. . . all the evolution we know of proceeds from the vague to the definite.

-CHARLES SANDERS PEIRCE.

ORDER FROM DISORDER.

Although the epitome of a local reversal of the second law is observed in living and thinking beings, related local deviations from orthograde thermodynamic change are also found in many non-biological phenomena. Inorganic order-producing processes are fewer and more fleeting than any found in life, nor do they exhibit anything resembling ententional logic-neither end nor function-yet many physical processes share at least one aspect of this time-reversed order-from-disorder character with their biological and mental counterparts. Understanding the dynamics of these inorganic order-production processes offers hints that can be carried forward into our explorations of the causality behind life and mind.

In these processes, we glimpse a backdoor to the second law of thermodynamics that allows-even promotes-the spontaneous increase of order, correlated regularities, and complex part.i.tioning of dynamical features under certain conditions. Ironically, these conditions also inevitably include a reliable and relentless increase of entropy. In many non-living processes, especially when subject to a steady influx of energy or materials, what are often called self-organizing features may become manifest. This constant perturbation of the thermodynamic arrow of change is in fact critical, because when the constant throughput of material and/or energy ceases, as it eventually must, the maintenance of this orderliness breaks down as well. In terms of constraint, this means that so long as extrinsic constraints are continually imposed, creating a contragrade dynamic to the spontaneous orthograde dissipation of intrinsic constraints, new forms of intrinsic constraint can emerge and even amplify.

There are many quite diverse examples of constantly perturbed self-organizing inorganic processes (several of which will be described below). Among them are simple dynamical regularities like whirlpools and convection cells, coherence-amplifying dynamics such as occurs in resonance (e.g., Figure 8.1) or within a laser, and the symmetrical pattern generation that occurs in snow crystal growth. Even computational toy versions of this logic produced by computer algorithms, such as cellular automata and a variety of recursive non-linear computational processes, exemplify the way that constant regular perturbation can actually be a factor that increases orderliness.

FIGURE 8.1: Resonance: a simple mechanical morphodynamic process. A regular structure that is capable of vibrating (a tubular bell: left) will tend to transform irregular vibrations imposed from without (depicted as a mallet striking it: top left) into a spectrum of vibrations (right) that are simple multiples of a frequency determined by the rate at which vibrational energy is transformed back and forth from one end to the other (bottom left). This occurs because as vibrational energy from varying frequencies "rebounds" from one end to the other, it continually interacts with other vibrations of differing frequencies. These reinforce each other if they are in phase and cancel each other if they are out of phase. Over many thousands of iterations of these vibrational interactions, it is far more likely for random interactions to be out of phase. So, as the energy is slowly dissipated, these recurring interactions will tend to favor a global vibrational pattern, where most of the energy is expressed in vibrations that coincide with even multiples of the time it takes the energy to propagate from one end to the other. This is well exemplified in a flute, where air is blown across the mouthpiece, disturbing the local internal air pressure, and this imbalance is transformed into a regularly vibrating column of air that in turn affects the flow of air across the mouthpiece. Image produced by Antonio Miguel de Campos.

In recent decades, a focus on these spontaneous order-producing processes has galvanized researchers interested in explaining the curious thermodynamics of life. However, the sort of order-generating effect observed in these non-living phenomena falls short of that found in living organisms. These processes are rare and transient in the inorganic world, and their presence does not increase the probability that other similar exemplars will be produced, as is the case with life. An individual organism may also be a transient phenomenon; but the living process has a robust capacity to persist despite changing conditions, to expand in complexity and diversity, to make working copies of itself, to adapt to ever more novel conditions, and to progressively bend the inorganic world to its needs.

The second law of thermodynamics is an astronomically likely tendency, but not an inviolate "law." You might say that it is a universal rule of thumb, even if its probability of occurring is close to certainty. But precisely because it is not necessary, there can be special circ.u.mstances where it does not obtain, at least locally. This loophole is what allows the possibility of life and mind. One might be tempted to seize on this loophole in order to admit the possibility of an astronomically unlikely spontaneous violation of this tendency. And many have been tempted to think of the origins of life in terms of such an incredibly unlikely lucky accident. Actually, as we'll see in the next chapter, life follows instead from the near ubiquity of this tendency, not from its violation. This loophole does, however, allow for the global increase of entropy to create limited special conditions that can favor the persistent generation of local asymmetries (i.e., constraints). And it is the creation of symmetries of asymmetries-patterns of similar differences-that we recognize as being an ordered configuration, or as an organized process, distinct from the simple symmetry of an equilibrium state. What needs to be specified, then, are the conditions that create such a context.

In what follows I will use the term morphodynamics to characterize the dynamical organization of a somewhat diverse cla.s.s of phenomena which share in common the tendency to become spontaneously more organized and orderly over time due to constant perturbation, but without the extrinsic imposition of influences that specifically impose that regularity. Although these processes have often been called self-organizing, that term is a bit misleading. As we will see in the next section, this process might better be described as self-simplifying, since the internal dynamical diversity often diminishes by vastly many orders of magnitude in comparison to being a relatively isolated system at or near thermodynamic equilibrium. However, since the term self-organizing is widely recognized, I will continue to use it, and when referring to the cla.s.s of more general dissipative processes that build constraints, I will describe them as morphodynamic.

Morphodynamic processes are typically exhibited by systems or collections of interacting elements like molecules, and typically involve astronomical numbers of interacting components, though large numbers of interacting elements and interactions are not a necessary defining feature. If precise conditions are met, as they can in simulated contexts or engineered systems, it is possible for simple recursive operations to exhibit a morphodynamic character as well. Indeed, abstract model systems generated in computers have provided much of the insight that has been gleaned concerning the more complex spontaneous order-producing processes of nature (some of which were discussed in chapters 5 and 6). Morphodynamic processes are distinguished from other regular processes by virtue of a spontaneous regularizing tendency that can be attributed to intrinsic factors influencing their composite dynamical interactions, in contrast to regularities that result from externally imposed limitations and biases.

