Tag Archives: Newton


Maxwell and the Treatise on Electricity and Magnetism:


Maxwell Between Two World-Views

Many of us may know what it means to feel “at sea”: without beacons to steer by, without terra firma on which to set our feet. A dialectical passage between two world-views is like that, and James Clerk Maxwell’s life-story might be read as the log-book of just such an expedition: a lifelong search for a clear and coherent view of the physical world. Maxwell’s voyage would almost precisely fill his lifetime, but it would in the end be rewarded by his recognition of one single principle, the principle of least action, which would be key to a virtually complete inversion of the Newtonian world order from which he was escaping.



In a sense, Maxwell was born into a dialectically-divided family. His father was Scottish, and Maxwell spent his early, formative years at the family home of Glenlair in rural southwestern Scotland. His mother on the other hand was English, and though she died while Maxwell was very young, her family was to have a strong influence on his career. While the English spirit would lead him eventually to Cambridge and the epicenter of an aristocratic, Newtonian concept of both science and society, the Scottish channel would lead him to a democratic view of society, and with it an appreciation of experiment and the evidence of the senses, together with a profound mistrust of the mathematical abstractions Newtonian theory.

These two themes met in abrupt confrontation when he was dispatched to Edinburgh to enter a new academy, designed to prepare students for entrance to English universities. In an encounter which must been a rude awakening, he was beaten up by his new fellow-students for his rural attire and his country ways. He stood his ground and soon became a leading student, but the encounter must have thrown light on an issue which would abide throughout his life.


Edinburgh University

Maxwell was clearly ready for entrance to Cambridge, for which his interest in science and his skill in mathematics surely qualified him; but he delayed for a year at Edinburgh University, and then, against the advice of family and friends, persisted in continuing there for a second year. At Edinburgh, he was encountered with excitement a truly liberal education; he loved, as he affirmed later, his professor of natural philosophy, and he became confirmed in his skepticism by the metaphysics of Kant as taught by Sir William Hamilton. Maxwell was not so much following Kant as agreeing with him: he left Edinburgh with a lifelong disbelief in the inert particles and forces upon them, on which Newtonian science rested.

After these two years he went on to Cambridge, where his skill in mathematics earned him entrance to Trinity College–the college of Newton–and high standing in the rigors of the tripos examinations. But he had brought his Edinburgh education with him, utterly abandoning Newton’s world, as we shall see when we turn to the first of his scientific papers.


Three Papers on Electricity and Magnetism

At this point, we find Maxwell, having obtained a fellowship at Cambridge, fully embarked on his voyage on the open seas. He is fascinated especially by the phenomena of electricity and magnetism, but he has no interest in joining the scientific community of his time elaborating Newtonian “laws of force” acting on electric “charges” or magnetic “poles”. He has met Michael Faraday, the self-proclaimed unmathematical philosopher, who has been dong brilliant experiments at the Royal Institution in London. Maxwell has, I think we can say, begun a lifelong devotion to this unassuming character, who represents the very opposite of the Cambridge/Newtonian concept of science–and almost defiantly takes up Faraday’s cause as his own. These are open seas: how to proceed?


Paper 1: An Analogy

Maxwell turns, not to theory, but to analogy. He shares common ground with Faraday regarding an interest in visual thinking–Faraday has presented his insights into the magnetic field by way of patterns formed by iron filings. Maxwell perceives these as the very lines of flow of a fluid. Here, then, is a gift from Faraday, a visual scientific language Maxwell can use! So is conceived the first of three papers on electromagnetism: On Faraday’s Lines of Force. This instrument of analogy, and with it, the goal of writing for the common man (for the democratic intellect, as one student of Scottish thought has put it) is to become one of the sure signs of the new world-view, towards which Maxwell has already begun steering.


