15. “A brilliant result”: the prelude to natural selection

Since fixing the size of a biological-ecological system using standard physical methods of walls and areas is unlikely to be successful in biology and ecology, we must find an alternative. That alternative must also facilitate the determination of ‘forces’, ‘areas’, and ‘distances’ … at least, in deep structure.

We can take our lead from James Maxwell who wrote to William Thomson, the Lord Kelvin, in 1854 as follows:

Suppose a man to have a popular knowledge of electrical show experiments … how ought he to proceed in reading & working so as to get a little insight into the subject wh [sic] may be of use in further reading? If he wished to read Ampère Faraday &c how should they be arranged, and at what stage & in what order might he read your articles in the Cambridge Journal? If you have in your mind any answer to the above questions, three of us here would be content to look upon an embodiment of it in writing as advice (Cooper, 1968, p. 228).

Under Thomson’s guidance, Maxwell directed himself to the theoretical problems created by Faraday’s discovery of induction, which was still unexplained. He initially visualized electrical field lines as lines of small particles, and similarly visualized magnetic fields as a series of whirling vortices. An electric current was then a line of small particles being pushed along by his spinning vortices. He then imagined that his moving particles, their field lines, and their vortices were all placed upon an elastic sheet which could then be deformed, by stretching, as they exerted their electromagnetic forces. This led him to appreciate that currents could diverge, which is a vector dot product symbolized by ‘ •’ and pronounced either ‘del dot’ or ‘nabla dot’. It also led him to understand this new Faraday induction. Vortices possessed an independent spin or circulation about themselves, and so could induce a rotation. It is now designated as a vector cross-product, symbolized by ‘ x’ and pronounced either ‘del cross’ or ‘nabla cross’. Maxwell thus saw that Faraday’s induction was induced in his vortices as a given current flowed around and about them, thus inducing them to respond, energetically, by varying their contributions to the net circulation through varying their independent rates of vector curls, and so inducing the observed current. And although Maxwell then abandoned his physical model so he could concentrate on the mathematical relations that it had helped to lay bare, those physical analogies have been retained as an aid to explicating these kinds of vector phenomena (Fleisch, 2008).

In the strictest terms, neither electrical nor magnetic fields, nor Maxwell’s particles, nor his vortices, exist. Only their deep structure can strictly be retained. Indeed when, to universal amazement, Maxwell produced his theory that light and heat were electromagnetic waves, his explanatory model provoked doubt about his entire theory:

The coincidence between the observed velocity of light and your calculated velocity of transverse vibration in your medium seems a brilliant result. But I must say I think a few such results are wanted before you can get people to think that every time an electric current is produced a little file of particles is squeezed along between rows of wheels (Cooper, 1968, p. 234).

Maxwell’s theory had, however, transcended his original physical model. The vector relations he discovered continue to hold good, with the physical model being a mere aid to comprehension. When it was abandoned, the given “points”, “lines”, and “fields” remained susceptible to divergences and to curls. That remains so howsoever they may be understood, or manifest themselves, in any phenomenon of interest … even biological ones. The Maxwell electromagnetic theory must, however, have a very different conception of size and volume over its objects.