Coincidentally, the term morphodynamic has been independently coined to describe related phenomena in at least two quite distinct scientific domains: geology and embryology. Since coining it in my own writings to refer to spontaneous self-simplifying dynamics, I discovered that it had been in use for nearly a century. And although I independently conceived of the term and this usage, I am not even the first to use it to characterize dynamical processes that produce spontaneous regularity. Coincidentally (and thankfully), these prior uses share much in common with what I describe below, and the phenomena to which it has been applied generally fit within the somewhat broader category that I have in mind.

Most authors trace its first use to a 1926 paper bearing that t.i.tle ("Morphodynamik"), written by the developmental biologist Paul Weiss. He was one of the founders of systems thinking in biology, along with Ludwig von Bertalanffy. Weiss' research focused on the processes that result in the development of animal forms. His conception of developmental processes was based on what he described as morphogenetic fields, which were the emergent outcomes of interacting cell populations and not the result of a superimposed plan. More emphatically, he believed that many details of animal morphology were not predetermined, even genetically, but rather emerged spontaneously from the regularities of cellular interactions. In a little known but prescient paper published in 1967 and enigmatically t.i.tled "1+12,"2 he described numerous examples of molecular and cellular patterns emerging spontaneously in vitro3 when biological molecules or cell suspensions were subject to certain global conditions.

Though recent years have seen a shift in emphasis back toward the molecular mechanisms of cell differentiation and structural development, the term morphodynamic is still used in approaches that focus instead on geometric properties involved in the formation of regular cellular structures, tissue formation, and body plan. A cla.s.sic example is the formation of the regular spiral whorls of plant structures, called spiral phylotaxis, where shoots, petals, and seeds often grow in patterns that closely adhere to the famous Fibonacci number series (1, 1, 2, 3, 5, 8, 13, 21, 34, 55, . . . ), which is generated by adding the two previous numbers of the series to produce the next. In these patterns, the distribution of plant structures form interlocking opposite curved spirals with adjacent Fibonacci numbers of arms. Thus, for example, a pinecone can have its seed-bearing facets arranged into spirals of eight arms clockwise and thirteen arms counterclockwise (as shown in Figure 8.2). This turns out to be highly advantageous. Plant structures like leaves and branches that follow Fibonacci spirals are arranged so that they are maximally out of each other's way, for nutrient delivery, for exposure to the sun, and so forth.

Mathematical models of this process have long demonstrated that this pattern reflects growth processes in which unit structures are added from the center out in a way that depends on how previous units have been added.4 In growing plant tips, this is regulated by the diffusion of molecular signals from previously produced buds that inhibits the growth of other new buds. Since there is a reduction of concentration with distance from each source and with the maturation of each older growing bud, new buds appear in positions where these inhibiting influences, converging from the previously erupted buds, are weakest. This indicates that the Fibonacci growth pattern is not dependent on any intrinsic template or archetypal form (e.g., encoded directly in the genome). It is induced to emerge by the interaction of diffusion effects, the geometry of growth, and the threshold level of this signal at which point new plant tissue will begin to be generated. Recently, this patterning of growth has also been demonstrated to occur spontaneously in inorganic processes. For example, Chinese scientists have demonstrated the spontaneous growth of mineral nodules on a metal surface with conical protrusions that conforms to either 5 x 8, 8 x 13, or 13 x 21 patterns of interlocking spirals, due to electrochemical effects.5 This further confirms that the spontaneous emergent character of this patterning is not unique to biology and not merely an expression of its functional value to the plant.

FIGURE 8.2: Three expressions of the Fibonacci series and ratio. Left: regular branching of a lineage in which there are regular splits (reproductive events for organisms) that occur at the same interval (distance) along each line. This produces the sequence 1, 2, 3, 5, 8, 13, 21, 34, 55 . . . that is generated by adding the two previous numbers in the series. Middle: dividing adjacent numbers in this series yields closer and closer approximations to the non-repeating decimal ratio 0.618 . . . which can define the adjacent sides of an indefinitely nested series of smaller and smaller rectangles. Such rectangles are self-similar to one another, and a spiral can be traced from corner to corner that is also self-similar in shape at whatever magnification it is shown. Right: spherical objects distributed around a central point in a closest-packed pattern also form a self-similar pattern at whatever size they are shown. As each new object is added, the next is found 137.5 around the center from the last. Depending on the size of the components, a self-similar array of this sort will demonstrate interlocking, oppositely curved spirals, such that the number of spirals in each direction corresponds to adjacent Fibonacci numbers. This is reflected in many forms of plant growth in which the addition of new components (e.g., seeds in a sunflower) occurs where there is the most s.p.a.ce closest to the center.

More recently, self-organizing logic (though not called morphodynamics in these contexts) has been used to describe the formation of regular stripe and spot patterns as adaptations for cryptic coloration or species signaling in animals. Examples include the regular stripe patterns on tigers and zebras, the complex spiral lines and spots on certain snail sh.e.l.ls, the spots on leopards and giraffes, and the beautiful iridescent patterns of color on b.u.t.terfly wings. The logic of these processes has been well studied both by simulation and by developmental a.n.a.lysis of the molecular and cellular mechanisms involved. All of these pattern-generation processes appear to involve a diffusion logic that is loosely a.n.a.logous to that just described for Fibonacci spiral formation in plants. Each takes advantage of local molecular diffusion dynamics to generate regularity and broken symmetries, though in each case utilizing quite distinct molecular-cellular interactions.

Within cells, there are also processes that can be described as morphodynamic. These are molecular interactions that produce spontaneously forming structures like membranes or microtubules. Even the regular protein sh.e.l.ls that surround many viruses are the result of spontaneous form generation. These molecular-level form-generating processes are often described as self-a.s.sembly processes, and they are responsible for much of the microstructure of eukaryotic cells. (They will be treated in greater detail in the next chapter, when we explicitly explore the morphodynamics of living processes.) In geology, the term morphodynamic also has an extended history of use. It is used primarily to describe processes involved in the spontaneous formation of the semi-regular features of landscapes and seascapes, such as river meanders, frost polygons, sand dunes, and other geologic features that result from the dynamics of soil movement. It can be seen as the solid dynamical counterpart to the physics of fluid movement: hydrodynamics. The physics of particulate movement and a.s.sortment in continually perturbed collections of objects, such as gravel movement in geology and object sorting in industrial processes, is surprisingly counterintuitive and remains an area where theoretical a.n.a.lysis lags behind descriptive knowledge. Some of the most surprising and interesting geomorphodynamic processes are those that produce frost polygons. The repeated freezing and thawing of water within the soil in arctic regions can result in the formation of gravel that is regularly distributed around the perimeters of remarkably regular polygons (see Figure 8.3).

