Newton believed that Pythagoras, in the course of his travels, had tapped into many an ancient and still bubbling wellspring of the prisca sapientia. This was true both for his science and for the moral laws he promulgated. Newton writes that,
Pythagoras, one of the oldest Philosophers in Europe, after he had traveled among the eastern nations for the sake of knowledge & conversed with their Priests & Judges & seen their manners, taught his scholars that all men should be friends to all men & even to brute Beasts & should conciliate the friendship of the Gods by piety, & his disciples were celebrated for loving one another. Th[is] religion . . . was therefore [called] the Moral Law of all nations put in execution by their courts of Justice until they corrupted themselves.19
Pythagoras’s moral and spiritual teachings were part and parcel of his discovery of Number. Number was eternal. Number was God’s structuring of the world. Number was sacred; it was to be mediated on, imbibed, understood—but never exploited. Philolaus wrote of Pythagoras’s discovery that “Number became great, all powerful, all sufficing, the first principle and the guide in the life of gods, of heaven, of men. Without it, all is without limit, obscure, indiscernible.”20
Future generations would agree. Johannes Kepler (1571–1630) wrote: “Geometry existed before the creation, is co-eternal with the mind of God, is God himself.”21 The twenty-first-century physicist Alex Vilenkin declares: “The Creator is obsessed with mathematics. Pythagoras, in the sixth century BC, was probably the first to suggest that mathematical relations were at the heart of all physical phenomena. His insight was confirmed by centuries of scientific research, and we now take it for granted that nature follows precise mathematical laws.”22 Pythagoras’s second great discovery was that the musical scale depends on numerical proportions: the octave represents the proportion of 2:1; the fifth, 3:2; and the fourth, 4:3. This led to the idea of harmony. Pythagoras discovered that the most “agreeable” harmonies—those whose tones seem to be “in sync” with one other—are formed by the simplest kinds of mathematical ratios. If the vibrations of one tone are twice as fast as the vibrations of another, the two tones will be an octave apart thus making a unity. The separate constituents of this musical marriage oscillate in the proportion of 2 to 1. This is a very basic ratio. But only through the simplest kind of proportion does pleasing harmony arise.
The dynamic seer of Croton, whose presence drew beauty and harmony out of all that surrounded him, first detected the numerical proportions of music in the soot and clamor of a blacksmith’s shop. Striding by a smithy one day, he saw five blacksmiths striking five anvils with hammers of five different weights. Beautiful harmonies irregularly cut through the cacophony. Pythagoras recorded the weights of the five hammers and when at home hung from his ceiling on stretched sinews of oxen and sheep’s intestines five equivalent weights.
He randomly plucked the strings in pairs, and discovered that bell-like harmonies sounded when the weights were in the proportions of 2:1, 3:2, and 4:3. The discovery that music arises from unchangeable mathematical relationships had profound implications. Since mathematical relationships were the groundwork of all being, it followed that ultimate reality expressed itself in music. Pythagoras and the Pythagoreans had come to believe, as Aristotle succinctly put it, that “the whole cosmos is a scale and a number.”23
All of this suggested to Newton the deeper mysteries of gravitation. His tortuous interpretation of the lyre of Apollo, the pipes of Pan, and the harmony of the spheres rests on the belief that the “true system of the world” was known to the ancients but had been turned into a “great mystery” that only the initiates could penetrate. His thoughts ran thus: since all bodies moving in space produce sounds whose pitch depends on the size and speed of the body, then each planet in its orbit about the Earth (or this was what Newton believed Pythagoras thought) makes a sound proportional to its speed which is a function of its distance from the Earth; and these diverse notes constitute a harmony or “music of the spheres” that we never notice because we hear it all the time.
According to Pythagoras, God, in placing the moon, the planets, and the fixed stars in motion around the Earth, had varied their sizes, their orbital velocities, and their distances from us (this last determinng how high or low the pitch was) in such a way that the distinct and different sounds that each of the nine celestial bodies produced created when sounded together a harmonious whole.
