Wednesday, May 15, 2013

Self-Organization and Emergence

The reason why higher-level subjects can be studied at all is that under special circumstances the stupendously complex behaviour of vast numbers of particles resolves itself into a measure of simplicity and comprehensibility. This is called emergence: high-level simplicity ‘emerges’ from low-level complexity. High-level phenomena about which there are comprehensible facts that are not simply deducible from lower-level theories are called emergent phenomena. –David Deutsch1

How has That Which Is manifested itself? What are the most fundamental principles which it seems to have given rise to, at least in this Universe? More broadly, what are the most basic rules that seem, in our perspective, to govern the physical reality  in which we find ourselves?

Everywhere there is decay and disintegration. Everywhere, things seem to be heading toward entropy, toward complete equilibrium. Everywhere, structure seems to break down into chaos. And yet, the Universe is filled with structures, many of them extremely huge and extremely ancient, containing innumerable other structures within them, oftentimes structures of great complexity. How did this occur? Moreover, some of these structures have gained the ability to replicate themselves and make more structures, even, eventually, to evolve unanticipated structures. How is this possible? What hidden realities are at work that make chaos resolve into order—the exact opposite of what we might expect? There seem to be two phenomena which, in the Universe we know and inhabit, govern the operation of all things: self-organization and emergence. It is these phenomena which seem to have given rise to every structured thing and organized process we know of and observe, and it is these two phenomena which appear to have created the increasingly ordered levels of physical reality that eventually gave rise to our tiny and isolated species. In the opinion of an increasing number of specialists, they are the great builders of the Universe. So how might they be understood?

We need to first understand that the classical method of examining nature by breaking its components into smaller and smaller parts, a process known as reductionism, has been very successful at systematically describing enormous numbers of naturally-occurring phenomena. But reductionism became a sort of intellectual dead-end; it could describe the smallest parts of the natural world, but it could not adequately explain the way these basic entities had come together to form the elaborate structures we observe around us. Thus, the sciences of complexity, self-organization, and emergence began to grow in response to the need for such an explanation.

There is an extensive literature on these matters—the number of papers, books, and articles in these fields has increased tremendously in recent years—and there is by no means a complete consensus among scientists with regard to the exact definitions of the terms involved and the internal operations and characteristics of the phenomena being described. To a layperson like me, the various disputes among these scholars can be daunting in their complexity, to say the least. But there are research findings I think I can present with some degree of confidence.


By self-organization, we mean the appearance of distinct patterns, processes, structures, or interactions without the specific direction or intentionality of any outside source. As Francis Heylighen  of the University of Brussels put it in a 1989 paper:

Self-organization may be defined as a spontaneous (i.e. not steered or directed by an external system) process of organization, i.e. of the development of an organized structure. The spontaneous creation of an “organized whole” out of a “disordered” collection of interacting parts, as witnessed in self-organizing systems in physics, chemistry, biology,[and]  sociology, is a basic part of  dynamical emergence.2

Heinz Pagels, who in the 1980s wrote presciently about the ability of the computer to simulate and model complex realities, put it this way, in remarking on the work of another researcher, Charles Bennett:

A self-organizing system lowers its entropy (a measure of its degree of disorganization) by expelling entropy into its environment and hence avoiding deterioration. An example of a self-organizing system is the growth of a plant or crystal. The point to be made about self-organizing systems is that first they are indeed complex—highly organized—and  second they got that way by starting from a much simpler system.3

The concept of self-organization is counter-intuitive, in some ways. It goes against much of our ordinary experience, where things seem to fall apart and become disorganized. But, repeatedly, we observe examples of how order arises with no outside influence. When energy in some form passes through a set of particles/units/individual entities, there seem to be definite patterns that emerge spontaneously. Examples would include varieties of cloud formation, the emergence of bubble-like structures in liquids that are heated, and a whole host of other effects that have been noted by all the natural sciences. It is this tendency of things to create spontaneous structure that allows for new structures to arise, structures which in turn make possible the construction of bigger and yet more organized structures, and so on. And although it would appear, according to several researchers, that there can be self-organization in isolation, in other words, without any ensuing emergence, (and emergence that is not brought on by self-organization) it would further appear that self-organization and emergence in combination largely produced the physical reality and its various levels of organization we see all around ourselves (in the human frame of reference).

