by David Orrell
Buried in the quasi-mystical text was the last of Kepler’s three laws of planetary motion. Together, these stated that
the planets rotate around the sun in elliptical orbits;
orbiting planets sweep out equal areas in equal time;
the squares of the period are proportional to cubes of average distance from the sun.
These rules held for all the planets. Like the theorem of Pythagoras, they were general principles that could be applied in different cases. Kepler saw them as manifestations of a force, the anima movens (which he equated with electromagnetism), that swept the planets around the sun. He was perhaps the first scientist to see the universe as a system with an underlying dynamic. A good theory does more than just reproduce data; it also gives a sense of why things happen. It tells a kind of story. The search for order is a search for meaning. Kepler’s identification of a single, universal force was the precursor to Newton’s law of gravity. Just as Renaissance painters such as Leonardo da Vinci had knocked the fixed, crystalline halos off religious art with a new sense of dynamism and movement, so Kepler broke away from the ancient concept of planets in crystalline spheres to the view that they were actively propelled by dynamical forces. “My aim,” he wrote in a 1605 letter, “is to show that the machine of the universe is not similar to a divine animated being, but similar to a clock.”20
The need to search for order and pattern seems to be a fundamental characteristic of human beings. Science, like religion, is a way of structuring and making sense of the world, a kind of bastion against chaos. While Kepler was working on books with titles like Secret of the Universe and Harmony of the World, his own world was in complete turmoil. Several of his children died from diseases that seemed to come from nowhere; the countries where he lived were embroiled in religious wars; his career was in the hands of a rather unreliable emperor; he was denied university positions because of his battles with religious orthodoxy; and finally, his mother, at around the age of seventy, was accused by her townsfolk of being a witch.
It is this last that shows the negative, shadow side of our desire for order. In a time when a child could die for no apparent reason, or a whole village could be devastated by plague, or a city could starve because of crop failure, it is not surprising that people would try to find scapegoats. Kepler’s mother, like thousands of women across Europe, was one of them. She was apparently a strange, argumentative woman with an interest in folk medicine. We would probably call her odd, but in the Pythagorean scheme, which associated odd numbers with the divine and even numbers with conflict, her number would be even. A dispute with a neighbour grew, through gossip and innuendo, into the accusation of witchcraft. Specifically, she was charged with injuring seven people by giving them potions or hitting them, killing three more, and riding somebody’s cow late at night (this was part of the folk tradition about witches). She spent over a year in prison while her case went to trial. It was only the intervention of her son—himself somewhat compromised by his disagreements with religious authorities—that saved her from being tortured and burned to death. Such a fate was not uncommon, and in fact had been suffered by the aunt who raised her.
It didn’t play in Kepler’s favour that as a young student, he had written a short piece of early science fiction that illustrated Copernican theory by imagining a flight to the moon to view the earth from an outside perspective. In the story, the boy is given the power to fly by his mother, who summons the spirits to usher him into the sky. This is the kind of thing you don’t want read out at a witchcraft trial.21
About the only thing in Kepler’s life that was predictable was the planets. And even they took on a different appearance when an Italian astronomer called Galileo Galilei, son of the musician whose book on harmony Kepler had read, took a custom-modified version of a new instrument known as a telescope and aimed it at the heavens.
THE LITTLE ICE AGE
The cold winter that Kepler correctly predicted in 1595 occurred in the depths of the Little Ice Age, a period of unusually chilly weather in Europe, North America, and elsewhere that started around 1550 and didn’t end until the mid-nineteenth century. It is associated with the widespread advance of glaciers, the freezing of rivers such as the Thames, frequent famines, increased storms and floods, and even the decline of Viking colonies in Greenland and Iceland. The Little Ice Age is also reflected in the art of the time, like the winter landscapes of the Flemish painter Pieter Brueghel the Younger.
What caused the Little Ice Age? Some think the blame can be pinned on sunspots—intense electromagnetic disturbances that appear as darker areas on the surface of the sun. The solar radiation that we receive from the sun varies slightly in intensity; the lower the sunspot activity, the lower the total radiation. The Little Ice Age correlates with a period of reduced sunspot activity known as the Maunder minimum (though Galileo still managed to see a few). Sunspot activity also fluctuates over a period of about eleven years; the Victorian economist William Stanley Jevons believed this cycle was linked to agricultural production. While sunspot fluctuations are no longer thought to strongly influence the short-term weather, their electromagnetic pulses can disrupt satellite communications or even the power grid.
Many scientists believe that the Little Ice Age ended because of global warming; others argue that what we see as global warming is in part the natural ending of the Little Ice Age. In complex systems like the climate, the answers are rarely clear-cut.
AT REST VS IN MOTION
When science takes one of its occasional lurches forward, it is often because of some technological innovation. The magnifying glass had been used as an aid for reading since the 1200s, and by 1300 lensmakers were regularly grinding convex lenses for elderly, longsighted people. These are easier to make than the concave lenses required for short-sightedness, which are thin in the middle and more easily broken. It was not until 1608 that a Dutchman called Lipperhey combined the two lenses to make a telescope.
