Truth is the offspring of silence and meditation. That's what Newton once said, and the quote makes him sound like a Far Eastern Zen master, who is at peace with himself and whom nothing can trouble. Newton certainly contemplated a lot, and he may well have discovered all sorts of truths about the universe. But calm and even-tempered—and silent? No, not at all, especially when people criticized him. This made him hypersensitive and fight back, and in the course of his career, he had countless extensive and vigorous disputes with his peers.

When Newton was still at the beginning of his scientific career, he attempted to escape criticism by remaining anonymous. The consequences of this would continue to shape his life decades later. Had he not had such a great fear of other people's criticism, many of his feuds would perhaps never have occurred.

It all began with mathematics, but the actual trigger, slightly surprisingly, was astrology. In 1664, Isaac Newton had finished his studies at Cambridge University and began to devote himself to mathematics. He had previously come across a book on astrology and had been unable to understand one of the diagrams in it.1 There was no focus on mathematics in university courses at the time, which tended to concentrate on theology and the classics. So Newton simply taught himself mathematics, and when he started something, he only ever stopped when he had thought through every aspect of it. From self-study, therefore, he graduated onto research into topics on the very limits of existing mathematical knowledge.

IN SEARCH OF INFINITY

In Newton's notebook, we can find all sorts of calculations. Infinite series, for example, i.e., the sum of infinitely many numbers. Such sums don't always need to be infinitely great, of course; if the figures get smaller and smaller, then they will converge to a finite value.2 In his notebook, there is a calculation in which he has worked out the value of such an infinite sum to the fifty-fifth decimal. “I am ashamed to tell you to how many figures I carried these computations, having no other business at the time,” he wrote to an acquaintance in 1666. “I had too much pleasure in these discoveries.” The discoveries of which he speaks were new methods of dealing with infinity. Though infinity was already a research branch of mathematics at the time, it was still considered to be rather mysterious and indecipherable. The Frenchman René Descartes, whose mathematical works Newton had studied carefully, wrote in his Principles of Philosophy:

We will accordingly give ourselves no concern to reply to those who demand whether the half of an infinite line is also infinite, and whether an infinite number is even or odd, and the like, because it is only such as imagine their minds to be infinite who seem bound to entertain questions of this sort.3

Well, Newton certainly seemed bound to entertain such questions. And he did so with great success. His thoughts on infinity culminated in a completely new mathematical discipline (see chapter 7), which changed the world at least as much as his findings about nature did. To begin with, however, Newton worked alone and out of the public eye. Only Isaac Barrow, who had held the mathematics chair at Cambridge since 1664, knew what Newton was up to and recognized the significance of his work. It was also Barrow who was later able to convince Newton to share at least some of his findings with the rest of the world.

In 1668, Barrow brought a book with him to the university. It was written by the German mathematician Nicholas Mercator, who had also worked on the calculation of infinite series. Newton must have been surprised and shocked in equal measure when he saw Mercator's book, for it contained precisely what he himself had thought out years before. His own work, however, was much more comprehensive than Mercator's and, at Barrow's insistence, Newton wrote up a little of what he had done.

Barrow sent the whole thing to the mathematician John Collins, who served a similar purpose in the seventeenth century to the major internet forums or mailing lists today. He was in contact with the most influential mathematicians of the day and made sure that information and new publications were swiftly and widely distributed. This didn't mean that the author Isaac Newton made an appearance, however, since Newton had only agreed to the publication of his work on the condition that Barrow would not reveal his name.

Newton avoided the public gaze. Until then, he had always carried out his research alone—discovering his new mathematical principles, investigating the nature of light and understanding gravity. But he had no idea what his scientific peers thought of all this, and he probably didn't really want to know, either. As an egomaniac, he would certainly have had no problem with public recognition, but this seems to have been outweighed by his reluctance to be exposed to criticism and the need to justify his work.

It was only when John Collins's answer not only contained no criticism, but was also full of enthusiastic praise for the work, that Newton finally agreed to make his name public. This was the first time that people outside of Cambridge University had heard of his scientific work. Collins distributed Newton's article about the calculation of infinite sums throughout Europe and began extensive correspondence with Newton—though this turned out to be increasingly frustrating.

