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Self-organized Criticality


sand_castleMany conceptual and experimental attempts have been made by evolutionists to explain the arise of the huge complexity and organization of nature based on unguided processes, that is without the intervention of an organizing intelligence. Among them I recall those related to chaos theory, evolutionary algorithms, emergent properties, far-from-equilibrium dynamical systems, self-organized criticality (SOC). Here I will briefly focus on SOC, the last on this list though not the recent one.

Wikipedia says about SOC:

“SOC is one of a number of important discoveries made in statistical physics and related fields over the latter half of the 20th century, discoveries which relate particularly to the study of complexity in nature. For example, the study of cellular automata, from the early discoveries of Stanislaw Ulam and John von Neumann through to John Conway’s Game of Life and the extensive work of Stephen Wolfram, made it clear that complexity could be generated as an emergent feature of extended systems with simple local interactions. Over a similar period of time, Benoît Mandelbrot’s large body of work on fractals showed that much complexity in nature could be described by certain ubiquitous mathematical laws, while the extensive study of phase transitions carried out in the 1960s and ’70s showed how scale invariant phenomena such as fractals and power laws emerged at the critical point between phases.”

In a previous post of mine (Potentiality and Emergence) I explained my doubts about real complexity emerging from nothing in systems by mean of “simple local interactions”. Moreover in another post (see my previous post: Formulas and Forms) I said what I think about complexity described by mathematical laws.

In his book “How nature works − The science of self-organized criticality” (1996 Springer-Verlag) the physicist Per Bak, perhaps the major proponent of SOC, begins explaining how many natural and artificial phenomena can be described mathematically by a power law. A power law is when some quantity N is power of another quantity s: N(s) = s^(-t). For example, the distribution of earthquakes as function of their power and how often a given word was used in literature texts follow a power law. The treatment of the power laws topic is very good in this book. As we will see in the following the problems are others and begin when the author tries to defend Darwinism.

To stress the fact that SOC is different from chaos theory Bak says that:

“Chaos theory shows how simple systems can have unpredictable behavior. […] Chaotic systems have no memory of the past and cannot evolve. […] The complex state is at the border between predictable periodic behavior and unpredictable chaos. Chaos theory cannot explain complexity.” (pag. 30-31)

After having rightly discarded chaos theory as a good explanation of the real organization found in nature, Bak starts to deal with his new paradigm, which in his view should work better than chaos theory, and provides a simple model or metaphor of it, the sandpile:

“The canonical example of SOC is a pile of sand. A sandpile exhibits puctuated equilibrium behavior, where period of stasis are interrupted by intermittent sand slides. The sand slides, or avalanches, are caused by a domino effect, in which a single grain of sand may interact with other grains in a chain reaction. Large avalanches, not gradual change, make the link between quantitative and qualitative behavior, and form the basis for emergent phenomena. If this picture is correct for the real world, then we must accept instability and catastrophes as inevitably in biology, history and economics […] Self-organized criticality can be viewed as the theoretic justification for catastrophism.” (pag. 32)

Why periods of stasis are quantitative while catastrophes are qualitative is a thing that I don’t understand. May be the author suspects that “emergent phenomena” need a source of quality after all because he recognizes somehow that quantitative sources alone are not enough to generate organized complexity. I agree with him here because the suspect is reasonable, but, differently from him, I would go to search for sources of quality in the direction of intelligent designers rather than in the direction of natural processes.

“Indeed sandpiles exibit their own equilibria. For long periods of time there is litlle or no activity. This quiescent state is interrupted by rapid bursts, namely the sand slides, roaming through the sandpile, changing everything along their way. The similarity between avalanches in the sandpile and the punctuations in evolution was astounding. Punctuations, or avalanches are the hallmark of self-organized criticality” (pag. 117)

Bak says that the sandpile is a “toy symbol” of his new SOC paradigm and dedicates most part of his book to it. A symbol or metaphor or model must always contain something pertaining the essence of the reality it symbolizes, metaphorizes and models. Otherwise, if a symbol/metaphor/model contains exactly nothing of the modeled reality then its utility would be zero and one could reasonably ask because an author has resorted to it to explain his thought. Therefore if Bak has chosen the sandpile and not another thing (among other infinite things available) it is because the sandpile is a good representation or “canonical example” of the processes Bak believes capable to create organization in nature. After all it is Bak himself to admit that “the similarity between avalanches and the punctuations in evolution is astounding. […] Avalanches are the hallmark of self-organized criticality”. Therefore given the sandpile is a meaningful and appropriate model we can examine it and whether we find it is not at all a generator of organization then we can deduct that the entire SOC paradigm is flawed.

