Swenson: Advances in Human Ecology, Vol. 6, 1997

AUTOCATAKINETICS: A THEORY OF EMBEDDED CIRCLES

Identity Through Flow

Symmetry Breaking And Symmetry Making: Autocatakinesis,
And The Generalized Metabolism Of Dynamic Flow Structures

An ecological science requires a demonstration of why, contrary to what most evolutionary theorists believe biological and cultural evolution are not a negation of physical evolution‹a principled basis for uniting the two rivers, or otherwise apparently two-direction universe, that Fisher, and many others have pointed out. It requires answering the question of Lorenz about why, with the fecundity principle, according to which life produces as much order as it can, and with evolution as a whole, the world produces what appears as a progressive process that goes from what appears to be more probable to increasingly less probable states. It needs to show why, if the transition from disorder to order is infinitely improbable, as Boltzmann argued, the world, in effect, is in the order-production business. What is more, it must show the basis for the meaningful relations by which the intentional dynamics of biological and cultural ordering are distinguished.
As noted briefly above, part of the attraction of Descartes' passive, "dead", qualityless world of physics to the proponents of the mechanical world view was that it required extra-physical ordering to get it ordered. The mechanical world, made of inert, reversible, particles incapable of ordering themselves, as Boyle (Lange, 1877/1950, p. 255) pointed out, like the "ingenious clock of Strasburg Cathedral" must have an intelligent artificer to account for it. In addition to Boyle, the argument from design was made repeatedly throughout the rise of modern science. Paley's famous version about finding a watch on a beach, and knowing that it had to have had a watchmaker to design it, is the one Darwin is credited with undermining with the idea of natural selection which Dawkins (1986) has consequently termed the "blind watchmaker". But there is a serious category error in these arguments, namely, that non-artifactual systems, such as living ones, are not the same kinds of things as mechanical artifacts. In different terms, if you found a watch on a beach, or wherever, it certainly would make sense to imagine that it had an artificer to design it because nothing like it has ever been found in the universe as far as anyone knows that was not artifactually produced.
Machines or artifacts are defined by static order‹their identity constituted and maintained by static components, the same components, external repairs excluded, in the same positions with respect to each other. Living systems from bacteria to cultural systems, as self-organizing, or spontaneously ordered systems, are defined by dynamic order‹their identity is constituted through the incessant flux of their components which are continuously being replaced from raw materials in their environments, and expelled in a more dissipated form. Persistence (the form of the thing) at one level (the "macro" level) is constituted by change at the component level (the "micro" level). In more technical terms, living systems are autocatakinetic systems while artifactual systems are not. The class of autocatakinetic systems includes more than just living systems, and this immediately suggests a connection between living and non-living things that will

a tornado is an autocatakinetic system or system of spontaneous order and dynamical flow

Figure 2. A tornado is an example of an autocatakinetic system, a dynamically ordered flow structure whose identity, in contrast to a machine, or artifact, is constituted not by a set of particular components typically occupying fixed positions with respect to each other, but by the ordered relations maintained by the incessant flow of its components. The dynamical order that defines the persistence of an autocatakinetic system as an object at the macro level, is maintained through constant change at the micro level. This incessant flux of components can be thought of as a generalized metabolism by which the system maintains itself by pulling environmental potentials (or resources) into its autocatakinesis, which it returns in a more dissipated form. All living things from bacteria to human cultural systems as well as the planetary system as a whole, which maintains a constant level of oxygen, for example, by this same generalized process, are all members of the class of autocatakinetic systems. Photo courtesy of the National Severe Storms Laboratory.

