If Isaac Newton had achieved nothing else in his life other than finding a mathematical demonstration of gravity, that would still have been enough to ensure he went down in history as one of the most important scientists of his time. The Principia—finally published in 1687 in spite of all the difficulties and a dreadfully expensive historical treatment of fish—has three volumes, however, and these contain much more than just a few ideas about gravity.
ON THE SHOULDERS OF…
The physics Nobel Prize winner Steven Weinberg said the following about Newton's work: “All that has happened since 1687 is a gloss on the Principia,”1 which may be a bit over-the-top, but only a bit. Despite its fundamental and timeless significance, however, the work is as difficult to read today as it was back then. The fact that the Principia is such an onerous read is not only due to its (mathematical) contents, but is also thanks to Newton himself, since he deliberately made sure that his work was incomprehensible.
Nevertheless, it is worth taking a closer look at the Principia, which goes beyond the law of gravity and, for instance, deals with the following question: gravity is a force of attraction, but if it is indeed the case that every object in the universe attracts every other object, why doesn't everything end up in a giant heap somewhere in the cosmos? Why are there planets, moons, and comets moving along their paths around the sun in a somewhat orderly fashion? In order to answer these questions, Newton didn't only need a mathematical explanation of the force of gravity; he first required a sensible concept of what “motion” actually was. He had thought about this in his youth and he had of course studied the works of his predecessors. In his notebook, we can find the following statement: “Amicus Plato amicus Aristoteles magis amica veritas,” which roughly translates as “Plato is my friend, Aristotle is my friend, but truth is a better friend.” And Newton was right to place truth above ancient knowledge. The interpretations of the ancient philosophers’ insights still formed a large part of the academic tradition in the seventeenth century, but Newton recognized that he needed to go further and to actually cast doubt on their findings. Aristotle, for instance, was convinced that an object's motion could only change if the object came into direct contact with another one that caused this change. He also believed in a “natural movement,” by which he meant that some things always strived to move upward toward the sky (air, fire, smoke, etc.), while others naturally moved downward without any external impulse. The natural movements on Earth were different from those in the heavens, where natural movement always had to follow a perfectly circular path.
With the work of Copernicus, Galileo Galilei, and Johannes Kepler at the latest, people knew that the motion of the celestial bodies didn't quite work in the way the ancient Greeks had imagined. But it was still unclear in Newton's time what motion actually was and how it could be accurately explained. In 1664, one year after Newton's birth, the French mathematician and philosopher René Descartes published his major work Principia Philosophiae. In these Principles of Philosophy, he pondered the nature of all manner of things, including the motion of the celestial bodies. He developed a vortex theory, according to which the cosmos was filled with a kind of liquid celestial matter called “ether.” All objects moved within this ether and their motion was caused by vortices emanating from the sun. Like Aristotle, Descartes was convinced that mechanical contact between the mover and the moved was necessary and so a vacuum could not therefore exist. The ether between the planets was needed so that the sun could drive it like a motor with its rays and thus set the entire cosmos in motion.
But Newton was not merely concerned with motion in the heavens. In his Principia, he wanted to answer two questions: How can motion in general be understood and explained? And how can one use this explanation to understand both the motion of the celestial bodies and that of objects on Earth? In his preface to the Principia, Newton makes it clear that, unlike Descartes, his aim is to grasp and explain natural phenomena using mathematical rules. He considered the Frenchman's philosophical approach to be nonsense—one might be able to use it to “make a name for yourself…[but it] is hardly better than a fairytale.”
Newton described the aim of his own work in an astonishingly modern way: “from the phenomena of motions to investigate the forces of nature, and then from these forces to demonstrate the other phenomena.” That's exactly how modern natural sciences work. One observes certain phenomena in nature and tries to deduce from them principles and theories with which one can make much more general statements and predictions about still unknown phenomena. This wish not simply to explain specifically why the moon orbits the earth, but to find a universal explanation, is made clear by Newton in another part of his introduction, when he describes what exactly he wishes to investigate: “the science of motions resulting from any forces whatsoever.” He is concerned not only with gravity, but also with everything that might have any sort of influence on the motion of objects.
THE INVENTION OF A NEW LANGUAGE
In order to achieve such a general understanding of nature, Newton first needed a completely new language. Words like “force,” “mass,” “momentum,” “space,” or “time” are clearly defined in the world of science today. But Newton didn't have such definitions at his disposal, and he accordingly faced a struggle when it came to finding clear descriptions. What is a “force” in a physical sense? How can it be demonstrated and how is it measured? Using the official standard unit, the “Newton,” of course, as all schoolchildren learn today in physics classes! But how did this unit come about?