Paper 2: A Physical Theory Maxwell has a great propensity for wit, though his friends remark on the difficulty of catching his intent. It may be a shield for a person who is living between worlds: not fully a member of the world friends suppose him to share with them. Maxwell is now in the position of having arrived at a whole view of the interrelations among the electric and magnetic phenomena: yet having no structure of theory in which to compose such a vision. I have proposed that his recourse is that of Aristophanes, in Peace, or the Birds–to stage his vision in the mode of comedy. Maxwell has been playing with the subject of mechanism (he and Karl Marx happen to have taken a course from the same teacher in London, though perhaps not at the same time!). He cannot mean that he proposes that such a mechanism actually exists, but he invents a great machine, for which he writes all the appropriate equations, which would do all the things the electromagnetic field actually does. Maxwell calls it A Physical Theory of the Electromagnetic Field, but he is not proposing that these vortices and idler-wheels actually exist. Like Aristophanes’ world of peace, it is an object for the mind, a project of pure thought. Again, this is a major step toward the goal Maxwell is seeking: in the new world, we will not take mechanisms seriously.

Maxwell’s jeu d’esprit is so successful that he can calculate from it the speed at which vibrations would be transmitted: it is very close to the speed of light! He is the point now of announcing the electromagnetic theory of light. But his discovery hangs in the air (or floats on the waves) it is no more than a beautiful play of thought.


Paper 3:Dynamical Theory

At last, the gods smile on Maxwell’s endeavor. He meets dynamical theory–and a new world begins to take shape. The mode of this encounter is deeply ironic, and correspondingly confusing. One of the most obdurate and imperious of Newtonian advocates is Lord Kelvin, once more modestly Maxwell’s colleague, William Thomson. He, with Maxwell’s close scientific friend P. G. Tait, have undertaken to write an ambitious, one might say proud, Treatise on Natural Philosophy. It’s intended to lay, once for all, the secure foundations of Newtonian science. An edifice of all physical science is to be built on this solid foundation, of which they’ve published only Volume 1.

At sea in uncharted waters, very strange things can happen! Kelvin and Tait, building their arguments on solid Newtonian foundations, expound a new approach to physical problems in terms of energy, rather than force: it is termed dynamical theory (they are importing it to England from the Continent, where it has been developed.) Though Kelvin resolutely insists that it is really still Newtonian, and nothing new, Maxwell sees light at the end of his tunnel (or a beacon on a new continent!) If equations can be written in terms of energy rather than force, nothing further needs to be said about forces acting upon those underlying particles, which he has always been convinced, do not exist!


The Treatise

The new dynamical equations are named after Pierre Lagrange, who wrote them, and Maxwell now uses them to characterize the electric and magnetic fields as regions on energy and momentum. Lagrange makes no explicit reference to ponderable mass, but that no longer matters–the equations carry all the energy that reaches Earth from the Sun. Maxwell publishes his Dynamical Theory of the Electromagnetic Field, and confidently announces his electromagnetic theory of light, based on the new equations.

Maxwell’s problem is not yet solved. Either the equations stand, as Kelvin maintains, on Newtonian theory – in which case we have only avoided the issue by not referring to some underlying particles, hardly more than a subterfuge, certainly not worthy of Maxwell, or they flow from some higher principle which Maxwell has not yet named. This is perhaps the darkest night of his voyage: he has glimpsed the new shore, but it has slipped away in the obscurity of this night.


The Principle of Least Action

Blessedly, Lagrange’s dynamical equations of motion can be derived from another source: indeed, this new source is their natural home, for this new origin is itself expressed in dynamical terms, i.e., in terms of the potential and kinetic energies of the system as a whole. Causality of the whole natural world is at stake here, so this “derivation” of Lagrange’s equations is no mere mathematical question! For Newton, causality flows from below to the whole: the “reason” things happen is mechanical, the whole moves as a consequence of the motions of its parts. So it was with Maxwell’s joking physical theory; he knows very well there are no such underlying parts. The new derivation of Lagrange’s equations flows from above–and with it, causality likewise flows downward, from some inclusive whole.

That inclusive whole–from which all the motions of he natural world flow–is the Principle of Least Action. The motions of the natural world arise ultimately from potential energies, such as the calories in a loaf of bread, or the BTUs in a gallon of gasoline. The conventional symbol for potential energy is V. Motions arise as potential energy is converted to kinetic energy, whose symbol is T. The difference (T–V) is called the Lagrangian, and the action (A) associated with any motion is nothing more complicated than the product of the Lagrangian and the time (t) the motion takes:

 A = (T – V) x t

 With that modest introduction, we can now state the principle on which it seems, nature runs. For any system:

The motion will be such that the action is least.