be more apparent later on. Dust devils, hurricanes, and tornadoes, for example, are all examples of autocatakinetic flow structures whose identities are constituted in just this way‹by the incessant flux of matter and energy pulled in from, and then excreted or expelled back into, their environments in a more degraded or dissipated form (see Figure 2). An autocatakinetic system is defined as one that
maintains its "self" as an entity constituted by, and empirically traceable to, a set of nonlinear (circularly causal) relations through the dissipation or breakdown of field (environmental) potentials (or resources) in the continuous coordinated motion of its components (from auto- "self" + cata- "down" + kinetic, "of the motion of material bodies and the forces and energy associated therewith" from kinein, "to cause to move")(Swenson, 1991a).
The importance of understanding living systems as flow structures with behavior generic to the class was emphasized in the first half of this century by Bertalanffy (e.g., 1952), and later by Schröedinger (1945), who popularized the idea of living things as streams of order which, like flames, constitute themselves by feeding off "negentropy" (energy potentials) in their environments. Prigogine (e.g., 1978) called such systems "dissipative structures". The root of the idea goes back at least to the Presocratic Heraclitus (536 B.C.) who, in contrast to Parmenides, for whom true reality was entirely static, characterized the world as a continual process of transformational flow, and its objects as constituted by a generalized metabolism or combustion. Fire, as Aristotle (1947, p. 182) wrote centuries later in De Anima, stressing the active agency and generalized metabolism, consumption, growth, and decay of such systems, "alone of the primary elements [earth, water, air, and fire] is observed to feed and increase itself." In modern times the idea was picked up by Leibniz who, following Heraclitus, described the dynamical persistences of the world as in a state of "perpetual flux, like rivers [where] the parts are continually entering in and passing out" (Rescher, 1967, p. 121). It was first used as part of a general theory of evolution by Spencer (e.g., 1852, 1857/1892, 1962; Swenson, in press-b). Figure 3 shows a schematic of a generalized autocatakinetic system. Circular causality, as
an autocatakinetic system is a dynamic energy flow system that converts thermodynamics potentials in their environments or ecology and turns them into entropy

Figure 3. A generalized autocatakinetic system. EI and EII indicate a source and a sink with the difference between them constituting a field potential with a thermodynamic force F1 (a gradient of a potential) the magnitude of which is a measure of the difference between them. is the energy flow at the input, the drain on the potential which is transformed into entropy production at the output. EIII is the internal potential carried in the circular relations that define the system by virtue of its distance from equilibrium that acts back to amplify or maintain input during growth or non-growth phases respectively with an internal force F2. From "Emergent Attractors and the Law of Maximum Entropy Production: Foundations to a General Theory of Evolution" by R. Swenson, 1989b, Systems Research, 6, p. 191. Copyright 1989 by Pergamon. Adapted by permission.

in closed-circle theory, and its various relatives, plays a central role in autocatakinetic systems, but in contrast to the autonomous circular relations of closed-circle theory which refer only to themselves, the circularity that defines an autocatakinetic system defines, and maintains it in relation to its environmental sources. Autocatakinetic systems are embedded circles whose existence is inseparable from their environments both in actuality, and by definition. In contrast to generalized Cartesian or closed circles, the circularity that defines the existence of autocatakinetic systems refers to the autocatakinetic-environment relation. There is no existence or self-reference for an autocatakinetic system independent of this relation. The rest of this section sketches some of the important generic behavior of autocatakinetic systems, and the following section the nomological basis for this dynamical ordering, and the way it is manifested in the intentional dynamics of living things.

Order Production, Symmetry Breaking, And Space-Time Dimensions

Symmetry, simply put, is invariance over change. Something is symmetric under certain operations or transformations if those operations leave it unchanged, it remains the same, or, put differently, is conserved under those operations. The greater the number of symmetry operations that can be performed on a thing to which it is indifferent, or remains unchanged the greater its symmetry. With geometric objects, for example, a sphere has greater symmetry than any other with respect to its rotational symmetry group because it is left invariant under arbitrary rotations around any axis passing through its center. Because these rotations can take on any value, the rotational symmetry group of a sphere is said to be continuous. In contrast, the symmetry group of a cube is discrete rather than continuous, and its symmetry is considerably lower. It is symmetric only under rotations around an axis through its face centers of 90š, 180š, 270š, and 360š (fourfold rotations). As this example shows, discontinuities constitute a break or reduction in symmetry, and from this we see that spontaneous order production, the appearance of an autocatakinetic system where there was none before, constitutes a symmetry-breaking event. There is now an object where there was no object before, and such an object constitutes a discontinuity in the field or environment from which it arises. When a tornado comes into being in a sky where there previously was no tornado it breaks the symmetry of the sky.
This is further illustrated with a classic laboratory example of spontaneous ordering, or self-organization, known as the Bénard experiment (see Figure 4). In this experiment a viscous

the Benard experiment is a easy to understand example of spontaneous order

Figure 4. Two time slices from the Bénard experiment. The first time slice (left) shows the homogeneous or disordered "Boltzmann regime" where entropy is produced by heat flow from the disordered collisions of the molecules (by conduction), and the second (right) shows entropy production in the ordered regime. Spontaneous order arises when the field potential is above a minimum critical threshold, and stochastic microscopic fluctuations are amplified to macroscopic levels as hundreds of millions of molecules begin moving in an orderly fashion together. From "Emergent Attractors and the Law of Maximum Entropy Production: Foundations to a Theory of General Evolution" by R. Swenson, 1989b, Systems Research 6, p. 192. Copyright 1989 by Pergamon. Reprinted by permission.