In the notebooks of his youth, Newton wasn't yet decided which word he should use for which meaning: “power,” “efficacy,” “vigor,” “strength,” and other similar terms are used interchangeably. They all have connected meanings, but for a mathematical natural philosophy of the kind Newton wanted to create, he needed clear definitions, not a dictionary of synonyms.
It is precisely with a list of such definitions that Newton's Principia begins. He starts off with mass, defining the mass of an object as the amount of material contained within it, and also explaining that in his definition he has no need for any old “ether” or anything else which might be found between the parts out of which an object is composed. Definition number two in the Principia is concerned with the highly important quality of momentum. Newton calls this “quantity of motion” and explains that it is measured using the speed and size of the material (i.e., the product of the mass and velocity). Of at least equal importance for Newton's physics is the third definition. Here he explains that “inertia” (or vis insita, as he calls it) is the characteristic with which every object works against a change to its current situation (either at rest or in motion). And he uses this definition in order next to establish what a “force” is: namely, an action that is exerted on an object in order to change its state of motion.
If all of that sounds a bit trivial from today's perspective, it just goes to show how much Newton's work has seeped into our very consciousness. Newton had just found his language, and what he had to say with it remains unforgotten by physics even after all these centuries. In the next part of the Principia come the three “laws” or “axioms” that bear Newton's name today and which can be seen as the founding stone upon which modern physics was built.
In their brief and precise choice of words, the three Newtonian axioms are expressed with an almost irresistible elegance:
1. “Every body perseveres [remains] in its state of rest, or of uniform motion in a right [straight] line, unless it is compelled to change that state by forces impressed thereon.”
2. “The alteration [change] of motion is ever proportional to the motive force impressed; and is made in the direction of the right line in which that force is impressed.”
3. “To every action there is always opposed an equal reaction; or, the mutual actions of two bodies upon each other are always equal, and directed to contrary parts.”2
In his first law, Newton describes a universe in which everything is either at rest or moving in a regular fashion along a straight line. Once created, everything remains as it is and nothing changes. Since our universe is obviously not made like that, however, Newton's second law explains what is required to change an object's state of motion. Each and every change is caused by a force acting. How the motion is changed depends on the direction and the strength of the force.
Newton explains that the force corresponds to the temporal change of momentum. Everybody learns the modern formulation of the second law at school as the basic equation of mechanics: force = mass times acceleration.3 The third law may sound a little confusing at first, but it is no less important than the first two. Only with its help is it possible to explain how several masses influence each other. Newton provides a pithy explanation: “If you press a stone with your finger, the finger is also pressed by the stone.” Or to express it a bit more scientifically: when a force acts between two objects, the momentum of both objects changes to the same degree. Since the momentum is the product of mass and velocity, however, the change in velocity depends on the objects’ individual mass.
Newton deduced everything else from these three fundamental statements,4 and his explanation of gravity also originates from them. The first ideas for how to explain lunar motion, about which Newton and Hooke had quarreled so bitterly, were based on a balance of forces: one force which becomes weaker with the square of the distance and emanates from the center of the earth, and a centrifugal force that acts outward and prevents the moon from falling down on the earth.
Newton's laws now enabled a more elegant explanation for the motion of the moon. The first law states that the moon actually moves through space along a straight line. This straight line is thus the “natural” state of its motion and so, if the moon doesn't follow a straight line—which is of course the case—then something must be responsible for this. This something is a force—one force and not two forces that need to be balanced out. The force that makes the moon deviate from the straight line and follow its curved path around the earth must originate in the earth itself; it is a so-called “centripetal force,” i.e., a force that is always directed at a certain point (Newton described such a force in definition five in the Principia). Every object that moves along a circular path must be controlled by a centripetal force at the center of its path.
A UNIVERSAL FORCE
What Newton is telling us, therefore, is that the moon doesn't fall to the earth, but rather toward the earth. And it is doing this constantly. The moon strives to move along its straight line, but is accelerated toward the earth by the centripetal force being exerted by the earth. Not just once, but in every single moment—it falls around the earth.5 There is nothing here yet about a “force of gravity,” however. To begin with, Newton only showed that the change in the moon's motion along its path must be caused by a force that is inversely proportional to the square of the distance from the earth.