In 2008, three physicists expressed the concept of self-organization in this way:

…if we think of empty spacetime as some immaterial substance, con­sisting of a very large number of minute, struc­tureless pieces, and if we then let these micro­scopic building blocks interact with one anoth­er according to simple rules dictated by gravity and quantum theory, they will spontaneously arrange themselves into a whole that in many ways looks like the observed universe. It is sim­ilar to the way that molecules assemble them­selves into crystalline or amorphous solids…

Similar mechanisms of self-assembly and self-organization occur across physics, biology and other fields of science. A beautiful example is the behavior of large flocks of birds, such as European starlings. Individual birds interact only with a small number of nearby birds; no leader tells them what to do. Yet the flock still forms and moves as a whole. The flock possesses collective, or emergent, properties that are not obvious in each bird’s behavior.4

The constant interaction of particles in a given space or region creates a dynamical system, because those particles can be in different states in relation to each other over time. Self-organization involves the presence in a changing, dynamic system of attractors, areas of the system that seem to “capture” the trajectories of particles or keep other elements of the set close to them. Attractors exist in what are known as basins of attraction, regions of a system where attractors can exert their influence. The simplest attractors seem to be point attractors (or sometimes, fixed point attractors) which allow for only one final position for any particles they attract (such as a ball thrown into a jug or bowl which is inexorably drawn to the vessel’s lowest point). Another example of how a fixed point attractor operates, one given in many places in the literature, is the movement of a pendulum. The pendulum comes to rest eventually because gravity and friction create a basin of attraction that draws it into a resting state. Periodic attractors (or limit cycle attractors) cause particles (however the term particle is defined) to pass through different states on a regular basis. An object orbiting another object in a mathematically ideal way would be exhibiting the influence of periodic attractors. Particles drawn to periodic attractors are being affected by some kind of regularly occurring energy or reaction. They are not held in a fixed position, but they cannot operate in a purely random one. Strange attractors are points in a system deeply affected by the initial state of a system. Any perturbation of the system causes them to act in unpredictable ways. The greater the disturbance, the more unpredictable the actions of these attractors become, because any stimulus they receive is enormously amplified. Novel, unpredictable states can arise quickly from such attractors. It was not until the development of the computer that strange attractors, these odd, continuously moving points that never return to the exact same place in a system, could be studied. Fractal images generated by computers are examples of strange attractors in action.5

Attractors are physical states in a system, therefore, that particles tend to move toward, such as fixed points, states where the particles can settle into some sort of equilibrium, or those which can bring forth unpredictable new relationships and structures. 

So how is self-organization possible in an extremely complex system?

Physician and biologist Stuart Kauffman, a member of the Santa Fe Institute, has done as much work as anyone in the world on the natural processes that underlie complexity and self-organization. In his 1995 book At Home in the Universe, Kauffman calls the spontaneous emergence of self-organized complexity “order for free”. He explains that depending on the initial state of a system it will cycle in certain ways through its possible states, or state spaces. If there are vast numbers of possible states a system can be in, it will be necessary for attractors to draw in particle trajectories, in effect forming subsystems within the larger system, and allowing these subsystems to follow orderly patterns and establish a measure of stability, or homeostasis. Not all systems eventually do this, and the ones that don’t end up descending into chaos.6

The heart of Kauffman’s argument lies in his examination of Boolean networks, networks with components which can display only two possible behaviors. To explain these networks, Kauffman uses the example of arrays of light bulbs. He explains that a network of such bulbs can be ordered, chaotic, or in a transitional state between order and chaos. The network of lights, when operating, goes through what Kauffman describes as a state cycle, a pattern of lights that might range from only one pattern (such as alternating on-lights and off-lights) all the way to a state cycle exhibiting every conceivable state that is possible within the network. With a small number of lights, going through every possible state is easy. With increasing numbers of lights, however, it becomes progressively more complicated.

The number of different states the network can be in is governed by the number of lights in it. A single lone light bulb can exhibit only 2 states, either on or off. Two lights can exhibit four possible states (22) namely,  both on, both off, the first one on and the second one off, or the second one on and the first one off. Three lights can exhibit eight possible states (23), and so on.  If we keep adding one light to the network, it doesn't take long for the number of possible states to grow very large. For example, a mere 20 lights can exhibit 1,048,576 different combinations (220). One hundred lights can exhibit 1,267,650,600,228,229,401,496,703,205,376 states! (That’s over 1.2 novillion.) Some idea of the magnitude of this number can be gained this way: if each of the possible 1.2 novillion+ light combinations manifested itself for only one one-millionth of a second, it would take more than 2.9 million times the estimated age of the Universe for each of them to be manifested.