Examples of other physical phenomena that I would include as morphodynamic processes range from simple inorganic dynamical phenomena like the formation of vortices and convection cells in fluids to more complex phenomena like the growth of snow crystals. The dynamical processes involved in the formation of these regularities will be described in more detail below, but at this point it is worth remarking that what makes all these processes notable, and motivates the prefix morpho- ("form"), is that they are processes that generate regularity not in response to the extrinsic imposition of regularity, or by being shaped by any template structure, but rather by virtue of regularities that are amplified internally via interaction dynamics alone under the influence of persistent external perturbations.

FIGURE 8.3: The formation of three different kinds of natural geological polygons. Left: soil and gravel polygons are the result of the way that the daily and seasonal expansion and contraction of ice in arctic soil causes larger stones to be pushed upward toward the surface, and outward from a center of more silty soil which more effectively holds the water, and from which ice expansion and contraction slowly expels the larger stones. The regular segregation of soil and stones is thought to result from the relatively even distribution of this freezing/melting effect, and the common rate at which the dynamics takes place in each polygon. However, multiple competing hypotheses seem equally able to explain this self-organizing effect, as is true for many self-organized, particulate segregation effects (see Kessler and Werner, 2003, for a more technical account). Center: regular polygonal cracks can also form for similar reasons as a result of ice crystal expansion and drying contraction of the soil. Right: basalt columns form in cooling sheets of lava, probably as a result of a combination of convection effects (see Figure 8.4) and shrinkage as the lava cools, with the cooler peripheries of convection columns shrinking first and forming cracks. Photos by M. A. Kessler, A. B. Murray, and B. Hallet (left); Ansgar Walk (center); L. Goehring, L. Mahadevan, and S. W. Morris (right).

In addition, I would also include a wide variety of algorithmic systems with a similar character due to a.n.a.logous virtual dynamics, such as in cellular automata (like Conway's computer Game of Life), and computational network processes, such as so-called neural nets. Although computational models are not truly dynamical in the physical sense, they do involve the regular highly iterative perturbation of a given state, and the consequences of allowing these perturbations to recursively amplify in effect. In this sense, the recursive organization of these computational processes can be seen as the abstract a.n.a.logue of the physically recurring perturbation of a material substrate, such as constant heating or constant growth. Ultimately, much of what we know about the logic of morphodynamic processes has come from the investigation of such abstract computational model systems.

Understanding how to take advantage of these special dynamical processes has played an important role in the development of many technologies, including the production of laser light and superconductivity. These too will be described in more detail below.

SELF-SIMPLIFICATION.

The concept of self-organization was introduced into cybernetic theory by W. Ross Ashby in a pioneering 1947 paper.6 Ashby defined a self-organizing system as one that spontaneously reduces its entropy, but not necessarily its thermodynamic entropy, by reducing the number of its potential states. In other words, Ashby equated self-organization with self-simplification. In parallel, working in physical systems, researchers like the physical chemist Ilya Prigogine explored how these phenomena can be generated by constantly changing physical and chemical conditions, thereby continually perturbing them away from equilibrium. A well-known example is the famous Belousov-Zhabotinsky reaction, which produces distinctive alternating and changing bands of differently colored chemical reaction products, which become regularly s.p.a.ced as the reaction continually cycles from state to state. This work augmented the notion of self-organization by demonstrating that it is a property common to many far-from-equilibrium processes; systems that Prigogine described as dissipative structures.

With the rise of complex adaptive systems theories in the 1980s, the concept of self-organization became more widely explored, and was eventually applied to phenomena in all the many domains from which the above examples have been drawn. However, the precision of Ashby's conception is often lost when it is employed in complex systems theories, where it is often seen as a source of increasing complexity rather than simplification. This demonstrates that the relationships between complexity, systematicity, dynamical simplification, regularity, and self-organization are not simple, and not fully systematized, even though the field is now many decades old. More important, I fear that a recent focus on understanding and managing complexity may have shifted attention away from more fundamental issues a.s.sociated with the spontaneous generation of order from disordered antecedents. Indeed, as I will argue below and in the next chapter, the functional complexity and synergy of organisms ultimately depends on this logic of self-simplification.

In general, most processes that researchers have described as self-organizing qualify as morphodynamic. So, it will typically be the case that the two terms can be used interchangeably without contradiction. However, I will mostly avoid the term self-organization, because there are cases where calling processes self-organizing can be misleading, especially when applied to living processes where both terms, self and organization, are highly suggestive without providing any relevant explanatory information about these properties.

The term is problematic both for what it suggests and what it doesn't explain.

First, self-organization implicitly appears to posit a sort of unity or ident.i.ty to the system of interacting elements in question-a "self," which is the source of the organizing effect. In fact, the coherent features by which the global wholeness of the system is identified are emergent consequences, not its prior cause. This is of course presumed to be an innocent metaphoric use of the concept of a self, which is intended to distinguish the intrinsic and thus spontaneous source of these regularities, in contrast to any that might be imposed extrinsically. But although the term has been used metaphorically in this way, and is explicitly understood not to imply anything like agency, it can nevertheless lead to a subtle conceptual difficulty. This arises when incautious descriptions of the globally regularized dynamics of such a system are described as causing or constraining the micro dynamics. As we discussed in chapter 5, the phrase "top-down causality" is sometimes used to describe some property of the whole systemic unity that determines the behavior of parts that const.i.tute it. This has rightly been criticized as circular reasoning, treating a consequence as a cause of itself. But even when understood in process terms, where a past global dynamical regularity constrains future microdynamic interactions which in turn contribute to further global regularity, the term fails to explain in what sense the global dynamics is in any sense unified, as the word "self" suggests.