Only later did Newton calculate how strong the force exerted on the moon must be: the moon has to fall 151/12 “Paris feet”6 toward the earth each minute in order to follow the orbit that can be observed. If that is how strong this force is despite the distance of the moon, and it is inversely proportional to the square of the distance, how strong must its effect then be on objects near the earth's surface, for example a falling apple? The force must be stronger here, and so the apple must fall more quickly to the earth than the moon. Newton's answer: the said apple would fall 151/12 feet per second, i.e., sixty times faster than the moon, which takes a minute for the same distance. That being said, science historians today are pretty sure that Newton must have played around with the figures a bit in order to get a perfect match at the end of his calculations. This changes nothing about the validity and brilliance of his theory, though it is further evidence of how far Newton was prepared to go to avoid potential criticism of his work.
The motion of the moon and the apple can therefore be explained by a single force. The force that causes the apple to fall in the direction of the earth's center is, at a greater distance, as strong as the centripetal force emanating from the earth that causes the moon to fall around the earth. Newton concluded that this centripetal force was the force of gravity. There is no difference and so it is pointless to differentiate them.
What is true of the earth and the moon is also true of the sun and the earth. Or the sun and comets. Or Jupiter and its moons. And thus Newton finally arrives at the peak of his findings about the motion of the celestial bodies and writes: “The force which retains the celestial bodies in their orbits has been hitherto called centripetal force; but it being now made plain that can be no other than a gravitating force, we shall hereafter call it gravity.”
That's what the story of the apple and the moon is really about. Not the “discovery” that there is a force of gravity that makes things fall to the ground, and also not the fact that this falling can be mathematically explained by a force that is inversely proportional to the square of the distance. That is certainly important, but of greater importance is the fact that Newton could clearly establish that gravity is universal; that it is this single force that keeps the cosmos in motion and ensures that the stars, planets, comets, and moons move around each other.
“It remains that from the same principles I now demonstrate the frame of the System of the World,” he writes. People would have imputed delusions of grandeur to any other scientist making such a declaration, but not to Isaac Newton. And in his Principia he did indeed do nothing less than explain the “System of the World.”
THE MAN WHO DIDN'T WANT TO BE UNDERSTOOD
It is just a slight shame that Newton took such little trouble in this revolutionary work to make it comprehensible. Much to all his contemporaries’ surprise (though not his own), he was in a position to explain the entire cosmos. You might have thought that he would want to share this with as many people as possible. But Newton, being Newton, had different ideas.
From the beginning, he had planned his Principia as a mathematical text and that's indeed what it was. Not only that, it was a text that was based on a completely new form of mathematics. In order to explain the motion of the celestial bodies and all the other dynamic phenomena, Newton required the mathematics that he had developed years before (see chapters 3 and 7), the mathematics that allowed him to explain the infinitely small and the infinitely large and to grasp changing values. This branch of mathematics, known today as differential and integral calculus, is a powerful tool without which the Principia could not have been composed. But when he wrote the book, Newton didn't bother sharing his new methods with the world.
Like at the beginning of his scientific career, when he had inhibitions about making his mathematical discoveries public, he was not prepared to do so now. Newton could have used his new analytical language7 in order to derive and prove his conclusions about the universe as clearly and simply as possible. Instead, he used the existing language of geometry: the Principia is full of circles, intersections, lines, geometrical shapes, and other complicated and abstruse diagrams.
Mathematically speaking, Newton compressed his thought processes to an extreme degree and all too often didn't bother to write down the intermediate steps he had taken (especially when they were connected with his new mathematical method). That made it difficult or even impossible for many of his contemporaries to follow his work. The philosopher John Locke, for example, didn't even bother trying. He only read the part of the Principia that includes the results and for the rest he simply asked the Dutch scientist Christiaan Huygens whether Newton's mathematical deductions could be trusted.
That was precisely Newton's plan. He didn't want everybody to be able to understand what he had written because, as we already know, he was a shrinking violet and had no desire to be criticized. “He designedly made the Principia abstruse,” wrote the clergyman and natural philosopher William Derham in a letter in 1733. He said that Newton had told him that he wanted to avoid “being baited by little Smatterers in Mathematicks” and only true mathematicians should be able to follow what he had achieved. In the introduction to the third volume of the Principia, Newton himself writes that he had actually intended to publish a version comprehensible to the general public, but had decided against this, because “such as had not sufficiently entered into the principles could not easily discern the strength of the consequences, nor lay aside the prejudices to which they had been many years accustomed, therefore, to prevent the disputes which might be raised upon such accounts, I chose to reduce the substance of this Book into the form of Propositions, which should be read by those only who had first made themselves masters of the principles established in the preceding Books.” Newton clearly wasn't interested in the general public reading his work and wanted his audience to consist of experts. Such an attitude is perhaps understandable given his experiences, but it isn't particularly congenial, nonetheless.