NEWTON CONSTRUCTS A TELESCOPE

It was a curious dance that took place between Collins and Newton. Collins wanted to know as much as possible about Newton's work and to have his findings published as quickly as possible. But Newton played hard to get. He would send Collins the odd equation or the occasional solution and hint at more to come, which he would then never send. And he liked to tease a little in his letters: when Collins was interested in a table with solutions, Newton answered that this would be “pretty easy and obvious enough. But I cannot persuade myself to undertake the drudgery of making it.”4 And time and time again, he insisted, at least to begin with, that Collins should under no circumstances mention Newton's name when publishing his answers: “I see not what there is desirable in public esteem were I able to acquire and maintain it. It would perhaps increase my acquaintance, the thing which I chiefly study to decline.” Newton also annotated a book by a Dutch mathematician—at the urging of Barrow and Collins—and insisted shortly before the book's publication that the sentence “extended by another author” should be added, not “extended by Isaac Newton.”

Even back then, Newton could have justifiably become world-famous with his new mathematical theories. But he had no interest in public opinion or that of the scientific community. Had he not been so coy at the time, the study of natural sciences might have developed differently. He certainly would have spared himself the biggest and longest row of his career (see chapter 7).

Before things came to that, though, he started an argument with his peers for quite different reasons. At the same time as he was discovering completely new realms in the field of abstract mathematics, he also came up with a wholly practical invention that was however no less revolutionary. It was the technical counterpart to his breakthroughs in physics. Theoretical physics and astronomy today couldn't do without Newton's findings about gravity and mathematics; practical astronomy is equally dependent on the thing he constructed around the same time: the telescope.

There had been telescopes for a while, of course; they had been around for about sixty years and, in the hands of the great Galileo Galilei at the beginning of the seventeenth century, had proved that they had the potential to bring entire world systems toppling down. It was probably in 1608 that the Dutch optician Hans Lipperhey came up with the idea of combining a few special glass lenses and thus constructed the first telescope. Or the telescope might also have been invented shortly before that by Zacharias Janssen, another Dutch optician. Or maybe it was Adriaan Metius, an astronomer and mathematician. All three men claimed at one time or another to have been the first. Whichever one of them it was, the fact is that he had the idea of combining two pieces of glass. Not any old pieces of glass, of course, but rather specially ground optical lenses. The first was a so-called converging (or convex) lens. If a bundle of parallel light rays passes through a converging lens, all of the light rays converge to a single point before spreading out again. The second lens was a diverging (or concave) lens, which has the opposite effect—a bundle of divergent rays is refracted to become parallel light rays. Light that passes through the converging lens can be focused and then dispersed again through the diverging lens to form an image that can be observed. The converging lens in this case is much larger than the pupil in our eye, which only measures a few millimeters across. It can therefore gather a lot more light and so, thanks to the diverging lens, we can transform this light into an image again that our small eye can see.

A telescope is therefore nothing more than an artificial, but much larger, eye. The larger the lens, the more light it can collect and the fainter heavenly bodies we can observe. The lens telescopes of the time, however, didn't always work properly. The images were often fuzzy, and colors appeared different in the telescope than in nature. Newton knew this too, but unlike his colleagues, he had an idea why this was.

He knew all about eyes and light. After all, he had already carried out experiments on them with no regard for personal damage. His optical research was not merely limited to sticking needles into his eyes, however. Between 1664 and 1666, when Newton was laying the foundations for the greatest scientific revolution of the early modern period, he was not only busy with mathematics and gravity. He was also researching optics and the nature of light.

In 1665, he had to leave Cambridge University. The plague had broken out and the university was closed, so he was forced to return to Woolsthorpe, the small, sleepy village where he had been born. Not much happened there—there were no famous institutions, research facilities, or attractions. Today, it is of course possible to visit the house where Newton was born, but nobody was interested in that back in 1665. Not even Newton himself, though he had no choice in the matter. At least he was able to continue his research and experiments there in peace and quiet, free from external distractions.

Back in Woolsthorpe, Newton did what he had done as a small child in his attic room: he observed the light. This time, though, he did so quite differently. He carried out an experiment that is now considered to be one of the most important in the history of science—one that opened up a completely new world for him and the rest of humankind, an experiment that could hardly have been simpler and yet ended up making an entire universe visible.

