The Principia was concerned, mostly, with Galileo’s heliocentric model: the orbit of the planets around the sun. Increasingly accepted as consistent with reality, Galileo’s solar system was still plagued with questions. Galileo himself had solved some of its major problems, but by no means all of them. He believed that heliocentrism was the best explanation for the movement of the tides, and his telescopic observations had revealed that it was possible for planets to rotate around heavenly bodies that were not the earth. His experiments with weights, whether or not dropped from the Leaning Tower, had shown that the earth could be rotating without objects flying off its surface.
But he had not tried to explain how the force that caused weights to drop (the gravitas, or “heaviness”) worked. In fact, although he had disproved some of the central aspects of Aristotelian physics, he had held on to the vaguely Aristotelian idea that gravitas was an intrinsic property of physical objects, not an outside force that affected them.5
And Galileo could not explain why, if planets orbited the sun, calculations about their circular orbits didn’t account for their movements. His contemporary Johannes Kepler had proposed laws for elliptical orbits that yielded much better results—but neither Kepler nor Galileo had been able to explain why the orbits should be elliptical rather than circular. In the Galilean universe there was no force, and no property possessed by physical bodies, that would propel a planet into an ellipse rather than a circle.
This was the presenting problem that Newton solved.
He did so by extending the results of Galileo’s earthly experiments with weights into the heavens. Galileo had theorized that the gravitas of objects meant they would continue to travel at the same rate, no matter how far they fell; Newton suggested that gravitas was not an inherent quality, but a force, exerted by the sun on the planets and by planets on the moons surrounding them. The same gravitas that drew Galileo’s objects to the earth also drew the moon toward the earth—but the strength of this force did not remain the same over distance. It changed. As the planets moved farther from the sun, the force that pulled on them weakened—thus, the ellipse.6
To fully explain the laws governing this new force—most vitally, the relationship of the distance between two objects and the strength of the gravitas between them—Newton had to come up with an improved mathematics, capable of accounting for continual small changes. This new math was a “mathematics of change,” able to predict results in a setting where conditions were constantly shifting, forces altering, factors appearing and receding.7
So, the Principia performed two groundbreaking tasks simultaneously. It explained the why behind the ellipses of the planets—and, in doing so, revealed for the first time a new force in the universe: the force of gravity. It also introduced an entirely new branch of mathematics; a dynamic mathematics that became known in the seventeenth century as calculus: from the Latin word for “pebble,” one of the tiny stones used as arithmetical counters.*
•
The four books of the Principia lay out the rules by which gravity functions. Throughout, Newton establishes and makes use of three principles (Newton’s Laws of Motion):
Books I and II establish these laws of motion, both in the abstract (without any friction present) and in the presence of resistance; the third book discusses gravity as a universal force.
None of this is easy going. The title of the Principia points to the book’s greatest difficulty: it is composed largely of impenetrable mathematical explanations, laid out in Newton’s new calculus. William Derham, Newton’s longtime friend and colleague, later wrote that the book’s obscurity was deliberate. Newton had confided in him that, since he “abhorred all Contests,” he “designedly made his Principia abstruse,” in order to “avoid being baited by little Smatterers in Mathematicks.” Since “little smatterers” is probably an accurate description for the majority of interested modern readers, including myself, the bulk of the Principia remains out of reach for most of us. (This isn’t necessarily a failing of modern education. As James Axtell has observed, Newton’s strategy “effectively rendered the Principia unintelligible . . . to the virtuosi and intellectual laymen” of his own day as well; a frustrated Cambridge undergraduate famously remarked, as Newton passed him on the street, “There goes the man who has writt a book that neither he nor any one else understands.”)8
But there are two sections of the Principia in which Newton abandons his dense formulaic prose and writes clearly: the “General Scholium” (which is to say, “Overall Explanatory Remarks”) at the very end of the entire Principia, and the “Rules for the Study of Natural Philosophy” that come at the beginning of Book III.
The “Rules” are, in a way, Newton’s final response to the Royal Society. He was aware that the conclusions of the Principia could be dismissed by the literal-minded as “ingenious Romance”—mere guesses, airy speculations. After all, he had not actually experimented with the moon, or spun planets at different distances from the sun to observe the rates of their orbits. Instead, he had taken the results of experiments carried out on the earth and had extrapolated their results into the heavens—a method that the pedantic Royal Society might not applaud.9
The “Rules” explain why Newton’s conclusions about the movements of the moon and planets, while not experimentally proven in the way that would make Hooke happy, are nevertheless reliable. The first three are:
1. Simpler causes are more likely to be true than complex ones.
2. Phenomena of the same kind (for example, falling stones in Europe and falling stones in America) are likely to have the same causes.
3. If a property can be demonstrated to belong to all bodies on which experiments can be made, it can be assumed to belong to all bodies in the universe.
The “Rules” do not appear in exactly this form in the first edition of the Principia, although Newton’s conclusions make clear that he was certainly operating with them in mind. Not until the second edition, published in 1713, was he able to put his working assumptions into words. And he did not add his fourth and final rule until the third edition of the Principia, in 1726:
4. A general theory that is based on specific phenomena or experimental results should be considered true unless new phenomena or additional experimental results make another theory more likely.
