Last time, I discussed the concept of **emergence as a general background for understanding life.**

I proposed that the best way to think of emergent phenomena in this connection is in the way that condensed-matter physicists do.

Namely, qualitatively new entities and properties arise due to symmetry breaking, and new effective fields emerge as we move from one level to another up the hierarchy of nature. Effective fields, according to quantum field theory (QFT), are fields with properties that are specific to a particular level, or length scale. This is the "more is different" principle.

I also stressed that the thing, above all, that we should be seeking to explain in biology is the *functional stability* of the cell (or any living organism). That means the way the chemical reactions that constitute the physiology, or "metabolism," of a cell are teleologically organized---directed towards the cell's own self-preservation.

In addition, every living thing has the capacity to react appropriately so as to compensate (within limits, of course) for internal or external perturbations. I have been calling this capacity "adaptivity," and the general power of the cell to strive and act on its own behalf, "intelligent agency."

These ideas represent a certain way of looking at life, and pose a certain set of scientific problems. But what is more interesting, of course, is whether the problems have a solution.

It is safe to say that no one scientist has yet succeeded in solving the stupefying intellectual puzzle that is the phenomenon of life. However, a number of scientists have proposed ideas that may well turn out to be individual pieces of the puzzle.

The remaining installments in this series will be devoted to looking at some of their suggestions.

F. Eugene Yates (top) was a highly distinguished physiologist. Born in 1927, he conducted pioneering research over a period of many years at Harvard, Stanford, USC, and UCLA. He cast his net wide, making contributions to our understanding of aging, biorhythms, the endocrine system, Alzheimer's disease, and congestive heart failure. He founded three new journals, in integrative physiology, endocrine systems, and biomedical engineering. He was involved in improving drug delivery systems. He was even a consultant for NASA. He was still scientifically active almost until his death on January 20, 2015, aged 87.(1)

Few careers in science have been as fruitful, or as successful, as Gene Yates's. And yet, it is likely that his place in history will be secured, not by his mainstream accomplishments, excellent as they are, but rather by the original, and as-yet under-appreciated, theoretical framework he developed for modeling the goal-directed, adaptive character of biological systems---*homeodynamics*.

With homeodynamics, Yates is endeavoring to bring the pioneering physiologist Walter B. Cannon's (right) notion of "homeostasis" up to date. Or, better to say, he is striving to give a fuller and more rigorous form to Cannon's idea by expressing it in terms of the concepts of the modern mathematical field of dynamical systems theory, and, in particular,* nonlinear dynamics*.(2)

Nonlinear dynamics traces its origins to the late nineteenth century and the polymath genius, Henri Poincaré, who developed a new mathematical approach to the celebrated three-body (or *n*-body) problem in celestial mechanics, which had long defied analytical solution on Newtonian principles.(3)

Poincaré (left) showed that, by bringing to bear concepts he had developed in the area of mathematics that would come to be known as "topology," it was possible to determine whether particular configurations of *n* bodies would lead to stable or unstable orbits.

That is, even though no exact solution solution to the *n*-body problem was possible, it *was* possible to give a more general or "qualitative" description of the future behavior of the system. For this reason, nonlinear dynamics is sometimes known as *qualitative dynamics*.

Yates's idea was to apply some of the concepts of qualitative dynamics to the problem of understanding the stability of living systems---in particular, physiological feedback systems. In order to understand why Yates's ideas are so original, it is important to understand that the conventional way of modeling the "homeostatic" behavior of various physiological systems is by means of an altogether different set of ideas---those of cybernetics, or feedback-control theory.

Now, there is no doubt that the concept of control via negative feedback is helpful in understanding the way that living systems operate. But it is also clear that organisms possess properties that no man-made feedback-control system has. There are many such properties, but for our purposes here, we may concentrate on two of them: robustness and plasticity.

While these terms are unfortunately not used consistently by all investigators, the way I use them here is now becoming standard. "Robustness" refers to the ability of a living system to return to an earlier functional regime following perturbation, while "plasticity" means the ability to find a novel functional regime that maintains overall system viability, in case a perturbation is so great as to make a robust response impossible.

According to this way of using the terms, the ability of a broken bone to heal would be an example of robustness, while the ability of a dog to shift to a three-legged gait upon losing a limb would be an example of plasticity.

The main reason that nonlinear dynamics is so well-adapted to describing the behavior of physiological systems is that it allows us to see why all living things possess both robustness and plasticity. The reason is that they are not two independent properties. From the point of view of nonlinear dynamics, we can see that they are two sides of the same coin.

