필사 모드: Why Newton Rewrote the World — The Apple, the Principia, and Prediction as a Test

Introduction — The Apple Did Not Fall on His Head

On April 15, 1726, in a garden in Kensington, London, an eighty-three-year-old Isaac Newton drank tea with a young visitor and talked about old times. They were under the shade of an apple tree. Sixty years earlier, sitting in the garden of his family home in Lincolnshire, an apple had fallen, and this thought had come to him. Why does an apple fall neither sideways nor upward but always straight toward the center of the earth.

The man who took down that conversation was the antiquarian William Stukeley, and he left the scene in the memoir of Newton he wrote in 1752. The Royal Society released the manuscript digitally in 2010, so anyone can now check the sentence for themselves. Two things become clear here. First, nowhere is there a passage about the apple falling on his head. That embellishment belongs to later hands. Second, the source of the story is not a witness but Newton himself, sixty years after the fact.

The second fact is the more interesting one. Past eighty, Newton told this anecdote to several people again and again. John Conduitt, the husband of his niece, wrote it down as well, and Voltaire spread it in France saying he had heard it from the niece of Newton. Of all times, this was the period when he had been fighting the camp of Leibniz over priority in calculus for nearly twenty years. The apple story was also a story that nailed his discovery down to 1666. That is why historians of science do not flatly deny the anecdote but read its function alongside it. The tree at Woolsthorpe in Lincolnshire is still standing, said to have grown back from the root after the wind knocked it down in 1816.

The Compressed Story Called the Miracle Year

In the summer of 1665, when a great plague ran through London, Cambridge University closed. Newton, twenty-two, went home and spent about eighteen months there. This period is commonly called the miracle year. The story goes that calculus, the theory of light and color, and the idea of gravity all poured out in those few months.

The source of that story too is in large part Newton himself. In a reminiscence he wrote in the 1710s, he set down that he had been at the best age for invention in those days and had applied himself to mathematics and natural philosophy more than at any time since. It is not untrue. The core ideas of infinite series and fluxions, the beginning of the experiments splitting white light with a prism, and the attempt to compare the motion of the moon with falling on earth were all around then.

But the research since the Newton biography by Richard Westfall (1980) shows a far less dramatic picture. The Newton of 1666 did not obtain an answer; he obtained a problem. When he checked the motion of the moon that year he used an inaccurate value for the radius of the earth, and the calculation came out only "pretty nearly" right. On top of that a decisive mathematical obstacle remained. In calculating a fall against a sphere as large as the earth, he had to prove that the attraction of the whole sphere may be treated as a single point gathered at the center, and Newton proved that theorem in 1685. Almost twenty years later.

The letters he exchanged with Robert Hooke in 1679 and 1680 pulled him back into the problem, and a single visit in 1684 finally produced the book. In other words, the miracle year is not an event that happened in one year but a story that folds twenty years of work into a single year. Stories of great discoveries are almost always compressed like this. Because we know the ending, we erase the dead ends along the way.

Halley, a Book of Fishes, and 1687

One day in January 1684, three men argued in a London coffeehouse. Robert Hooke, Christopher Wren, and Edmond Halley. The subject was this. If a force acts in inverse proportion to the square of the distance, what orbit does a planet trace. Hooke boasted that he could prove it, and Wren staked a book worth forty shillings on whoever brought a proof within two months. Nobody brought one.

That August, Halley went to Cambridge to see Newton and put the same question. Newton answered at once: an ellipse. Asked how he knew, he said he had calculated it, and he looked for the paper but could not find it. He said he would work it out again and send it, and that November he sent a nine-page tract. And the tract did not stop; it grew into a book in three volumes.

The circumstances of publication include a detail that still raises a smile. The Royal Society had just spent its entire publishing budget bringing out a history of fishes. The book did not sell, and the Society paid Halley in bundles of unsold fish books instead of salary. One of the most important scientific books in human history was published out of the pocket of Halley because the treasury of the Society had been emptied by an illustrated book of fishes. The imprimatur of Samuel Pepys, president of the Royal Society, was stamped on the title page dated July 5, 1686, and the book came into the world in the summer of 1687. The Mathematical Principles of Natural Philosophy, the Principia for short.