Let’s imagine that each of these celestial bodies is attached to the Earth by a taut violin string. God touches each string, and that is what produces the sound. Let’s further imagine that these bodies, revolving around the Earth, are analogous to anvil hammers whose weights as they hang from the end of strings differ in the proportions first discovered by Pythagoras.
Newton believed Pythagoras knew that when varying the weights attached to the ends of the strings, rather than string length, the proportions had to be squared and inverted. To Newton, the Pythagoras story was hidden science; the “music of the spheres” was a myth meant to conceal the true scientific fact that “the weights of the planets towards the sun were reciprocally as the squares of their distances from the sun.”24 This was nothing less than an early iteration of Newton’s principle of universal gravitation, which states, in modern terms, that the force of gravity varies inversely as the square of the distance; that is, this force grows smaller as the distance grows larger; and if the distance increases by a ratio of x, the force increases by a ratio of x2.
Newton was able to make this application because in his time Marin Mersenne, the French theologian, philosopher, mathematician, and music theorist, often referred to as the “father of acoustics,” and Vincenzo Galilei, the Italian lutenist, composer, and music theorist who was the father of Galileo Galilei, had discovered a quantitative relation in which two equally thick strings stretched by suspended weights would be in unison when the weights were reciprocally as the lengths of the strings. Newton contended that this must have been the quantitative relation that Pythagoras applied to the heavens, that he must have recognized that the harmony of the spheres required the force of the sun to act upon the planets in that harmonic ratio of distance by which the force of tension acts upon strings of different length—that is, inversely as the square of the distance.
So Mersenne and Galileo were only rediscovering what Pythagoras has discovered! David Gregory tells us that “Pythagoras afterwards applied the [much later Mersenne/Galileo] proposition he had thus found by experiments, to the heavens, and thus learned the harmony of the spheres.”
Newton’s own explanation of how Pythagoras made this application, which may be found in the draft Scholium to Proposition VIII, is, for most modern readers, very difficult to understand.
Pythagoras discovered by experiment an inverse-square relation in the vibrations of strings (unison of two strings when tensions are reciprocally as the squares of lengths); that he extended such a relation to the weights and distances of the planets from the sun; and this this true knowledge, expressed esoterically, was lost through the misunderstanding of later generations.25
By way of further explanation, we don’t find ourselves much better off with the explanation of Newton’s most brilliant pupil, Colin Maclaurin.
A musical chord gives the same notes as one double in length, while the tension or force with which the latter is stretched is quadruple of the gravity of a planet at a double distance. In general, that any musical chord may become unison to a lesser chord of the same kind, its tension must be increased in the same proportion as the square of its length is greater; and that the gravity of a planet may become equal to the gravity of another planet nearer to the sun, it must be increased in proportion as the square of its distance from the sun is greater. If therefore we should suppose musical chords extended from the sun to each planet, that all these chords might become unison, it would be requisite to decrease or diminish their tensions in the same proportions as would be sufficient to render the gravities of the planets equal. And f
rom the similitude of those proportions the celebrated doctrine of the harmony of the spheres is supposed to have been derived.26
Maclaurin goes on to say that
these doctrines of the Pythagoreans, concerning the diurnal and annual motions of the earth, the revolutions of the comets . . . and the harmony of the spheres, are very remote from the the suggestions of sense, and opposite to vulgar prejudices; so we cannot but suppose that they who first discovered them must have made a very considerable progress in astronomy and natural philosophy.27
The average reader does not come away from this enlightened; it is almost as if Newton and Maclaurin (and perhaps David Gregory) were themselves wrapping up deep truths in arcane language to keep we common people from learning things we won’t be able to handle.
