STRUCTURAL PROPERTIES OF COMPLEX ADAPTIVE SYSTEMS Adapted/expanded from John Holland A. Each Complex system is a network of many 'agents' acting in parallel. EXAMPLES: Nerve cells in a brain, organelles in a cell, ants in a colony, species in an ecological biome, producers and consumers in an economy. B. Each Complex system tends to be decentralized in decision- making. EXPLICATION: In cells, chemical and micro-electronic processes arise from each free ion, molecule and organelle in the ecosystem of that cell. In an economy, its dynamical state is a function of millions of decisions made by separate agents. C. A Complex System has many levels of organization. EXPLICATION: A set of amino acids constitute a protein; proteins, lipids, and free ions constitute a cell; a set of cells constitute a physiological system [bone, heart, skin); a set of systems constitute an organism; a set of organisms constitute a niche in a biome. Interacting sets of organisms constitute an ecological system. These, in turn, draw upon and adapt to energy/materials from inorganic systems [rock, sun, water, excrete, and carrion. D. Complex Systems continuously rebuilt and re-pattern its constituent sub-systems as it adjusts to and learns from other systems in an ecosystem. This is called Equi- finality. EXPLICATION: Firms promote employees who are helpful to its survival; cells admit water molecules when its molar density exceeds a given point; people turn to new and different foods in a time of drought; new species arise as a biome becomes energy rich or energy poor compared to previous states. E. In some way or another, all Complex systems anticipate the future. EXPLICATION: Workers in an industry learn its cycles and adjust their buying toward the day when income will be higher or lower; firms in a niche know the buying patterns which come with the seasons and order in anticipation of them; bears feed and store fat for the coming Winter; brains develop software sub-routines built around anticipation of pain and/or pleasure; deer do not drop their fawns until food supply is likely to increase; moths produce more eggs when food is abundant. These routines are continually tested, adjusted and replaced. F. Complex Systems offer many niches to individuals and species within it. EXPLICATION: In the human body, there are many places where bacteria can live and, perchance, contribute to the integrity of the whole. At the same time, in the same body, there are places where the same bacteria cannot live... and other kinds of bacteria or viruses might. In a biome, there are many niches in which such species as ants, rabbits, trees, shrubs, bacteria, butterflies, bears and grasses can live. As plants succeed each other, new niches are formed which may... or may not ... be used by still other, new species. The new species in turn, offer energy/material resources for still more new kinds of animals and plants to survive. G. Complex Systems may be conceptualized as process until niches are filled; at which time, the whole system-as- process takes on the character of structure for those included sub-systems. EXPLICATION: Process transforms into structure as those routines and sub-routines within it become predictable enough to serve as reliable energy sources for 'agents' within it. When the ice cap recedes, plant seeds are blown in by the wind or dropped by birds ... their activity is pure process until animals [bacteria to bears] settle into the niches plant life provides. Bacteria, moles, rabbits, hawks, and foxes then form ever adjusting cycles to each other while the plants are limited, in turn, by the activities and by-products of that animal life. The whole system becomes structure while the activity-as-process of each component sub-system becomes structure to every other species in every other niche. DYNAMICAL PROPERTIES OF COMPLEX SYSTEMS I. Most natural and social dynamics are nonlinear. EXPLICATION: A. Small changes can produce large, untrackable changes in the dynamics of natural and social systems. B. Large changes in key parameters can be absorbed by a nonlinear system. This ability to absorb change depends upon proximity to the feigenbaum points mentioned below. C. Variations in the behavior of a system is such that no given iteration ever repeats itself precisely. Self-- similarity replaces sameness in the Chaos paradigm. D. Simple nonlinear dynamics can produce very complex structures. The Mandelbrot Set of attractors is, perhaps the most complex structure in the universe. It is produced by the nonlinear interaction to two values; one of which is kept constant and the second allowed to vary without restraint. II. Interactions of key parameters produce varied outcome states called attractors. A. The degree of chaos of each attractor changes dramatically to entirely new Attractors [configurations] with small changes at key moments. B. There are five generic attractors; 1) Point, 2) Limit, 3) the Torus, 4) a Butterfly with a 2n outcome basin, 5) more complex attractors with 4n, 8n, and 16n basins. In addition, there is a dynamical state with a great many endstates we can call full or deep chaos. Attractors 3, 4, and 5 offer a mix of order and disorder most congenial to the human need for predictability and planning while, at the same time, conducive to creativity and human agency. C. Nonlinearity increases qualitatively as system dynamics move from limit to tori; from tori to butterfly and from butterfly to deep chaos. D. There is a precise point at which transitions from one state to another occurs. These are marked by the 'Feigenbaum' numbers. III. Nonlinear Dynamics Produce Structures which have a Fractal Geometry; process and structure are thus united in Chaos. A. Both Order and Disorder are found together in every region and at every scale in fractal structures. B. The amount/ratio of order to disorder depends upon which region in an outcome basin one samples; both precision of dynamics and replicability of research findings are a function of sampling decisions. C. The geometrical dimensions of a dynamical system vary with scale of observation. One speaks of degrees of reality/facticity rather than of sharply delineated euclidean geometry such as dense lines, unbroken planes, or solid three dimensional objects. D. Any given mapping of the dynamics of a complex system at any given scale of observation is