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Mathematically Ordered Universe: Little Known Facts About Isaac Newton, Johannes Kepler, and other Luminaries

Edward Dolnick shares fascinating details about Isaac Newton, Johannes Kepler, and others in his book, The Clockwork Universe: Isaac Newton, the Royal Society, and the Birth of the Modern World.

He writes, “All these thinkers had two traits in common. They were geniuses, and they had utter faith that the universe had been designed on impeccable mathematical lines. What follows is the story of a group of scientists who set out to read God’s mind.’’

My philosophy mirrors what these luminaries determined: Nature and the universe are mathematically ordered.

Thousands of years of empirical research suggest humans are connected to that order as symbolized by comprehensive astrology and numerology.

Below are excerpts from Dolnick’s book (bold emphasis, mine).

“Newton himself owned some thirty Bibles in various translations and languages that he endlessly perused and compared one against another. Every word in the Bible was meaningful, just as every twig and sparrow in the natural world offered up a clue to God’s intent. The Bible was not a literary work to be interpreted according to one’s taste, but a cipher with a single meaning that could be decoded by a meticulous and brilliant analyst. Newton devoted thousands of hours—as much time as he spent on the secrets of gravity or light—in looking for concealed messages in the dimensions of the Temple of Solomon and trying to match the prophecies in Revelation with the battles and revolutions of later days.”

“If God was a mathematician, it went without saying that He was the most skilled of all mathematicians. And since nature’s laws are God’s handiwork, they must necessarily be flawless—few in number, compact, elegant, and perfectly meshed with one another. ‘It is ye perfection of God’s works that they are all done with ye greatest simplicity,’ Isaac Newton declared. ‘He is ye God of order and not of confusion.’

“The primary mission that seventeenth-century science set itself was to find His laws. The problem was that someone would first have to invent a new kind of mathematics.”

“As able as the Greeks had been, they never found a way around one fundamental obstacle. They had nothing to say about motion. But if mathematics was going to describe the real world, it had to find a way to deal with moving objects. If a bullet is shot into the air, how fast does it fly? How high does it rise?”

“The conceptual breakthrough was called calculus. It was the key that opened the way to the modern age, and it made possible countless advances throughout science.”

“‘His peculiar gift was the power of holding continuously in his mind a purely mental problem until he had seen straight through it,’ wrote John Maynard Keynes, who was one of the first to examine Newton’s unpublished papers. ‘I fancy his pre-eminence is due to his muscles of intuition being the strongest and most enduring with which a man has ever been gifted.’ An economist of towering reputation and intelligence, Keynes could only marvel at Newton’s mental stamina. ‘Anyone who has ever attempted pure scientific or philosophical thought knows how one can hold a problem momentarily in one’s mind and apply all one’s powers of concentration to piercing through it, and how it will dissolve and escape and you find that what you are surveying is a blank. I believe that Newton could hold a problem in his mind for hours and days and weeks until it surrendered to him its secret.’”

“Alchemy, which was a scientific quest for a magical-sounding goal, provides perhaps the most striking example of the coexistence of old and new. The aim was to find a substance called the ‘philosopher’s stone,’ despite its name a liquid, which held the power to transform ordinary substances into silver and gold and to convey immortality to anyone who drank it.”

“A devout belief in alchemy was standard in the seventeenth century, but no one exceeded Isaac Newton in persistence. His small, crabbed handwriting fills notebook after notebook with the records of his alchemical experiments. In all Newton lavished some half million words on alchemy, about as many as in War and Peace. He and countless other researchers spent long hours at their flasks and fires mixing potions according to closely guarded recipes. (Leibniz’s only fear was that if gold became too readily available its price would fall.) An assistant watched Newton’s experiments with reverence but without understanding. ‘Whatever his aim might be, I was not able to penetrate into, but his Pains, his Diligence at those Times made me think he aimed at something beyond the Reach of human Art & Industry.’ A peek inside Newton’s notebooks would have left an observer scarcely more enlightened. He never spoke of anything as crass as growing rich; his focus, it seems, was solely on uncovering nature’s secrets. In any case, alchemical formulas were too valuable to state openly.”

“The language was encoded—‘Saturn’ stood for ‘lead,’ for instance—and the procedures sound like something from an X-rated Hogwarts spell-book. Newton jotted down recipes with such ingredients as ‘the Green Lion’ and ‘the menstrual blood of the sordid whore.’”

“…Newton started out by studying chemistry but abandoned it in favor of what he saw as the deeper mysteries of alchemy.”

“Chemistry dealt with matter-of-fact questions like what salt is made from. Alchemy sought to explain the invisible forces of living nature.”

“‘God always complies with the easiest and simplest rules,’ Galileo asserted.”

“On the one hand, delving into the world’s mathematical secrets gives a feeling of having one’s hands on nature’s beating heart; on the other, in a world of chaos and disaster, mathematics provides a refuge of eternal, unchallengeable truths and perfect order.”

“But mathematics is a cruel mistress, indifferent to the suffering of those who would woo her. Only those who themselves have wandered lost, wrote Einstein, know the misery and joy of ‘the years of searching in the dark for a truth that one feels but cannot express; the intense desire and the alternations of confidence and misgiving, until one breaks through to clarity and understanding.’”

“‘A mathematician, like a painter or poet, is a maker of patterns,’ wrote G. H. Hardy, an acclaimed twentieth-century mathematician and an ardent proponent of the Greek view. ‘If his patterns are more permanent than theirs, it is because they are made with ideas.’”

