Self-Organizing Systems

Self-organization refers to spontaneous ordering tendencies sometimes observed in certain classes of complex systems, both artificial and natural. Such systems have a large number of components that interact simultaneously in a sufficiently rich number of parallel ways; are at best only partially decomposable; are sensitive to initial conditions when they are in the chaotic regimen; are constrained away from their most probable state; and exhibit nondeterministic bifurcations in their dynamic trajectories. Self-organization occurs in these systems when chance fluctuations are spontaneously amplified by nonlinear feedback. This sort of spontaneous ordering has been observed in computational systems that are programmed for nonlinear, parallel interactions under local constraints. Examples in nature range from dust devils and hurricanes to certain sorts of chemical and biological systems, such as Benard cells and chemical oscillators (see below). The topic of self-organization has also been explored under other rubrics, such as "emergent structuring," "self-assembly," "autocatalysis," and "autopoiesis." In each case, the contrast emphasized is between the additive building of structures from elemental building blocks in a decomposable or nearly decomposable system (in the sense defined by Simon 1962) by means of measured increments of force and the spontaneous emergence of nonadditive, nonlinear, highly integrated, highly interactive wholes in less decomposable systems.

Ilya Prigogine's model of dissipative structures, which obey the second law precisely by building structures that increase the entropy of their surroundings while decreasing it within their own boundaries, has facilitated both the recognition of self-organizing structures and their explanation (Prigogine 1973). The wider significance of Prigogine's work has been made known by Isabelle Stengers, Erik Jantsch, Jeffrey Wicken, and C. Dyke (Prigogine and Stengers 1984; Jantsch 1980; Wicken 1987; Dyke 1988). Stuart Kauffman has been prominent among those who have argued that the self-ordering properties of cellular AUTOMATA provide good dynamic models for self-organizing biological systems (Kauffman 1993). Cellular automata were originally developed by John VON NEUMANN and Warren MCCULLOCH as tools for analyzing NEURAL NETWORKS.

The line between genuinely self-organizing systems and the self-ordering properties of a wider class of complex systems is difficult to draw. Those who stress the autocatalytic, self-promoting aspect of self-organizing systems, in which a reaction feeds on itself, and the far-from-thermodynamic-equilibrium locus of paradigmatic instances of it, may hesitate to recognize the self-assembly of microtubules, for example, as any more than a case of crystalline self- ordering. Similarly, a distinction might well be drawn between self-organizing systems generally and "autopoietic" systems, in the sense of Maturana and Varela's use of the term (Maturana and Varela 1980). The latter term connotes the kind of agency that appears when a complex dissipative system is coupled to its environment through autocatalytic feedback in such a way that it is capable of changing the parameters that govern its interactions with its surroundings. (Maturana and Varela suggest that the ability of some living things to represent their environment, and in some cases even themselves, to themselves is a function of self-organization, which creates a bond between self and environment that is more intimate than our philosophical tradition has hitherto allowed.)

One ought not, however, be too rigid about such definitional matters. Research into these issues is only in an early stage, and usage is in flux. Nonetheless, it is highly significant that the computational revolution has now given science mathematical tools to track and display the dynamics of systems that do not reduce either to ordered simplicity, as in classic mechanics, or to disordered complexity, as in statistical mechanics and thermodynamics. This allows the ordered complexity of phenomena that have hitherto remained beyond the reach of science itself, or that have been subjected to inappropriately reductionist forms of analysis, to be brought within the charmed circle of mathematized knowledge.

The best understood cases of natural self-organization occur in physical and chemical systems that are stabilized far from thermodynamic equilibrium. Benard cells are a classic example of self-organizing physical systems. A honeycomb of hexagonal cells forms at the bottom of the pan when a thin layer of oil is heated from below. This happens because the kinetic energy of the molecules becomes insufficient to dissipate the energy flux when it exceeds a certain threshold value. Macroscopic order then emerges in which billions of molecules move coherently in a convection stream, thereby more efficiently dissipating the energy gradient and increasing the entropy of the surroundings of the system. Increasing the gradient further can lead to a development of still more complex convection cells. Ultimately, however, excessive gradient will result in turbulence.

