Isaac Newton came up with the theory of gravity when an apple fell on his head. This occurrence is one of the great stories in the history of science, along with Galileo Galilei throwing things from the Leaning Tower of Pisa, or Archimedes running naked through the streets, shouting “Eureka!” after he had discovered the principle named after him in the bathtub.1 Today, we know that Galileo didn't carry out his experiments on a tower and that Archimedes probably didn't carry out research in a bathtub. And it was different with the apple, too. Above all, though, we do know that the development of Newton's theory of gravity was accompanied by no end of quarreling with his archenemy Robert Hooke.

UNCERTAIN KNOWLEDGE ABOUT THE UNIVERSE

With gravity in Newton's day, it was a bit like it was with light. Nobody really knew what it actually meant. Of course, people realized that things fell downward and that there must be a reason for this. But what was it that made things fall? What made the moon always move around the earth, and the earth around the sun? And what actually was motion?

It is difficult to imagine how scientists of that time must have felt. In view of the enormous number of unanswered questions, it was difficult to establish anything with any certainty. Along with all the knowledge about the universe that we take for granted today, an entire language was missing. If somebody uses the word “gravity” today, it's pretty clear what they mean by it. Perhaps not everybody understands the specific scientific significance of the term, but most people know at least that we're talking about a force that acts between all objects with mass.

The word “gravity” was already in use in Newton's time, but it had a different meaning from our understanding of it today. Like “light,” nobody at the time really had any idea what “gravity” actually was. In his notebook, the young Newton imagined it to be something material—something that was contained in all matter and caused a certain “massiness.” A kind of “gravitational liquid” that was contained in everything and made things heavy. Some people thought of gravity as a sort of radiation; other contemporaries of Newton's believed it to be a place, some special location in the universe to which all objects were attracted. They thought there was a tendency within matter to move toward this location, and since everything always fell down to the ground, this special place could only be located at the center of the earth, which thus had to mark the center of the universe. This reasoning led to problems, however—what about all the other heavenly bodies? Wouldn't a stone that was dropped on the surface of the moon also move in the direction of the earth? Surely there couldn't be two such special locations in the universe? And if gravity really was a kind of liquid, what happened to it? Logically, it could only ever move downward and so must gather, as Newton wrote in his notebook, in giant hollow spaces in the earth's interior. So you can see that there were at the time all sorts of conflicting ideas and concepts.

The question of “gravity” is closely connected with the question of the general nature of motion. Things fall downward—that much was clear to Newton. But not always—a cannonball first flies upward in a wide arc, before it then falls toward the earth's surface again. The water in the oceans rises and falls with the regular cycle of the tides. There had to be an explanation for all of these different motions and a language with which to describe them.

During his studies, Newton regularly read about the experiments and theories of his predecessors, for example Galileo Galilei's reports about the speed at which objects fall to the ground, about which Newton noted down the following: “According to Galileus [Galileo] a iron ball or 100 Florentine (that is 78 lb. in London of Adverdupois weight) descends an 100 braces Florentine or cubits (or 49.01 Ells, perhaps 56 yds.) in 5 seconds of an [hour].”2 Florentine pounds, London avoirdupois, Ells? The only unit in this list that we still commonly use today is the second.³ This entry from Newton's notebook is further evidence of how different from today the situation was for scientists back then. There were no clear and generally accepted definitions for words like “motion,” “space,” or “gravity.” There were no uniform measurements and generally not even practical measuring instruments. But at least there was Isaac Newton, his burning desire to understand everything, and the famous apple.

AND SO IT FELL…

If we are to believe William Stukeley, a friend of Newton's and the author of a biography that was published back in 1752, then the famous apple really did exist. It didn't fall on Newton's head, however. Instead, with no sense of a good story, it simply fell to the ground, as apples sometimes do. Unlike all the other ones that throughout the centuries had fallen from apple trees all over the world, however, in the case of this particular apple there was a genius sitting nearby who happened to have nothing better to do than to ponder the nature of the world, since the university where he should have been working had been shut down because of an outbreak of the plague. When Newton was taking involuntary leave in his home village of Woolsthorpe between 1665 and 1666, he didn't only busy himself with needles and the nature of light (see chapter 1), but also with mathematics (see chapters 3 and 7). Practically all of his other revolutionary ideas were conceived during that time, and none of them were as revolutionary as those about gravity.

