Equifinality in Physical System

One important characteristic of biological systems is circum­scribed by terms like “purposiveness,” “finality,” “goal-seeking,” etc. Let us see whether physical considerations can contribute to a clarification of these terms.

It has often been emphasized that every system attaining an equilibrium shows, in a certain way, “finalistic” behavior as was discussed previously (pp. 75f.).

More important is the following consideration. Frequent at­tempts have been made to understand organic regulations as establishment of an “equilibrium” (of course, of extremely com­plicated nature) (e.g., Kohler, 1927), to apply LeChatelier’s and similar principles. We are not in a position to define such “equi­librium state” in complicated organic processes, but we can easily see that such a conception is, in principle, inadequate. For, apart from certain individual processes, living systems are not closed systems in true equilibrium but open systems in a steady state.

Nevertheless, steady states in open systems have remarkable characteristics.

An aspect very characteristic of the dynamic order in organismic processes can be termed as equifinality. Processes occurring in machine-like structures follow a fixed pathway. Therefore the final state will be changed if the initial conditions or the course of processes is altered. In contrast, the same final state, the same “goal,” may be reached from different initial conditions and in different pathways in organismic processes. Examples are the development of a normal organism from a whole, a divided or two fused ova, or from any pieces as in hydroids or planarians, or the reaching of a definite final size from different initial sizes and after a different course of growth, etc.

We may define:

A system of elements Qi(x, y, z, t) is equifinal in any sub­system of elements Qj, if the initial conditions Qi0 (x, y, z) can be changed without changing the value of Qj (x, y, z, ∞).

We can stipulate two interesting theorems:

  1. If there exists a solution of form (5.9), initial conditions do not enter into the solution for the steady state. This means: If open systems (of the kind discussed) attain a steady state, this has a value equifinal or independent of initial conditions. A general proof is difficult because of the lack of general criteria for the existence of steady states; but it can be given for special cases.
  2. In a closed system, some function of the elements—e.g., total mass or energy—is by definition a constant. Consider such an integral of the system, M(Qi). If the initial conditions of Qi are given as Qio, we must have:

independent of t. If the Qi, tend toward an asympotic value, Qil

M, however, cannot be entirely independent of Qi0; with change of Qi0, also M and therefore M(Qi1) are altered. If this in­tegral changes its value, at least some of the Qi1 must also change. This, however, is contrary to the definition of equifinality. We may therefore stipulate the theorem: A closed system cannot be equifinal with regard to all Qi

For example, in the simplest case of an open chemical system according to equation (5.2), concentration at time t is given by (5.3); for t =∞ , Q = E/k, i.e. it is independent of the initial concentration Q0 and dependent only on the system constants E and k. A derivation of equifinality—i.e., the reaching of a steady state independent of time and initial conditions—in diffu­sion systems can be found in Rashevsky (1938, Chapter 1).

The general consideration, of course, does not provide an ex­planation for specific phenomena if we do not know the special conditions. Yet, the general formulation is not without interest. We see, first, that it is possible to give a physical formulation to the apparently metaphysical or vitalistic concept of finality; as is well known, the phenomenon of equifinality is the basis of the so-called “proofs” of vitalism of Driesch. Secondly, we see the close relation between one fundamental characteristic of the organism, i.e. the fact that it is not a closed system in thermo­dynamic equilibrium but an open system in a (quasi-)stationary state with another one, equifinality.

A problem not here considered is the dependence of a system not only on actual conditions, but also on past conditions and the course taken in the past. These are the phenomena known as “after-effect,” “hereditary” (in mathematical sense: E. Picard) or “historic” (Volterra) (cf. D’Ancona, 1939, Chapter XXII). In this category belong phenomena of hysteresis in elasticity, elec-tricity, magnetism, etc. Taking dependence on the past into con­sideration, our equations would become integro-differential equations as discussed by Volterra (cf. D’Ancona) and Donnan (1937).

Source: Bertalanffy Ludwig Von (1969), General System Theory: Foundations, Development, Applications, George Braziller Inc.; Revised edition.

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