The Belouzov-Zhabotinskii, or BZ, reaction is a well-known example of self-organization in a chemical system. In a BZ reaction, citric acid, sulfuric acid, potassium bromate, and an iron salt, when combined in certain proportions, produce sudden and repeated alternations between blue and red states in stirred solutions. In thin layers, circular or spiral chemical waves of color can result. As in the case of Benard cells, increasing the gradient produces nondeterministic bifurcations and more complex patterns. But when the energy gradient (which in this case inheres in the chemical bonds between constituents) grows too steep, chaotic behavior results.

Chemical oscillators, such as the BZ reaction, may have implications for self-organization in biological systems, particularly in development. Alan TURING's paper on limit cycle solutions to reaction-diffusion equations has long been thought by some to model certain aspects of embryogenesis (Turing 1952). The life cycle of slime molds, a sort of colonial amoeba, also appears to embody a self-organizing pattern. It alternates between mere aggregation when food is plentiful and differentiation into a cellulose base and a fruiting body when it is scarce. The fruiting body eventually bursts, scattering spores that begin the cycle over again (Garfinkel 1987).

As these examples show, self-organization is potentially relevant to fundamental questions about EVOLUTION. One issue is whether life itself came into existence through a self-organizing process. Those who have used computers to explore the mathematically self-ordering properties of complex adaptive systems have studied this subject under the rubric of ARTIFICIAL LIFE. Those whose definition of life is less formal have looked for chemical conditions in the early history of the planet in which some form of prebiotic selection might have amplified the autocatalytic properties of self-organizing protocells into functional, adapted traits. Such studies begin with the plausible insight that life probably did not originate solely in the accidental assembly of nucleic acids, but in the coevolution of proteins and nucleic acids, with protein evolution perhaps playing the leading role. Sidney Fox's pioneering work on proteinoid microspheres reveals them to be spontaneously self-organized systems that might have provided the hydrophobic boundaries within which the subsequent coevolution of protein and nucleic acids can take place (Fox 1984). Harold Morowitz's and David Deamer's notion of abiotically forming vesicular amphiphile bilayers provides another possible such "cradle" for the emergence of life (Morowitz, Heinz, and Deamer 1988). Manfred Eigen's notion of hypercycles provides a model of how this interaction might have occurred. One can think of a hypercycle as a system of linked autocatalytic cycles, in which each member is catalyzed by at least one other member (Eigen and Schuster 1979.)

A second issue is the relationship between natural selection and self-organization once life is up and running. On the face of it, self-organization rivals natural selection as the basis of both individual development and of the larger contours of phylogenetic order. For the acquisition of functional traits by self-amplifying feedback is not the same thing as selection-by-consequences by means of a forcelike "selection pressure" that operates against an inertial, and indeed inert, dynamic background, which is how natural selection is usually conceived. The notion that self-organization and natural selection are rivals has been defended by several authors (Goodwin 1994; Oyama 1985; Salthe 1993). A more integrative, mutually reinforcing approach is, however, possible. Recognizing that when any system analogous to Boolean networks is set into motion it can be expected spontaneously to explore its space of future states and if mild "fitness" conditions are imposed it can be expected to reach peaks on "adaptive landscapes." Kauffman, Holland, and others who have studied genetic algorithms and EVOLUTIONARY COMPUTATION have suggested that "spontaneous order is available to natural selection for the further selective crafting of well-wrought designs" (Kauffman 1993: l; Holland 1995). One might readily imagine, in accord with this suggestion, that natural selection has stabilized the self-organized life cycle of slime molds, and in the process has conferred an explicitly biological function on a spontaneously generated pattern. Kauffman himself argues that the regulatory systems of genetic networks, among whose many nodes much connectivity and parallel processing are at play, are self-organizing, functionally decomposable (see FUNCTIONAL DECOMPOSITION) systems that have been stabilized by natural selection in this way. Weber and Depew have argued that, considered as a natural phenomenon in its own right, natural selection emerges only in autocatalytic chemical systems that have managed to internalize information in macromoleules, the error rate of which provides the fuel of natural selection (Weber and Depew 1996). In this account, genes have the function of enhancing and stabilizing the coupling between organism and environment that self- organization first generates.