How so? Here, in a nutshell, is the idea that lies at the foundation of Yates's homeodynamics.

First, we recognize that most physiological processes are periodic, or cyclical, in nature. This is no mere accident, but rather is a deep insight into the nature of living, as opposed to nonliving, systems. In Yates's words:

In any persistent system, whose operations are sustained over periods of time very long compared to the characteristic process and interactional times within it, cyclic energy transformations must be present. Certain processes must occur again and again if the system is to persist. Otherwise we would observe only relaxational trajectories to equilibrium death. Thus, limit cycle--like, nearly periodic, oscillatory behavior is the signature of energy transformations in open, complex, thermodynamic systems . . .(4)

That is, we recognize that physiological processes are, in general, types of oscillators, and thus may be appropriately modeled using the concepts of nonlinear dynamics. In particular, we represent the behavior of the oscillator over time as a collection of trajectories through an abstract "phase space." This ensemble of trajectories will usually be confined to a small volume of the available space---that is, it will be "non-ergodic." Such a mapping of the oscillator's behavior is called a "basin of attraction," or "attractor," for short.

Different sorts of attractors exist with various mathematical properties, but the fact that physiological oscillators are, in general, highly nonlinear---with trigger-like, weak energetic inputs leading to high-energy outputs---means that nonlinear attractors (either "limit cycles" or "strange attractors") are the right sort of mathematical construct with which to model most, if not all, biological phenomena.

Using the nonlinear attractor as our basic tool for modeling biological activity, in turn, allows us to understand why robustness and plasticity are two sides of the same coin. Nonlinear attractors have two mathematical properties, called "equifinality" and "metastability," which allow us to represent these phenomena in a natural way.

Equifinality is the tendency of a system to return to its former equilibrium regime following perturbation, so long as its trajectory remains within the boundaries of its basin of attraction. Equifinality, thus, corresponds to robustness.

Metstability is the ability of a system to find a new equilibrium regime following a perturbation that is too strong, and which sends the system's trajectory over the edge of its attractor (a "bifurcation event"). Metastability means that attractors are not isolated, but exist within a larger landscape of alternative virtual basins of attraction. Thus, metastability corresponds to plasticity.

It should be pointed out, of course, that the general property of metastability does not guarantee successful plastic adaptation. It is always possible that the system may fall into a "point attractor"---that is, an attractor that ceases to oscillate altogether. That, of course, is the mathematical representation of death for that system.

Another important aspect of Yates's homeodynamics is the idea that the behavior of physiological oscillators is, in general, delicately poised at the intersection of competing physical forces, or influences. This means that perturbations need not necessarily be conceived of as severe, or even as exogenous. Rather, biological systems are inherently sensitive, fluid, and dynamic.

Here is how he expresses this point:

A key concept of [homeodynamics] is that physical models of complex systems require competing components in the equations of motion. The competing influences may be potential energy versus kinetic energy, or energy versus entropy, or symmetry versus broken symmetry, or incoherent diffusive transport versus coherent convection or coherent wave propagation.(5)

This way of looking at biology as a competition between inherent influences throws additional light on robustness and plasticity, as well:

An internal or external fluctuation may tip the competition one way or the other, and then either of two possibilities will be realized: (a) the system may absorb or damp-out the fluctuation and so continue its current stability regimes or (b) the system structure may change. If the system structure changes, there are two further possibilities: it may change toward a new stability regime or it may change toward an instability, even leading to death of the system.(6)

Another important feature of homeodynamics is that it provides us with a natural representation of the field-like features of living systems. Here is what Yates says on this topic:

. . . the important characteristic that distinguishes complex atomisms in a field is that their interactions do not rapidly equipartition energy among the accessible translational and internal degrees of freedom. Instead, very significant time delays appear in the distribution of energy among the internal degrees of freedom of the system. A complex field can be thought of as a cooperative, in which the chief processes are fluid-mechanical, gel-like, dissipative---very unlike the more spring-like, conservative interactions of simple, idealized statistical mechanical systems. The net effect of such complexity is to make an account of motion by translational momentum (i.e., by Newton's law of motion) inappropriate. Instead, one must integrate over a time much longer than the relaxation times of translational interactions in order to close the thermodynamic books on energy and entropy changes. This is the process cycle time in which action modes characteristic of the field emerge. Complex systems are thus "soft" systems without many tight, direct, or "hard" causalities or couplings.(7)

This point is important, not only because homeodynamics is an appropriate heuristic for modeling the field-like characteristics of living things, but also because eventually we must connect up the "phenomenology" described by homeodynamics with some deeper physical theory, which is bound to be a field theory in mathematical form.

