent, slope) and flicker (temporal — time to reach critical state) fingerprints of alluvial fans be?
2. Many of these examples seem so conveniently contrived. How do they apply to real world forests and sand piles (erosion patterns?) Why is the goal producing power law distributions — is this just humans reaching for an inconsequential measure? In Brown et al, for example, their three power law classes are not very convincing. Are they saying some things fit nicely into the SOC model (class 1), and others do not?
3. In Brown, do real-world empirical power-law relationships plot up so clearly and globally? Should this statement increase my skepticism: “Other statistical distributions, such as lognormal or exponential, can appear quite linear on logarithmic plots, especially if the data include only part of the total distribution, or span only a limited range of variation.” So to judge quality of fit, besides the r value and the graph itself, we should be looking at the distribution/variation of the log plot. How tight and rigorous is this power law definition/distinction?
4. In Carlson and Doyle 1999, do they explain heavy tailed distributions? Is it just a slowing after an initial burst of speed? I don’t understand how a web file can have a heavy tail? It’s just a bunch of bits sitting in memory. Are they talking about file transfer over networks? This paper seems heavy-tailed! Will it ever end?
About heavy-tailed distributions:
http://en.wikipedia.org/wiki/Heavy-tailed_distribution