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The Transfinite Principle of Light:
The Saga of the `Poisson Spot'

by Jonathan Tennenbaum

Reprinted from FIDELIO Magazine, Vol . 8, No.3, Fall 1999
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We are in Paris, at the highpoint of the oligarchical restoration in Europe, the period leading up to and following the infamous, mass-syphilitic Congress of Vienna. Under the control of LaPlace, the educational curriculum of the famous Ecole Polytechnique is being turned upside-down, virtually eliminating the geometrical-experimental method cultivated by Gaspard Monge and Lazard Carnot and emphasizing mathematical formalism in its place.

The political campaign to crush what remained of the republican faction at the Ecole Polytechnique reaches its highpoint with the appointment of the royalist Auguste Cauchy in 1816, but the methodological war had been raging since the early days of the Ecole.

With Napoleon's rise to power and the ensuing militarization of the Ecole in 1799, Laplace's power in the Ecole was greatly strengthened. At the same time, Laplace consolidated a system of
patronage with which he and his friends could exercize increasing control over the scientific community. An important instrument was created with the Societe d'Arcueil, which was founded in 1803 by Laplace and his friend Berthollet and financed in significant part from the pair's own private fortunes.

Although the Societe d'Arcueil supported some useful scientific work, and its members included Chaptal, Arago, Humboldt and others in addition to Laplace and his immediate collaborators (such as Poisson and Biot), Laplace made it the center of an effort to perfect a neo-Newtonian form of mathematical physics in direct opposition to the tradition of Fermat, Huygens, and Leibniz. In contrast to the British followers of Newton, whose efforts were crippled by their own stubborn rejection of Leibniz' calculus, Laplace and his friends chose a more tricky, delphic tactic: use the superior mathematics developed from Leibniz and the Bernoullis, to "make Newtonianism work."

Poisson, whose appointment to the Ecole Polytechnique had been sponsored by Laplace and Lagrange, worked as a kind of mathematical lackey in support of this program. He was totally unfamiliar with experimental research, and had been judged incompetent as a draftsman in the Ecole Polytechnique.

But he possessed considerable virtuosity in mathematics, and there is a famous quote attributed to him: "Life is good for only two things: doing mathematics and teaching it." An 1840 eulogy of Poisson gives a relevant glimpse of his personality:

"Poisson never wished to occupy himself with two things at the same time; when, in the course of his labors, a research project crossed his mind that did not form any immediate connection with what he was doing at the time, he contented himself with writing a few words in his little wallet. The persons to whom he used to communicate his scientific ideas know that as soon as he had finished one memoir, he passed without interruption to another subject, and that he customarily selected from his wallet the questions with which he should occupy himself."

In the context of Laplace's program, Poisson was put to work to elaborate a comprehensive mathematical theory of electricity on the model of Newton's Principia. Coulomb had already proposed to adapt Newton's "inverse square law" to the interaction of hypothetical "electrical particles", adding only the modification, that like charges repel and opposite charges attract--the scheme which is preserved in today's physics textbook as "the Coulomb law of electrostatics".

Poisson's 1812 Memoire on the distribution of electricity in conducting bodies, was hailed as a great triumph for Laplace's program and a model for related efforts in optics.

Indeed, between 1805 and 1815 Laplace, Biot and (in part) Malus created an elaborate mathematical theory of light, based on the notion that light rays are streams of particles that interact with the particles of matter by short-range forces. By suitably modifing Newton's original "emission theory" of light and applying superior mathematical methods, they were able t "explain" most of the known optical phenomena, including the effect of double refraction which had been the focus of Huyghen's work.

In 1817, expecting to soon celebrate the "final triumph" of their neo-Newtonian optics, Laplace and Biot arranged for the physics prize of French Academy of Science to be proposed for the best work on the theme of {diffraction}--the apparent bending of light rays at the boundaries between different media.

In the meantime, however, Augustinn Fresnel, supported by his close friend Andre-Marie Ampere, had enriched Huygens' conception of the propagation of light by the addition of a {new
physical principle.} Guided by that principle--which we shall discover in due course--Fresnel reworked Huyghens' envelope construction for theself-propagation of light, taking account of distinct {phases} within each wavelength of propagational action, and the everywhere-dense interaction ("interference") of different phases at each locus of the propagation process.

In 1818, on the occasion of Fresnel's defense of his thesis submitted for the Academy prize, acelebrated "show-down" occurred between Fresnel and the Laplacians. Poisson got up to raise a seemingly devastating objection to Fresnel's construction: If that construction were valid, a {bright spot} would have to appear in the middle of the shadow cast by a spherical or disk-shaped object, when illuminated by a suitable light source. But such a result is completely absurdand unimaginable. Therefore Fresnel's theory must be wrong!

Soon after the tumultuous meeting, however, one of the judges, Francois Arago, actually did the experiment. And there it was--the "impossible" bright spot in the middle of the shadow! Much to the dismay of Laplace, Biot, and Poisson, Fresnel was awarded the prize in the competition. The subsequent work of Fresnel and Ampere sealed the fate of Laplace's neo-Newtonian program once and for all.

The phenomenon confirmed by Arago goes down in history with the name "Poisson's spot," like acurse.

Before proceeding to work through the essentials of these matters, it is necessary to insist on some deeper points, which some may find uncomfortable or even shocking. Without attending t those deeper matters, most readers are bound to misunderstand everything we have said and intend to say in the future.

It is difficult or even virtually impossible, in today's dominant culture, to relive a scientific discovery, without first clearing away the cognitive obstacles reflected in the tendency to reject, or run away from, the essential subjectivity of science.

Accordingly, as a "cognitive I.Q. test" in the spirit of recent provocations on economics by Lyndon LaRouche, challenge yourself with thefollowing interconnected questions:

1. Identify the devastating, fundamental fallacies behind the following, typical textbook account:
"There were two different opinions about the nature of light: the particle theory and wave theory. Fresnel and others carried out experiments which proved that the particle theory waswrong and the wave theory was right."

2. Asked to explain the meaning of "hypothesis," a student responds:
"An hypothesis is a kind of guess we make in trying to explain something whose actual cause we do not know." Is this your concept? Is it right?

3. What is the difference between what we think of as a property of some object, and a physical principle? Why must a physical principle, insofar as it has any claim to validity, necessarily apply to all processes in the Universe, {without exception}?

If you encounter any difficulty in answering the above, reread in particular Lyndon LaRouche's book-length essay, "Project A."

Project A is a section of Lyndon H; LaRouche Jr.'s book, The Science of Christian Economy


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