There would have to be, in any such system of lights, a way of controlling whether each individual light was on or off. There would be a system of “inputs” for each bulb, connections to other bulbs  and/or to itself. In a network where each light had 4 or 5 random inputs, the network would be unpredictable and chaotic, going through its state cycles in extremely long sequences, even accounting for the presence of attractors that might give it some organization, and highly vulnerable to any outside disturbances of its operation. But if each bulb were only controlled by one or two others, and each bulb could only be on or off, order would spring into existence regardless of the size of the network and how many states (patterns of  lights either lit or not lit) it could display. Kauffman discovered something utterly amazing. Even in a system of 100,000 lights, which has 2100,000 possible combinations, if each light controls only itself and one other random light (2 inputs per light), the system will fall into a mere 317 different state cycles out of all the enormous number of possible cycles it could go through. (And 317 is about the square root of 100,000.) The conclusion is compelling: Given the right initial conditions and interactions, order can arise spontaneously in even the largest arrangement of entities, without any outside intervention and without any intentionality.7

Scientists are also investigating the phenomenon of self-organized criticality, a hypothesis most associated with the late Danish physicist Per Bak. The idea behind it is typically illustrated by picturing grains of sand being dropped on to a surface. The pile of sand that results can only grow so high before it begins to exhibit a characteristic shape and a structure that produces avalanches of various sizes if additional sand is added to it. The pile is self-organized in the sense that no one has to shape it. In fact, it spontaneously forms substructures of various kinds. And it is in a state of criticality because it is unstable and the results of adding more sand to it are unpredictable. Will adding more sand cause a minor avalanche or a catastrophic one? Bak saw the sand pile’s structure and behavior as a metaphor for all kinds of processes in the physical world that are driven to self-organization and instability by the constant addition of some crucial component. In the words of M. Mitchell Waldrop,

a steady input of energy or water or electrons drives a great many systems in nature to organize themselves in the same way. They become a mass of intricately interlocking subsystems just barely on the edge of criticality—with breakdowns of all sizes ripping through and rearranging things just often enough to keep them poised on the edge.8

It would appear, therefore, that not only is it possible for structures in nature to self-organize, it is rather common for them to do so. The means by which this happens are still being elucidated and debated over, but that it does happen can no longer be doubted. It is this tendency of nature to self-organize, to create structures and substructures which are mathematically describable, and to create spontaneous networks of interlocking and interacting components that allows for the existence of emergence—the appearance of a new “level” of reality.


How do the professionals researching emergence define its properties? The question is still being investigated intensely, but some consensus now seems to be developing.

In a study entitled Causality, Emergence, Self-Organisation, published in 2003, the editors of the study, Vladimir Arshinov and Christian Fuchs, prefaced the book with a summary of what they believe to be the principal characteristics of emergence. They are: synergism, the interaction between two or more entities in a “co-operative” manner; novelty, the emergence of previously unobserved qualities; irreducibility, meaning that the process cannot be reversed to create the same entities that produced it; unpredictability, the creation of an unanticipated result; coherence/correlation, meaning that the emergent phenomenon creates a unity that encompasses its sources; and historicity, meaning that emergent phenomena are not pre-ordained.9

Tom De Wolf and Tom Holvoet  of the Catholic University of Leuven, in Belgium, did an extensive review in 2005 of the literature concerning emergence. They concluded that  genuine emergence has the following characteristics: Micro-macro effect. The behaviors and properties of the emergent system are a result of the interaction of the entities within it. This is considered by almost all researchers to be the essential feature of an emergent system. Radical novelty. The emergent entity cannot be something that would be anticipated by examining the parts of the system in isolation. Coherence. The organization maintains itself over time. Interacting parts. Parts existing in parallel to each other are not sufficient, and cannot produce emergence. Dynamical. The emergent system materializes over time because of new attractors in the interacting system that produces it. Decentralized control.  No individual part controls the whole system. Two-way link. The interacting parts give rise to the new system. The new system in turn affects its parts. Robustness and flexibility. The overall emergent structure is less sensitive to disturbance  or destruction than any single entity within it, and can maintain itself even if it sustains some damage.10

So the essence of emergence appears to be an interaction of elements that brings about an unanticipated, unpredictable outcome, an outcome that can only exist in the presence of this interaction. (See the chapters Synergy and Feedback Loops and Chains of Unanticipated Consequences in this section of the book for more elaboration on these points.)  The emergent system in turn creates a new interactive dynamic that can set the stage for a still higher level of organization. This process does not need any conscious direction and its ultimate result—if there is an ultimate result—will be the sum of all of the unpredictable outcomes generated at every level of the emergent process.

