One of the clearest dividing lines is over the matter of intention in nature. Despite the overwhelming evidence of a purposefulness in natural development, the modern view has replaced the idea of intention with that of mechanism. A theory is called scientific if it provides a credible mechanism, or model, to describe an observable natural phenomena.

In one such model, dead objects (often called particles) are assumed to exist and are assigned certain properties, such as attraction, repulsion, or inertia, which must be assumed as axiomatic. These objects exist in an empty, triply-extended container, called space, to which certain self-evident properties are attributed, while a fourth dimension, called time, extends linearly into the before and after. In another version, the space is not empty, but filled with a substance capable of transmitting waves, which replace the particles as the self-evident elementarity.

In modern times, we have added various complex variations to these mechanistic systems. In one, the ether disappears, but the waves, and particles, still exist. And there are others, but none that has challenged the essential premises of mechanism.

Wide acceptance of a fraudulent version of the history of science has allowed the flourishing of the modern prejudice that the method of mechanism has produced scientific discovery. (We can show that it has never led to scientific discovery, but only to its suppression.) We take the case of Fermat's Principle of Least Time to help the modern reader to understand that a true universal physical principle will be an expression of intention in the universe. A close examination of the criticism to which Fermat's Principle was subjected by the Cartesians, will help the reader to see the prejudices he likely brings to the subject.

Snell's Discovery
The law of reflection of light, that the angle of incidence equals the angle of reflection, was known in classical times. Heron of Alexandria recognized that this law obeyed a minimal principle; that is, that were the angles to differ from each other, the time and distance of travel of the light would not be the least possible.

The law governing the refraction of light proved more difficult to discover. When a ray of light passes from one medium to another, it is bent (refracted). If the passage is from a less dense to a more dense medium, the light bends toward the normal to the surface forming the boundary between the two media. However, the angle of refraction varies, in some non-linear way, with the angle of incidence. The problem of lawfully determining this angle had been under investigation since Classical times. Neither the great optical theorists of the Arab renaissance, nor those of Europe could solve it.

Finally, in 1621, Willebrord Snell, a leading mathematical physicist of the Dutch republican tradition, found the solution. The light ray is refracted in such a way that the sines of the angles of incidence and refraction remain in the same proportion for any given pair of media (see Figure 1).

Snell's discovery was welcomed by René Descartes (1596-1650), the leader of a philosophical school which proposed that all natural phenomena could be explained by mechanical causes. In fact, Descartes so welcomed the discovery that he claimed it for his own, and his writings being more widely read than Snell's, Descartes was thought to be the discoverer of the law, until the matter was cleared up after his death.

Descartes was not content, however, to express the law as Snell discovered it. It was necessary to fit it into his mechanistic philosophy of nature, in which he represented light as consisting of ballistic particles. In order to thus account for the law of refraction, Descartes had to make the unusual assumption that the particles speed up when they pass from a less dense to a more dense medium. This seemed absurd to many. However, as no one was able to accurately measure the velocity of light in its passage from one medium to another, this assumption was not finally disproven experimentally until the middle of the 19th Century, when Leon Foucault and Armand Fizeau designed an experimental apparatus which proved Descartes wrong.

Fermat's Principle
Pierre de Fermat (1601-1665) was one of those classically educated geniuses, who, like Ampère, never went to college. Having received an early education in Greek and Latin, Fermat read the mathematical classics of antiquity in the originals, and so developed his mind. (Ampère never even went to elementary school, but learned by reading in his father's library; he taught himself Latin at the age of 11, in order to be able to read Bernoulli's calculus.)

Fermat did not believe Descartes's assertion about the velocity of light. After a long and fruitless correspondence with the followers of Descartes, he came upon a new flank of attack. In 1657, in a letter to Cureau de la Chambre, Fermat stated for the first time his idea that the law of refraction might be deduced from a minimum principle, like that which Heron had noted for reflection.¹

In a letter of Jan. 1, 1662, to Cureau de la Chambre, Fermat announced that he had accomplished his proof.² Fermat showed that the path of a refracted ray of light was that which takes the least time! (See Figure 2.) The discovery, now known as Fermat's Principle of Least Time, was more than the Cartesians could stand. In fact, it is probably more than most readers can stand—they just don't know it.

"1. The principle you take as a basis for your proof, to wit, that nature always acts by the shortest and simplest path, is only a moral principle, not a physical one—it is not and can not be the cause of any effect in nature."

Does anyone disagree? Clerselier continues:

"This principle is not the cause, because it is not the principle which makes the action, but rather the hidden force and power which reside in each thing, which things are never directed to a given effect by this principle, but rather by the force which results from all the causes that come together into a given action, and by the present disposition of all the bodies on which this force acts."

I argue that there is still nothing for the modern physicist to disagree with. If the phrase "hidden force and power which reside in each thing" sounds a bit strange, then what do you mean by a force of attraction, or by inertia?

Clerselier, again:

"And [Fermat's] principle can not be the cause, for otherwise we would be attributing knowledge to nature: and here, by nature, we understand only that order and lawfulness in the world, such as it is, which acts without foreknowledge, without choice, but by a necessary determination."

Don't we agree? Nature cannot act with foreknowledge. Is not evolution the result of random events, ordered by the survival of the fittest? Back to Clerselier:

"2. This same principle must make nature irresolute, not knowing which way to go when it makes a ray of light pass from a less dense to a more dense medium. For I ask you: if it is true that nature must always act by the shortest and simplest path, and given that the straight line is undoubtedly shorter and simpler than any other, would it not make nature hesitate, (if you wish that it act by this principle), when a ray of light, passing from a point in a rare medium to a point in a dense one, must simultaneously follow both the straight line and the bent one, since if the one proves shorter in time, the other is shorter and simpler in length? Who will decide, and who judge?"

Who indeed?