What this book did can be summed up in one sentence. It bound heaven and earth under the same law. Until then the heavens were the realm of perfect and eternal circular motion, and the earth the realm of corrupt and irregular falling. The two worlds were held to follow different rules. With three laws of motion and one law of attraction Newton put the fall of an apple and the orbit of the moon, the rise and fall of tides, the paths of comets and the slow wobble of the axis of the earth inside the same calculation. The idea that there is no special place in the universe, that a law holding here also holds over there, becomes in this book a basic premise of physics.

Reading it was brutally hard. Newton rewrote the results he had obtained by calculus in the language of classical geometry, and later said he had deliberately made it difficult so as not to be pestered by people with a smattering of mathematics. There is a story of a Cambridge student who saw Newton passing in the street and said there goes the man who wrote a book that neither he nor anyone else understands. Even so, the book went through edition after edition on the circuit of error correction that printing created and became a common language of Europe.

Whose Calculus Is It — A Twenty-Year War of Priority

Newton had the core of calculus in hand in the 1660s and did not publish it. He only circulated manuscripts among a few acquaintances. He printed fluxions formally in 1704, as an appendix to his book on optics. Nearly forty years in a drawer.

Meanwhile Leibniz (Gottfried Wilhelm Leibniz) built the same tool independently around 1675 and published it in 1684. His notation was far better. The symbols we use today for differentiation and integration are not the dots of Newton but those of Leibniz.

Into the 1700s the quarrel turned ugly. Accusations of plagiarism went back and forth, and in 1712 the Royal Society convened a committee of inquiry that issued a report the following year. The conclusion came down on the side of Newton. The trouble is the fact that the president of the Royal Society at the time was Newton himself, that he appointed the committee, and that he wrote a good part of the report personally. He even published an anonymous review of that report in the journal of the Society. By the standards of today it is a textbook case of conflict of interest.

The settled view now is independent discovery by both. And the price of the victory was paid in an unexpected place. British mathematics clung to the notation of Newton out of patriotism, and as a result fell behind continental analysis through the whole of the eighteenth century. The side that won the priority fight lost a hundred years.

The Newton We Invented — Alchemical Manuscripts and the Shoulders of Giants

In July 1936, at the Sotheby auction rooms in London, the papers Newton left behind were split into 329 lots and sold. They were the so-called unscientific manuscripts, kept by descendants for generations and then let go. The total came to less than ten thousand pounds. The man who bought up the alchemical manuscripts in bulk at that auction was the economist John Maynard Keynes. A large share of the theological manuscripts went to the collector Abraham Yahuda and is now in the National Library of Israel.

Keynes was shaken by what he read. In a famous piece of 1946 he called Newton not the first figure of the age of reason but the "last of the magicians". The sheer volume says as much. The writing Newton devoted to alchemy is estimated at around a million words, and what he wrote on biblical chronology and theology comes to more than that. It exceeds the volume he gave to physics and mathematics. He concealed a heretical faith that denied the Trinity all his life, he labored over calculations converting the prophecies of scripture into dates, and in one manuscript he wrote that the end of the world would not come before 2060 at the earliest.

To take this and conclude that Newton was a strange man is to miss the point. The point is that the boundaries were drawn far later than we imagine. In the seventeenth century the word scientist did not even exist. William Whewell coined it in the 1830s. Newton considered himself a natural philosopher, and alchemy that handles the transformation of matter, theology that reads the design of God, and mechanics that calculates the motion of heavenly bodies were for him a single project. The modern scientist Newton we know is a portrait assembled by later hands after stripping half the papers away.

The same sort of assembly happened to his most famous sentence. In a letter to Robert Hooke on February 5, 1676, Newton wrote that if he had seen further it was by standing on the shoulders of giants. It is quoted as a specimen of modesty.

And yet the sentence carries two layers of shadow. One is authorship. The image of a dwarf sitting on the shoulders of a giant goes back to Bernard of Chartres in the twelfth century, and John of Salisbury set it down and passed it on in a book of 1159. The sociologist Robert Merton wrote a whole book in 1965 simply tracing the travels of this phrase. That is, the sentence of modesty was itself a commonplace borrowed from someone else.