So there was Newton, sitting under, next to, or at least within sight of an apple tree, when he saw an apple fall (or at least later claimed to have seen it). Whatever may have actually happened—Newton pondered deeply about falling and moving objects. Not just humdrum apples, but also celestial bodies like the moon. Apples move toward the earth, he thought to himself. And the moon moves around the earth. What if there was a single cause that was responsible for both phenomena? What if the earth exerted an influence that affected both the apple and the moon? What kind of influence could that be? The moon is much larger than an apple. But the apple is much closer to the earth than the moon. The moon “hangs” above the earth; the apple hangs on the apple tree. The moon moves around the earth, while the apple hangs or falls down in a straight line. There seemed to be some sort of connection between all these thoughts, but what exactly was it?

Viewed from a distance of a few meters, an apple can appear to us to be just as large as the moon. That's logical, since the closer something is to our eyes, the larger the perceived image. Whatever is true for the apple must also be valid for the moon. If the moon were therefore twice as close, would it then appear twice as large? No—Newton knew that the surface area of the moon would then appear four times as big. And if the moon were four times closer, it would look sixteen times bigger. The appearance of the surface area does not therefore appear proportionally greater as the distance gets smaller—it changes exponentially. Mathematically, this is referred to as the inverse-square law.

The tiny apple and the gigantic moon seem to be equally large, therefore, but only because the apple is much closer and the appearance changes not in proportion with the distance, but is rather inversely proportional to the square of the distance. Perhaps this is also true of the influence that Newton is trying to find? Using the limited data available to him at the time about the distance and size of the moon, he made a small, rough calculation. And it was indeed the case that an influence that was inversely proportional to the square of the distance was suitable to affect both the apple and the moon.

Today, we like to imagine the conception of the theory of gravity as a typical flash of inspiration, a spontaneous and instantaneous brainwave that was set off by the apple falling. In reality, it was a longer and much more complicated process. The ideas that Newton had in the Woolsthorpe orchard merely formed the basis for his later scientific work. There was still a long way to go first—and plenty of trouble, too.

First of all, Newton returned to Cambridge. He studied mathematics, constructed his telescope, published his first findings about the nature of light and color, and got involved in his first dispute with the members of the Royal Society. After all of that, he devoted himself to completely different subjects (see chapter 6). He only returned to gravity in the 1680s, and the catalyst for this was a comet.

THE WRATH OF THE COMET

In the seventeenth century, as might be expected, comets were still largely a mystery. Nobody knew what they consisted of. Nobody knew why they shone so brightly. Nobody knew why they always appeared so suddenly in the sky and then disappeared again just as suddenly. What people thought they knew at the time was nonsense.

When a comet appeared in the sky at the end of 1680, there was great excitement. It was described as a “sword of vengeance and rod of wrath of Almighty God” in a pamphlet in Nuremberg, which spoke of “a terrifying torch, rod, and sword as a benevolent warning of pending doom.”4 The comet was seen as a warning from God, designed to bring about “dread and transformation in hardened sinful souls.” But not only in Nuremberg were people convinced that comets were the harbingers of doom. This view had been held all over the world for some time. Unlike the stars and planets, the motion of the comets was irregular and unpredictable, and their appearance was out of the ordinary. They weren't points of light that shone brightly and steadily, but rather dull clouds without regular form and with tails that could stretch across the whole sky. The Roman historian Pliny the Elder had already explained that the appearance of a comet signified a looming disaster in his Natural History from the year 77 CE, and up until Newton's day, this view had scarcely changed.

Hundreds of scripts, leaflets, religious pamphlets, and other texts were written about the comet of 1680 and all of them outdid each other in painting the most terrible picture of the future.