What might stimulate this process? In Robert Hazen’s 2005 study on the origin of life, he identified what he sees to be the factors contributing to the emergence of complex patterning: Concentration of agents. By this Hazen means that there must be sufficient numbers of units (grains of sand, stars, neurons) in close proximity to each other. “Below a critical threshold, no patterns are seen.” Interconnectivity of agents. The more numerous and complex the interactions of individual entities, the greater the chance of emergent phenomena. Energy flow through the system. “The emergence of complex patterns evidently requires energy flow within rather restrictive limits: Too little flow and nothing happens; too much flow and the system is randomized—entropy triumphs.” Cycling of energy flow. Periodic fluctuations in energy and the presence of periodic cycles of  change seem to have a dramatic effect on emergence.11  So emergence seems to involve the effect of energy passing through a system of densely concentrated and closely interacting particles in a particular way, with the term “particle” defined very broadly. As we go backward in time or downward in scale, the interactions between particles (of various sizes and complexities) is less organized and more and more subject to purely stochastic processes.  

The implications of all this are enormous. Nobel laureate Robert B. Laughlin, in discussing the effect the growing study of emergence is having on the sciences, observes that there is a great deal of resistance in the scientific community to abandoning reductionist ideas and embracing emergent ones. Nonetheless, he contends that emergence is such a powerful and useful concept that it will come to dominate humanity’s study of nature, alter our perception of what mathematics is capable of, and usher in what he calls The Age of Emergence, the era when our view of reality is defined by what he calls “the higher organizational laws of the world”.12 If Professor Laughlin is right, then we will come to see the presence of emergent phenomena not just in the sciences but in every area of existence, including an explanation of the emergence of human society and culture.

Personal Conclusions

So what do I conclude from all of this? Here are my hypotheses, based on my (limited) understanding of these phenomena:

First, self-organization and emergence seem to be evolutionary and self-perpetuating in nature. Self-organization (usually) causes emergent phenomena to come into being. Various and diverse emergent phenomena can in turn self-organize to produce a new, larger, more comprehensive  emergent phenomenon. Where this process will end cannot, by its very nature, be predicted. Each level of reality is more and more unexpected; the cumulative effect of all these levels, one “on top” of the other, is the least predictable thing of all in the process. As individual phenomena emerge into the next level of organization, they become subsumed within it. These phenomena are harnessed, so to speak, and become part of an integrated system.

At every level of physical reality, particles tend to link up with other particles because they are drawn together by distinct areas of space-time. (Could we say that they are simply following the path of least resistance?) This linking up becomes more complex as the levels of physical organization become more elaborate. At the highest level of organization—human society—so many variables are at work in this linking process that the effects become more and more unexpected.

It is difficult to see how basic physical interactions can directly lead to the emergence of life. The emergence of chemical principles seems to be a necessary intermediate step. The transition from basic physical particles to human society required a great many intermediate steps.

The micro brings forth the macro; increasing amounts of energy are required to reduce the macro at various levels to the micro. As Timothy Ferris has pointed out, enormous energies are required to tear matter down to its most fundamental levels, energies that more and more approximate those which must have existed at the time of the Big Bang. It would be quite possible, for example, to destroy a complex structure by breaking it apart into small pieces. But breaking it into its constituent molecules would require much more energy, breaking it into its atoms would require an enormous amount of energy, and breaking it into its quarks and leptons would require an inconceivable amount of energy. The end results of emergence are not necessarily permanent; emergent phenomena can be undone, but doing so requires undoing a great many steps and the marshaling of energies that are not easily acquired.