It can get complicated when systems are complex, or when relativity or quantum principles are involved, but it works, too, for systems as simple as a falling stone. Since each system is characterized first of all as a whole, it is inherently organic, and applies especially well to ecologies, which nature appears to see primarily as wholes, and organic.

Maxwell learned of this from the writings of William Rowan Hamilton of Dublin; he jokes of his “two Hamilton’s, saying their metaphisics are valuable in proportion to their physics. He means, I think, that the Kantian metaphysic espoused by Sir William Hamilton of Edinburgh was geared to the Newtonian world-view. The “new” Hamilton of Dublin is geared to a new, very different world-view in which the whole is primary as such, and not an assemblage of parts, and causality flows organically from whole to part. Wholes of course do not have to be big, the quantized hydrogen atom, a protein molecule, or the living cell, are instances.

We spoke earlier of Maxwell’s devotion to Faraday. Now we must ask, has he brought Faraday with him to this new land of Least Action? The answer, I can say confidently, is Yes.

How do we characterize a “system”? In the old, Newtonian way in which the parts were causal, it was important to describe a system in terms of those parts which constituted it and caused it to move. But now, parts are no longer causal. Our concern will be, instead, to characterize the state of a whole connected system. Interestingly, there is no one right way to do that! Any set of measurements sufficient to characterize the state of the system will serve. They don’t have to be readings of meters; Faraday’s diagrams of lines of force will serve very well to characterize a magnetic field. His intuitive interpretations of the behavior of his galvanometers serve him better than columns of numbers. Further, Maxwell’s analogy to fluid flow may serve very well to comprehend the structure of the magnetic field. Indeed, the Principle of Least Action in effect restores life to nature, which tends to move, as Faraday observed of his magnets. We have indeed arrived at a whole new world, yet one which Faraday, and Maxwell in his devotion to Faraday, already had in view.

Why has the modern world so resisted recognition of this principle, leaving it to rather esoteric studies within mathematical physics rather than teaching and embracing it generally as a far better way of understanding and caring for the natural world? Any thoughts on this will be very much appreciated.



This is the continuation of a discussion of “Newton/Maxwell/Marx”, a new work of mine, from Green Lion Press. This overview has been envisioned as a “dialectical cruise”, visiting in succession the world-views of Newton, Maxwell and Marx. Here we visit the first of these “worlds”, that of Isaac Newton. Read part 1 here.




The work known familiarly as Newton’s Principia is the foundation stone upon which our concept of science has been erected. Despite all the transformations by way of quantum physics and relativity, this bedrock image of objective, scientific truth remains firm. Arriving now, however, as if from outside our own world, we may feel a new sense of wonder, and presume to ask a few impertinent questions about core beliefs normally taken for granted:


Why, in our system of modern western science, do we suppose that the natural world is composed throughout of inert masses, with no inner impulse to move? Why are we convinced that nature is thus ruled by external forces, and that truth lies in finding mathematical laws of force?


In short, why do we suppose that nature is purely quantitative and, despite all appearances, deep down, essentially mechanical? Is the life we see everywhere infusing the natural world merely an illusion? Who killed nature?


These are dialectical questions, meaning that they go straight to the first principles of our systems of belief. Such principles normally go unquestioned, but challenging them is exactly our business here, on this dialectical world cruise! They all lead back to a fresh reading of Newton’s Principia. And as we shall be seeing in the course of this cruise, they do have interesting answers.



What Newton actually wrote, and what the world has on the whole supposed him to have written, are two very different things, as we shall see. Let us begin, however, by taking Newton at his own word, with a thumbnail sketch of his Principia Mathematica Philosophiae Naturalis (“Mathematical Principles of Natural Philosophy”). In relation to this title itself, we might point out that Newton’s topic is by no means limited to the discipline we now call physics. Newton is prescribing for the entire natural world – the universe of objects, living or non-living, that meet our senses in the directions of the large or the small, by means of any instruments, however advanced, in any domain which assumes the role of science. The Principia is discussed in detail in the essay on Newton in Newton/Maxwell/Marx; here we give only a thumbnail sketch.