The contents of the Principia certainly deserved a wider audience. Planets, comets, centripetal forces, momentum, and inertia might have been a bit too abstract for the average layman at the time. But Newton demonstrated in the third part of his work what his theory was capable of achieving. With it, not only the heavens but also many phenomena on Earth could be explained, and the most impressive example of this, and the one that was most entwined with people's daily lives in Britain at the time, was certainly the tides.
THE WILD NATURE OF THE TIDES
It is one of the ironies of history that it was Isaac Newton, a man who probably never saw the sea in his life—he spent his life in Woolsthorpe, Cambridge, and London, away from the long coastline of the British Isles—who finally found a practical explanation for the phenomenon of high and low tides. On the other hand—who, if not Newton, could have done so? Even though he never saw the sea, the world of mathematics in his head contained everything that was needed for such an explanation.
This was long overdue. Back in ancient Greece, unsuccessful attempts had been made to find one. One of the first (or at least one of the first we know of) to try to find the cause of the tides was the Greek geographer Pytheas, in the third century before Christ. He traveled from the Mediterranean as far as England and was subsequently convinced that the moon definitely had a role to play in the matter. But he had no idea what form this influence might have. The other Greek scholars, too, had little to contribute to clarifying the issue. In the Mediterranean, the tides are not particularly pronounced,8 and it was difficult to obtain decent observation data. In the Middle Ages and the early modern period, there was no shortage of attempted explanations with differing degrees of absurdity. The Anglo-Saxon Benedictine monk Beda Venerabilis, born in the seventh century, also considered the moon to be responsible for the tides and thought that it “blew” on the sea and thus moved the water. In the thirteenth century, the Persian scholar al-Qazwini surmised that the sun and moon heated the water of the seas, with this leading to it spreading out at regular intervals. The (re)discovery of America at the end of the fifteenth century inspired the Italian natural scientist Julius Caesar Scaliger to believe that the water swashed back and forth between the European and the American continents. Johannes Kepler was on the right path in the seventeenth century, and supposed a force of attraction exerted by the sun and moon on the water of the oceans—but he thought along the lines of something similar to magnetism; his contemporary Galileo Galilei, on the other hand, believed this was nonsense and sought the cause of the tides in the rotation of the earth. René Descartes once again brought his vortices into the equation—but nobody could really provide a logical explanation for how the whole thing actually worked in detail.
Nobody apart from Isaac Newton, of course. He had created the tools to be able to calculate exactly how strong the moon's gravitational pull was on the earth. He also knew how to calculate the combined influence of several different forces and could show that the moon's influence alone was not enough to explain the alternating high and low tides observed. Both the moon and the sun together with their combined forces of gravity are responsible. The height of the tides depends on the relative position of these two heavenly bodies. Sometimes, their influences complement one another, sometimes they partly work against each other—but Newton was able to irrevocably prove that it was gravity we have to thank for the tides.9
Many readers of the Principia were extremely surprised by Newton's analysis of the precession10 of the earth's axis. The phenomenon itself had been known since ancient Greek times: the direction in which the rotation axis of the earth points is not always the same, but rather changes over time. Today, its northern point is directed almost exactly toward the North Star. This was not always true, however, and will also not be the case in the future. The axis describes a small circle in the heavens, for the completion of which it requires about 25,800 years.
The first person to describe this phenomenon was the Greek astronomer Hipparchus in the second century BCE. Just like with the tides, there were numerous attempts to explain the phenomenon. Ptolemy, for instance, who was fully convinced that the earth was fixed at the center of the universe and therefore couldn't rotate around its axis, considered precession to be a slow rotation of the heavens themselves. Later astronomers, who had a heliocentric view of the world, correctly recognized that it must be connected to the rotation of the earth—but nobody knew exactly how it happened. Until Isaac Newton came along and simply demonstrated it in his Principia.