Geometrically speaking, as raw approximation, the ideal sand pile is a cone. In real sand piles avalanches somehow destroy the geometric perfection of the cone. Before this destruction of perfection sure one cannot say properly that avalanches represent organization and order, rather disorganization and disorder. The destruction of a building is definitely another thing than its construction. From the point of view of time the construction of a system (natural or artificial) always needs far more time than its destruction. This is a banal ascertainment, however this difference in time evidences the qualitative difference between construction and destruction. Why does a sand pile collapse giving rise to an avalanche? The avalanche happens when the addition of sand on the top constitutes a weight than the bottom structures cannot support and consequently crash. This is exactly what the design of a building, among other things, always tries to avoid.

One can note that the sand pile evolutionary model is somewhat inverse of the sand castle ID model. Obviously an IDer would chose the latter and never the former to represent the ID paradigm. The sand castle is an ID “toy symbol” (to use Bak’s term) of a very building and, according to the above general concept of symbolism, it contains a little of the essence of a building. In fact a building and its toy symbol share an essential thing: both are intelligent designs. It is interesting to compare these two opposite “toy symbols” from a general point of view, because this comparison may help to clear some aspects of the two opposite and incompatible perspectives of unguided evolution and ID.

A sand castle involves complex specified information (CSI) and as such is constructed by an intelligent agent. While a sand castle (as any true project) needs a top-down design, it grows bottom-up, in height from the foundations to its top, in size from little to big, as any building does. We must distinguish between design and fabrication. Design is always top-down. There is not such thing as bottom-up design (to greater reason in the case of complex systems, as the biological ones). Fabrication is another thing: it is always bottom-up: in fact in the case of organisms embryo developments go in size from small to big.

This particular inversion between design and fabrication is simply a special case of a more general law: when the extra-cosmic principle creates cosmological manifestations, it operates in a top-down way while its manifestations develop
bottom-up. This is a consequence of the inverse analogy existent between
physics and non physics. The design-fabrication inversion is a special case of that because in a sense design is non physical and abstract while fabrication is physical and material.

In the sand pile evolutionary paradigm, the generation of the sand pile doesn’t need a designer because it is sufficient a constant supply of sand at the pile’s top. Therefore we have an inverted situation respect the sand castle: top-down “construction” and bottom-up “non-design” (in the sense that the unintelligent sand source doesn’t provide CSI: it is simply powered by the physical laws, which stay at the bottom in the hierarchy of causes). Therefore, also from this point of view, the sand pile evolutionary scenario is exactly the inverse of the ID sand castle. Of course also the effects will be different and somewhat reversed. A sand pile creates avalanches while a sand castle usually does not (if this happens it is considered by the constructor an accident or defect rather an improvement or creation of organization). Since the two models are inverse, while in the sand castle there is creation of organization in the sand pile there is destruction of organization.

There would be nothing evil per se in Bak’s studies of sandpiles, but unfortunately he claims that SOC can create true complexity and, last but not least, Bak explicitly declares that his SOC mathematical models are attempts of defense of Darwin’s evolution and Gould’s punctuated equilibrium theory:

“Our approach is to explore, by mathematical modeling, the consequences of Darwin’s theory. Perhaps then we can judge if some other principles are needed. If the theory of self-organized criticality is applicable, then the dynamics of avalanches represent the link between Darwin’s view of continuous evolution and the punctuations representing sudden quantitative and qualitative changes. Sandpiles are driven by small changes but they nevertheless exhibit large catastrophic events.” (pag. 131) “Our model is in the spirit of Darwin’s theory, but nevertheless exhibits puntuated equilibria. […] Our simple model barely constitutes a skeleton on which to construct a theory of macroevolution. […] It is a toy model that demonstrates how, in principle, complexity in an interacting biology can arise.” (pag. 141-142)

Again we have the confirmation that the dynamics of avalanches is a model of the biological qualitative changes and that the sandpile has a lot to do with biological macroevolution, even it demonstrates how macroevolution arose.

