October 2011 - Updated illustrations
Gateway To The Fourth Dimension: The Hypecube As Theater
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New From Green Lion Press
The basis of the art of rhetoric is the distinction between what is said, in a simple declarative sentence, and the way that thought is expressed. A nuanced statement may convey meanings very different from the literal content of a sentence. Surprisingly, perhaps, the same is true of a mathematical equation. Its literal content is the numbers which it serves to compute; but its rhetorical content is the thoughts it suggests to the mind of the reader. Rhetoric is often used to win arguments, but Maxwell’s intention is very different. His aim is to suggest new ideas, and he shapes his equations to open our minds to new ways of viewing the natural world. Read More
Much of my work has its roots in a long study of the writings of James Clerk Maxwell on the electromagnetic field. The concept of the field has been for me, as I believe it was for Maxwell, a window into the wholeness of the natural world. From this vision of nature stems, in turn, a fresh sense of the unity of society, and indeed, of ourselves. I have tried to trace this thread of wholeness through its many ramifications, in education, in literature and the arts, in philosophy, and in our very conception of science itself. Through it all, the image of the field has been my guide.
Thomas K. Simpson
Tutor emeritus, St. John’s College,
Annapolis, Maryland and Santa Fe, New Mexico
Image from Maxwell’s Treatise on Electricity and Magnetism, Fig. XVII.
The image above is a drawing of a plane section of the field surrounding a current-carrying conductor in a uniform magnetic field; the field from which this section is taken is, classically understood, a three-dimensional continuum which fills the world with energy. Every least change in this current will cause the field to tremble with a signal, radiating with the velocity of light throughout the whole.
To capture the global character of this process–and hence the very idea of the field–it was of central importance to Maxwell to derive the equations of the field, not from force laws in the Newtonian tradition, but from Lagrange’s equations of motion–equations formulated in terms of energy, and deriving from the principle of least action. ‘Action’ and ‘energy’ are here conceived globally, and belong primarily to the system as a whole.
This insight, at the core of an alternative approach to nature stemming from Leibniz, and hence ultimately from Aristotle, expresses a concept of wholeness which has, in one way or another, guided most of the work described on this website.