Newton builds his Principia in a geometrical mode with a clarity reminiscent of Euclid’s Elements. Like Euclid, he lays a secure foundation, now of definitions and laws of motion, from which propositions flow with the same intuitive conviction we feel as we follow Euclid’s Elements. A world is unfolding before our eyes; if the foundations are secure. The edifice must stand.

Newton thus builds an edifice of science as firm as Euclid’s, though crucially now this consists of nothing but inert masses, deflected from rest or straight lines only under the action of external forces. Bodies move according to strict, mathematical laws of motion, and the forces are defined by equally precise mathematical relations. All this unfolds in a structure of true and mathematical time and equally absolute, mathematical space. Within the Principia, Newton develops the range of all possible motions under central forces, and applies these results to describe with precision, as merely one possible case, the system of planetary motions about our sun. This beautiful result emerges as just one example of his universal method at work; he will go on, for example, in his Optics to provide an equally mathematical system of color and the visual spectrum. Where Euclid gave us the precise forms of the things of our world, Newton gives us the things themselves, though they enter strictly as quantities. Apart from inert matter whose measure is mass, there is nothing behind these mathematical forms.

This reduction to stark mathematics might well strike a modern reader as the very spirit of mathematical physics today, an account we might call mechanical. At this point, however, an important distinction arises. In fact, Newton writes in fierce opposition to mechanism.

Newton is responding to Rene Descartes, who had indeed described the world as mechanical – a plenum, each part acting on its neighbors by simple rules of contact. Once set going, the cosmos runs on its own, like a fine watch. God’s role at the Creation was as watchmaker, but since that moment, the cosmos has run, and will forever continue to run, on its own.

This exclusion of God from His cosmos is anathema to Newton, and motivates the Principia. Where Descartes had filled the heavens with ethereal mechanism, Newton sweeps the cosmos clean. And where Descartes had seen nature moving entirely on its own, Newton very deliberately cancels any such powers, leaving nature utterly inert, everywhere dependent entirely on the ongoing operations of God’s active law. Hence the introduction of law at the foundation of the Principia. The orderly motions of the planetary system, which Newton calls The System of the World, is for him a vivid testament to the wisdom and active power of God. To bring this vision to mankind is, he says in the Principia, the reason he wrote. Might we not add, it’s the reason the concept of law structures our scientific discourse today?

We see now, indeed, the answer to our question, “Who killed nature?” It was Newton! And we see, too, why he did it Newton made sure that nature would be strictly powerless, and thus fit subject for God’s continuing rule. Nature must be mathematical to admit the precision of divine rule. Force is the modality of divine command, and law enters physics as the voice of God, who speaks in the medium of mathematics. Scientists today who, in their opposition to “creationism”, may cite Newton as the founder of modern science, freed from religion, are assuredly calling the wrong witness!



Newton, then, intended his Principia as a testimonial to God’s active presence in His Creation. He thus writes as a theologian, but by the strangest of fates, has been read as a mechanician! How this happened is indeed a fascinating story, recounted in my Newton essay, but need not detain us long at this point.

Briefly, it turns out that Newton was dedicated experimenter and theorist in the realms of alchemy, and devoted much effort to detailed interpretation of scripture. It seems clear that for him the Principia itself was but one component of a far larger project. It appears that all this was regarded as an embarrassment by his executors, who took pains to sequester it from public view. In turn his denuded Principia was welcomed by a society more interested in science than in theology. A strictly mathematical world picture. Only in recent years have manuscripts been recovered, revealing the role of the Principia in a much larger, and very different, project.

Believing however that it was loyal to its mentor, the west has accepted embraced the structure of the Principia, with its assumption of nature as in itself inert, moved by forces defined by law, as if Newton had intended such a vision as the very truth of the natural world. We have conjured a Principia divested of God, a feat comparable perhaps to reading the Old Testament without mention of the Lord. We have an empty shell, a narrative with no plot, law with no lawgiver. The appearance of life, but assuredly, no role for life itself.

No one could doubt that modern science works; its success in its own terms speaks for itself, though the direction of its interests and the delimitation of its scope leaves room for important questions. Now that our dialectical inquiry has probed the foundations of our notion of modern science, which turn out to be curiously accidental, we are in a good position to ask, reasonably, whether some alternative, a different foundation for modern science, might be possible. As we shall see at our next port of call, visiting James Clerk Maxwell, the answer will be a resounding “Yes!” And nature will indeed spring to life once again, before our very eyes.