fluid (silicone oil) is placed in a dish and heated uniformly from below. As a consequence of the difference in temperature, or gradient, between the hot bottom (source) and the cool air on top (sink) a potential exists which results in a flow of energy as heat from source to sink. Figure 4 shows two time slices from this experiment. The left-hand photo shows the disordered or Boltzmann regime where the potential is below a minimal threshold, and the source-sink flow is produced by the random, or disordered, collisions of molecules. In this regime, the surface of the system is smooth, homogeneous, and symmetrical. Any part can be exchanged with any other without changing the appearance or dynamics of the system at all. When the potential is increased beyond the critical threshold, however, the situation changes dramatically as spontaneous order arises and the symmetry of the disordered regime is broken. The dynamical ordering of the system produces macroscopic discontinuities with distinct space-time orientations that make it no longer possible to arbitrarily exchange one part for another.
The relation between order production, symmetry breaking, and space-time dimensions is an important one, and can be brought further into focus by looking at the Bénard experiment in
more detail.
a line drawing showing the energy flow from source to sink (entropy production) characterizing the Benard cell experiment

Figure 5. The autocatakinetic flow of the fluid constituting a Bénard cell is shown by the small arrows. is the heat gradient between the heat source below and the sink above that constitutes the potential that motivates the flow. Because density varies inversely with temperature there is also a density gradient from bottom to top giving groups of molecules ("parcels") that are displaced upwards by stochastic collisions an upward buoyant force. If the potential is above the minimum threshold, parcels will move upward at a faster rate than their excess heat can be dissipated to their surrounds. At the same time such an upward flow of heat will increase the temperature of the upper surface directly above it creating a surface tension gradient which will act to further amplify the upward flow by pulling the hotter fluid to the cooler surrounds. The upward displacement of fluid creates a vacuum effect pulling more heated fluid from the bottom in behind it which in turns makes room for the fluid which has been cooled by its movement across the top to fall, be heated and carry the cycle on, and autocatakinesis has been established. From Spontaneous, Order, Evolution and Natural Law: An Introduction to the Physical Basis for an Ecological Psychology by R. Swenson, 1997, Hillsdale, NJ: Lawrence Erlbaum and Associates. Copyright 1997 by Lawrence Erlbaum and Associates. Used by Permission.

Figure 5 shows the ordered autocatakinetic flow of molecules constituting an individual Bénard cell. Here, by way of the stream lines, we can see in detail the way the continuous flow of components at the microscopic level constitutes the structure at the macroscopic level. As this figure helps visualize, because the intrinsic space time dimensions for any system or process are defined by the persistence of its component relations, the transformation from disorder to order increases its dimensions dramatically. Put in different terms, the symmetry breaking that occurs in the production of order from disorder implies a dramatic increase in a system's space-time dimensions.
In the ordered regime of the Bénard experiment the intrinsic space-time dimensions are of the order of seconds and centimeters‹it takes the fluid some seconds to make an autocatakinetic cycle between source and sink, and the distance covered, or the dimensions of a single cell, such as that shown in Figure 5, is in numbers of centimeters. This is in stark contrast to the disordered regime where the intrinsic space-time dimensions are defined by mean free path distances and relaxation times (the distances and times between random or disordered collisions), and are on the order of 10-8 centimeters and 10-15 seconds. From this it is seen that with the breaking of symmetry in the production of spontaneous order the system accesses, and fills, new dimensions of space-time beyond the reach of its previous regime. The same generic dynamics can be seen with respect to terrestrial evolution in Figure 1. Here, spontaneous ordering occurs at symmetry breaking events as minimal critical thresholds of atmospheric oxygen are reached with the system, as a consequence, progressively filling new dimensions of space-time, and moving, contrary to the Boltzmann interpretation of the second law, increasingly further from thermodynamic equilibrium. This relationship between spontaneous ordering and the filling, or extension of space-time dimensions, as the final section of this paper will show, provides an important piece to the apparent puzzle of the river that flows uphill. From this, evolution on Earth can be seen as a process of symmetry-breaking events by which the terrestrial system as a whole accesses new dimensions of space-time, and moves progressively further from equilibrium. This provides a set of observables that establishes the direction or time-asymmetry of evolution.

