At The Best Schools, James Barham continues his series with “Seeing Past Darwin VI: F.E. Yates’s Homeodynamics” (June 24, 2012) on one scientist’s effort to use the conceptual tools of nonlinear dynamics to model physiological systems:
“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.”
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.