What is “Action”, that Nature Should be Mindful of It?

We have been tracing the course of the book, NEWTON/MAXWELL/MARX by way of a dialectical tour of three worlds of thought. We have seen Maxwell replace Newton’s “Laws of Motion” with the Principle of Least Action as the foundation of the natural world. Here, we seek the meaning of this curious phrase, Least Action.

Let’s grant that Maxwell – along with perhaps most of the mathematical physicists of our own time – is right in supposing that the Principle of Least Action governs all the motions of he physical world. How can we make sense of this truth? What is Action, and why is essential that it be Least?

First, we must begin by recognizing nature is not inert, but in some sense purposeful: every motion in the natural world (and that includes practically everything we can point to, once we take our hands off the controls!) will begin with a goal (Greek TELOS). Think, for example, of that complex process by which an acorn develops into a flourishing oak. This Motion will unfold in such a way that its goal will be achieved in the most efficient way possible. Sound like good economics? We’re asked to see every natural motion as directed to some goal, and as unfolding in such a way that waste or loss en route be the least possible under the given circumstances.

This principle can be expressed elegantly in mathematical terms, rather esoteric and belonging to the hushed domain of mathematical physics. But since it is actually in play everywhere around us, in actions going on at all times, it’s time we reclaimed it and demanded to know what it means. Let’s make a serious effort here to understand the implications that the physicists – Maxwell chief among them – have been saying.

For Maxwell, the true paradigm of physics is the laboratory of Michael Faraday, working immediately with phenomena and tuned always to hear, without complication of intervening symbols, the authentic voice of nature. The Principle of Least Action is about the world we live in.

However we may distort and engineer it, it is always nature, ever-active, with which we begin, and our projects end. We may think we begin with a tabula rasa and design with total mastery to purposes of our own, but every blade of grass, infinitely quantum-mechanical-wise, will laugh at us. It is in the fields and the mountains, the atmosphere and the oceans, and the endlessly-complex workings of our own bodies, that Nature’s economics is inexorably unfolding. High time, that we take notice of it!

We begin always with some process – the fall of a stone, from cliff’s edge to the beach below or the slow unfolding of an acorn into a flourishing oak. The principle applies in every case. Further, nature thinks always in terms of the whole process as primary: the economic outcome cannot be conceived as the summation of disparate parts, however successful each might seem in its own terms.

The unifying principle throughout any motion is always its TELOS, and it is this which in turn entails an organic view of the motion as one undivided whole process. Each phase of the motion is what it is, and does what it does, precisely as it contributes to the success of the whole. If this seems a sort of dreamland, far from practical reality, we must remind ourselves that we are merely rephrasing a strict account of what Nature always does! Things go massively awry (the seeding gets stepped on by the mailman) but these events are external constraints upon the motion: under these constraints, the Principle holds, strictly. Ask any oak tree, blade of grass, or aspen grove. Each has endured much in the course of its motion, yet each has contributed, to the extent possible, to the success of the ecology of which it is a part.

Economic achievement of the goal, we might say, is Nature’s overall fame of mind. Within this frame, exactly what is the economic principle at work? Everything moves in Nature in such a way that Action over the Motion will be least.

So, what is action? Action is the difference, over the whole motion, between two forms of energy: kinetic and potential Nature wants that difference to be minimal: that is, over the whole motion, the least potential energy possible to be expended, en route, as kinetic – i.e., as energy of motion. (One old saying is that Nature takes the easy way.) Or we might suggest: nature enters into motion gracefully.

Think of the falling stone: the stone at the edge of a high cliff has a certain potential energy with respect to the beach below. That potential is ready to be released – converted into kinetic energy, energy of motion. Thus the TELOS is given: to arrive at the beach below, with that high velocity equivalent to the total potential with which the fall began.

Our principle addresses the otherwise open question, how exactly to move en route? There is just one exact answer: the rule of uniform acceleration – steady acquisition of speed. Galileo discovered the rule; Newton thought he knew the reason for the rule. But Maxwell recognized that Newton was wrong, and we need now to get beyond this old way of thinking.

The real reason for the slow, steady acceleration is that the final motion, which is the TELOS, be acquired as late in the motion as possible, and thus that total-kinetic-energy-over-time be least.

Our principle may turn out to be of more intense interest to biologists than to physicists, as the ”kinetic energy” in this case becomes life itself. The seed bespeaks life in potentia. The ensuing show, steady conversion of potential—its gradual conversion to living form as the seedling matures – is the growth of the seeding, the biological counterpart of the metered, graceful fall of the stone.

Our principle governs the whole process of conversion: the measured investment of potential into kinetic form defines the course of maturation. Nature is frugal in that investment: the net transfer of energy-over-time is minimal; transfer in early stages of growth is avoided. Growth, like the fall of the stone, is measured, and graceful. Growth is organic in the sense that every part of the plant, at every stage of the way, is gauged by its contribution to the economic growth of the whole plant.