Second, describing these processes as self-organizing tends to suggest that the system in question is being guided away from a more spontaneous unorganized state. Used in this sense, it is metaphorically related to a concept like self-control. The problem with this comparison is that the organization is not imposed in opposition to any countervailing tendency. Self-organizing processes are spontaneously generated. The process could even be metaphorically described as "falling toward" regularity, rather than being forced into it, as is also the case with change toward equilibrium in simpler thermodynamic conditions. The specific forms of such processes are explicitly not imposed; they arise spontaneously, due to intrinsic features of the components, their interaction dynamics, and the constant perturbation of the system in question. In contrast, it often takes work to disrupt the regularity of a self-organized dynamical system, while constant perturbation is actually critical to its persistence.

Consider an eddy in a stream. It can be disrupted by stirring the water in opposition to the rotation of the vortex, or in any sufficiently different pattern, but stirring in the same direction is minimally disruptive. With sufficiently vigorous disruption, the rotational symmetry can be broken and a chaotic flow can be created-at least briefly. But so long as the stream keeps flowing, when the irregular stirring ceases, the rotational regularity will re-form. This is because the vortex flow is itself a consequence of constant perturbation as water flows past a partial barrier. The circular flow of the water is disrupted only by a contrary form of perturbation. In general, an intervention that can disrupt a stable morphodynamic process must diverge from it in form. This will differ for each distinct morphodynamic process, because there are many ways that a process can exhibit regularity.

Finally, the regularity that is produced is a consequence, not a formative influence or mechanism. Though all of the processes I will describe as morphodynamic are identified by virtue of converging toward a particular semi-regular pattern, what counts is that this consequence is approached, but need not ever be achieved. The asymmetric orthograde directionality of change is what matters. It is the tendency toward regularity and increasing global constraint that defines a morphodynamic process, not the final form it may or may not achieve. In this sense it is a.n.a.logous to the way that the increase in entropy, but not the achieving of equilibrium, defines the orthograde tendency of a thermodynamic process. This is because using the production of a stable orderly dynamic as the sole criterion for identifying a morphodynamic process would cause us to overlook many relevant types of processes that fail to fully converge toward a regular state. In fact, as morphodynamic processes become more complex and intertwined, as they do in living organisms, none may actually converge to a regular pattern. Each may be generating a gradient of morphodynamic change with respect to others, even though none of the component processes ever reaches a point of morphodynamic stability.

Nevertheless, in either a thermodynamic or morphodynamic process, the same dynamical conditions that would ultimately converge to a stable end state, if left to run unaltered, are already at work long before there is any hint of stability. The point being that both thermodynamic and morphodynamic processes are defined by a specific form of orthograde change, not the end stage that such a change might produce. Thus, a morphodynamic process can be discerned in systems that will never ultimately converge to a stable end state. Even if a dynamical system only converges to a slightly less than chaotic regularity, it may still be morphodynamic.

How are we to recognize these processes in cases where there is limited time or contravening influences preventing convergence to regularity? The answer is, of course, that we must identify a morphodynamic process by virtue of a specific form of spontaneous orthograde change. So, while we have named morphodynamic processes with respect to their tendency to converge toward regular form, we must define them in terms of the dynamic process and not the form it produces. A brief and superficial description of the common dynamical principles characterizing morphodynamic processes is that they all involve the amplification and propagation of specific constraints. Of course, this brief statement requires considerable unpacking and qualification.

FAR-FROM-EQUILIBRIUM THERMODYNAMICS.

Thinking in these terms can be confusing because of a double-negative logic that is hard to avoid. For example, in typical discussions of thermodynamic processes, we tend to think of energy as a positive determinant of change. Introduce energy into a system and it will eventually be dissipated throughout the system (and the surroundings if it is not isolated). But thinking in terms of constraint and entropy, the description becomes a bit more convoluted and counterintuitive. When a thermodynamic system-such as a gas in a closed container-is disturbed, say by the asymmetric introduction of heat, a constraint on the distribution of molecular movements has been imposed. Although the system is now more energetic, it is not merely the added energy that is responsible for the directional change that will eventually take the system to a new equilibrium. This would in fact occur whether one part was heated or one part was cooled. Removing heat in an asymmetric fashion is just as effective at initiating a re-equilibration process as is adding it. So, what is the cause of the asymmetric change, if not the addition of energy?

As we saw in the last chapter, this orthograde tendency in an equilibrating gas is the result of the biased distribution of molecular motions that this perturbation created, and it occurs irrespective of whether heat is added or removed. What matters is the creation of an asymmetric distribution of molecular motions. This perturbation lowers the entropy of the system, making some molecular movements more predictable with respect to their location within it. Or, to put it in constraint terms: the distribution of molecular velocities is more asymmetric (thus constrained) just after perturbation than when in equilibrium. The second law of thermodynamics thus describes a tendency to spontaneously reduce constraint, while thermodynamic work involves the creation of constraint. This complementarity will turn out to be a critical clue to the explanation of morphodynamic processes.

To see the relationship between this most basic thermodynamic process and morphodynamic processes, consider the following simple thought experiment: Imagine attaching a device to an otherwise isolated container of gas at equilibrium that will simultaneously cool one side of the container and heat the other side equivalently, but in a way that will keep the total energy (specific heat) in the container constant. Heat will be added exactly as rapidly as it is removed. If such a perturbation occurred only at one point, and then the system was isolated, the asymmetric state would have immediately started changing toward a state of equilibrium, attaining progressively more symmetric distributions of molecular motions with time. But what happens if the perturbation is continuous? In one sense, there is no intrinsic difference in the way the second law tendency is expressed. There is still a tendency toward redistribution of faster molecular velocities to one side and slower velocities to the opposite side in a way that runs counter to the perturbation, and yet every incremental change in distribution due to this spontaneous tendency is balanced by the perturbing influence of the heated and cooled sides of the container. The result is, of course, a stable gradient of temperature from hot to cold from one side to the other that never gets closer to an equilibrium state. And if somehow one were to stir things up, in a way that disturbed this gradient, as soon as the stirring stopped the same gradient would begin to re-form and re-stabilize.