Newton made a hole in the wall of a room that was otherwise fully darkened. A narrow ray of sunlight penetrated through this hole and passed through a prism, with colors then appearing on the other side. So far, so unspectacular—since glass had been in existence, there had been people who noticed that colors appeared in this glass when light passed through it in the right way. It was also known that this phenomenon could be observed particularly well when a special, triangular-shaped piece of glass—a prism—was used. But it was not known why this was the case. Or rather, the reason seemed obvious to people: they assumed the colors were produced in the prism. This was the prevailing opinion, and hardly anybody questioned it.

But Newton wasn't satisfied, particularly when he came up with a method for testing this assumption, for which he needed nothing more than a second prism. In the colorful rainbow that was created behind the first prism, he placed a dividing wall with a small hole in it that was so designed that only light of one particular color would pass through it. He thus now had just one ray of light consisting of a single color—and he then had this ray pass through the second prism. If the colors really did arise in the glass itself, then a second rainbow ought to have been visible behind the prism. But this wasn't the case. A ray of blue light remained a ray of blue light even behind the second prism. A ray of red light remained red.5

The prism didn't therefore create the colors, it separated them, Newton discovered. White light is a mixture of colors—all colors. Newton established this, too, by making the complete rainbow of rays become white light again after passing through a second prism. And he made a further discovery: the light changed direction when passing through the glass, but not uniformly—blue light deviated more than red.

It was thereby clear to Newton why the telescopes didn't work so well: each color in the white light was diverted to differing degrees in the lenses inside. This meant that there was no uniform image at the end, but rather a number of images in the different colors that were slightly adjacent to and superimposed upon each other. This “chromatic aberration” could be avoided by using mirrors instead of glass lenses. It was already known at the time that light rays could also be diverted using mirrors.6 Up until then, however, nobody had actually managed to construct a practical and working telescope with mirrors. But then along came Newton and did just that.

When the plague disappeared after 1666 and Cambridge University commenced operations again, Newton repeated and expanded his optical experiments there. In 1668, he was then ready to build a telescope that used mirrors instead of lenses. He was extremely proud of his achievement, explaining later to the husband of his niece that he had indeed made everything himself—including the necessary tools, since “If I had waited for other people to make my tools and design things for me, I had never made anything.”

Newton's telescope was a masterpiece. The reflecting telescope was not his invention, but he was the first person to understand why and how it worked in the way it did. He had investigated the scientific principles of optics and then put them into practice. His telescope was small—only about thirty centimeters long. The lens telescopes that were common at the time were much longer. They had to be, since the larger the converging lens at the front was, the further back was the point at which the light was focused. If you wanted to see more, you needed bigger lenses and therefore longer—and more unwieldy—telescopes. But even though Newton's telescope was smaller, it was still clearly better. His instrument achieved a magnification of approximately thirty-five times, almost three times as much as the best lens telescopes already in existence.7

Newton made the mirror himself, using a mixture of copper and tin that was later known as speculum metal. Along with the main mirror, Newton also incorporated a second, smaller mirror into his telescope. From the telescope's opening, the light first fell upon the main mirror, some thirty-three centimeters wide, being reflected there and then being diverted by the secondary mirror out through another opening, where the observer could view the image. This construction enabled Newton to achieve the maximum light yield and it was thereby possible to observe the heavens without standing in the way of the light.

RAISE THE CURTAIN FOR NEWTON'S FAVORITE ENEMY

Collins and Barrow were once again the first to hear of Newton's invention. Barrow then took the telescope to London in 1671, in order to show it to his colleagues from the Royal Society, who were all suitably impressed. The Society's secretary, Henry Oldenburg, immediately wrote to Newton, asking him to publish a report about the new instrument. He said Newton should apply for a public patent, in order to prevent other scientists from abroad from copying the telescope and presenting it as their own work. Newton was also invited to become a member of the Royal Society.

But Newton reacted coyly once again, writing in reply: “I was surprised to see so much care taken about securing an invention to me, of which I have hitherto had so little value.”8 Had he not been asked so often, he wrote, he would have kept his telescope as a matter of private interest. But he ended up sending the appropriate information to the Royal Society for publication, again insisting on anonymity—although he did feel flattered enough by the Society's praise that he agreed to become a member. And he said that he was looking forward to sharing his “poor and solitary endeavours” in the future (which is, however, rather doubtful and can be interpreted as an expression of false modesty).

