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

The Aristotelian Pathway to the Modern World and Beyond

I’m just back from a week of seminars in Maine: an overview of Aristotle’s world-view, based on a sequence of selected readings.  Although I’ve long been curious about Aristotle’s thinking, and written about this to some extent on this website, I’ve never before caught the full coherence and impact of his world-view. I’ll leave details to future posts to this blog, but here’s an overview of a few highlights. Tradition has misleadingly titled many of Aristotle’s works. His “Physics” is not limited to what we today call “physics”, but actually addresses the foundations of the entire natural world, of all things that move, from stones to living creatures, including ultimately ourselves. Aristotle’s “Physics”, then, lays the foundation for his other works, and in the “Metaphysics”, of the cosmos itself. We ourselves he will say, are rational by nature.

What is “nature”?  An inner principle of motion, Aristotle says; things move not because they are pushed or pulled, but through inner tendencies. This is by no means nonsense. Within what we call “physics”, think for example of the second law of thermodynamics, which asserts, in more formal terms, that heat “tends” to flow downhill. Within our own lives, think of fear or love, and our innate desire to know. Thus in Aristotle’s inclusive world-view, there’s no occasion for the infamous split which today appears to divide our sciences from the humanities.

Such unification need not threaten the integrity of the sciences. Remarkably, within this encompassing perspective Aristotle lays a secure foundation for a fully valid alternative approach to modern science. Key is his concept of “energy” (the word, energeia, is his!); motion consists in the unfolding of energy from potential to kinetic form. Importantly, energy belongs primarily to whole systems, so wholeness and living, organic unity are foundational in Aristotelian science.

In the 17^th century Leibniz, who knew his Aristotle, put this into mathematical form. He introduced, in open opposition to Newton, a version of the calculus which served to open alternative path into not just modern physics, but modern thought more generally.

As a result, we can discern two very different, parallel pathways through the history of western thought – one leading to Newton, Descartes, and a world of force, competition and mechanism; the other, prefigured by Aristotle, leading to wholeness, cooperation, friendship and life.

The path through Newton, Locke and Hobbes is very familiar to us; it has led t the world we know today, a world of strife, competition, and ever-escalating warfare. That other thread, which runs from Leibniz, Euler, Lagrange, Hamilton, Faraday, Maxwell and Einstein, bespeaks unity and intelligent cooperation. Within physics, this appears especially in the concept of the field; but more generally, it looks to a society of intelligent cooperation in the solution of our common human problems. It is easy to see, I believe, which is better suited to address the problems of warfare and environmental catastrophe which beset human society today.

Nobody, of course, is offering us this choice of roads into the future.  But we have independent minds, and it would be good to know that there is a difference in principle even if we see no way at present to pursue it in practice. I propose to write more about this in upcoming postings – and it will be good to know what others think of this Aristotelian way I’m convinced I’m seeing.

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!

Can An Ecosystem Model Help Us Think About Wholeness?

Readers of this website will be aware of my preoccupation with the question of "wholeness". The more I observe the world's current struggle to find its way through complex economic structures or global systems, the more convinced I become of the degree to which our deep-rooted commitment to individualism is betraying us. Individualism is both an ethic, which we are determined to impart to the world, and a habit of thought. This is not the moment to follow that line of thought further; it has been the subject of other postings, and it will be of more in the future. My concern at the moment is to offer a new approach to this issue. On a visit to the Key School in Annapolis recently, on the shores of the Chesapeake, I was struck by the widespread awareness there that the Bay is sick: 27% of true health was the figure I was hearing. That led me to wonder about the concept of "health" of an ecosystem, and how it might be grasped. With the aid of the computer, I knew, the human mind is today able to reason about problems hitherto too complex to analyze. Could I find a computer model of an ecosystem?

By good luck, I've found not only such an ecosystem model, but a revealing account of a team project by which it was achieved. Teams of experienced scientists agreed to set aside their normal researches into separate compartments of the ecosystem, and direct their efforts  instead to a different kind of learning: to the common goal of constructing a coherent computer model which would capture the intricate interrelationships of these many components of one single system.

The system to which fortune had led me was a salt marsh at Sapelo Island on the coast of Georgia. The Book, edited by L. R.Pomeroy and R.G.  Wiegert, is "The Ecology of a Salt Marsh" (New York, 1981). Its innocent title fails to suggest the very special interest of the project it narrates. Quite elegantly, the book pulls together a fascinating account of the scientists' experience in disciplining their work to this goal.