Newton was no great listener of music as a form of art to be appreciated. He hardly ever listened to music at all. Newton told William Stukeley that he “never was at more than one Opera. The first Act, he heard with pleasure, the 2nd stretched his patience, at the 3rd he ran away.” On another occasion, emerging from a concert at which Handel had played the harpsichord, the only thing he could think of to comment on was the elasticity of the great composer’s fingers.28
But Newton was fiercely interested in music in the abstract. He wondered if the spacing of the seven colors of the spectrum (which Newton had discovered) imitated “the proportional ‘distances’ between the tones in a musical scale.”29 Had nature created laws for melody and harmony in the same way that it had created hues of light? Strangely enough, writes Stuart Isacoff, Newton decided that man “is not inherently musical . . .[, that] natural singing is the sole property of birds. In contrast to our feathered friends, humans perform and understand only what they are taught. . . . Still, he acknowledged, the proportions ‘which the God of Nature has fitted’ were now impractical. A system in tune with both man and heaven was needed.”30 But, wait! Before we go on, we need to visit with Pythagoras one last time.
During this visit, Pythagoras will introduce us, if indirectly, to perhaps the only master of the prisca sapientia of high antiquity who was his equal.
This was the prophet Moses.
Let’s travel to the port of Sidon, in Phoenicia, in about 530 BC. Pythagoras is on the dock. He has just arrived from Croton. He wears white robes and pants and a gold tiara, the standard outfit for a seer of his high rank. Probably an eagle is circling obediently overhead.
If any animals have wandered down from the adjoining fields he’s probably talking to them. They listen with ears pricked wildly to the master. (Pythagoras may be exchanging a word or two with the lapping waves beneath the dock.) Behind him, in a large trireme, the crew sits huddled on the huge deck, watching the master’s back. They gaze at him like a farmer stares at the sky, looking for signs of wind or rain or sun.
A procession is advancing slowly along the dock toward Pythagoras. It seems to be one family; they look alike, and they are dressed in similarly brightly colored robes. The man in front is a high priest. Pythagoras knows these are Phoenician Jews, and they have come here to perform a high office. The high priest carries before him a cedar chest the size of a large book. He reaches Pythagoras, bows; explains that he and his family are descendants of the prophet Moses; that their illustrious ancestor had bequeathed this chest to his family; that it was not to be opened by any of them, but that, probably several centuries in the future, an eagle would swoop down from high in the sky, perch on the chest, and, speaking to them in Hebrew, tell them for whom this cedar chest was for and how to find him and give it to him.
All had transpired as Moses had foretold. And now the priest passed the chest to Pythagoras, who opened it—just as the eagle swooped down, perched on his arm, and peered down into the chest. It contained a book in rich gold binding; Pythagoras opened it and for several minutes could not read the strange-looking words at all. Then he began to realize he was looking at a textbook on atomic physics.
Isaac Newton believed that many of the ancient Greek philosophers who had tapped into the wisdom of the prisca had learned all of the secrets of the atom, not just what Lucretius and Democritus knew, but everything Isaac Newton knew. These Greek physicist-seers included, along with Lucretius and Democritus, Epicurus and Ecphantus and Empedocles and Zenocrates and Heraclites and Aesculapius and Diodorus and Metrodorus of Chios—and many more.*5531
Newton could back up his assertions with a chestful of citations. For him the greatest atomic physicist among the ancients was Moses. Moses’s accumulation of knowledge was so important that the prophet had somehow arranged for it to be preserved and passed along to Pythagoras.
Here is Newton summarizing the Cambridge Platonist Ralph Cudworth:
Posidonius, an ancient & learned Philosopher, did (as Strabo & Empiricus tell us) avouch it for an old tradition, that the first inventor of atomical Philosophy was one Moschus [Moses] a Phoenician, who as Strabo notes, lived before the Trojan war. Perhaps this Moschus was then that Mochus a Phoenician Physiologer in Iamblichus with whose successors Priests & Prophets he affirms that Pythagoras sometimes sojourning at Sidon (his native city) had conversed.32
Would an atomic physicist, even of the most primitive sort, ever say that Earth was created in six days? Here, Newton is as fertile with answers as was scientist-theologian William Whiston, his surrogate apologist for Moses. Newton argued that the entire creation could have taken place in six twenty-four-hour periods, because God had started the world rotating on its axis only on the fourth or fifth day; at first it had rotated very slowly, or not at all. The Deity could make the days as long or short as he wished so as to accomplish in a given time period anything that he wanted.