Isaac Newton also observed the comet almost every night, eagerly following its traversal of the sky, as did the Royal Society's other natural scientists: Edmond Halley (then aged just twenty-one),5 Robert Hooke, and of course the Astronomer Royal John Flamsteed. When the comet first appeared in the sky in November 1680, though, Flamsteed missed it. It was only visible shortly before dawn at that time and soon disappeared completely from the sky. Flamsteed conjectured that comets didn't perhaps behave as unpredictably as was thought, and forecast that it would soon return. And so it was: in mid-December, the comet could again be seen shining brightly in the night, although not everybody was convinced that it really was the same celestial body as the one a few weeks before.

Flamsteed wrote a letter to a friend at the University of Cambridge, in the hope that he would pass it on to Isaac Newton. The two men's major dispute (see chapter 2) was still a thing of the future and Flamsteed was interested in Newton's mathematical expertise. He had developed a (relatively vague) theory about the motion of comets and wanted to hear Newton's opinion. What if, Flamsteed thought, the sun attracted the comet in some way, perhaps magnetic? The comet would move in a straight line toward the sun and, when close enough to it, would be repelled again, just as magnetism can sometimes attract and sometimes repel.

Newton wrote back and explained outright to Flamsteed that his hypothesis was nonsense. He said the sun was hot and it was a well-known fact that objects lost their magnetic properties when they were heated up. In addition, Newton himself wasn't quite certain whether comets were not perhaps actually two different objects. His own records showed that the motion of the celestial body (or bodies) wasn't consistent, being sometimes faster and sometimes slower. But, Newton wrote to Flamsteed, even if the comet didn't move in a straight line toward the sun and then away from it again, it would be possible that it followed a path around the sun. That could also be caused by an exclusively “attracting force in the sun.” “Force” was another word whose scientific meaning had not been clearly defined at the time. But Newton's work on the motion of the celestial bodies was to change that once and for all. He pondered deeply about forces emanating from the sun, the earth, the moon, and other bodies in the cosmos. He wondered how these forces might be mathematically described and in what way they were interdependent. He came to the conclusion that the motion of the comet could be a simple juxtaposition of two forces: first, its tendency to move along a straight line, and then the deviation from this straight line by a force of attraction emanating from the sun.

HOOKE V. NEWTON: ROUND 2

The comet had inspired Newton's first concrete, and above all public, statement about the manner and cause of celestial bodies’ motion. It was also the catalyst for another altercation with Robert Hooke. For Newton wasn't the only one to ponder the nature of the motion of planets and comets. Hooke had similar ideas and had told Newton about them back in 1679. Wanting to settle their dispute about optics, he asked Newton for his opinion on his theory. Hooke had also had the idea of explaining the motion of planets by a force of attraction, the strength of which changed with distance. He didn't know that Newton had had exactly the same idea back in 1666, long before Hooke (he couldn't have known, since Newton had as usual told nobody about his thinking). In his response, Newton acted as though he was unaware of such a theory. But he did get involved in an exchange regarding a thought experiment.

The question sounds very simple: What happens when you drop a ball from a high tower? Naturally, it falls downward—this much was obvious and, even for an argumentative pair like Isaac Newton and Robert Hooke, there was no reason to fall out over that. But where does the ball land? The earth rotates on its axis, once a day, from the west toward the east. If, therefore, the earth under the ball rotates eastward, then the ball should land a little to the west of the tower. At least one might think so—but Newton had other ideas. The top of the tower rotates with the earth, and the further it is from the ground, the more quickly it rotates.6 That means the ball has a greater starting velocity toward the east than objects on the ground. It must therefore land to the east of the tower, Newton believed. And not only that: in a diagram, he illustrated what would happen with the ball if it could fall unobstructed toward the center of the earth. If the motion of the ball is constantly only downward, toward the center of the earth, then the rotation of the planet ensures that it approaches the center along a spiral-formed path.