The human brain has about 10¹⁰ neurons, any of which can have up to 10⁴ connections with other such neurons, stimulated and regulated by a large number of chemical neurotransmitters. This fact alone brings the study of cognitive and other psychological phenomena within hailing distance of the study of self-organizing complex systems. This distance has been reduced by those advocating DYNAMIC APPROACHES TO COGNITION, who recognize that learning is a process that occurs only in systems that are "environmentally embedded, corporeally embodied, and neurally entrained" by feedback (see Port and Van Gelder 1995; Smith and Thelen 1993; Kelso 1995; Cook and Murray 1995). If digital computationalism gives way to more dynamical studies of connectivity in neural networks, self-organization can be expected to play a more prominent role in both the ontogeny and phylogeny of mental functions. The purely adaptationist stories people like to tell about the Pleistocene origins of localized mental functions (Barkow, Cosmides, and Tooby 1992), as well as the inclination to model neurological development closely on Darwinian mechanisms (Edelman 1987), might then give way to a more nuanced view, in which neural organization is taken to be governed in part by self-organization working through intense feedback between organism and environment.

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-- David Depew and Bruce Weber

References

Barkow, J., L. Cosmides, and J. Toomy. (1992). The Adapted Mind. New York: Oxford University Press.

Cook, J., and J. D. Murray. (1995). Pattern formation, biological. In M. A. Arbib, Ed., Handbook of Brain Theory and Neural Networks. Cambridge, MA: MIT Press, pp. 705-710.

Dyke, C. (1988). The Evolutionary Dynamics of Complex Systems. Oxford: Oxford University Press.

Edelman, G. (1987). Neural Darwinism. New York: Basic Books.

Eigen, M., and P. Schuster. (1979). The Hypercycle. Berlin: Springer.

Fox, S. (1984). Proteinoid experiments and evolutionary theory. In M.-W. Ho and P. T. Saunders, Eds., Beyond Neo-Darwinism. London: Academic Press, pp. l5-60.

Garkinkel, A. (1987). The slime mold Dictyostelium as a model of self-organization in social systems. In F. E. Bates, Ed., Self-Organizing Systems: The Emergence of Order. New York: Plenum Press.

Goodwin, B. C. (1994). How the Leopard Changed Its Spots: The Evolution of Complexity. London: Weidenfeld and Nicolson.

Holland, J. A. (1995). Hidden Order: How Adaptation Builds Complexity. Reading, MA: Addison-Wesley.

Jantsch, E. (1980). The Self-Organizing Universe. Oxford: Pergamon Press.

Kauffman, S. A. (1993). The Origins of Order: Self-Organization and Selection in Evolution. New York: Oxford University Press.

Kelso, J. A. S. (1995). Dynamic Patterns: The Self-Organization of Brain and Behavior. Cambridge, MA: MIT Press/Bradford Books.

Maturana, J., and F. Varela. (1980). Autopoiesis and Cognition: The Realization of the Living. Dordrecht, Reidel.

Morowitz, H. J., B. Heinz, and D. W. Deamer. (1988). The chemical logic of a minimum protocell. Origins of Life and Evolution of the Biosphere l8: 28l - 287.

Oyama, S. (1985). The Ontogeny of Information. Cambridge: Cambridge University Press.

Port, R., and T. van Gelder. (1995). Mind as Motion: Explorations of the Dynamics of Cognition. Cambridge, MA: MIT Press.

Prigogine, I. (1973). Irreversibility as a symmetry breaking factor. Nature 248:67-7l.

Prigogine, I., and I. Stengers. (1984). Order Out of Chaos: Man"s New Dialogue with Nature. New York: Bantam.

Salthe, S. N. (1993). Development in Evolution: Complexity and Change in Biology. Cambridge, MA: MIT Press.

Simon, H. A. (1962). The architecture of complexity. Proceedings of the American Philosophical Society 106:467-482.

Smith, L. B., and E. Thelen. (1993). A Dynamic Systems Approach to Development. Cambridge, MA: MIT Press/Bradford Books.

Turing, A. M. (1952). The chemical basis of morphogenesis. Philosophical Transactions of the Royal Society London.Series B. Biological Sciences 237:37-72.

Weber, B. H., and D. J. Depew. (1996). Natural selection and self-organization: Dynamical models as clues to a new evolutionary synthesis. Biology and Philosophy 11:33-65.

Wicken, J. (1987). Evolution, Information and Thermodynamics: Extending the Darwinian Program. New York: Oxford University Press.

Self-Organizing Systems

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