An aesthetic of wholeness is invoked at the outset, with lines from  Sydney Lanier's poem, "The Marshes of Glynn". We learn much about this new sort of scientific endeavor when the book closes with a section on the aesthetic of the marsh, and a final quotation from that same poem.

Though a layman in matters of biology, I've since been making an effort to follow the turns of this inquiry. I won't say more how, beyond the remark that the effort proved successful only after the scientists had learned of a fundamental error they had been making, and accepted correction from the computer.

People whose judgment I very much respect have expressed their doubts as to the whether such a computer model is an appropriate means for approaching wholeness, or whether at this point I'm confusing true wholeness with a mere assemblage of parts by complicated aggregation. (My thoughts go back to Plato's "Parmenides", and the paradigm there of Hesiod's wagon: I agree that the "wagon" is something quite other than an assemblage of its parts!) In these terms, is a working computer model helping us to grasp the wholeness of a system, or betraying us into confusing true wholeness with a merely clever example of aggregation? In the case of a living ecosystem, in which the wholeness is manifestly organic, is the computer misleading us, tempting us to confuse organism with a complex structure of inherently inorganic parts?

My case for the computer as a welcome aid in advancing toward a  grasp of true wholeness must be made in future remarks which I plan to post soon.

What Do we Mean by the Term "Elementary"?

What do we mean when we use the term ,”elementary”, in relation to a science? Does it refer to an easy introduction, as contrasted with an “advanced” treatment of the same subject? Or does it mean a solid account of the very foundations of the science? Or, for that matter, are these the same thing?

Maxwell had a tendency toward writing “elementary” texts: he wrote one on heat, and another on mechanics, both for use in classes for workingmen – a project to which he was deeply committed. Finally, at the time of his death he was at work on his “Elementary Treatise on Electricity and Magnetism, intended to serve as the Cambridge text to support a new degree in experimental natural philosophy at Cambridge University.

My sense is that Maxwell endowed each of these with earnest attention – that he regarded the “elements” not as evident, but as a topic to be approached with great care. Our decision as to what is elementary in a science has a great deal to do with our sense of the form the finished product will take – so that the most difficult issues may focus on the most elementary beginnings.

For example, Maxwell wrote his workingmen’s text in mechanics, Matter and Motion, only after he had hit on the fundamental idea, new to him, of Lagrnagian mechanics and generalized corrdinates. This would not be a mechanics in Newtonian form, in which the elements would be assumed to be hard bodies acting upon one another according to laws; rather, elements of this sort would be the least known components of the system, represented by generalized coordinates.

In this view, what we observe initially is a whole system of some sort; it is this whole which is fundamental, and truly elementary. The parts which compose it, we may never know. Our science can be complete and secure even if that question remains unresolved, or unresolvable.

This is the point of view I believe Maxwell had come to, underlying his approach to the new program at Cambridge as well. If so, must it not represent a truly revolutionary inversion of our very concept of scientific knowledge?

It fitted the primacy he – following the path of Farday – was giving to the concept of the electromagnetic field. In this view, he field would not be a secondary phenomenon, a composite or consequence of simpler “elements”, but itself both simple and whole.

If the elementary is what is primary, then in the case of the field it is the whole which is the element, from which we deduce what we can, concerning lesser components. Faraday had felt strongly that in the case of electricity, there was no “charge” lying on the surface of a charged body, but what we call a “charge” was a field, which filled the room.

Isn’t it the case that when we ask for the “explanation” of a physical system, we are asking for an account in terms of its elements? If so, then the field is itself explanatory, and we would not seek explanation in terms of the actions of some lesser parts. What will be the consequences if we extend this view to physical explanation – or explanation beyond the realm of physics -- more generally?

"Faraday's Mathematics"

“Faraday’s Mathematics” is a lecture I gave at at a conference on Faraday at St. John’s College in Annapolis.  Its subtitle is “On Getting Allong Without Euclid”, for Faraday had neither studied Euclid, nor taken on board the plan of formal demonstration which most of us learn from the study of geometry.  In short, Faraday thought in his own way, following the lead of nature and experiment.  He was in effect  liberated from the presuppositions about thought and physical theory with which others in the scientific community were encumbered. 