This is Bacon’s inductive reasoning, always progressing from specifics to generalities, but extended by Newton to breathtaking lengths: across the entire face of the universe.
But the “General Scholium” (which also contains a famous discussion of the place of God in natural philosophy) places limits on the method. Gravity, Newton explains, is a force
that penetrates as far as the centers of the sun and planets without any diminution of its power to act, and that acts not in proportion to the quantity of the surfaces of the particles on which it acts . . . but in proportion to the quantity of solid matter, and whose action is extended everywhere to immense distances, always decreasing as the squares of the distances.10
But, he cautions, “I have not yet assigned a cause to gravity.” He could deduce the laws of gravity from his experiments on the earth, but the reason for gravity lay beyond his grasp.
To go from laws to cause was, in Newton’s view, theorizing in the absence of proofs—the sort of grand paradigm-inventing carried out by the ancient philosophers. He calls this, scornfully, “feigning the hypothesis”: “I have not as yet been able to deduce from phenomena the reason for these properties of gravity,” he concludes, “and I do not ‘feign’ hypotheses.” He felt no need to provide a universal explanation for why the universe functions as it does—a theory of everything. In his “experimental philosophy,”
propositions are deduced from the phenomena and are made general by induction. The impenetrability, mobility, and impetus of bodies, and the laws of motion and the law of gravity have been found by this method. And it is enough that gravity really exists and acts according to the laws that we have set forth and is suffici
ent to explain all the motions of the heavenly bodies and of our sea.11
It is enough: with this, Newton was content. He had extended the reach of the experimental method across the universe, but he had also erected a boundary fence on its far side.
To read relevant excerpts from the Principia, visit http://susanwisebauer.com/story-of-science.
ISAAC NEWTON
“Rules for the Study of Natural Philosophy” and “General Scholium” from Philosophiae naturalis principia mathematica
(1687/1713/1726)
Readers who want to tackle the entire Principia have several options. The clearest modern translation, done by I. Bernard Cohen and Anne Whitman, is available in a massive 950-page paperback; the entire first half of the book is commentary, explanation, and how-to-read-this-difficult-book guidance.
Isaac Newton, The Principia: Mathematical Principles of Natural Philosophy: A New Translation, trans. I. Bernard Cohen and Anne Whitman, assisted by Julia Budenz, University of California Press (paperback, 1999, ISBN 978-0520088177).
Multiple editions of the 1729 translation by Andrew Motte are also available. Although dated, and in places inaccurate, the prose is not significantly more difficult than that of the Cohen and Whitman translation.
Isaac Newton, The Principia: Mathematical Principles of Natural Philosophy, trans. Andrew Motte, Daniel Adee, publisher (free e-book, 1846).
Isaac Newton, The Principia: Mathematical Principles of Natural Philosophy, trans. Andrew Motte, Snowball Publishing (e-book and paperback, 2010, ISBN 978-1607962403).
Selected excerpts from the Principia (including the “Rules” and parts of the “General Scholium”) and many other Newtonian writings, along with commentary, can be found in the Norton Critical Edition of Newton’s work.
I. Bernard Cohen and Richard S. Westfall, eds., Newton: Texts, Backgrounds, Commentaries, W. W. Norton (paperback, 1995, ISBN 978-0393959024).
* * *
* Isaac Newton and his contemporary Gottfried Leibniz were simultaneously, and independently, working toward this new “calculus.” Afterward, they fought bitterly about who had invented which aspects of calculus, and who had copied from whom; this quarrel takes up a lot of literature about Newton, but it is irrelevant to our interests here. A useful overview is found in Chapter 15 of Niccolò Guicciardini’s Isaac Newton on Mathematical Certainty and Method (MIT Press, 2009).
PART
III
READING
THE EARTH
Georges-Louis Leclerc, Comte de Buffon, Natural History: General and Particular (1749–88)
James Hutton, Theory of the Earth (1785)
Georges Cuvier, “Preliminary Discourse” (1812)
Charles Lyell, Principles of Geology (1830)
Arthur Holmes, The Age of the Earth (1913)
Alfred Wegener, The Origin of Continents and Oceans (1915)
Walter Alvarez, T. rex and the Crater of Doom (1997)
THIRTEEN
The Genesis of Geology
The creation of the science of the earth
The general history of the earth ought to precede that of its
productions.
—Georges-Louis Leclerc, Comte de Buffon,
Natural History: General and Particular, 1749–88
While physics and astronomy were flourishing, the study of the earth had remained mostly geographic.