Why didn’t Moses simply say this in the Hebrew Bible? Frank Manuel responds: “Moses knew the whole of the scientific truth—of this Newton was certain—but he was speaking to ordinary Israelites, not delivering a paper to the Royal Society, and he popularized the narrative without falsifying it.”33
Newton Project director Rob Iliffe adds that in the early post-Flood era religious leaders “concealed these [scientific] truths from the vulgar. At this time, there was a ‘sacred’ philosophy—communicated only to the cognoscenti—and a ‘vulgar’ version, promulgated openly to the common people.”34
Newton seems to have believed that the ancients withheld great truths from the “vulgar” for reasons that were noble. In the beginning, primal truth had shone in the souls of humankind. We were infants of genius—but we were infants. We couldn’t handle the knowledge; it gave us power we couldn’t help wielding often for the wrong reasons. We harmed the planet, and eventually God felt he had no choice but to wipe us out and start over with a clean slate.
So Newton felt that it must be true that the last of the sages of the antediluvian period—the “remnant,” led by Noah—who had, however incompletely, preserved the prisca from the Flood, had felt it was necessary to obscure the deepest truths from the vulgar; they had learned, at the expense of the loss of a world, that ordinary men and women couldn’t handle them. This wasn’t because we were stupid, Newton thought. It was because we forgot to keep worshipping God; the old devil idolatry kept slipping and luring us once again down the path of moral corruption.
Today we believe Newton came up with his discoveries on his own. Did his immersion in ancient scientific doctrines, however disguised in myth, help him make these discoveries? Some critics wonder if notions like the pipes of Pan and the music of the spheres, lengthily and zealously pondered by Newton, didn’t decisively jog his mind so far outside the box as to actually play an indispensable role in enabling him to come up with his amazingly innovative theories. Did the prolonged meditation of Pythagoras on the mystical number of seven provide Newton with an indispensable impetus pushing him to the discover that light is composed of seven colors? Did Pythagoras’s seminal notion of the music of the spheres not anticipate the theory of universal gravitation so much as inspire it?
If the ancient sages knew so much, what
happened to all that knowledge? Why didn’t we build steadily on the discoveries of Archimedes and Aristarchus; if we had, wouldn’t we be just as advanced today as our descendants will be in the twenty-third or twenty-fourth century?
How did it happen that, in the words of mathematician Alfred North Whitehead, “by the year 1500 Europe knew less than Archimedes, who died in 212 BC”?35
Scholar Piyo Rattansi explains that “it was the Greeks who first inaugurated the search for truth, unfettered by authority. But Aristotle had dimmed that light.”36 Aristotle rejected many of the most daring ideas of his time, and his dominance became such that no other daring ideas could break through his eminence as the ultimate authority on everything. “The light of truth,” continues Rattansi, “was almost wholly extinguished after the Gothic invasions [of Italy]. Christianity had prospered among the ruins of Rome, and the world returned to credulity and superstition.”37
So complete was the loss of the “sacred philosophy” of the ancients that it did not reemerge until after the fall of Constantinople in 1453, when it was rediscovered in ancient texts, many thought lost forever, many never known. Much of this lost knowledge was fairly quickly restored, and to the philosophers of the Italian Renaissance as well as the natural philosophers of Newton’s century, its superiority over modern ideas was such that it was very easy to believe there was a prisca sapientia of which this newfound knowledge was a part.
The French mathematician René Descartes (1596–1650), who tried to bring mathematical precision to philosophy, had been forced to do so by a series of terrifying, irrational visions that beset him when he was twenty-three. Descartes believed that “certain primary seeds of truth [had been] implanted by nature in our human minds.” But their growth had been “stifled owing to our reading and hearing, day by day, so many diverse errors.” Descartes hated the ancients for concealing those truths in esoteric symbols. He suspected their motives, declaring cynically that “they have perhaps feared that their method being so very easy and simple, would if made public, diminish, not increase public esteem.”38
The Metaphysical World of Isaac Newton Page 37
