This image from from Maxwell’s Treatise on Electricity and Magnetism (Fig. XVII.) 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.