The Greeks (of course) had created geography. Maps had been drawn since the days of the ancient Babylonians, but the conquests of Alexander the Great in the fourth century BC had suddenly opened up new possibilities to Greek mapmakers. A hundred years later, the librarian at Alexandria, Eratosthenes, wrote the first scholarly study of the earth’s topography. The three volumes of his Geographika (the earliest known use of the word) laid out a new, worldwide system of parallels and meridians. Not long after, the Greek astronomer Hipparchus used his observations of the moon to create the grid of lines that we now know as latitude and longitude, improving the accuracy of Greek-created maps even further.1
So earth science began. But Greek geography simply observed the present state of the earth’s surface. It offered no explanations about how the planet had come to be as it was, or why it functioned as it did. After all, Aristotelian philosophy held that the history of the earth was an infinite one, in which cycles of time were repeated ad infinitum; this did not suggest to the Greeks that research into the origin of the globe was even possible, let alone that it would be useful in understanding the world’s present form.2
Advances in chemistry and in physics provided some useful insights about physical processes taking place on the earth. But it was not until the science of the stars had begun to develop toward greater maturity that the earth itself (extraordinary, but now seen to be one heavenly body among many; sharing qualities with the wandering planets, but unique as the home of the human race) became an object of study. Geology, as Charles Van Hise observes, was the child of astronomy.3
During the first part of the seventeenth century, though, geology was not quite ready to take its place as a new science. It was merely another branch of natural philosophy, still wondering what questions to ask. And those first questions were asked not by astronomers and physicists, but by theologians and philosophers.
In 1647 the natural philosopher John Lightfoot used the genealogical accounts of the Old Testament to calculate the age of the earth. It had been created, he announced, in September of 3928 BC. Three years later, the Irish bishop and amateur astronomer James Ussher merged the Bible chronologies with his own astronomical observations, and placed the time of creation slightly earlier. “In the beginning God created the heaven and the earth,” Ussher wrote, in his Annals of the World. “The beginning of time, according to our chronology, happened at the start of the evening [midnight] preceding the 23rd of October, 4004 BC.”4
This was not exactly science. Still, the Christian and Hebrew tradition that the earth’s life span began at the moment of creation was an advance over the Greek tradition of endlessly repeating cycles. Assigning the earth a real, linear, chronological history suggested that its rocks and soil, its mountains and valleys, bore tracks of the actual past.
Nineteen years after Ussher set his date, the Danish clergyman Nicholas Steno, trained in anatomy at the universities of Copenhagen and Amsterdam before his ordination, published an essay about that past—the first real attempt at earth science.
The work, “Preliminary Discourse to a Dissertation on a Solid Body Naturally Contained within a Solid,” dealt with the puzzle of fossils: stone formations, often found in mountains far removed from the sea, that resembled living creatures. The first-century Roman philosopher Pliny had guessed that they were rocks fallen from the sky. The medieval philosopher and physician Avicenna suggested that they had been formed, mysteriously, by a “plastic” force in the earth that molded rock into new shapes. Robert Hooke, eyeing them under a microscope, had concluded that fossils were petrified remnants of living organisms, but he had been unable to explain why they were found in the midst of solid earth.5
Steno took Hooke’s conclusions a little further. In 1666, Steno had carried out a careful dissection of the head of a strange shark, caught off the Italian coast and sent to him by an influential acquaintance, Ferdinando II de’ Medici. The shark’s teeth were identical to small tooth-shaped fossils that Steno and other seventeenth-century natural philosophers knew well: glossopetrae, stones resembling tiny forked serpent’s tongues that had been gathered at numerous locations across Europe. The “Preliminary Discourse” aimed, first of all, to prove that glossopetrae, like the shark’s teeth, were parts of previously living animals; and second, to explain how they came to be contained in stone.
Steno’s explanation for the latter is obscured by clarifications, qualifications, unnecessary details, and unpruned language. But it can be pared down to three essential principles:
Steno’s Principle of Superposition. Layers of rock are formed when rock particles settle at the bo
ttom of water and are then compressed. So, lower layers of rock and artifacts were deposited earlier than higher layers.
Steno’s Principle of Original Horizontality. Layers of rock always form horizontally. If a layer slants, or runs vertically, it was pushed that way by later factors.
Steno’s Principle of Lateral Continuity. Layers of rock do not just end. So, if two layers of rock are near each other and have the same mineral content, soil content, and artifact content, but are separated from each other, they were originally the same layer but were disrupted by a later event.
All three of these principles point to the same deep insight, one that had never been articulated before: the layers of the earth, the strata (the “blankets” of rock and dirt that lie one on top of another) had been deposited, one at a time, over the course of many years. Digging down through them, the natural philosopher could travel back in time.
There was still no such thing as geology, but Steno had now made the invention of this science a possibility. He had identified the raw material that natural philosophers could exercise their Baconian methods upon: the earth’s layers, and the fossils within them, were the things that could be observed, analyzed, theorized about.
At once, that raw material began to cast doubt on the conclusions of the theologians and philosophers.
Steno himself saw no difficulty with the creation date of 4004 BC. He was convinced that fossils were remnants of living creatures that had settled at the bottoms of streams, and it stretched credulity that fragile objects such as shells and claws (even petrified) could last for thousands of years. In the “Preliminary Discourse,” Steno is clearly worried that a creation date of 4004 BC might actually be way too far back in the past.6
The Story of Western Science Page 11