Let’s consider the terminology of SOC. To speak of “self-organized” is improper because no organization is involved (rather destruction) and to greater reason is not involved self-organization (a concept properly contradictory per se…). To use the term “criticality” means to say that the system is eminently unstable and its evolution is driven by entropy. Critical states are not states of creation of active information, rather states of abrupt lose of information and functionality. Hence, just in the name, we have an absurdity (self-organization) added to a thing (criticality) that entails the inverse of what the author hopes.

Bak provides also data reports obtained by lab experiments and computer simulations on sandpiles:

“Our data fall approximately on a straight line [on a logarithmic plot], which indicates that the number of avalanches of size s is given by the simple power law N(s) = s^(-t) where the exponent t, defined as the slope of the curve, is approximately equal to 1.1.” (pag. 47)

The fact that a power law describes the sandpile behavior, far from to prove that true complexity can arise from SOC processes, in a sense proves just the reverse, that they obey to statistical laws. Differently complex specified information (CSI) is free from contingency and cannot be generated by laws. Sand castles (and a fortiori cathedrals and computers) are not generated by natural laws.

In his chapter 6 “The ‘game of life’: complexity and criticality” Bak investigates the similarities between his sandpile paradigm and the famous cellular automaton invented by John Horton Conway. Cellular automata are determined by the rules of interaction among the cells on the grid. Some sets of rules generate richer geometrical configurations and give the illusion of generating “pseudo-organisms”. This rules tuning is a thing that has more to do with intelligent design than pure chance. Anyway needless to say the objects arising in the ‘game of life’ are light-years far from the simplest forms of real life. The application of a SOC jargon to the ‘game of life’ tried by Bak of course changes nothing to the basic failure of the SOC paradigm to create or explain real organization. A partnership between two poor doesn’t create one rich man.

Whether one yet doubts about the SOC equation catastrophes = biological evolution here is a quote from Wikipedia that clearer is impossible:

“SOC has nevertheless become established as a strong candidate for explaining a number of natural phenomena, including: earthquakes […]; solar flares; fluctuations in economic systems such as financial markets (references to SOC are common in econophysics); landscape formation; forest fires; landslides; epidemics; and biological evolution.”

It is indicative of the intrinsic logical inconsistency of these evolutionary attempts that what are the highest examples of advanced organization (organisms) are considered created by the same “self-organized and critical” processes producing … earthquakes, fires, epidemics, etc., that is all what destroy any life and organization.

And with this astonishing evolutionary paradox we can arrive at the conclusion that also SOC is a unsuccessful attempt to explain the complexity that only intelligent design can create.

Nakashima #1 Thank you for the errata corrige. Yes I agree that after all to study natural sciences entails to construct models of phenomena. These models never are the reality and their fitness or correspondence to reality is what distinguishes good rather bad science. You are right to say that "until someone can show that sand castles can be studied in the same way [of sandpiles]" the first explicative option of sand castles is design ... also because we see with our own eyes their designers at work. niwrad
Even granting there can be self-organized "complexity", these examples happen under conditions of low noise. The problem with biotic reality is we are dealing with copy errors, damage to systems all the time. Quantum tunneling, thermal noise, radiation, chemical threats, mechanical threats, etc. In such an environment, the equilibrium condition is toward total disorganization. That is what we see when an organism dies, any propensity for self-organization is run over by disorganizing agencies, the plug is essentially pulled on any prospective "game of life". Whatever theory is put forward for self-organization, what counts in the end is what we see in real life. When something dies,we don't see spontaneous self-organization to what it was when it was healthy. Never happens except maybe by a miracle... scordova
Mr Niwrad, A small erratum - the cellular automata ruleset commomly called the Game of Life was invented/discovered by John Horton Conway. I think you are absolutely correct, you have to understand when and where a model accords with reality, and where it does not. Hasn't this been the problem with so much talk about Dawkins' Weasel? I raised sandpile models recently on UD in response to this topic of how could small imcremental changes in genotypes (such as Darwin himself favored) lead to observed punctuated equilibria in speciation. But I agree that simply noting a coincidence in distribution functions is not enough to declare that biological speciation is an SOC phenomena, that is merely a hint in that direction. You need to build up a set of correspondences between model and reality, correspondences that can be measured and that lead to predictions. That is what makes studying sand piles a scientific pursuit. Until someone can show that sand castles can be studied in the same way, I will find your analogy between ID and sand castles very apt indeed. Nakashima

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