Galileo learned of the new invention within months; realizing the instrument’s potential, he set upon improving it. By learning to grind his own lenses and increasing the strength of the concave component, he boosted the magnification from 3X to 9X and more. He demonstrated his telescope to the Venetian senate and pointed out its obvious military applications. In a letter to the doge, he described how it enabled one “to discover at a much greater distance than usual the hulls and sails of the enemy, so that for two hours or more we can detect him before he detects us.”
While the military applications of the telescope guaranteed Galileo’s continued funding, the forty-six-year-old mathematics lecturer was soon pointing his lenses at the sky rather than at boats. Classical astronomers insisted that the moon was a perfect spherical orb, but Galileo was seeing what appeared to be craters and mountains. He also discovered four moons around Jupiter. Having realized that pure science could pay if done properly, he achieved another funding coup—and a position as mathematician and philosopher to the grand duke of Tuscany—by naming the moons after the wealthy Medici family. (They are now known as the Galilean satellites.) The fact that Jupiter had moons appeared to back up the Copernican theory, since it made it more plausible that our moon could go around the earth while we circle the sun. Furthermore, the ancient belief that the heavenly bodies were perfect spheres was undercut by the observations of features such as sunspots.
Galileo was already skeptical about the classical Greek Circle Model, not because of his observations of the heavens, but because of his far more prosaic experiments here on earth. One of Aristotle’s theories had been that objects of different masses fall to the ground at different rates. While the effect of air resistance means that this might be true of a feather and a stone, Galileo showed that it was not generally the case. The story goes that he proved his point by dropping stones of different mass from the Leaning Tower of Pisa. He also demonstrated it by means of a thought experiment: if a falling brick broke in two in midair, then according to Aristotle the two p
ieces should slow, instead of continuing at the same rate. If the Greeks were wrong when it came to the motion of stones and bricks, then they could also be wrong when it came to the motion of planets.
The only way to divine the true nature of the universe, Galileo believed, was through careful observation and the use of mathematics. As he wrote in 1623, echoing both Pythagoras and Leonardo: “Philosophy is written in this grand book—the universe—which stands continuously open to our gaze. But the book cannot be understood unless one first learns to comprehend the language and interpret the characters in which it is written. It is written in the language of mathematics, and its characters are triangles, circles, and other geometrical figures, without which it is humanly impossible to understand a single word of it; without these one is wandering about in a dark labyrinth.”22 An object’s qualities, like taste and smell, were secondary to the quantifiable properties of position, shape, number, and motion. A stone of a different colour would fall as fast.
In 1632, Galileo published his Dialogue Concerning the Two Chief World Systems, which argued for the Copernican model over the Greek Circle Model. (He ignored Kepler’s version, still preferring circular motion to ellipses.) It was presented as a discussion between three characters, called Salviati, Sagredo, and Simplicio. The simple-minded Simplicio represented the classical Greek viewpoint, and the character was widely assumed to be based on the pope of the time. Salviati represented Galileo’s position. Sagredo pretends to be neutral but often backs Salviati, as here, where he mocks the dryness and sterility of the Aristotelian view of the cosmos: “I cannot without great astonishment—I might say without great insult to my intelligence—hear it attributed as a prime perfection and nobility of the natural and integral bodies of the universe that they are invariant, immutable, inalterable, etc., while on the other hand it is called a great imperfection to be alterable, generable, mutable, etc. For my part I consider the Earth very noble and admirable precisely because of the diverse alterations, changes, generations, etc., that occur in it incessantly. If, not being subject to any changes, it were a vast desert of sand or a mountain of jasper, or if at the time of the flood the waters which covered it had frozen, and it had remained an enormous globe of ice where nothing was ever born or ever altered or changed, I should deem it a useless lump in the universe, devoid of activity and, in a word, superfluous and essentially nonexistent. This is exactly the difference between a living animal and a dead one.”23
Like Plato, Galileo had a flair for writing dialogue. He wrote some not terribly successful plays, and as a young man, he had even ventured into art–science fusion territory by delivering two lectures on the topography of Dante’s Inferno based on a scientific analysis of the text. It was probably his taste for writing and drama that got him into trouble. If he had composed the usual dry, sterile scientific text, presenting the Copernican system as only a theoretical possibility, then his work probably would have received little attention from the Inquisition. Instead, he wrote an entertaining dialogue in which the classical model was completely ridiculed. Most dangerous, it was in Italian, so it could be widely understood.