Newton had fused natural philosophy and theology into one, truly apocalyptic vision. With that union dissolved, religion has been left to go its own way, with natural philosophy as the stark bedrock of our daily lives, our social and political associations, even our concept of freedom. We see ourselves as by nature separate and individual, while liberty becomes no more than the absence of restraint. At all levels, our associations are deliberate, held together by law in the form of agreements, to which we willingly bind ourselves for rational expectations of ultimate gain.

Our practical relationships thus rest ultimately on this understanding of the nature of nature – like Newton’s planets, we are separate bodies constrained by law, following trajectories in time and space. We group by aggregation; we are not social by nature.

In this world in which community is essentially an option, reasonable people can be heard to speculate that the brutality of war is part of our human nature. Despite all evidence, we find no place for life in the natural world: what appears as life we must accept, in scientific reality, as an artifact of complex mathematics – nothing real.

Religious convictions of course are another matter, not founded in nature but independently, in direct relation to the divine. The result, perhaps understandably, is that religious differences divide us even more fiercely than our perpetual struggle for the resources of the earth.

Surely there must be a better way – a more promising understanding of nature and natural philosophy. And indeed there is, as we shall see in our next port of call. Stay tuned!


This has been the first in a series of three ports of call in a Dialectical World Cruise. The second, to James Clerk Maxwell and his “Treatise on Electricity and Magnetism”, will appear in this space soon. Stay tuned – and meanwhile, your comments will be most welcome.

Organism vs. Mechanism: Science at the Lagrangian Divide

The Lagrangian equations are a powerful set of differential expressions describing the motion of a complex system.  With one equation for each component of the system, they would seem to offer a powerful expression of the relation of part to whole.

They are, however, seriously ambivalent: they can be read in either of two opposite ways. They present, then, a stark problem for the art of interpretation, the highest branch of rhetoric, as it comes from Augustine to Bacon and Newton.  The same statement becomes a watershed; it may belong to one world, or its opposite – but not both.  Each is a containing frame, within which we picture, and live, our lives

Read in one way – the way most common today – they are seen as derived from Newton’s laws of motion, and thus adding nothing fundamentally new. From this perspective, they merely rephrase Newton in terms of the concept of energy, a mathematical convenience in certain circumstances but making no fundamental change in our understanding of the natural world. In this interpretation, they express what we today call mechanism, which sees the motion of any system as the mere aggregation of the motions of its individual parts. Causality flows upward; motions of the parts explain the motion of the whole.

Seen from the other side of the Lagrangian watershed, however, the same equations express a world of a totally different sort. Here, the same equations are derived from the Principle of Least Action – a concept which readers may recognize as one of the recurring themes of this website.  The system itself as a whole, described in terms of potential and kinetic energy, becomes the primary reality and the source of the motions of the parts. Causality arises from the  interplay of these energies, and flows in the reverse direction, from whole to part.

Within the world of mechanism – the first interpretation – there is no place for goalor purpose. These are concepts considered far too vague to meet the standard of objectivity, the signature of modern science.

Remarkably, however, Least Action reconciles purpose with quantitative objectivity. By means of the mathematical technique of variation, which considers all possible paths, this principle seeks the optimum path by which potential energy may, over he whole course of any natural motion, be transformed to kinetic. In this interpretation of Lagrange, then, our world-view is transformed. Science itself, while remaining strictly objective and quantitative, becomes at the same time goal-oriented – all at once!

More than this, however, science on the Least Action side of the Lagrangian divide becomes, at last, fundamentally organic. This arises from a further, crucial feature of Least Action: if a system as a whole moves in such a way as to minimize action,so also will, within the bounds of external constraints, every part of that system. The goal which belongs primarily to the whole, is pervasive: it is shared by every part.

It was important in stating this principle to add “within given constraints”, because a rigid part of a man-made machine has few options. By contrast, the myriad components of a leaf, or of a cell or enzyme within the system of a leaf, navigate among unimaginable options toward the common goal of turning sunlight into life, over the season of the leaf, the life of the tree, or the evolution of photosynthesis on earth.