Nonsense, said Hooke—and he was completely right. His own suggestion was that the ball falling through the earth would behave like a planet that moves around the middle of the earth, probably moving, he thought, along an elliptical path. Accusing Newton of having made a mistake was enough to get a rise out of him. The fact that such an accusation came from Robert Hooke only exacerbated the problem. But what probably made Newton angriest was the fact that Hooke criticized his idea before the members of the Royal Society. The two of them had actually agreed to keep their exchange private, but Hooke broke this promise when he read out Newton's letters in public.

The old quarrel between the two scientists was now in full swing once more. Newton sketched a new diagram that showed clearly what the ball's elliptical path would look like, since Hooke's suggestion was also not completely correct and, above all, mathematically rather vague. The two men continued to argue for a while what the connection between the path of one body and the force of attraction of another might look like. Hooke's final conjecture was that the strength of the force of attraction was inversely proportional to the square of the distance, and he asked Newton for an answer to the following question: What path would be followed by a celestial body on which such a force was exerted? Hooke was aware of Newton's mathematical skill and so threw down the gauntlet with this problem. But Newton preferred to remain silent.

It took a few more years for the next important step in Isaac Newton's scientific revolution to be taken. In 1684, Edmond Halley, Robert Hooke, and Christopher Wren7 met in a coffee house and discussed—once again—the question of the motion of objects. All three of them believed that the force that makes the celestial bodies move around the sun ought to be inversely proportional to the square of the distance. But this was just a supposition; they lacked a rigorous mathematical interpretation. Over coffee, Robert Hooke claimed, however, that he had long since demonstrated how the motion of all celestial bodies could be explained by a force that was inversely proportional to the square of the distance. He simply wished to keep his findings secret and to only go public with them when they would be truly appreciated.

Halley wasn't convinced that Hooke wasn't simply bluffing and preferred to ask Newton once more. He visited him in Cambridge in August 1684 and once again posed the question: What path is followed by a celestial body on which a force of attraction is exerted that is inversely proportional to the square of the distance? Newton's response was immediate: an elliptical path. He said that he had long since established this using mathematical calculations. Unfortunately, he had lost these calculations, but he would repeat them and send them to Halley.

THE SILENCE IS BROKEN

Astonishingly, that is exactly what Newton did. Unlike previously, he actually delivered what he had promised. First, Halley received a short manuscript titled “On the motion of bodies in an orbit.” But that was merely the beginning. Newton kept on writing, devoting himself to comets, planets, and the moon. He gathered data, asking the astronomer Flamsteed (their major dispute was still to come) for observations that he could use for his calculations. He developed a new language, providing definitions for words like “space” or “time.” He used the new mathematics he had developed years before (of which hardly anybody apart from himself yet knew) to explain not only the motion of the planets, but also numerous other phenomena in the skies and on the earth. Just like that, he created an entirely new approach to natural sciences, or a “natural philosophy,” as it was still called at the time. Above all, he developed mathematical principles that formed the basis of this new natural philosophy. These were the “Mathematical Principles of Natural Philosophy,” which was the title he gave to his work: Philosophiae Naturalis Principia Mathematica.

The initial brief treatise was enough to convince the members of the Royal Society that something truly new and significant was to be expected here. They agreed to print and publish Newton's book, when it was finished, and commissioned Edmond Halley to supervise the matter. It is thanks to him that the book did indeed appear in 1686, since the project was almost scuttled because of a few fish. Or to be more precise, because of a work by the naturalist Francis Willughby, whose name has slipped into obscurity today. He wrote books about birds, insects, and fish (and football too, rather surprisingly).8 He had died in 1672, and his works were only published after his death. In 1686, the Royal Society decided to publish Willughby's History of Fish.⁹ The book contained a great number of illustrations of fish, which made the printing process extremely expensive—without, however, boosting sales. This history of fish was very much a shelf warmer and the Royal Society was reluctant to spend money on printing another book,¹⁰ which meant that the publication of Newton's work was on the verge of being abandoned because of a fish lover. Without further ado, however, Halley defrayed most of the printing costs out of his own pocket; posterity and the entire world of science have reason to be grateful to him. His contemporaries repaid him in a rather curious manner, on the other hand. An agreed fee of fifty pounds for various tasks carried out for the Royal Society was withheld. Instead, he was offered fifty copies of the History of Fish.11

