Part 8 (1/2)

. . . 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 s.h.i.+ft 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 relations.h.i.+ps 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 s.h.i.+fted 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 fas.h.i.+on 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?