BIFURCATIONS AND BIOLOGICAL OBSERVABLES

I t is a truism that biological systems are complex. I t has further come to be regarded as axiomatic that complex systems in general are “counter-intuitive.” TO set the stage for the subsequent discussion, it will be helpful to study these two propositions a bit further, and establish some relationships between them. The term complex is almost as hard to define as is life itself. Many approaches to complexity attempt to treat it as if it were an intrinsic property of a system, or class of systems, related somehow to entropy or “information.” These approaches seek to obtain a single quantitative measure of complexity in terms of the number of elements, interactions, o r operations required to characterize some aspect of system behavior. I would rather suggest that complexity is not an intrinsic property of a system-it must also reflect something about the manner in which we, as observers, can interact with the system. Roughly, then, I would suggest that complexity is a property of system descriptions rather than a property of the systems themselves. Indeed, we may say that a system appears complex when it is possible to generate many apparently independent descriptions of its behaviors. Each such independent description must arise out of a different process for observing the system, and hence out of a distinct available mechanism that enables us to interact with the system. For example, a stone usually appears simpler than an organism, because we have only a few ways to interact with the stone, and many ways to interact with the organism. As we increase our capabilities for interaction with the stone, its complexity grows; as we narrow our capabilities to interact with an organism, its complexity diminishes. Thus, complexity appears as a contingent, rather than an intrinsic. property and ultimately reflects interactive capabilities reflected in observation or measurement. It is these capabilities that provide the elements for corresponding system descriptions. With this as background, let us consider what is meant by the proposition that complex systems are counter-intuitive. Roughly, such a proposition connotes the absence of an expected implication between two or more aspects of system behavior. I f each such system behavior arises from a particular mode of interaction or observation and generates a corresponding system description, then the assertion of counter-intuitive behavior implies a logical independence between these modes of descriptions. Let us be more precise about this: imagine a class K of systems, each of which can be described in two ways. Suppose that a body of experience exists which indicates that in some available subclass K ‘ C K, one of