It is this community of purpose, nested and shared, which renders a system trulyorganic – a living being, something fundamentally beyond any bio-molecular mechanism, however intricate.

It is hardly necessary to add that it is this sense of nested purpose and shared membership in natural communities which has been so lacking during the long reign of mechanism. Our so strongly-held worldview has diverted us from that other option, which has nonetheless long formed a strong alternative flow of thought and practice in science, mathematics, politics and the arts. Now in many ways, not least the earth’s biosphere itself, the demand is upon us to recognize that we do have an option of immense importance. Viewing this whole scene now, we might say, from the Lagrangian ridge-line itself, with both worldviews clearly in view, our task is truly dialectical: leaving none of the insights of the past behind, we are in a position to move forward into a new, far richer and wiser world.

That new world-view, which has appeared here as a richer interpretation of Lagrange’s equations, is the ongoing theme of this website – always with an eye to Maxwell’s turn to Lagrange as mathematical vehicle for the launch of his concept of the electromagnetic field, paradigm, if ever there was one, of that whole system of which we have been speaking.

[A brief introcution to the Principle of Least Action is given in my lecture, “The Dialectical Laboratory” .

It is important to add that in this thumbnail sketch, many nuances of the application of Least Action have been left without mention]

Newton on the Field

I’ve just returned from a gathering in New Mexico, the first, pilot workshop of the Cosmic Serpent project, in which Native Americans and others-such as myself-gathered to compare Native American views of the natural world with those of “western science”. With the essential help of Jim Judson from the Sister Creek Center in San Antonio, I brought along an “open lab” on magnetism. It seemed to me that the concept of the “field”-specifically, here the (electro-) magnetic field-might prove helpful in relating these two domains of thought about nature.

For the moment, here, I just want to comment on a document that was circulating during the conference concerning the mystery of magnetism. Asking very simply “What is Magnetism?”, it was written by Bruno Maddox and published in a recent edition of Discover magazine. He reports that after exploring all options, he finds no scientific explanation of the cause  of magnetism.  If it remains a mystery, as he seems to conclude, then it may well be open to interpretation in terms compatible with Native American points of view.

That’s a point of view I’ll want to return to in future postings.  For the moment, I want to call attention to one of Maddox’s findings. He hit on a text in which Isaac Newton-looking in this case at the mystery of gravitation-opines that “the notion that one body may act upon another at a distance through a vacuum without the mediation of anything else…is to me so great an absurdity that I believe no man who has in philosophic matters a competent faculty of thinking could ever fall into it.”What did Newton have in mind?

I’m confident that he is not thinking in terms of any sort of mechanical explanation. Newton was not a mechanist: in fact, he wrote the Principia essentially as a polemic against mechanism, and in particular, against Descartes. No. His aim is to reveal the role of what he called Spirit in the world: the fact that the laws of these actions are mathematical in no way implies for Newton that they are mechanical, but is fully compatible with his concept of Spirit and its operation throughout the realm of nature.

I’m not arguing that Newton “had” the idea of the field-though his “intensive” quantity of a force seems to ascribe it to space itself, and is remarkably compatible with later ideas of the “field”. My point is only that as he describes the mathematical System of the World, Newton feels himself to be in the immediate presence of mystery-in his view, divine mystery in the form of the Holy Spirit as God’s agent in the natural world.

Newton’s thoughts along these lines, together with those on alchemy and theology, were systematically buried by his followers, and have been uncovered only in recent years. But now that we have a better sense of what he actually meant, we may be the more ready to contemplate this bridge between “spirit” as Newton intended it, and “spirit” in Indigenous accounts of the operations of the natural world. Either way, we are contemplating something which has all the feel of wonder and mystery.

While in Santa Fe, I learned that students at St. John’s College there would be gathering to witness this very mystery, in an experiment which Newton himself had thought would be impossible to carry out. Just as the Sun and Earth are joined by the gravitational force, so any two bodies on Earth must attract another by a very slight, yet calculable force. The experiment can in fact be done, with lead weights suspended by a delicate metal thread. To watch them, by way of a light beam and mirror, move toward one another slowly but surely, is to be present at a solemn ceremony at the foundation of the cosmos-as much a mystery, still today, as it ever was. I wonder if others agree with this reading of Newton’s text?