Priests of any religion like to have control over what gets written, and one of the best ways to do this is to use a specialized language. A century before Galileo, the Englishman William Tyndale was so upset by the foolishness and corruption of the local clergy that he decided to circumvent them and publish a version of the Latin Vulgate Bible in plain English. The Church strongly disapproved, since this would mean that priests would lose their monopoly as interpreters of the word of God. The archbishop of Canterbury had already declared translation of any part of the Bible a heresy punishable by burning. (And he wasn’t talking about the books.) Tyndale was forced to leave England. In 1524 he travelled to Germany, then kept moving from place to place to evade the attention of English agents and assassins. All the time, he wrote and published. His enemy Thomas More complained that he “is nowhere and yet everywhere,” like an early version of an Internet publisher. At the age of forty, in Antwerp, Tyndale was trapped by an agent and arrested. He was charged as a heretic and burned at the stake.
In Galileo’s case, he was hauled in front of the Inquisition and forced to recant his view that the earth went round the sun. Unlike Tyndale, as well as the dissident scholar Giordano Bruno and many thousands of accused witches, Galileo managed to avoid the stake, but he was put under house arrest.
Being confined to his villa didn’t stop him from working. In 1638, a copy of his Discourse on Two New Sciences was smuggled out and published in Leyden. The “two sciences” referred to the study of objects at rest—that is, mechanical properties of static objects— and in motion. Much of the book was based on experiments he had performed earlier but not yet written up. The work also represented Galileo’s main contribution to the field of prediction, and explored the concepts of time, velocity, and acceleration.
These ideas seem mundane to any modern person who is used to working the accelerator and brake pedals in her car to achieve the right speed and get to her destination on time. But in Galileo’s age, little was known about how things move. The problem with moving objects, after all, is that they don’t stay still; a stone dropped from a tower was soon moving too fast to be timed using the primitive clocks of the day. Galileo realized, however, that he could slow down the experiments by studying the motion of balls rolling on an inclined plane, rather than in free fall.
He prepared a wooden plane with a channel about the width of a finger. He then rolled a bronze ball down the channel, starting from different heights, and timed its descent using a simple water clock. He reasoned that if the ball always fell at the same rate, then the descent time should vary directly with the initial height. So if the initial height was increased by a factor of four, then the amount of water released by the water clock during the fall should increase by the same factor. Instead, he found that the time increased only by a factor of two, and in general it varied with the square root of the height. It therefore followed that the object was speeding up as it fell down. He proposed that a falling object experiences uniform acceleration. If it is travelling at a given rate after one second of descent, then after two seconds it will have doubled its speed, and so on. He had succeeded in finding an unvarying principle, a kind of stillness at the heart of motion. The object moves, but the law that underpins the motion remains at rest.
Kepler showed, using the observations of Tycho, that the sun, earth, moon, and planets could be viewed as a single system that followed geometric laws and was united by a single force. Galileo studied the dynamics of motion here on earth and demonstrated that falling objects accelerate in a uniform fashion according to a mathematical law. It was Isaac Newton who synthesized these developments, proving that the plurality of falling objects here on earth and the motion of planets in the solar system were different instances of the same underlying principle: gravity.
ONE VS PLURALITY
Isaac Newton was born, prematurely, in Lincolnshire, England, on Christmas Day in 1642. The Christmas present might have been a little overwhelming for his mother, since her husband, an uneducated farmer, had died just three months before. Three years later, she married and went to live with a wealthy clergyman from the next village, leaving young Isaac behind to be looked after by his grandmother.
As a boy, Newton showed great talent at making models, a skill that proved useful when he began constructing his own experimental apparatus. He did well enough at grammar school, and was bad enough at farming, that it was decided he should attend Trinity College, Cambridge. He had to pay his way by waiting on faculty members and the richer students. His initial aim was a law degree, but he also studied mathematics and philosophy. In 1665, the university closed down when the plague, which had been sweeping its way across Europe, reached Cambridge.24 Newton retreated to Lincolnshire, and started to work on problems of mathematics and physics.
The notoriously private and anti-social Newton later said that it was duri
ng these two years of near isolation that he formed his main theories. In perhaps another myth, a scientific version of the Garden of Eden, he observed the famous apple falling from the tree in his garden and, in a sudden flash of insight, realized that . . . it was lunchtime. Or that planets and apples are one and the same. Or that objects attract each other with a force that decreases in strength with the square of the distance. (The mathematician Karl Gauss thought the apple story, about the discovery of the law of gravity, was something Newton had fabricated to get rid of an annoying questioner.)
In 1667, once the plague had receded, Newton returned to Cambridge to continue his studies not just of mathematics and philosophy but of alchemy. While at grammar school, he had lodged with the local pharmacist, and he was fascinated by the smells and textures of the different chemicals that were used to make up the treatments of the time. The passion for experimenting with chemical compounds never left him, and he continued to pursue alchemy throughout his life. He also dabbled in other areas of mysticism, such as kabbalism, and searched for prophetic passages in the Bible. In fact, it could be said that Newton’s scientific work was only a part-time pursuit, since his religious writings—including a 300,000-word tract on the book of Revelation that was published for the first time in 2004—constitute most of his output.25 He believed that his scientific discoveries were in fact rediscoveries of ancient knowledge that had been passed from God to Noah to Moses to the Egyptian philosophers, and from them to Pythagoras (whom he credited with knowing the law of gravity).26