In his next letter, Newton had obviously convinced himself to finally stand by his work. He said he would not only present his telescope, but also the research that had led to its construction, it being “in my judgment the oddest if not the most considerable detection which hath hitherto beene made in the operations of Nature.” So much for his modesty…

In February 1672, Newton sent his article to Henry Oldenburg. The title held little back: “New Theory about Light and Colours.” The article was read out to the members of the Royal Society two days later, and precisely what Newton had always feared then happened: he received feedback. The members of the Royal Society set up a committee to study and evaluate Newton's work on light and colors, with Robert Hooke chosen to write the final report. Which he did—and in so doing landed himself a lifelong enemy in Isaac Newton.

Hooke was seven years Newton's senior, but, unlike the younger man, already a renowned scientist. He had been accepted into the Royal Society back in 1663 and was its first curator, responsible for all experiments. He was also assigned with the task of bringing to the weekly meetings drawings of the things he had observed with his microscope. Like the telescope, this instrument had only been invented at the beginning of the seventeenth century. And as with the telescope, there is some dispute as to who was the first person to construct it. Robert Hooke was in any case the first person to make extensive use of it in order to better understand the world of small things. His illustrations of enlarged insects, needlepoints, razor blades, or mildew9 were so impressive that the Royal Society commissioned an entire book of them. Micrographia appeared in 1665 and became one of the first scientific bestsellers. While the print run only amounted to 1,200 copies, it completely sold out within just a few days.

Along with these pictures, Hooke also published a theory of the nature of light and colors in his Micrographia—namely, that light arose through movement and that everything that was shining was vibrating in some way. He also said that there were only two basic colors—red and blue. When pulses of light came into contact with the eye, these two color impressions were created, and where they were superimposed on one another, “many sorts of greens” arose.10

This was a bit sparse for a complete theory. Hooke himself wrote in his book: “It would take a little too long to explain all of that in detail and to prove what kind of movement is responsible.” And: “It would take too long to insert here how I found out the characteristics of light.” This didn't prevent him from claiming that he had now explained all color phenomena in the world, however.

It's no wonder that Newton's reaction was a little unfriendly. Somebody who said he knew everything, but wouldn't say what exactly he knew or how he had attained this knowledge, was only likely to irritate somebody like Newton, who had after all stuck needles into his eyes in order to understand how light worked. Particularly since Newton had himself carried out experiments during his exile in the countryside which in his opinion clearly demonstrated that Hooke's theory of colors could not be correct.

Hooke, for his part, claimed that he himself had already carried out the experiments that Newton described in his article, and this much earlier, and that Newton had also falsely interpreted the findings from the experiments. Newton was outraged at this. For him, the “most considerable detection” announced in his letter was not merely a simple observation. It was a mathematical certainty that he was presenting here to his colleagues. It was not a hypothesis, not an assumption, but rather the beginning of a new, mathematical understanding of optics. He had found the ultimate solution to one of the mysteries of nature and this “without any suspicion of doubt” as he wrote to Secretary Oldenburg. He had drawn up a hypothesis and developed an experiment that confirmed his statement about the nature of light and colors. Hooke's theory, on the other hand, was “not only insufficient, but in some respects unintelligible.”

Newton seemed incapable of putting himself into the position of his peers. Yes, his explanation of light and colors was indeed (largely) correct. But he had come up with it years before and had had more than enough time to consider it and improve it. In the same period of time, he had developed his new theories of mathematics and physics and was accustomed to having completely new and innovative ideas which went far beyond what was known to the rest of the world. Now he was firing these revolutionary ideas without warning at the rest of the world, and he shouldn't have been surprised that it would take a little time before people could appreciate them. He should have been expecting criticism at first, but he wasn't. His first appearance in the scientific public eye must have seemed to him to be quite a disaster.