What about the entropy of the gas in the container? Here is where things can get a bit counterintuitive. Clearly, energy in the form of heat is channeled through the gas, flowing from one side to the other, generating a constant increase in the entropy in the larger system that includes the heating and cooling mechanisms. Because the system is continually far from equilibrium due to constant perturbation, however, the gas within the container doesn't increase in entropy. So, although the dynamical interactions within the gas medium are in the process of increasing entropy, the entropy of the gas remains constantly well below its maximum, because of the continual disturbance from outside. Of course, the external heating-cooling device must do continual thermodynamic work to maintain this local constancy. This extrinsically generated contragrade dynamic continually counters the spontaneous orthograde dynamic within the gas medium. It is generally a.s.sumed that in such dissipative processes, the dynamical organization of gas molecule interactions eventually stabilizes to produce an entropy production rate (EPR) for the whole system (including heating and cooling mechanisms) that balances the rate of perturbation.

Locally within the gas we thus have a curious dynamical situation in which contragrade and orthograde processes are in balance. If the constant heating-cooling mechanism is adjusted to produce a higher or lower differential, the EPR will also shift to a new value. In a simple thermodynamic system, entropy increase occurs more rapidly if the temperature difference is greater and more slowly if the temperature difference is less (in this sense, a temperature difference is a.n.a.logous to a pressure difference).

To understand what this means in terms of constraints, and thus the organization of the system, imagine that this constant extrinsic perturbation is suddenly removed and the system is again isolated. At this initial point, the fluid medium would be in a highly constrained state (thus highly organized) and would also spontaneously destroy that constraint (order) more rapidly than if it were in a less constrained state. Reflecting on what this means for thermodynamics in general, we can now see that the rate of constraint elimination is higher the more constrained the system (e.g., exhibiting a high heat gradient), and this rate will eventually decrease to zero when the system reaches the equilibrium state. What the external perturbation accomplishes then is to increase constraint (and drive the entropy down); or, in other words, it drives the system in a contragrade direction of change, thus becoming more highly ordered.

But there is an upper limit to this diffusion process that has a critical effect on the overall global dynamic. This is a threshold at which dynamical discontinuities occur. These are often called bifurcation points, on either side of which distinctively different dynamical tendencies tend to develop. At this threshold, local variations can produce highly irregular chaotic behaviors, as quite distinct dynamic tendencies tend to form near one another and interact antagonistically. But exceeding this threshold, radical changes in orthograde dynamics can take place. As the heat gradient increases to a high value, the potential influence of any previously minimal interaction biases and extrinsic geometric asymmetries will also become relevant, such as the viscosity of the medium, the shape of the container, the positions of the heating and cooling sites, and any possible impediments to dissipation or conduction through the container walls. This is because these additional biases-while irrelevant in their influence on the microdynamics of molecule-to-molecule interactions-are able to bias larger-scale collective molecular movements and allow differences to acc.u.mulate regionally. This can lead to the asymmetric development of correlated rather than uncorrelated molecular movements.

RAYLEIGH-BeNARD CONVECTION: A CASE STUDY.

This is most easily demonstrated by a liquid variant of the simple non-equilibrium thermodynamic condition just described. Perhaps the paradigm example of self-organizing dynamics is found in the formation of what are termed convection cells in a thin layer of heated liquid. Highly regular shaped convection cells (hereafter termed Benard cells) can form in a process known as Rayleigh-Benard convection in a uniformly heated thin layer of liquid (e.g., oil).7 In 1900, Claude Benard observed that a cellular deformation would form on the free surface of a liquid with a depth of about a millimeter when it was uniformly heated from the bottom and dissipated this heat from its top surface. This often converged to a regular pattern of tiny, roughly hexagonally shaped columns of moving fluid, producing a corresponding pattern of hexagonal surface dimples (see Figure 8.4). These Benard cells form when the liquid is heated to the point where unorganized (i.e., unconstrained and normally distributed) molecular interactions are less efficient at conducting the heat from the container bottom to the liquid surface than if the liquid moves in a coordinated flow. The point at which this transition occurs depends on a number of factors, including the depth, specific gravity, the viscosity of the liquid, and the temperature gradient. The depth and dynamical properties of the liquid become increasingly important as the temperature gradient increases. The large-scale coordinated pattern of fluid movement reliably begins to take over the work of heat dissipation from random molecular movement when a specific combination of these factors is reached.

FIGURE 8.4: One of the most commonly cited forms of morphodynamic processes involves the formation of hexagonally regular convection columns called Benard cells in shallow, evenly heated liquid. They form in liquid that is heated to a point where simple conduction of heat is insufficient to keep the liquid from acc.u.mulating more heat than it can dissipate. This creates instabilities due to density differences, and induces vertical currents due to weight differences. The heat dissipation rate increases via convection, which transfers the heat faster than mere pa.s.sive conduction. The geometric regularity of these currents is not imposed extrinsically, but by the intrinsic constraints of conflicting rising and falling currents slowing the rate. These rate differentials cause contrary currents to regularly segregate and minimize this interference. Hexagonal symmetry reflects the maximum close packing of similar-size columns of moving liquid.

At moderate temperature gradients, local molecular collisions transfer heat as faster-moving molecules near the bottom b.u.mp into and transfer their momentum to slightly slower-moving molecules just slightly above them, so that collision-by-collision, molecular momentum is conveyed from the hot to the cool surface, where it ultimately gets transferred to air molecules. As the temperature gradient is increased, this process begins to be overshadowed by the direct movement of whole regions of faster-moving hot molecules toward the cooler surface because of their relative buoyancy. Hotter regions contain more energetic molecules that, as a result, maintain slightly larger distances between one another, and thus are collectively less dense and lighter than cooler regions. Cooler and thus heavier regions of liquid nearer the surface tend to descend and drive the lighter regions upward. The transfer of molecular momentum via collision inevitably follows highly indirect trajectories, whereas the collective movement of larger ma.s.ses of liquid is less impeded by collision and their trajectory toward the surface is therefore more direct. So the rate that heat can be dissipated is inevitably higher if moving molecules, aligned with the direction of the heat gradient, are minimally impaired by collision. When the temperature gradient is slight, viscosity effects limit the rate at which nearby streams of liquid can move past one another, and so transmission of molecular momentum differences (heat) can occur more readily via molecular collisions. But at higher-temperature gradients, there is a reversal of this bias.