Finally, perhaps the most important aspect of homeodynamics---at least from a philosophical perspective---is the way it helps us to rationalize the phenomenon of teleology.(8)

Teleology---or goal-directedness, or purposiveness---is a manifest property of practically all biological phenomena. It has been considered anathema since the time of Francis Bacon, because it has seemed impossible to square with ordinary physical causation. Homeodynamics is valuable, above all, as a way of reconceptualizing teleology in biology.

Traditionally, teleology has been considered unacceptable because it seems to presuppose either "backwards causation" or else a mind capable of forming conscious intentions.

The former is unacceptable because it seems impossible that a non-actual, future state of affairs (the goal state) should causally influence the present. The latter is unacceptable because most biological systems apparently lack a mind in the relevant sense of a capacity for forming conscious intentions.

Homeodynamics solves this riddle by injecting the mathematical apparatus of nonlinear dynamics into the discussion, which introduces the element of virtuality. Virtuality---a notion well attested in physical science---is built into the concept of an attractor, in regard both to equifinality and to metastability.

In this way, homeodynamics allows us to model teleological phenomena while dispensing entirely with both backwards causation and conscious intentions.

Yates goes on, in both the papers cited here and elsewhere, to discuss a great many more topics than I have space to explore at present.(9)

Let me close, then, by allowing Yates to sum up his ideas in his own words:

I have attempted to provide a glimpse of a general, physical "theory" (more correctly, an heuristic) for a fundamental understanding of the complex dynamic character of energetic metabolic networks and their regulations. The heuristic, [homeodynamics], is free of unjustified intentional or "smart" elements, of vitalisms, or of KiplingesqueJust So Storiesabout causalities. It is synoptic and level-independent. It supports both reductionist and holistic approaches to complex systems and avoids two dominant intellectual constraints of recent times, viz., genetic determinism from molecular biologists, and the notion that contemporary particle physics has the wherewithal to come up with a "theory of everything."(10)

Earlier installments in this series are as follows:

**Part III: Mary Jane West-Eberhard**

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(1) John Urquhart, "Living History: F. Eugene Yates," *Advances in Physiology Education*, 2009, **33**: 234--242; http://www.huffingtonpost.com/walter-m-bortz-ii-md/dare-to-be-100-gene-yates_b_6547332.html.

(2) Nonlinear dynamics, also known as chaos theory, may be defined as the study of systems whose behavior is highly sensitive to small changes in one or more variables. See E. Atlee Jackson, *Exploring Nature's Dynamics* (Wiley, 2001).

(3) Florin Diacu and Philip Holmes, *Celestial Encounters: The Origins of Chaos and Stability* (Princeton UP, 1996).

(4) F. E. Yates, "Order and Complexity in Dynamical Systems: Homeodynamics as a Generalized Mechanics for Biology," *Mathematical and Computer Modelling*, 1994, **19**(6--8): 49--74; p. 62.

(5) F. Eugene Yates, "Homeokinetics/Homeodynamics: A Physical Heuristic for Life and Complexity," *Ecological Psychology*, 2008, **20**: 148--179; p. 155.

(6)* Ibid.*

(7) F.E. Yates, "Order and Complexity in Dynamical Systems," *op. cit*.; p. 63.

(8) The French school of dynamicists has laid particular stress on this philosophical point. See Pierre Delattre, "An Approach to the Notion of Finality according to the Concepts of Qualitative Dynamics," in Simon Diner, *et al.*, eds., *Dynamical Systems: A Renewal of Mechanism* (World Scientific, 1986), pp. 149–154; and Alexandre Favre, *et al.*, *De la causalité à la finalité* (Éditions Maloine, 1988) [translated as *Chaos and Determinism* (Johns Hopkins UP, 1995)].

(9) Two other useful papers by Yates are "Quantumstuff and Biostuff: A View of Patterns of Convergence in Contemporary Science," in F. Eugene Yates, ed., *Self-Organizing Systems: The Emergence of Order* (Plenum Press, 1987), pp. 617--644; and "Self-Organizing Systems," in C.A.R. Boyd and Denis Noble, eds., *The Logic of Life: The Challenge of Integrative Physiology* (Oxford UP, 1993), pp. 189--218.

(10) F. Eugene Yates, "Homeokinetcs/Homeodynamics," *op. cit.*; pp. 166--167.