A SMALL THEORY FOR A BIG UNIVERSE

Besides all of these problems, Halley also had to take care of the dispute between Hooke and Newton, which had broken out once more shortly before the final publication of the work. At the request of the Royal Society, Halley wrote a letter to Newton in April 1686 to thank him for his work on the Philosophiae Naturalis Principia Mathematica. In it, however, he also mentioned that Robert Hooke had a slight problem with the manuscript for the first volume of the work. Hooke was of the opinion that the idea that a force was exerted between the celestial bodies, with its strength inversely proportional to the square of the distance, originated with him and Newton should mention this in his book.

It should now be clear to the reader how Newton would react to such accusations. In an enraged reply, he pulled no punches: “Now is not this very fine? Mathematicians that find out, settle & do all the business must content themselves with being nothing but dry calculators & drudges & another that does nothing but pretend & grasp at all things must carry away all the invention.” In a letter to Halley, Newton attacked Hooke directly: “Mr. Hook has erred in the invention he pretends to & his error is the cause of all the stir he makes.” Newton was prepared to admit that Hooke had told him about his thoughts on gravity. But he, Newton, had not asked about them and therefore felt no obligations in connection with them. Hooke had imposed the exchange of ideas upon him and Hooke's errors in his description of gravity had been the catalyst for Newton's own work and discoveries concerning the subject. Newton added that it was absurd for Hooke now to claim that all of this had originally been his own work. He called Hooke “a man of a strange unsociable temper” and promptly set about deleting every mention of Hooke from his manuscript.

As he so often did, Newton reacted far too aggressively and far too quickly, though in this particular case, he wasn't completely wrong. Of course there were other scientists at the time who were thinking along the lines of a force of attraction that was inversely proportional to the square of the distance. But these were merely ideas and suppositions. Nobody had developed a mathematical foundation or a unified and large-scale view of the world from which the law of gravity must necessarily follow. Nobody, that is, apart from Isaac Newton.

For that is what is truly revolutionary about his work. Not the discovery that one can explain the motion of the celestial bodies when one presupposes a force of attraction that is inversely proportional to the square of the distance. That was by no means the only realization contained within the three-volume Philosophiae Naturalis Principia Mathematica (see chapter 5). Newton created a completely new view of the world—not for nothing is the third and final volume of his work called De mundi systemate (Of the system of the world).

Newton had realized that the force that is responsible for the motion of the celestial bodies is not limited to the sky, but is rather a fundamental force, one that is exerted throughout the entire cosmos—on apple trees and entire stars alike. It is difficult to imagine the creative achievement that was necessary for Newton to come up with the idea of such a universal force of gravity—and not to leave it there, but rather to then explain it in mathematical terms.

It's not a question of Newton having “invented” or “discovered” gravity. He showed that it was possible to understand gravity, and that it is a universal force. He created a formula—a single theory that can be used to explain an entire universe.¹² What Newton did at that time formed the basis for modern science. He showed that the world can be understood and explained, that there are natural laws that apply everywhere. He took the first step toward the unification of the natural sciences and started a process that is still going on today. When modern quantum physicists search for a theory of everything, or when they attempt to unify quantum mechanics with the theory of relativity, they are able to do so because Isaac Newton started it all off all those years ago.

Newton clearly demonstrated that gravity is a universal force, that it acts as much in our daily lives as it does on the great cosmic stage of the stars and planets. He showed the natural scientists that the world need not only be understood piece by piece and that there are links between the different, seemingly isolated phenomena around us, and that it is possible to conceive of these links in mathematical formulae and understand them.

GO IN SEARCH OF DISPUTE!

But was all that quarrelling really necessary? Couldn't Newton have settled his differences with his colleagues in a slightly more peaceful way? One thing is clear: it's impossible to avoid disputes in science. That's because scientists are completely normal human beings with human characteristics. And even if your typical scientist doesn't have as many unpleasant character traits all at once as Newton did, he or she generally has enough for the odd confrontation. And confrontation is also absolutely indispensable for science to function properly. That's down to the very nature of the matter—the role of science is to make two diametrically opposed concepts compatible.