Why do regularly s.p.a.ced hexagonal columns of organized flow result? To see this, we need to focus on mid-scale dynamics between molecular and fluid dynamics. Because of the relatively more direct transmission of heat by aligned fluid flow at high-temperature gradients, regions of vertically aligned correlated movements will more effectively transfer heat out of the liquid than regions with less correlated molecular movements. But in the process of fluid convection, as more buoyant heated liquid rises from the bottom and heavier cooled liquid sinks back toward the bottom, there is an inevitable interaction between oppositely flowing streams. Consequently, the friction of viscosity affects the rate of convection. Regions with less correlated molecular movements will build up undissipated heat (higher local intermolecular momentum) more rapidly than neighboring regions, and create localized temperature gradients that are slightly out of alignment with the large-scale gradient. This creates a bias of movement out of regions with disoriented and less correlated flow toward regions with more aligned and correlated flow. Thus, centers of aligned and correlated convection in either direction will expand, and regions of chaotic flow will have their volumes progressively diminished. The result is that regions of countervailing flow will become minimized over time.

Hexagonal columns of fluid flow develop because the heated and cooled surfaces are planar, and the most densely packed way to fill a surface with similar-size subdivisions is with hexagons.8 Subdividing the plane of liquid into hexagonal subregions thus most evenly distributes the inversely moving columns of flowing liquid, and represents the most evenly distributed pattern of heat dissipation that can occur via fluid movement. This action both spontaneously evens out the rate of heat dissipation from region to region, and optimizes the rate of dissipation overall. So, as convection becomes critical to maintaining a constant high gradient of heat transfer through the liquid, the whole volume becomes increasingly regularized, until hexagonal columnar convection cells form. At this point, no more efficient movement patterning is available. From this point on, the local value of entropy within the liquid will tend to remain fairly stable. But because of the highly organized global convection patterning, stable global-level constraints are also generated that do not dissipate. The total rate of entropy production, and thus constraint dissipation, is maximized as far as convection can generate it.

Benard cells thus exhibit an effective reversal of the typical thermodynamic orthograde tendency: that is, for macroscopic constraints to be progressively eliminated through microscopic dynamical interactions. Instead, as these convection patterns form, the intrinsic constraints of fluid movement become amplified and propagated throughout the system, taking on some of the potential differential that otherwise would have been borne by microscopic intermolecular momentum differences, trading movement gradient effects for heat gradient effects.

To understand what this more complex condition means in terms of constraint (and thus the organization of the system), imagine once more that this constant extrinsic perturbation is suddenly removed and the system becomes isolated. At this point, the fluid medium is even more highly constrained, and part.i.tioned into subregions with highly divergent parameters, than if it were just exhibiting a high heat gradient. Consequently, the rate at which these constraints would tend to spontaneously decay will also be more rapid than in a simple heat gradient of the same value. In the far-from-equilibrium constantly perturbed condition, then, where convection has taken over much of the heat dissipation from molecular collision, the extrinsic perturbation is also driving the system into an even more constrained (and thus organized) state than it would be with a simple heat gradient. In the absence of convection, this contragrade process would have resulted in a significantly higher gradient of heat difference within the fluid; but in effect, the formation of convection cells has redistributed this level of global constraint to slightly more local constraints of a different sort-constraints on correlated movement-with the result that the temperature gradient is less steep than in their absence. Because correlated movement of large collections of molecules involves fewer dimensions of difference than uncorrelated local molecular movement, the system is by definition in a simpler and thus more orderly state. What the external perturbation coupled with the effects of buoyancy and the geometric constraint of hexagonal close packing together accomplish is to increase and redistribute constraint in a more symmetric way. This redistribution of constraint into other dimensions of difference provides more ways for constraints to be eliminated as well. This is what creates the higher rate of constraint elimination (and thus entropy production).

In summary, morphodynamic organization emerges due to the interaction of juxtaposed constant work opposing a homeodynamic process (e.g., processes involving both constant external perturbation and constant internal equilibration). High, uniform rates of perturbation lead to the production of second-order intrinsic constraints that eventually balance the rate of constraint dissipation to match the introduction of constraints from outside the system. Balanced rates are achieved when the rate of entropy production increases to the point that it keeps pace with the rate of disturbance by generating more dimensions of internal constraint that can now be simultaneously eliminated. Again, if the system is suddenly isolated, not only will temperature begin to equilibrate, but correlated movement will also begin to break down. This demonstrates that some of the heat energy went to create convection. Constraint dissipation was able to occur at a higher rate because fluid movement was doing work to increase the rate of heat transfer.

This may sound counterintuitive, but notice that the correlated movement of the convection cells is itself capable of being tapped to do work, and to generate this level of correlation in the first place, work was required, and that must have come from somewhere. It cannot have come for free. It cannot have come from gravitation, because although the falling, heavier liquid does work to push hotter, more buoyant liquid upward, this is the result of the density differential that was produced by the asymmetry of the heating and cooling. Gravitation merely introduces a bias, as does hexagonal close packing, which organizes the flow but doesn't initiate it. The only available source of work to organize convection is the constantly imposed temperature differential. Inevitably, then, some of the microscopically distributed molecular momentum differential must be reduced as it is transferred into the correlated momentum of the convection flows. Heat in the form of microscopic motion differences thus is transformed into global correlated movement differences.

The morphodynamic process that results is an orthograde process, because it is an asymmetric orientation of change that will spontaneously re-form if its asymmetry is somehow disturbed and so long as lower-order dynamics remain constant. But this higher-order asymmetry is dependent on the persistence of lower-order thermodynamically contragrade relationships: thermodynamic work. It is because of this lower-order work that the higher-order orthograde dynamic exists.

What does this tell us in terms of morphodynamic processes in general? Using the Benard cell case as an exemplar, it demonstrates that if there are intrinsic interaction biases available (buoyancy differences, viscosity effects, and geometric distribution constraints in this case), the persistent imposition of constraint (constant heating) will tend to redistribute this additional constraint into these added dimensions of potential difference. Moreover, these additional dimensions are boundary conditions, to the extent that they are uniformly present across the system. This includes the geometric constraint, which is not derived from any material feature of the system or its components. Because these additional dimensions are systemwide and ubiquitous, they are also of a higher level of scale than the constraints of molecular interaction. So this transfer of constraints from molecular-level differences to global-level differences also involves the propagation of constraint from lower- to higher-order dynamics.