 The result was that Faraday hit on a fundamentally new way of understanding the phenomena of electricity and magnetism – by way of the new concept of the “field”. Maxwell deeply respected Faraday’s way, and dedicated much of his own life to comprehending how Faraday worked, and what it was that Faraday had done.  The field is a fully connected system, and fields interact, not by way of their parts, but as wholes.  This was clear enough to Faraday, but it required recourse to a new sort of mathematics – Lagrangian theory – and a major reversal of conventional thinking, to articulate a formal theory in which the whole is primary, and with it a new rhetoric of explanation.   This was Maxwell’s accomplishment in his Treatise on Electricity and Magnetism, a transformation I trace as a rhetorical adventure in my book Figures of Thought.

  In the end, Maxwell emerged with the astonishing claim that of them all, it was the uneducated Faraday who was the real mathematician.  If that could be so, what is mathematics?   That’s the question pursued in this lecture, which aims to find out what Maxwell could have meant.

Maxwell was clearly in earnest, and seems to be pointing to a mathematics embodied in nature, which lies deeper than either its symbolic or its logical forms.

"Reason", Old and New

Somewhere in the course of our western history, something fundamental has been lost: we have lost track of the wholeness of the psyche, and its membership; in a world which was whole and in which it might feel at home.   

Where did this happen?  The psyche was whole in Athens – its membership in the family, the polis and the cosmos were so presupposed that there were perhaps no words to express the separation and fragmentation so vivid to us today.   I don’t think there was a word for “objective” or “subjective”, nor was there a mind which might be thought of as a blank tablet, upon which an outside world might write. In society there was work, but no word for “job”, with the radical alienation that term implies.  I’m not suggesting life was in any sense idyllic – only that for better or for worse, the psyche was intact, and seated in the world. 

I’ll leave it to others to explain how this has come about, but somehow we now find ourselves equipped with a mind which is well-furnished with knowledge, indeed, but all too easily likened to a calculative engine, with a memory bank stored with data from an “outside” world.  We understand the mind better and better – but only as a marvelously equipped machine.  

What is missing would seem to be that faculty once called “intellectual intuition” – the power to see directly and immediately, without the intervention of words, truths which are timeless and fundamental.  That old intellect -- for which the Greeks did have a word: NOUS -- was inherentlyi drawn to beauty, which it deeply loved. 

I don’t see this as an exercise in nostalgia: there are ways open to us today by which we can recover this power, which is perhaps rather hidden than lost.  Other cultures have preserved it in ways we haven’t, and we have much to learn from them.  To a large extent it is our conception of “modern science” which denies the evidence of intuitive reason, and reduces the concept of “reason” to accurate symbolic calculation.  But there is another way within modern science, equally mathematical and rigorous, but founded in a concept of wholeness, and looking to the whole rather than the parts as the ground of “explanation”.  I have spoken about this way – the “Pinciple of Least Action” -- in my lecture, “The Dialectical Laboratory”, elsewhere on this website.   

Nothing prevents, I believe, our mending this split between that classic concept of intuitive reason, seated in the world and knowing and loving truth directly -- and the concept current today of reason as a calculative engine making what it can of an “outside” world.   We need only retrace our steps and pick up that thread of truth wherever we dropped it.  Not easy to do, of course, but worth every effort!

Any suggestions as to how to begin? 

In Praise of Generalized Coordinates

I've been expressing my enthusiasm for a holistic approach to the understanding of nature -- in relation to my favorite topic, the electromagnetic field, this takes the form of the Lagrangian equations for the field as a single, connected system characterized by its energy, not by forces.  It was crucial to Maxwell's development of the equations of the field in his "Treatise on Electricity and Magnetism" that they be formulated as instances of such a connected system -- i.e., in Lagrangian terms, and NOT on the basis of Newton's laws of motion.  (The difference -- very fundamental to our understanding of nature -- is developed in "The Dialectical Laboratory", in my "Lectures" menu.) Now, the question arises: "If we start in this way, from the 'top down', how do we ever arrive at the elements?"   The answer is, "We DON'T!" We move logically "downward" by finding the dependence of the energy of the whole system upon ANY set of measurements we want to make -- provided only that it's a complete (i.e. sufficient to determine the state of the system), with each measure "independent" of the others. We find such a set of measurements by doing experiments -- and when we get them, they are called "generalized coordinates".  The important thing is that there may be many ways we can define them, each set as good as the others: and in the whole process we never get any"real,underlying elements" -- we don't need them!  Reality is founded at the top, not the bottom, of the chain of explanation.   This is Maxwell's new view of physical reality, founded upon the field.  It is the opposite of the notion of "mechanical explanation", and it is the direction which our approach to nature desperately needs to take as we approach the challenges which lie before us today.  In terms of the philosophy of science, Maxwell it seems was far ahead of his time.  I propose to call this the "Maxwellian Revolution". 