JUST LIKE IN KINDERGARTEN

Over the next few years, there was lively correspondence between Newton and the members of the Society. Ten critical articles were published in the Philosophical Transactions and eleven times Newton sent angry replies to this criticism. He was particularly upset that his discoveries about light were always referred to as “hypotheses.” And he was extremely irritated when Hooke was the author. For Newton, his optical theories were mathematics and not some goddamned hypothesis. He refused to accept such a claim from anybody—particularly not somebody like Hooke, who had absolutely no understanding of the true nature of light. Newton was not prepared to permit any criticism of his work, even when it might have been valid for once. The Dutch scholar Christiaan Huygens, for instance, noted that white light is not only obtained when all the colors are mixed; two colors are sufficient, as long as they are the right ones, like blue and yellow.11

Huygens was right, but that didn't diminish Newton's rage against the Dutchman. He took criticism as badly as a small child, and behaved just as sulkily. He even announced that he would leave the Royal Society, in order to “avoid such things in future,” as he wrote.

He didn't actually make good his threat, of course. Instead, he wrote another article about optics, containing his thoughts on the true nature of light. As defiant as ever, he specifically titled it a “hypothesis,” one “explaining the Properties of Light, discoursed of in my several Papers.” But regardless whether he was producing mathematical certainties or hypotheses, criticism still only provoked antagonism in Newton. His dispute with Robert Hooke entered its next phase: Hooke believed that light consisted of waves, while Newton thought it was a current of particles. Hooke said that he had done an experiment that showed the wave nature of light. Newton explained that this experiment had been carried out by other scientists much earlier and Hooke shouldn't call it “his” experiment. Hooke accused Newton of having copied out the hypotheses in Micrographia without stating his source. In other words, the two of them behaved as though they were in kindergarten.

The question as to whether light is a wave or consists of particles was definitively answered, not by either Newton or Hooke, but instead a few hundred years later by a new revolution in science—the development of quantum mechanics. Meanwhile, Newton and Hooke did pause in their quarrelling—but not for long, with the next round being even fiercer. Newton also stopped publishing his works for the time being, and his mathematical writings, which had been intended for publication after the works on optics, remained unknown to most of his peers, while he kept his work on gravity completely to himself. Newton's first exposure to the criticism of his colleagues seems to have discouraged him so much that he preferred to say nothing more, rather than face public judgment. His work was indeed ingenious and revolutionary. But hardly anybody learned anything about it because he had no desire to be criticized—in other words, because he was a shrinking violet.

GOOD CRITICISM IS HALF THE BATTLE

In the world of science today, Isaac Newton's attitude would be disastrous. Constant review is the foundation on which modern research is based. Naturally, it isn't always a pleasant experience to expose oneself to criticism, but it is nevertheless indispensable. What the Royal Society did with Newton's article about his theory of light and color is now a standard process and is called a peer review.

The actual research work still forms the basis of all scientific findings. But in order for these to be taken seriously, they need to be published. And before this can happen, they need to be exposed to a review. If you want to publish scientific results, you have to submit them to a specialist publication, where an editor will first decide whether the research in question is sound or just complete nonsense. This initial review is based on rather formal criteria: does the subject fit in with the publication's focus? Is the text sufficiently well-written? Have the authors kept to the standard structure, presented their methods and findings in a suitable way, and provided appropriate sources for their assertions? And so on and so forth. Once an article has passed this first test, the actual peer review follows.

The editor chooses one or more reviewers. These are just normal scientists who work in the same field as the authors of the article in question. They are experts in the type of research that is being presented (or at least they are supposed to be) and it is their job to test the detail of the article's content. The reviewers then take a very close look at the work and attempt to reproduce the results. They check for mistakes and indicate when, in their opinion, there are unresolved questions, flaws in the methods, or problems with the conclusions. According to what they find, they then advise the editor to accept or reject the work for publication. The authors typically receive a detailed list of questions and suggestions for improvement, and these are to be answered and implemented. If they can do this to the satisfaction of the reviewers and the editor, the work can then be published.

This peer review process is designed to minimize the number of false research results that are published. Of course, it doesn't always work to perfection. Even the best reviewers can overlook mistakes. Or they don't take enough time for their assessment.12 The subject is often so specialized that there is barely anybody who knows enough about it, and those that do are generally either colleagues or direct competitors of the authors and thus not fully objective. Despite all these flaws, however, the peer review process is still indispensable in modern science. If you don't expose yourself to this process, you can't have your work published. And those who don't publish any work don't really count—“publish or perish,” as the saying goes.