On the one hand, of course, we always want to find out new things about the world. That is after all the very reason why we get involved in science. There are heaps of things that we don't know, and that's what we want to learn more about. And because our knowledge is incomplete, the same is true for the models that we use to explain the world. Each new model must therefore correct certain assumptions of the old ones—and in some cases, it can completely push them out of the picture.

On the other hand, however, there is also the tendency during research to stick to what you already know. In order for something to become a part of accepted science, it has to actually work. That's true of Newton's model of gravity, for example. His equations enable us to predict the movements of the celestial bodies. We can use them to steer space probes so accurately through the solar system that they can land precisely on planets that, when the probes were launched, were still in a completely different location. Newton's theory of gravity works—even though we know today that it is “wrong.” In 1915, Albert Einstein developed a completely new model of gravity. With Einstein's equations, we can calculate everything that we can with Newton's mathematics, but we can do so more accurately and also in cases where it wasn't possible before. One could say that Einstein works better than Newton—which doesn't change the fact that Newton still works. At least, he does within certain limits, and thanks to Albert Einstein, we now know exactly what those limits are. The greater accuracy in the general theory of relativity comes at the cost of greater complexity; it is much more onerous to calculate using the new equations than the old ones. And because the old ones are still good enough within their limits, we still use them as well today.

A certain caution, however, is generally a good thing when it comes to new scientific theories. A great deal of the research being undertaken on the outer limits of current knowledge is by definition doubtful. One speculates and makes assumptions, and doesn't always have the chance to immediately test such speculation with concrete experiments. If scientists were to reject the status quo straightaway every time anybody had a new idea, then nothing more would be achieved. An accepted scientific theory has been checked in countless experiments and tested using countless observations. Such hard-won theories shouldn't then be rejected just like that, and this somewhat conservative attitude is essential. At the same time, however, science must be open to new concepts and prepared to entertain ideas that nobody has ever had before.

It is logical that conflicts should arise, therefore. If you have a new idea, you are generally fully convinced by it and have no time for existing knowledge. That's where your peers come in—their job is to view and judge the potential advance as soberly as possible, in order to see whether it is really a revolutionary idea or simply wishful thinking. Such a situation can easily give rise to disputes—and these disputes are sometimes necessary.

Science isn't democratic. What happens isn't necessarily what the majority wants, and the truth is not always to be found in the middle. Even if all of your colleagues and peers are ranked against you, it is still possible that you are right. In which case, you mustn't allow the waves of criticism to overwhelm you—and you have to be prepared for animated discussions and disputes. On the other hand, we mustn't take this idea too far. Just because you face criticism, it doesn't automatically follow that you are right.13 There are reasons for sensible criticism, and you have to take these reasons seriously. And it isn't necessary to let every animated discussion escalate into an argument. But if you want to be a successful scientist, a certain amount of pugnacity isn't necessarily a bad thing. You need to be able to stand up for your own ideas and not to throw in the towel at the first sign of criticism. Equally, you need to be able to criticize other people's ideas, where appropriate, and not to accept everything simply because somebody claims it is true. Science requires from all involved the willingness to engage in vigorous discussion; otherwise it cannot function properly. You just don't need to take this to extremes as Newton did.

Regardless of any readiness for an argument, in one respect, you definitely shouldn't take Isaac Newton as an example. You should recognize the established achievements of other people, even if you cannot stand those people. Simply to ignore their contributions—as Newton did with Hooke (and also Flamsteed or Leibniz—see chapters 2 and 7)—is a serious mistake. It has nothing to do with confrontation and criticism any more. It is at best unnecessarily impolite and at worst a clear case of plagiarism, which means presenting the thoughts and findings of others as your own. Today, this is quite rightly considered to be a serious malpractice—even if you are as brilliant as Isaac Newton.