Why Aristotle? Why Now?

 Here’s a brief posting, not unrelated to the previous two. I spoke in the first of a “tap root” running back from what we think of as “modern science” to sources in an ancient past. Such a tap root is not just a connection to the past, something of interest to academic historians, but potentially a powerful source of nourishment today.  This may seem a strange claim to make for Aristotle in relation to modern science, but I do put it forward in earnest. Aristotle generally gets a bad rap from those who tell the story of modern science, but to a large extent it’s latter-day Aristotelians (such as Galileo’s Simplicio), not Aristotle himself, who are the targets of such criticism.  It is well-known, and widely acknowledged, that Aristotle was a serious empiricist, conducting dissections and drawing such generalizations as he could perceive. But what was his account of scientific method, that we might give it serious attention today?  I’m writing this from memory, so my references for the moment must be inexact.  But in crude summary, here is the account which culminates in his “Posterior Analytics”.  

He has said elsewhere that the objects of true knowledge which Plato calls the “forms” are “nowhere”, not in the sense that they do not exist, but that they do not exist in separation.  The forms are everywhere in the observable world. We meet them when mind grasps something as whole and true. He says somewhere that scientific inquiry, as we gather data, is like an army in retreat: first one soldier takes a stand, then another, then more - and soon, the whole column stands fast. That standing fast is the mind grasping something true: “seeing something” whole, as we say, or achieving an intellectual intuition.  Such an intuition is not the additive sum of the component data. Between such an empirical summation (which Plato calls the “all”), and the grasp of a truth, (a “whole”), lies the difference between data-processing and great science. 

 We are so concerned today to emphasize the “objectivity” of true science, that we fail to acknowledge the role of mind - a function which grasps something the data do not themselves present. In that sense, great science, serious science, cannot be reduced to objectivity.  It cannot fly in the face of the data, but it cannot be reduced to those data, either.  We live at a time when it is becoming increasingly urgent that we rise to the challenge of recognizing whole systems as such. An ecology is something more than the sum of any quantity of data.  In biology, this whole beyond the parts is termed an “organism”; perhaps Aristotle would be reminding us today that we are in danger of failing to recognize life itself when it lies before us in our laboratories or in the seas.   

Indigenous Views of Nature and the Deep Roots of Western Science

When I wrote yesterday about the "deep roots" of Western science, I intended to point to a possible relation this opens up between the domain of "science" and Indigenous views of the natural world.  If we follow that line of development which leads from Aristotle through Leibniz to the holistic mathematical physics based on the Principle of Least Action, we find ourselves in a position much closer to that of Native American thinkers than we might have expected.Modern science in its mechanical mode cuts off "science" from any sense of wholeness or, especially, of purpose. It wants to reduce all quality to quantity, all motion to the operation of laws which bind matter apart from any sense of goal or meaning, and sees "nature" exclusively as an object from which we stand apart as mere observers. None of these limitations apply to the physics in the holistic mode.  Least Action applies to whole systems, and sees systems moving directionally toward the optimization of a quantity which applies to the system as a whole.  Although this goal may be no more than the optimization of a mathematical quantity, it opens the way to thinking of systems such as organisms or ecologies as moving as wholes toward ends -- a line of thought of which the modern world is in desperate need.One more link in this line of thought: the modern computer is bridging the gap ;between "quantitative" and "qualitative" thinking.  What goes in as number typically comes out on the computer screen as a graphical image readily grasped by the intuitive mind and conducive to interpretation in terms of purposes and goals. We can see how systems are moving, and where they "are going".   Nothing stands in the way of reading these in terms of purposes, and that is what we do on a daily basis -- think for example of evidences of the consequences of global warming emerging from complex computer modeling.  Thinking in this way in terms of whole systems,  understanding their motions in terms of a mathematics of optimization, and bridging the gap between quality and quantity -- all this is yielding an approach to science at once new and old -- in a continuous thread leading from Aristotle into the age of the modern computer.  If we follow that path and think of modern science in terms like these, then it seems to me the gap between a holistic science and Indigenous relations to the natural world is not as deep as it had seemed.  Set aside mechanistic thinking, embrace the sense of nature as a whole of which we ourselves are part, admit goal as a category amenable to science -- and then the old gap between Indigenous, or simply hunan views of the world, and those of "western science", begins to dissolve.   Thus the Cosmic Serpent project, designed to consider this relationship, begins to look much more promising than it otherwise might have.