As it stands, our analogy to the falling stone may be misleading. It is not, of course, the case that the seed holds in itself (like loaded gun!) the potential energy of the oak; the case is far more interesting. The acorn holds in its genome the program for drawing energy from the environment in a way which will assure Least Action over the whole growth process. Once again, frugality reigns, since that energy not drawn-upon by the seedling will be available to other components of the ecology. Since the solar energy is finite, whatever is not used by one is available to the others.

We are ready now to ask in larger terms, “What sense does it make, that Nature be thus frugal in expending potential energy – minimizing its “draw” upon potential in early stages of growth, though total conversion by the end of motion be its very TELOS?

The question is a difficult one, touching on the very concept of life itself. Here, however, is my tentative suggestion. Let us consider Earth’s biosphere as a newborn project, awaiting Nature’s design. Our Earth (like, no doubt, countless other “earths” in Nature’s cosmic domain) is favored with a certain flux of energy, in the form of light from our Sun: just enough, on balance, to sustain water in liquid form, one criterion, at least, for the possibility of life. With regard to Earth, then, Nature’s overall TELOS may reasonably be characterized as the fullest possible transformation of sunlight into life. Earth also offers a rich inventory of mineral resources, which Nature will utilize to the fullest, over time, in the achievement of this goal.

Might we not think of this immense process, still of course very much ongoing, in the terms we’ve used earlier – as one great motion, transforming as fully as possible the potential energy of sunlight, into the living, kinetic energy of life? (It might be objected that the flux of solar energy is kinetic, not potential. It is so in space, en route, but is made accessible as potential by that immense solar panel, the green leaf system of the world – which by its quantum magic captures photons, uses them to split water, and thus generate the electrochemical potential on which the motion of life runs.)

That said, we may apply the logic of Least Action to life on every scale: life’s TELOS is to encapsulate our allotted solar potential energy in living form, always by way of the most frugal path possible. What is saved by the Least Action of one life-motion, is grist for the mills of others – so that overall, the solar flux is utilized as fully as possible. “As fully as possible” at this stage: but the long, slow motion of evolution continues – always, no less governed by Least Action, towards a TELOS we cannot envision, yet of which we must be organically a part, today.

For an expansion of this concept, you can read an earlier lecture: The Dialectal Laboratory: Towards a Re-thinking of the Natural Sciences

NEXT: Karl Marx and his place in Newton/Maxwell/Marx.

The Two Minds of Charles Darwin

I’ve wanted for some time to write this note, but have hesitated because there are so many others who know Darwin far better than I. Nonetheless, I have a certain conviction I’d like to share. Two minds seem to be at work as Darwin surveys the natural world and its evolution. One sees natural selection in terms of confrontations between individuals or species in the search for limited resources. We all know that scenario, which in most of our discussions has become the very paradigm of Darwinian selection.

But Darwin has unmistakably another line of thought, which grasps the utter complexity of the selection process: not as a competition between individuals, but as a system whose complexity defies analysis. If we were to make an improvement in a breed in order to increase its chances of survival, we would not, he remarks, know what to do. In another passage, he remarks on the flourishing of a certain flower in one particular English village. What advantage does this plant have here, which it lacks elsewhere? The answer, he has decided, is the absence of dogs. (Dogs, he reasons, eat cats; cats eat mice; mice eat seeds.) I’ve forgotten why there are no dogs, it might be some village regulation. Whatever it is, there lies the strength of the flower: not in its own design alone, but in the structure of that ecosystem, which has at least for a time stabilized in a pattern collective survival –a pattern, we might say simply, of collective health.

This I believe is an overriding principle, which we have tended since Darwin’s time to miss. That principle, almost systematically ruled out of all facets of our thinking – even our very ideas of medicine or science itself, is the overriding concept of organism, the recognition that we live, flourish and evolve as a whole – not as a sum of individual parts. Only in recent years have we begun to study ecosystems, of all sorts and levels, as wholes. As a society, we’re far behind the demands pressing upon us in catching Darwin’s other, and I believe higher, insight.

The stereotype in describing the components of living systems, to ever-higher levels of resolution, is mechanism. Wrong! We will never understand living organisms as summations of mechanisms. A living system is a different concept altogether from a machine, and study of it calls for different strategies, and different conceptual tools.

Much new work is being done now in the spirit of this new understanding. I’ve found exciting studies of ecosystems to which I want to call attention in an upcoming blog posting. Indeed, it’s not a new thought on this blogsite, which has traced the idea of organism back to its rich source in the writings of Aristotle, and fast-forward through western history to Leibniz, Euler, Lagrange, Maxwell, Hamilton, Feynman and modern physics. But in the din of our celebration of Newton, isolation and competition, we haven’t heard, or perhaps have deliberately rejected, these other voices. We’ve caught only the lesser of the two voices of Charles Darwin.