Insensitivity to Initial Conditions, Downward Causation, or Macrodeterminacy, And the Genericity of Populations Of One

The preceding sections dealing with closed-circle theory and Darwinism as the theory of evolution showed a number of major problems, or anomalies, that render both of these approaches inimical to a comprehensive evolutionary theory, an account of intentional dynamics, or the active epistemic dimension of the world, and as a consequence to ecological theory. Given the anti-ecological Cartesian postulates at each of their cores, however, this is inevitable. Neither has a universal embedding, an embedding in a physical world that is commensurable with the behavior they would like to explicate. The study of autocatakinetic systems, on the contrary, which by definition, and by their behavior, namely, that they exist through, as differentiations of, the larger systems or world from which they arise, implies commensurability.
Living systems are a kind of autocatakinetic system. In particular, they are autocatakinetic systems with replicating components. Autocatakinesis, self-organization, or spontaneous ordering, however, is a universal property that is not dependent on, and therefore not explained by replicating components, or, in different terms, by biology, or culture. It is the universality of spontaneous ordering, or autocatakinesis, that provides the basis for understanding the commensurability of all self organizing systems in general. In this subsection, although it is understood that the fact of autocatakinetic systems (viz., the nomological basis for the river that flows uphill in relation to the river that flows down) remains to be explained until the next section, here it will be shown that major problems, or anomalies, of insensitivity to initial conditions, downward causation, and populations of one, are generic properties, and behaviors‹everyday expected behavior, and not anomalies, or problems, within the context of autocatakinetic systems.
Real-world systems, particularly, but not by any means exclusively, living things and the intentional dynamics that distinguish them, are remarkably insensitive to initial conditions. Because orthodox theory adheres to an impoverished causal description of the world, namely, that it is essentially microdetermined, it has no basis to admit what amounts to macroscopic causality, or downward causality into its explanatory framework. It is for this same reason that it cannot address the problem of the population of one. Put in simple, and blunt terms, it fails to recognize the universality of autocatakinesis or self-organization, and assumes with its Cartesian postulates, and Boltzmannian thermodynamics, an incommensurable physics. Insensitivity to initial conditions, downward causality, or macrodeterminism is a generic property of autocatakinetic systems. We return to the Bénard experiment, again in more detail for an illustration.
Returning to Figure 4, the right-hand photo shows the system filled with Bénard cells of variable size and shape shortly after the critical threshold has been crossed. As time continues, however, a spontaneous process of selection occurs that includes the subsumption of smaller cells by larger ones, the competitive exclusion of smaller cells by larger ones, and the spontaneous division, or fission, of larger cells to smaller ones (e.g., see Swenson, 1989a, 1989b, 1992, and in press-c, for the time series). The end result is a regular array of hexagonal cells of uniform size and shape. Now, the point to make is that the variability that is seen in Figure 4, which is at the beginning of the process, is a consequence of the fact that order production is stochastically, or randomly, seeded. The end state, however, is macrodetermined.
In particular, in the disordered regime the dynamics are characterized by random collisions between microcomponents which constitute fluctuations around an average state. When the critical threshold is crossed spontaneous order is seeded by any fluctuation anywhere in the fluid that is of a minimal amplitude. Since the location and actual amplitude of such fluctuations is stochastically determined the cells will form at different places in the fluid and grow at different rates every time the experiment is done. Seconds after the critical threshold is crossed the fluid thus fills with cells of variable size, but each and every time the experiment is run the variability in the size and shape is progressively eliminated by a process of selection to produce a final state of regularly arrayed hexagonal cells of uniform size and shape. In a decidedly non-Laplacian fashion, unlike micro antecedents lead to like macroscopic consequences. Here we see a process of "blind variation" in the stochasticity of the microcomponents in the disordered regime, and a lawful process of selection leading to a macrodeterminate result. Random initial conditions at the micro level do not mean that the evolution of the system is random or undetermined. Initial conditions, which can vary dramatically relative to their own frame of reference, need only meet some minimal general conditions, and the laws of form do the rest.