The distinct higher-order orthograde tendency that characterizes the morphodynamics of Benard cell formation thus emerges from the lower-order orthograde tendency that characterizes fluid thermodynamics. This tendency to redistribute constraint to higher-order dimensions is an orthograde tendency of a different and independent kind than the spontaneous constraint dissipation that characterizes simpler thermodynamic systems. Yet without the incessant process of lower-order constraint dissipation, it would not occur. The higher-order orthograde morphodynamic tendency is in this sense dynamically supervenient on the lower-order orthograde thermodynamic (homeodynamic) tendency, though it is not supervenient in a mereological sense.

Benard cells are entirely predictable under the right conditions, and will thus re-form spontaneously, like a whirlpool in a stream, if disturbed by stirring the fluid and temporarily disrupting the regular flow patterns. This spontaneous tendency to return to a dynamical regularity that will persist unless again disturbed is what defines an attractor in the s.p.a.ce of dynamic possibilities (in the terms of dynamical systems theory). The combination of an up-level shift in the form of constraint and the generation of a distinct higher-order orthograde attractor is the defining characteristic of an emergent dynamical transition. This is because, ultimately, the capacity to do work to change things in a non-spontaneous way depends on the presence of constraints, and so a new domain of orthograde constraint provides a new domain of causal powers to introduce change.

THE DIVERSITY OF MORPHODYNAMIC PROCESSES.

This detailed exploration of Benard cell formation demonstrates that in order to realize the potential of emergent causal power at the morphodynamic level, the interaction of contragrade dynamics is required at the next lower level of scale. Just as the spontaneous increase in the rate of constraint dissipation (and entropy production) can be realized in diverse ways, and not merely via the jostling of molecules in a heated gas or liquid, the amplification-propagation of higher-order constraints can also be realized in diverse ways, producing quite different sorts of attractors. This second-order orthograde logic characterizes all morphodynamic processes, including those that are not strictly speaking thermodynamically embodied (e.g., computational processes); and while they only occur when special conditions are met, they typically stand out as surprising apparent violations of the tendency toward disorder that is the most ubiquitous tendency in the universe.

First, consider a couple of close cousins to Benard cells: geological a.n.a.logues to convection, that include the formation of basalt columns and soil polygons.

Basalt columns are hexagonal columns that form in molten rock due to convection, as heat dissipates upward toward the surface.9 As the molten lava cools and hardens, it also tends to contract. The columns break apart at the boundaries between the hexagonal cells where the rock is coolest and least plastic. The large size of the hexagons in comparison to Benard cells is in part a consequence of the very different fluid properties of lava.

Soil and frost polygons (shown in Figure 8.3) form in multiple ways, due to different mechanisms driven by the expansion and contraction of ice particles in the soil, or alternatively as a consequence of the drying and shrinking of mud. Cracks formed into roughly rectangular polygons often result from contraction of soil due to drying. This does not involve regular movement of soil components, and so cracks form more or less along fracture lines, creating crisscross patterning with fissures that are roughly evenly s.p.a.ced because of the relatively equal rates of drying. In contrast, more or less hexagonally arranged roughly circular rings of stones form due to the differential upwelling of larger particulates (such as stones), driven by cycles of freezing and thawing of the surrounding soil. In this respect, there is a loose a.n.a.logy to Benard convection, as the larger stones are driven upward in part because they do not expand and contract with the surrounding soil. A related sorting of particulates occurs on rocky seash.o.r.es, where the action of waves helps to arrange different-sized, -shaped, and -weighted objects in different strata close to or further from the sh.o.r.e. The sorting of particulates according to shape, size, and/or weight is not only a common geological feature, but is also used in the development of mechanical agitation mechanisms employed to sort different objects for various industrial purposes.

A quite different example of morphodynamic change is exhibited by the amplification and propagation of constraints that takes place in the growth of snow crystals. The structure of an individual snow crystal reflects the interaction of three factors: (1) the micro-structural biases of ice crystal lattice growth, which result in a few distinct hexagonally symmetric growth patterns; (2) the radially symmetric geometry of heat dissipation; and (3) the unique history of changing temperature, pressure, and humidity regimes that surrounds the developing crystal as it falls through the air (see Figure 8.5).

FIGURE 8.5: Selected snow crystals from the cla.s.sic collection of photographs made by Wilson Bentley (18651931), obtained from the NOAA National Weather Service Collection Catalog of Images. All exhibit an elaborate hexagonally symmetric form, made up of plate, spire, and surface-etching components. This remarkable regularity is a result of the way temperature, humidity, and pressure determine ice crystal lattice formation, radial heat dissipation, and the compounding of geometric constraints on growth surfaces as the crystal grows. Snowflakes typically consist of many crystals stuck together.

Snow crystal growth occurs across time in the process of traversing these variable atmospheric conditions. But an ice crystal lattice tends to grow according to only a few quite distinct patterns (spires, hexagonal sheets, and hexagonal prisms, to name the major forms), depending on the specific combination of temperature, pressure, and humidity of the surrounding air. As a result, the history of the differences in atmospheric conditions that a growing crystal encounters as it falls to earth is expressed in the variants of crystal lattice structure at successive diameters and branch distances in its form. In this way, the crystal is effectively a record of the conditions of its development. But snow crystal structure is more than merely a palimpsest of these conditions. Prior stages of crystal growth progressively constrain and bias the probability of further growth or melting at any given location at subsequent stages. Thus, even identical conditions of pressure, temperature, and humidity, which otherwise produce identical lattice growth, can produce different patterns depending on the prior growth history of the crystal. In this way, the global configuration of this tiny developing system at each stage of growth plays a critical causal role in its microscopic dynamics. The structure present at any moment in its growth history will strongly bias where molecular accretions are most and least likely, irrespective of the surrounding conditions, which will instead influence the mode of growth that will occur at these growth points. Since partial melting and refreezing are also possible, and this too will depend on the constrained distribution of heat at any given position, the resultant crystal shape will not necessarily exhibit precise angular crystalline structure, but may also yield highly regular symmetrically distributed amorphous patterns as well, including ridges and trapped bubbles (shown in Figure 8.5). This is what contributes to the proverbial individuality of each crystal.