The other is tone. Hooke was short and had a curved back, so the reading that the sentence was a taunt was popular for a long time. It is attractive but thinly grounded. The phrase was an ordinary commonplace in that period, the letter in question was conciliatory in tone and meant to close an optical dispute, and the records describing the body of Hooke are mostly from his old age. A widely spread interpretation is not always the interpretation with thick evidence. Still, it is also true that Newton afterward erased the name of Hooke from the Principia, so it is probably more accurate to say that modesty and hostility coexisted in the same man.

The Correction Two Hundred Years Later — What Einstein Actually Did

For two hundred years after the Principia the Newtonian system worked almost perfectly. In 1737 the Lapland expedition confirmed by survey the prediction of Newton that the earth is flattened toward the poles, and at Christmas 1758 the comet returned exactly as Halley had calculated. In 1846 the discrepancy in the orbit of Uranus was calculated to point at the place where Neptune ought to be, and a planet was actually there.

But one thing would not fit to the end. The perihelion of Mercury advanced 43 arcseconds per century more than theory allowed. It was a very small error, and for nearly a hundred years astronomers tried to fill the hole by positing an invisible planet. In 1915 the general theory of relativity of Einstein calculated the value exactly, with no new planet. Four years later, when starlight was observed bending as it passed beside the sun during a total eclipse, the ground shifted completely.

Here a common misunderstanding has to be cleared up. Einstein did not show that Newton was wrong; he showed the range in which Newton is right. Under conditions where speeds are slow compared with light and gravity is weak, the equations of general relativity fall back into the formulas of Newton. That is why satellite orbits and rocket trajectories and bridge design are still calculated with Newtonian mechanics today. As Isaac Asimov put it in a piece from 1989, there are degrees of being wrong. The belief that the earth is flat and the belief that the earth is a perfect sphere are both wrong, but the second is far less wrong.

What has to be read out of this table is not who won. The clocks on GPS satellites drift from clocks on the ground by tens of microseconds a day, and without correcting for that the position error would open up to several kilometers within a single day. A theory that worked well for more than two hundred years collapses under particular conditions, and a broader theory takes it in as a special case — that is not a failure but the very way science works.

What Does This Explanation Predict

The most practical habit to take from Newton is not the formula for universal gravitation. What made the Principia great was not the power to explain what had already happened but the power to say in advance what had not yet happened. The earth will be flattened; the comet will return in about seventy-six years. Both predictions could have been wrong, which is exactly why it meant something when they were right.

This standard can be used just as it is outside physics. When you meet a claim, ask five things in order.

1. What does this explanation predict. It separates after-the-fact interpretation from advance prediction. An explanation that supplies a reason after the stock has fallen can explain anything, and an explanation that explains anything is saying effectively nothing.
2. What observation would make this claim wrong. If the person making the claim cannot answer this question, or is reluctant to, then it is not a claim but a position.
3. Are numbers and deadlines attached. Words like soon, considerably and sharply dodge verification. The moment how much, by when, and within what margin get attached, a claim goes onto the test bench.
4. How far does it hold. Every theory has a range of application. As Newtonian mechanics did, a good claim can state for itself the territory where it does not work.
5. What was fixed when it was wrong. Look at whether a past prediction that missed survived by quietly changing the conditions, or whether the model was repaired. The former is the method of astrology and the latter the method of science.

None of the five questions demands knowledge from the person asking. You can ask them without knowing physics and without knowing statistics. And usually the character of the conversation shows itself at the first question.

Closing — The Things That Survive Because They Can Be Corrected

Sort out the story of Newton and what remains is not one genius but a strange combination. An old man repeating the apple anecdote at eighty-three, a book published on someone else's money because of an illustrated volume of fishes, a man who wrote the verdict on his own case into the society he presided over, a natural philosopher who spent more nights on alchemy and biblical chronology than on physics.

And yet the system he built held for two hundred years, and even the manner of its collapse was useful to those who came after. Because Newtonian mechanics was not refuted and discarded but preserved by having a boundary drawn around it. A claim that survives a long time is not a claim that cannot be refuted but a claim that can say where it goes wrong. When you meet a plausible explanation in the news or in a meeting today, try throwing out a single sentence. So what does this explanation say will happen next. Whether or not there is an answer is the heart of a method that began three hundred years ago in a garden in Lincolnshire.