Teleology, Least Action, and Variational Principles

["Tim Gwinn" <***>]

To all,

 

I was thinking about the recent discussion of anticipatory systems and the way it touches upon aspects of such systems which seem to have teleological overtones.

 

It brought to mind a reference in Essays by Rosen:

"...it was early recognized that the variational principles of physics, which we reviewed above, seems already to violate this maxim; we need both a present and a future configuration to determine a path. Thus, the Principle of Least Action, say, which is at the very heart of theoretical mechanics, looks more telic than mechanics itself allows. This has always bothered people, and many have taken the trouble to try and rationalize it away on various grounds, which we need not pause to review here. But these facts point to a perhaps deep relationship between the nature of optimality principles in general and the things we do not understand about organic phenomena." [EL 216]

 

This led me to review Ernst Mach in his book "The Science of Mechanics", on the topic of the Principle of Least Action. Mach remarks:

"Euler's view is, that the purposes of the phenomena of nature afford as good a basis of explanation as their causes. If this position be taken, it will be presumed a priori that all natural phenomena present a maximum or minimum. Of what character this maximium or minimum is, can hardly be ascertained by metaphysical speculations. But in the solution of mechanical problems by the ordinary methods, it is possible, if the requisite attention be bestowed on the matter, to find the _expression_ which in all cases is made a minimum or maximum. Euler is thus not led astray by metaphysical propensities, and proceeds much more scientifically than Maupertuis. He seeks an _expression_ whose variation put=0 gives the ordinary equations of mechanics." [ch. III, sec VIII.5]

 

This view of purpose as a basis of explanation seems striking to me. This brings up an intriguing notion, stated 3 different ways below:

- Is there some _expression_ which can be ascertained and which will be a minimum (or maximum) for biological organisms?

- Is there some variational principle at work (no pun intended) for organisms?

- Is there an overarching "purpose" (in the sense in which Mach and Euler use the term) which organisms abide by, and can thus be  discerned "if the requisite attention be bestowed on the matter"?

 

It may well be that IF complex systems have such a solution, it will be very difficult to discern, and even harder to formalize, since complex systems possess noncomputable models, and therefore, it is highly likely that any variational principles analogous to a Least Action principle will likewise have noncomputable characteristics.

 

Still, the idea of purpose seems closely tied to organisms in the form of final cause associated with closed causal loops. So it leads me to muse on what might be the organismic analog of a Least Action kind of principle, and whether such a principle would exist across the span of an individual organism's lifespan, or perhaps only across an evolutionary span, or perhaps there are distinct principles for each span.

 

Regards,

Tim