The notion that matter could be, at least in thought, analyzed down to ultimate atoms, that is, bodies incapable of being further divided, was in no wise due to Dalton, but was adopted by him as the only reasonable hypothesis of the ultimate constitution of matter. Democritus further assumed that the atoms, rotating as they were imagined to do, must collide with one another, as a result of which certain properties of matter were established. This is virtually none other than the modern "kinetic theory of gases."
To Aristotle the inherent motion of the atoms was a difficulty; but this is a difficulty only to one who assumes that rest is more primitive, more of the original state, than motion. Our latest view is the early Grecian—that everything is in motion, and nothing is at rest, that rest is a relationship, the illusory result of movements in opposite directions.
That substance is infinitely extended and is primally one, that it is possessed of inherent motion, are Greek conceptions which though modified by centuries of subsequent thinking, are still of the warp and woof of modern physico-chemical working ideas.
Parmenides wrote on the oneness of substance, and was thence led in the sphere of religion to Pantheism.
It is admitted that Pythagoras and his school founded the science of mathematics and indeed gave the very name to the study. The Pythagoreans raised geometry to a pure science, severing it from its earlier association with the means of measuring actual distances on the earth's surface (mensuration). The Pythagoreans instituted the quadrivium or fourfold way to knowledge—the study of logic, rhetoric, geometry and astronomy—which lasted until the close of the middle ages and was always contrasted with the trivium or junior course of grammar, arithmetic and music. It is really to Pythagoras that the retaining of geometry and mathematics as a compulsory subject in all higher education is due; and we are sure that he has been thoroughly cursed by many generations of classically-minded but mathematically-incompetent aspirants after the degree of Artium Magister.
Pythagoras is also responsible for all the curious fancies about numbers such as, the odd and even, lucky or unlucky, right and left, dark and light, the good and evil numbers. He even attributed sex to numbers; three was male and two female, therefore five symbolized marriage.
These ideas linger on to this day: I have heard people tell me that if there were 7 of a thing, all must be well, since 7 is a "perfect number"; and I am repeatedly informed that some number or other is unlucky. The theory of numbers was of course illustrated in the 7 planets—the heavenly heptachord, which, being perfect, could not do otherwise than make "the music of the spheres." Pythagoras, however, did discover the objective vibrational relationships between the various tones in an octave.