“When Newton declared that he stood on the shoulders of giants…one of the great predecessors he had in mind was the astronomer Johannes Kepler. A contemporary of Galileo, Kepler was a genius and a mystic whose faith in God and faith in mathematics had fused into an inseparable unit. Kepler was both astronomer and astrologer, though he never sorted out just how much the heavens influenced human affairs. ‘In what manner does the countenance of the sky at the moment of a man’s birth determine his character?’ he wrote once, and then he answered his own question. ‘It acts on the person during his life in the manner of the loops which a peasant ties at random around the pumpkins in his field: they do not cause the pumpkin to grow, but they determine its shape.”

“Since he had no idea of the forces that moved the planets, Kepler took on the code-breaking challenge as if it were purely a task in numerology. Like a safecracker armed with nothing but patience, he tried every combination he could think of. If there was no pattern in the lengths of the different planets’ years, for instance, perhaps there was a pattern if you took the lengths of the years and squared them. Or cubed them. Or perhaps you could see a pattern if you computed each planet’s maximum speed and compared those. Or the minimum speeds. For more than a dozen years, Kepler tried one combination after another. He failed every time. Then, out of the blue, ‘On March 8 of this present year 1618, if precise dates are wanted, the solution turned up in my head.’ The discovery itself was complicated. Characteristically, so was Kepler’s response, which combined gratitude to God, immense pride in his own achievement, and his customary willingness to paint himself unflatteringly. ‘I have consummated the work to which I pledged myself, using all the abilities that You gave to me; I have shown the glory of Your works to men,’ he wrote, ‘but if I have pursued my own glory among men while engaged in a work intended for Your glory, be merciful, be compassionate, and forgive.’ What Kepler had found was a way—a mysterious, complicated way—to tie the orbits of the various planets together.

“Kepler had taken the first giant steps toward showing that mathematics governed the heavens. Galileo showed that mathematics reigned here on Earth. Newton’s great achievement, to peek ahead for a moment, was to demonstrate that Kepler’s discoveries and Galileo’s fit seamlessly together, and to explain why.”

“‘My aim is to show that the machine of the universe is not similar to a divine animated being,’ Kepler declared, ‘but similar to a clock.’”

“What Galileo did, and what no one before him had ever done, was find a new way to think about time.”

“The breakthrough was to identify time—not distance or temperature or color or any of a thousand other possibilities—as the essential variable that governs the world. For years Galileo had tried to find a relationship between the speed of a falling object and the distance it had fallen. All his efforts failed. Finally he turned away from distance and focused on time. Suddenly everything fell into place. Galileo had found a way to pin numbers to the world.”

“Algebra was a forest of symbols, geometry a collection of pictures. Now Descartes had come along and showed that algebra and geometry were two languages that described a shared reality.”

“From the moment he unveiled the theory of gravity Newton was hailed as almost superhuman. Voltaire observed Newton’s funeral and was stunned to see dukes and earls carrying the casket. ‘I have seen a professor of mathematics, simply because he was great in his vocation, buried like a king who had been good to his subjects.’”

“Newton had been the first to learn how to pin down the mysterious infinitesimals that held the key to explaining motion. He kept his discoveries secret from all but a tiny circle for three decades.” 

“This new tool for describing the moving, changing world was called calculus. With its discovery, every scientist in the world suddenly held in his hands a magical machine. Pose a question that asked how far? how fast? how high? and then press a button, and the machine spit out the answer. Calculus made it easy to take a snapshot—to freeze the action at any given instant—and then to examine, at leisure, an arrow momentarily motionless against the sky or an athlete hovering in midleap. Questions that had been out of reach forever now took only a moment. How fast is a high diver traveling when she hits the water? If you shoot a rifle with the barrel at a given angle, how far will the bullet travel? What will its speed be when it reaches its target? If a drunken reveler shoots a pistol in the air to celebrate, how high will the bullet rise? More to the point, how fast will it be traveling when it returns to the ground? Calculus was ‘the philosopher’s stone that changed everything it touched to gold,’ one historian wrote, and he seemed almost resentful of the new tool’s power. ‘Difficulties that would have baffled Archimedes were easily overcome by men not worthy to strew the sand in which he traced his diagrams.’”

“Calculus was a device for analyzing how things change as time passes.” 

“America’s founding fathers argued explicitly that the success of the scientific approach foretold their own success. Free minds would make the world anew. Rather than defer to tradition and authority, the new thinkers would start from first principles and build on that sturdy foundation. Kings and other accidental tyrants would be overthrown, sensible and self-regulating institutions set in their place. In the portrait of himself that he liked best, Benjamin Franklin sat deep in thought in front of a bust of Newton, who watched his protégé approvingly. Thomas Jefferson installed a portrait of Newton in a place of honor at Monticello. As they spelled out the design of America’s political institutions, the founders clung to the model of a smooth-running, self-regulating universe. In the eyes of the men who made America, the checks and balances that ensured political stability were directly analogous to the natural pushes and pulls that kept the solar system in balance. ‘The Constitution of the United States had been made under the dominion of the Newtonian theory,’ Woodrow Wilson would later write. If you read the Federalist papers, Wilson continued, the evidence jumped out “on every page.” The Constitution was akin to a scientific theory, and the amendments played the role of experiments that helped define and test that theory.”

“’If we evolved a race of Isaac Newtons, that would not be progress,’ Aldous Huxley once remarked, with a mix of wonder and horror. ‘For the price Newton had to pay for being a supreme intellect was that he was incapable of friendship, love, fatherhood, and many other desirable things. As a man he was a failure; as a monster he was superb.’”

“At Cambridge, Newton could occasionally be seen standing in the courtyard, staring at the ground, drawing diagrams in the gravel with a stick. Eventually he would retreat indoors. His fellow professors did not know what the lines represented, but they stepped carefully around them, in order to avoid hindering the work of the lonely genius struggling to decipher God’s codebook.”

Copyright © 2024 Scott Petullo

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