similar to that of an adjacent region or to some larger region in the total pattern of dynamics mapped by its behavior over time, but it is never identical. IV. Multiple systems with fractal geometries can occupy the same region in either real time/space or phase space. If they maintain their boundaries, they are called Solitons. Solitons maintain their integrity through nonlinear feed back loops. V. There are three kinds of feedback which affect the dynamics of complex systems: 1) Positive linear feedback loops tend to break up an attractor and, (after exhausting 3 dimensional space), tend to bifurcate that attractor until it occupies the time-space available to it. 2) Negative feedback loop work to draw a system down to a point attractor or extinguish it. 3) Nonlinear feedback tends to maintain an unstable system in a semi-stable attractor. VII. The number of basins in any outcome field increases as bifurcations in key parameters occur. A. With each bifurcation, causal basins double. Similarity is found within each different basin; uncertainty is found between outcome basins. B. Uncertainty increases qualitatively at each bifurcation. 1. The bifurcation from a limit attractor produces first order nonlinearity. It is small and often dismissed as observer error, technical error, incomplete measurement or just plain bad theory. 2. A second order form of change occurs when a torus transforms into a butterfly attractor. [In fact, a Butterfly Attractor can be viewed as two connected Tori]. This change is qualitatively different from the small variations found in a torus. The great difference in behavior observed in the two wings of a Butterfly attractor is often interpreted as proof of the existence of unknown intervening variables. Alternatively, that difference is used, erroneously, to falsify theory based upon findings from one or the other wing. 3. Third Order change occurs when another small increase in a key parameter drives a system [or set of systems] into deep chaos. This change is qualitatively different from the two above in that entirely new 'causal' relationships emerge; entirely new dynamical forms evolve out of the free energy from dissipative systems [After Prigogine]. VIII Bifurcations occur at precise intervals as changes in key parameters reach any one of four Feigenbaum points: 1) Limit attractors transform into tori when a key parameter reaches 3.0; 2) Tori transform in butterfly attractors at 3.4495; 3) 4n, 8n, and 16n Attractors are found in the narrow range of between 3.56 and 3.596. 4) there is a cascade to deep chaos with another small change at 3.596. B. Attractors with 2n, 4n, 8n, and 16n outcome basins combine enough order to serve the human need for planning and prediction; enough variability to serve the human need for flexibility, creativity and transformation. B. The value at which a key parameter becomes progressively and linearly smaller. The change in bifurcation points over the entire range of such points has been shown to be 4.6692016...this number is called Feigenbaum's constant (not to be confused with the feigenbaum points above. Glass and Mackey: 1988:33). VIII Bifurcations cascade a system (or set of system) into full chaos after the 4th bifurcation. A. Uncertainty increases by orders of magnitude at that bifurcation. (Glass and Mackey, 1988: 32). B. There are macro-structures in a bifurcation map which show points of unstable equilibrium. Small changes which refit the dynamical key at those points will maintain unstable equilibrium (Hbler, 1992; Kutchkoff, 1992) IX. New forms of order emerge out of fully chaotic fields. A. Even in fully chaotic regimes, there are regularities with which pockets of order appear (Glass and Mackey, 1988:32) B. Prediction is impossible but certainty is. That is, we cannot know the direction in which systems at the boundaries of an outcome basin will move but the ratio between order and disorder in the outcome field as a whole can be measured (Mandelbrot, 1977:363; Glass and Mackey: 1988:53). X. What is process at one scale of observation can be understood as structure at a more macro-scale of observation. A. Structure in chaotic regimes emerge as iterations proceed and transient states disappear. B. Structure in chaotic regimes is stabilized [locked-in] as other systems begin to occupy the niches provided by the new system [or set of systems]. In turn, the energy and raw materials from companion systems limits the behavior of the first. Think of a new species of tree in a biome which harbors other plants and animals which in turn provide pollen, seed dispersal, protection from insects, fertilizer, and aeration of soil. The whole eco-system becomes stabilized in second order change patterns until a key parameter [weather, predator, food supply, moisture] exceeds a critical Feigenbaum point. B. These structures are, themselves fractal and self- similar resolve back into process with micro-analytic techniques. C. The system in process is itself a product of other, more basic systems in process. D. Chaotic regimes thus produce very stable structures at macro-analytic scales. [vide Barnsley throwing dice; any given throw does not change the uncertainty of the next throw but all throws taken together define a very stable structure]. XI. Only Chaos can Cope with Chaos. A. If one wants a strategy with which to maximize proximity to a given attractor in a larger outcome field, one must adopt a chaotic strategy which is set by the dynamical key of that attractor (Hbler, 1992). B. In any nonlinear field, a nonlinear system has survival advantages over linear systems. (See XII, below C. In any nonlinear field, small systems are preferable to large, well ordered systems since they match variety better. XII. Chaotic Dynamics are preferable to Linear in many applications: Holden, (1986:10) suggests three advantages of nonlinear dynamics in a chaotic environment. 1. Chaotic diversity compensates for genetic stability. 2. Chaotic behavior improves survival chances. [It is difficult for a predator to track nonlinear behavior]. 3. Chaos prevents entrainment. Entrainment would either amplify deviation (toward full chaos) or reduce variety (toward a steady state). 4. Bruce West (UNT) adds that an irregular heartbeat is better able to meet unpredictable needs for oxygen and energy than is a regular heartbeat. (TWU lecture, 28 Feb. 1992)