Snow crystals are self-simplifying in a quite different way from convection cells, and yet both share a deep commonality. A snow crystal's growth is a.n.a.logous to Benard cell formation in the way it too is a consequence of persistent non-equilibrium dynamics. It is continually made thermodynamically unstable by the accretion of new molecules which release heat into the crystal lattice as they fuse, and from which heat is continually being dissipated through the highly constrained geometry of the crystal. In the process of exporting heat as fast as it is acc.u.mulated during growth conditions, the crystal tends to spontaneously regularize at a macroscopic level (i.e., macroscopic with respect to the scale of molecular interactions) because asymmetric growth leads to asymmetric heat dissipation, which tends to slow overgrown and accelerate undergrown regions. And as the process continues, the constraints of prior growth and heat dissipation further constrain the possibilities for growth. Along with the geometrically limited growth possibilities of ice crystal lattice, these factors amplify contingent events in the growth history of the crystal. Because of the compounding of constraints from the prior growth history, a snow crystal incorporates and amplifies the unpredictable influence of these random accretions into its complex symmetry, including even the effects of melting and refreezing. The quite exquisite symmetries that can spontaneously form are thus the result of a complex interplay of many different kinds of constraints, amplifying the extrinsically acquired biases introduced by a historically unique sequence of changing boundary conditions.

FIGURE 8.6: Laser light is also generated by a morphodynamic process that is roughly a.n.a.logous to resonance. It is generated when broad-spectrum (white) light energy is absorbed by atoms (a), making them slightly unstable. This energy is re-emitted at a specific wavelength, corresponding to the energy of this discrete quantum level (b). Re-emission is preferentially stimulated if an unstable atom interacts with light of the same wavelength (c and d). The critical effect is that the emitted light is emitted with the same phase and wavelength as the incident light. If this emitted light is caused to recycle again and again through the laser material by partially silvered mirrors, this recursive process progressively amplifies the alignment of phase and wavelength of the light being emitted.

Laser physics provides an example of morphodynamic logic in a very different domain (see Figure 8.6). It is based on a constraint amplification effect that is due to the temporal regularity of quantum resonancelike effects involving the atomic absorbance and emission of radiation. Lasers produce intense beams of monochromatic light such that all the waves are in precise phase alignment-that is, with the peaks and troughs of the waves emitted from different atoms, all aligned. Light with these precisely correlated features is called coherent light. It is generated from white (polychromatic) light, which contains mixed wavelengths aligned in every possible phase. The conversion of white light to coherent light is accomplished by virtue of the recurrent emission and resorption of light by atoms whose emission features correlate with their excitation features. When the energy of out-of-phase polychromatic light is absorbed into the electron sh.e.l.ls of the atoms of the laser material, it is incorporated into a system with very specific (quantized) energetic regularities. The energy is incorporated in the form of a shift of electron energy level to a higher and less stable quantized state.

An unstable excited atom reverts to its relaxed ground state (able to be re-excited) by dissipating the excess energy as re-emitted light. The light it emits carries a discrete amount of energy corresponding to the discrete quantum difference in energy levels of stable electron sh.e.l.l configurations, and is thus emitted at a specific wavelength. If the laser material is uniform, the excitation results in uniform color output. Amplification of the regularity of the emission of light by different atoms in this medium is achieved by causing the emitted light to reenter the laser by virtue of partially silvered mirrors. Thanks to the common quantized character of the light-absorbing-and-emitting spectra of atoms capable of lasing, light at the emission frequency is also most likely to induce an energized atom to revert to its more stable ground state, and emit its excess energy as light. When it does this in response to light emitted by another atom at the same precise wavelength, it does so in a phase that is precisely correlated with the exciting light. Repeated charging with white light and recycling of emitted light thus amplifies this correlation relationship by many orders of magnitude.

The continual pumping of energy into the atoms of the laser in the form of white light makes them unstable and predisposed to dissipate this energy. It is the a.n.a.logue of asymmetrically heating the fluid in Benard cell formation or accreting water molecules to the snow crystal lattice. A laser is similarly a dissipative system. The orthograde tendency of the atoms is to offload this excess energy and return to a more stable configuration; but the excited state is also somewhat stable, though far more easily disrupted even by the random fluctuations of the electrons themselves. Although spontaneous emission tends to be entirely uncorrelated, and is in this way a.n.a.logous to the random dissipation of heat in a thermodynamic system via molecular interactions, emission that is stimulated by interaction with photons with precisely the same energy (and thus wavelength) is in effect biased (or constrained) to be emitted in resonance with the stimulating light. So, although light-emitting atoms are distributed in s.p.a.ce throughout the laser, as previously emitted light travels recurrently back through the population of continuously excited atoms, it recruits more and more phase-matched photons. Since the system is being continually perturbed away from its ground state, and constantly dissipating this disturbance in the form of emitted light, the facilitation of emission results in an amplification of the matched constraints of stimulation and emission.

To summarize, let's reiterate the common dynamic features that characterize each of these morphodynamic phenomena, and which make them an emergent level removed from subvenient homeodynamic processes, whether at a thermodynamic or subatomic level. In each case we find a tangled hierarchy of causality, where micro-configurational particularities can be amplified to determine macro-configurational regularities, and where these in turn further constrain and/or amplify subsequent cycles of this process, producing a sort of compound interest effect. Although mechanistic interactions, aggregate thermodynamic tendencies, or quantum processes (as in the case of lasers) const.i.tute very different domains with different dynamical properties, the specific reflexive regularities and the recurrent causal architecture of the cycles of interaction have in these cases come to overshadow the system's lower-order orthograde properties. These systems must be open to the flow of energy and/or components, which is what enables their growth and/or development, but they additionally include a higher-order form of closure as well. Such flows propagate constraints inherited from past states of the system, which recurrently compound to further constrain the future behaviors of its component interactions. The new higher-order orthograde dynamic that is created by this compounding of constraints is what defines and bounds the higher-order unity that we identify as the system. This centrality of form-begetting-form is what justifies calling these processes morphodynamic. And the generation of new orthograde dynamical regimes is what justifies d