A number of other generic properties that can be observed in this example bear pointing out. When the critical threshold is reached in the Bénard cell experiment, and the fluid fills with cells, every cell arises initially as a population of one. The population of one is not anomalous with respect to autocatakinesis, autocatakinetic systems are populations of one, and the general conditions for the establishment of autocatakinetic systems is generic across scales. In each case it involves 1) stochasticity or "blind variation" at the micro level that "seeds" order at the macro level, 2) circular causality that amplifies the microscopic seeding to establish autocatakinesis at the new macroscopic level, and 3) a source-sink gradient above some minimal critical level sufficient to pump up or fill out the new dimensions of space-time that the establishment and maintenance of autocatakinesis entails. The specific details of the establishment of macroscopic order in the Bénard experiment are discussed in the figure legend of Figure 5.
As the generic description implies, autocatakinetic systems are deviation amplifying systems, to use Maruyama's (1963) term. They come into being as a consequence of positive feedback which acts to amplify small deviations or displacements away from thermodynamic equilibrium. Although negative feedback and homeostasis follows naturally from positive feedback as a consequence of various limits to growth or laws of form that follow from the finite nature of space-time, autocatakinetic systems come into being, and are characterized by growth, and the departure from thermodynamic equilibrium. Typically, providing sufficient environmental potential exists, when the system reaches a limit (a critical minimal threshold), order production continues either horizontally, by fissioning, or vertically through the production of a new macroscopic level.
Because autocatakinetic systems are dependent on their surfaces for pulling in environmental potential, and because in isometric growth surfaces increase as the square of a linear dimension while the volume increases as the cube, some form of surface-volume law, or related laws of form, typically determines a minimum and maximum size a system can be before fissioning. Again, fluctuations play an important role in the symmetry breaking process. Below a critical threshold they are dampened, and above, they are amplified. This generic order-producing dynamic is seen from simple physical systems, such as the Bénard experiment (see Swenson, 1989a, 1989c, 1992 for photos of fissioning of Bénard cells) to bacteria, and through to the autocatakinesis of cultural ordering, and planetary autocatakinesis as a whole.
From the early Paleolithic to early Neolithic times, to see this in a cultural example, the hominid population increased from some few tens of thousands to something like 5-10 million, but not through a corresponding increase in the size of autonomous communities (not by building new levels of order, or vertical ordering or growth), but through the proliferation by fissioning of their number (by horizontal growth)‹from something like 1500 at the beginning of the Paleolithic to some 75,000 or so at the end (Carneiro, 1987). The fissioning of autonomous villages, given a supply of initial conditions within tolerance, as with the Bénard case, is a macrodeterminate process. Below a critical size or threshold, social interactions which can be thought of as fluctuations or deviations from the mean (e.g., adultery, theft, disharmonious acts of witchcraft) are damped. When an autonomous unit exceeds a certain minimal size, however, these same microconditions are amplified to macroscopic proportions and fissioning occurs. This fissioning was the almost exclusive means of growth of human culture for some ninety-nine percent of its history until suddenly, and within a short period of time, after certain critical environmental thresholds were reached, vertical ordering occurred when previously autonomous units were pulled into the emergence of nation states, not once, but repeatedly and independently in numerous separate locations. As Carneiro (1970, p. 733; 1981; Swenson, 1991b; Swenson & Turvey, 1991) has shown "[w]here the appropriate conditions existed, the state emerged...[and e.g., in the Valley of Mexico, Mesopotamia, the Nile Valley, and the Indus Valley) "the process occurred in much the same way for essentially the same reasons.

Spontaneous Ordering Occurs Whenever it Gets the Chance

Finally, returning once again to the Bénard experiment to emphasize here perhaps the most important point with respect to spontaneous order production, it is seen that order arises, not infinitely improbably, but with a probability of one, that is, every time, and as soon as, the critical threshold is reached. Spontaneous ordering occurs, in other words, as soon as the opportunity arises. This conforms with the biological extremum (the fecundity principle) that takes it to be the "inherent property" of life to produce as much biological order as it can, and the evolutionary record writ large which suggests that the production of higher-ordered forms, including the origin of life itself occurred, not as a repeated series of astronomically improbable accidents (which certainly would be "infinitely improbable"), but a soon as it had the chance (viz., the origin of life on Earth not after some long lifeless time, but as soon as the Earth was cool enough to support oceans, and the origin of higher-ordered forms as soon as minimal levels of atmospheric oxygen were reached [Figure 1]). If the world in general produces as much order as it can, what is the nomological basis? The answer is given in the next section, which, as a consequence provides the principled basis for unifying the otherwise apparently two incommensurable rivers.