Cancer and Ecosystems

Peter Gann was a member of our Aristotle discussion group at Pemaqud Point in Maine this summer.  In response to a question I had raised in the wake of our discussions, Peter has written a letter which I find so interesting that, with his permission, I’m reproducing it here a a sort of “guest blog”.  Dr. Gann is Professor and Director of Reearch in the Department of Pathology of the University of Illinois in Chicago.

Dear Tom,

Your question about cancer and ecosystems naturally leads to Virchow! It was he who recognized cancer (and other diseases)as disorders within the community of cells that make up an organ or an organ system. I find this to be a very useful analogy.

The healthy function of the organ requires that each differentiated cell carry out its designated role while remaining in its designated space. How this unfolds during organ development is fascinating and deeply mysterious, but it seems to involve special “tunes” – primitive ones – played out within the genome as well as lots of direct chemical communication between nearby cells.

At some point, once the organ has developed, these signals must change so that such rapid growth and morphogenesis can stop and a more “mature” ecosystem of stable, collaborating cells can emerge.

Cancer cells overcome the signals that maintain this stable ecosystem, and, even appear to hijack some of the genetic programs that are used to control normal development.

This is not too far from how the Ailanthus tree in our backyard (which Wendy identified this summer) threatens our local ecosystem by hyperproliferation, exploitation of local energy sources, and evasion of organisms that would otherwise control its spread. Left undeterred, the Ailanthus could be viewed as a pathological force that would eventually destroy the native Midwestern woodland that we consider to be healthy.

I suppose one could look at all invasive exotic species through the same analogical lens. [But then, thinking of that awful tree in the backyard, maybe this is just demonizing the enemy before going to war!]

The response of an ecosystem to this type of imbalance raises very interesting questions and it would not surprise me to learn that there are numerous examples of stressed ecosystems righting themselves, through adaptation, since the invasive force can be seen as a stimulus to natural selection, just as a change in climate would be. It would take a serious ecologist to deal with that question.

I believe I do recall that some of the early thinkers in the field of ecology (as well as some of the post-Darwin evolutionary biologists) were very interested in the analogy between cell communities and ecosystems. It would be interesting to know what Virchow thought of Darwin.

All the best,

Peter

An Ecosystem As A Configuration Space

In my most recent posting, I've been exploring a quite classic mathematical model of an ecosystem: the Salt Marsh ecosystem model developed at Sapelo Island and described in the fascinating 1981 volume, "The Ecology of a Salt Marsh". For those of us who are devoted to grasping the "wholeness" of an ecosystem, the question arises whether matching such a system to a mathematical model helps in grasping this wholeness - or whether it may even detract. The concern would be that true unity is broken when a whole is described in terms of relationships among discrete parts: as if the "whole" were no more than a summation of parts - in Parmenides' distinction, an ‘ALL" (TO PAN), exactly the wrong approach to a true "WHOLE" (TO HOLON). An excellent guide in these matters is James Clerk Maxwell, who faced this question as he searched for equations that would characterize the electromagnetic field in its wholeness. As soon as he learned of them, he embraced Lagrange's equations of motion, and as he formulated them, his equations derive from Lagrange's equations, not from Newton's. For Lagrange, the energy of the whole system is the primary quantity, while the motions of parts derive from it by way of a set of partial differential equations. Fundamentally, it is the whole which moves, the moving entity, while the motions of the parts are quite literally, derivate.

The components of such a system may be any set of measurable variables, independent of one another and sufficient in number to characterize the state of the system as a whole. Various sets of such variables may serve to characterize the same system, and each set is thought of as representing the whole and its motions by way of a configuration space. If we have such a space with the equations of its motion, we've caught the original system in its wholeness: not as a summation of the components we happen to measure, but in that overall function in which their relationships inhere.

Now, it seems to me that a mathematical model of an ecosystem, to the extent that it is successful, is exactly such a configuration space, capturing the wholeness of the ecosystem whose states and motions it mirrors. Specifically, the authors of the Sapelo Island Marsh Model were if effect working toward just this goal, though it may not have appeared to them in just these terms. All their research on this challenging project was directed toward discovering and measuring those connections, and the integrity of the resulting mathematical system was exactly their goal.

They had chosen to construct their model in terms of carbon sinks and flows; the measures of these quantities were sufficient to characterize the state of the system and its motions, and therefore constituted a carbon-configuration space of the marsh. A different set of measures might have been chosen, and would have constituted a second configuration space for the same system: for example, they might have constructed an energy-model, which have been equivalent and represented in other terms the same wholeness of the marsh. Carbon serves in essence as a representative of the underlying energy flows through the system.

I recognize that this discussion may raise more questions than it answers, and I would be delighted to receive responses which challenged this idea. But I think it sets us on a promising track in the search for the wholeness of an ecosystem - an effort, indeed, truly compatible with the wisdom of Parmenides!