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.
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.
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]
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?