A few chapters earlier, he had looked into another longstanding question: What form does the earth have? Like all other learned people before and after, he knew that it was not a disk,11 but a globe, though not a perfectly round one, as he could work out with his theory about forces and motion. The rotation of the earth around its axis and the centrifugal force resulting from this lead to (put very simplistically) material being pressed “outwards” toward the equator. If we measure the radius of the earth from its core to one of the poles, the distance is slightly less than if we measure it to the equator.12 The earth bulges out a little at the equator, and this thickening creates precession: because the gravitational fields of the sun and moon have a greater surface area on which to work, this makes the earth wobble while rotating. This is precisely what Newton was able to work out and, at the end of his analysis, he arrived at a value for the speed of the precession that more or less matched what was observed.13
The extracts about the earth's form, the tides, and the precession of the earth's axis are perhaps the most astonishing parts of the entire Principia. The starting point for the work on the book was the question about the form of the orbital paths of comets. In the course of his answer, Newton not only created a completely new theoretical basis for explaining forces and motion and demonstrated that the force that keeps heavenly bodies moving along their paths is a universal one; he was also able to provide concrete evidence that the sun and the moon affected the phenomena of the earth itself with the same force of gravity. Universal gravity is much more than just a simple formula to calculate orbital paths. It is what gives the universe its form and dominates the entire cosmos in every aspect.
The Principia is one of the great masterpieces of humanity, comparable with the Mona Lisa, Beethoven's Ninth Symphony, or the Pyramids. Yet in contrast to art and culture, Newton's system of the world and what his successors constructed upon it are still understood and appreciated by far too few people.
BETTER TRANSPARENT THAN SORRY
Isaac Newton was not in the least concerned to make his research accessible to his colleagues or the general public. And I fear that he wouldn't have any problems getting away with this in the world of research today. Like back then, public relations play far too minor a role in science today.
Which is astonishing: of course research is still the main thing in science, but unlike in the seventeenth century, we live in a world today that is very much shaped by the insights and results of scientific research. What Newton and his peers found out was certainly revolutionary, but generally speaking it had nothing to do with most people's day-to-day lives. Today, things are different. Biogenetics, stem cell research, renewable energy, pharmaceutics, climate change, nanotechnology; not only is research carried out in all these fields—they also have a direct influence on our daily lives. Politics and society have to make the appropriate decisions and decide where and how the new knowledge gained can or may be used. That can only seriously happen if society, at least to an extent, understands these issues. Public relations in science is therefore indispensable, and not only in the context of applied research. Providing information about (seemingly) abstract basic research is also crucial if we do not wish to live in a world that is becoming more and more incomprehensible for more and more people. The computers that we use every day are based on the findings of quantum mechanics. The algorithms that show us personalized advertising on the internet and, without our noticing, evaluate our personal data, have their origins in abstract mathematics that could also come from Isaac Newton himself. And so on and so forth: if we want to have a tiny bit of control over the world in which we live, we have to know at least a little about science.
It would also be in the interests of scientists themselves to engage in as wide a range of public relations work as possible. Most of them work at state universities or research institutes and are funded by taxpayers’ money. The public therefore has the right to receive information about the use of its money. But even if one doesn't care about that, one should care about the people who distribute the money. If the politicians have to save money, they will do so where they can expect least resistance from the general population. The more and the better the public is informed about the reasons and necessity for research, the simpler it is for scientists to get funding for their work.
In Isaac Newton's day, science was still to a large extent a private hobby for well-to-do men and they could afford to ignore the public. But today, it should actually be taken as self-evident that the findings of science should be communicated to as many people as possible. Nevertheless, the idea of the “ivory tower” in which scientists carry out their work, cut off from the rest of the world, is unfortunately still somewhat more than just a cliché.
If you want to have a successful career in science, there is still one thing above all that you need to do: publish scientific papers. The range and quality of your publication list are the number 1 assessment criterion when it comes to getting a job or receiving funding for a research project. If you spend too much time on public relations, then you will be displaced by those who don't bother with that and instead prefer to publish a few articles.
Somebody like Isaac Newton, therefore, who concentrated exclusively on research and had no interest in interaction with the public, would still get along very well in the world of science today. But I still wouldn't recommend basing oneself too much upon him in this regard. There is still the hope that the current situation will change some time. Slowly but surely, the scientific funding organizations and big research institutes seem to understand that it is worth communicating directly with the public. In the USA, for example, it is already almost a matter of course that every major NASA space mission is accompanied by special social media appearances to provide information to the public. In Germany, too, young scientists address the public in YouTube videos, internet blogs and podcasts, or appear at Science Slams in order to present their research in a clear and fun way. Sooner or later, the value of science communication will find its way into the structure of the universities and then it will hopefully be beneficial rather than detrimental to one's career to devote oneself to public relations.