When we reach down to the most fundamental level of physical reality, using reductionist methods, there seems to be nothing but chaos. Emergence theory allows us to account for the order we find at various levels higher than the chaotic, basic level of physicality. Emergence theory therefore puts the reductionistic view in a new perspective. No longer is reductionism simply a descent into chaos; it becomes a descent into origins.

Using reductionistic methods in combination with the emergent perspective allows us to trace our story backward through time, starting with the “highest” level (that is to say, the  level that is the ultimate result of all the preceding emergent levels) and ending up at the most fundamental level of physical reality, the point at which we can go back no further.  We would therefore start with the human cultural and social worlds, their intricate rules and interrelationships, and all the “structures” which are no more than approximately understood common ideas held in the neurons of human brains. We would trace the emergence of human society and culture to consciousness, which is less organized and more random than the social and cultural worlds. We trace the origin of consciousness to the evolution of a particular kind of brain, noting that the steps that led to the biological evolution of higher-order nervous systems were more random than the ordered functions of the brain produced by these steps. We see that the evolution of the brain was an emergent result of the general evolution of multicelled beings, which was a broader, less defined, less organized phenomenon than the emergence of highly advanced collections of neurons. The evolution of multicelled beings emerged from the relatively more chaotic world of one-celled organisms. These one-celled organisms were in turn brought about by the emergence of nucleic-acid based life existing without membranes, brought about by the interactions of molecules built around carbon atoms. These molecules were themselves the product of a long chain of basic, evolving, self-reproducing chemical units (perhaps preceded by simple metabolic processes) which existed in a highly chaotic state of seemingly random movement, and which began to undergo changes because of the interaction between their own replication errors and changes in the physical environments in which they existed. The atoms which came together to form these molecules were in turn assembled and held together by fundamental particles, which in turn were the product of the emergence of the four fundamental forces of nature at the first moments of the Universe’s existence.

Every level of organization is both more coherent and more information-dense at the same time. Every level of organization contains all the information of all the levels from which it emerged. In one perspective, reality can simply be seen as the generation, transference, accumulation, and aggregation of information.

Is the social organization created by human consciousness the ultimate stochastic dynamical system, because of the number of possible outcomes or actions of the “particles”? When a “particle” knows that it is a particle, and that it is possible do things that are not pre-determined, does that create a unique form of dynamical system?

Not all areas of the Universe have been resolved into order. There are still areas, for example, where the basic level of physical reality is the only one, and nothing has emerged from it. Other areas have gotten no farther than basic chemistry; others no farther than basic biology. The ways of life and social interaction created by the human species involve an extraordinary—and quite possibly, very rare—number of emergences “stacked up” on each other. And there would have been no conceivable way of predicting that the randomly interacting quarks that came into being moments after the Universe’s beginning would ultimately bring forth human society and culture.

Self-organization and emergence have produced certain fixed regularities in the operation of physical reality. In the human perspective, these regularities appear to take a particular form:

They are called the laws of nature. So now we turn to them.

1.   Deutsch, David, The Fabric of Reality, pp. 20-21
2.   F. Heylighen,  "Self-Organization, Emergence and the Architecture of Complexity", in:
      Proceedings of the 1st European Conference on System Science, (AFCET, Paris), p. 23-32., 1989
3.   Pagels, Heinz, The  Dreams of Reason,  pp. 65-66
4.   Jan Ambjørn, Jerzy Jurkiewicz, and Renate Loll, “The Self-Organizing Quantum Universe”, in Scientific American, July 2008
5.   Kauffman, Stuart, At Home in the Universe: The Search for the Laws of Self-Organization and Complexity, pp. 79-110
6.   Kauffman, pp. 74-79
7.   Kaufmann, pp. 77-83
8.   Waldrop, M. Mitchell, Complexity: The Emerging Science at the Edge of Order and Chaos, pp. 304-306
9.   Arshinov, Vladimir, and Fuchs, Christian, editors. Causality, Emergence, Self-Organization, pp. 5-8
10. Tom De Wolf, , and Tom Holvoet, “Emergence Versus Self-Organisation: Different  Concepts but Promising When Combined”,  Department of Computer Science, Kuleuven, Celestijnenlaan Leuven, Belgium, 2005
11. Hazen, Robert, Genesis: The Scientific Quest for Life's Origins, pp. 17-22
12. Laughlin, Robert B., A Different Universe: Reinventing Physics from the Bottom Down, pp. 173-221 

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