Scientific careers are judged in terms of your publication lists. The more you have published, the better your chances of getting a good job or more funding. It's not an ideal state of affairs, of course—there are plenty of other criteria that ought to be taken into account: dedication to teaching, for example, or commitment to public relations work. But as long as having work published is the ultimate benchmark, then it is necessary not only to be able to tolerate your peers’ criticism—you need to actively seek it.

Besides publication in specialist journals, attending symposia is also part and parcel of a natural scientist's life. Here, you can present your work to your peers, mostly with a lecture, which is inevitably followed by the part where the audience can ask questions or pass comment. The peer review process is mostly impersonal and anonymous; the authors don't generally know the names of their reviewers. The Q&A session following a lecture, on the other hand, is extremely personal and public. Many young scientists fear their first appearance at a major conference—not always without justification. Rivalries and bitter animosity were not only a feature of Isaac Newton's time—today as well you can witness fierce quarrels at conferences. Some people are kind enough to give you their feedback in private, but others have no qualms about provoking an argument in front of the assembled crowd.

The criticism isn't always justified, but in most cases one would do well to at least think about it. The real aim of the peer review isn't to discover actual fraud or deliberately manipulated results. It is to check for the mistakes that all people inevitably make. Ideally, science should be completely objective, but we do find it incredibly difficult to think in this way. We are subjective creatures—that's just the way it is—and perhaps we just overlook certain mistakes because the results seem to fit in so well with our ideas.

Years ago, for example, I was investigating the planet system of the Beta Pictoris star. That is to say, I was investigating the question whether there can actually be any planets there. I was keen to deduce the existence and characteristics of possible planets based on certain conspicuous features in the observation data available. I then carried out comprehensive computer simulations and was delighted to finally be able to explain all of these features with the presence of a single planet. It was an elegant solution to the problem and I was looking forward to writing up my findings at last and publishing them in an article. First, however, I sent the whole thing to a colleague and asked him for his opinion. He replied a few days later by email: “Something isn't right—the results look too good to be true. I'd be surprised if they really are correct.” My initial reaction was similar to Isaac Newton's—I was annoyed and angry that I had even bothered to show him my work. What did “too good to be true” mean? Of course the results were okay—if somebody was wrong, it was him and not me! Nevertheless, I had another look at the work and was forced to admit that I had indeed overlooked a small and insignificant flaw in my computer program. A flaw that would normally have been of no consequence but had here produced the exact result that I had wanted. It is precisely for such cases that the peer review process is required. Scientific procedures are designed to protect us from ourselves, as far as that is possible. But this is only made possible by constant criticism, which we have to seek out, listen to, and finally also accept.13

Sometimes, though, it really is difficult to take criticism. Even the best scientists can have problems doing so. Albert Einstein was actually an affable man. But there was at least one occasion when he was just as defiant as Newton when it came to criticism of his work. In 1936, he and Nathan Rosen wanted to publish an article about the existence of gravitational waves. In a publication twenty years previously, he had predicted that accelerated mass gives off energy in the form of gravitational waves. In his new article, however, he now came to the conclusion that gravitational waves didn't exist after all. He submitted the article to the Physical Review journal, and the editor sent the text to a reviewer. The reviewer concluded that Einstein and Rosen had made a mathematical mistake. Einstein then wrote to the editor: “We (Mr. Rosen and I) had sent you our manuscript for publication and had not authorized you to show it to specialists before it is printed. I see no reason to address the—in any case erroneous—comments of your anonymous expert. On the basis of this incident I prefer to publish the paper elsewhere.”14

He was so upset by the reviewer's comments that he decided never again to publish work in the Physical Review, a vow he kept until the end of his life. The article on gravitational waves was published one year later in another journal. However, it appeared in a corrected form and with the conclusion that gravitational waves could actually exist. Einstein had obviously taken the criticism to heart after all and let go of his uncharacteristic defiance.¹⁵

Those who wish to work in science today have to be able to live with constant evaluation by their peers. If you can't take criticism, then you're in the wrong profession. Those who want to be successful have to both seek and accept other people's judgment. Being a genius like Isaac Newton is highly useful, but it doesn't shield you from criticism—on the contrary—and Newton himself was forced to realize this when he next entered into dispute with Robert Hooke.