by David Orrell
The questioning, skeptical attitude soon worked its way into astronomy. In early 1543, the sixty-year-old Polish astronomer Nicolaus Kopernik, who preferred to be known by his Latinized name of Copernicus, lay on his bed in the castle turret where he lived, staring into a different kind of threatening, dark cavern: impending death. In his arms was an object of intense fear and desire, his freshly published work, On the Revolution of Heavenly Spheres. It contained a theory that he had been working on for thirty years, since he had received his doctorate in Italy. Like Aristarchus over a millennium before, Copernicus believed that the earth rotated around the sun, rather than vice versa. The universe might be based on circles, but we were not at their centre.
No doubt anticipating the reception his ideas would receive, he had delayed publication until near the end of his life. The manuscript he had sent to the publishers had the motto “For mathematicians only” and included the following pre-emptive strike against his critics: “Perhaps there will be babblers who, although completely ignorant of mathematics, nevertheless take it upon themselves to pass judgement on mathematical questions and, badly distorting some passages of Scripture to their purpose, will dare find fault with my undertaking and censure it. I disregard them even to the extent as despising their criticism as unfounded.” He must have been shocked to find that in the version of the book in his arms, this defiant statement had been removed. The publishing process had been supervised by the Lutheran theologian Andreas Osiander, and he’d replaced the original preface with an unsigned letter claiming that the results of the book were intended not as truth but only as a more efficient method to calculate the positions of the sun and the planets.
The switcheroo by Osiander probably outraged the ailing Copernicus, but it did make his ideas more palatable to other astronomers. After all, his model avoided many of the tortuous complexities of the Greek Circle Model, and was therefore a useful device for computing orbits. However, because it still incorporated circular motion, it could not avoid the use of epicycles, and in fact employed even more than the Ptolemaic system (forty-eight versus forty).3 And theology aside, few were willing to believe for real that the earth was spinning at high speed around the sun. At a time when rapid transit meant a fast and bumpy carriage ride, one would expect to be conscious of such motion.
THE OBSERVER
Almost thirty years after Copernicus’s death, on the evening of November 11, 1572, a young Danish astronomer named Tycho Brahe emerged from his alchemical laboratory. Looking up into the night sky, he immediately noticed that something had changed. For the best part of ten years, he had studied the constellations; they were as familiar to him as a lover’s face. Yet that night, almost straight above him in the constellation Cassiopeia, there shone a new star, as bright as Venus. Perhaps wondering if this was a side effect from inhaling the fumes of one of his alchemical experiments, he called his assistant to confirm. But there was no doubt: a star was born.
The sudden arrival of this star, or supernova (as they are now known), which remained visible for seventeen months, caused a panic across the continent. Some believed that it signalled the coming of a plague, and they were apparently proved right when there was an outbreak in Europe shortly afterwards. It also came as a shock to astronomers. The authorities on matters of the stars were the ancient Greeks, and if there was one thing the Greeks knew, it was that there was nothing new under the sun. Tycho, who at that moment decided to dedicate himself to astronomy instead of alchemy, carried out detailed observations of the new star. When published in 1574, they conclusively proved that the star was at such a distance that it was really an addition to the firmament—which, it seemed, was not so firm. He dealt a further blow to orthodoxy in 1577, when his calculations showed that a comet he observed on November 13 had passed through the realm of the planets, and therefore should have smashed into Aristotle’s crystalline spheres, if they really existed.
Tycho, who had Latinized his name from Tyge, was born into nobility. His uncle Joergen, who was also his foster father, had saved King Frederik II of Denmark from drowning, then died himself of pneumonia. The king returned the debt by granting Tycho, whose brilliance had impressed him, his own observatory, called Uraniborg. It was located on the island of Hven (now Ven) in Copenhagen Sound, across the water from Hamlet’s Elsinore. (Tycho was also a relative of Friedrich Rosenkrantz, who was immortalized in Shakespeare’s play of 1600.) The island contained around forty farms and a village, and the residents became Tycho’s subjects. Tycho himself designed the laboratory, based on buildings he had seen in Venice.
The observatory was stocked with the best instruments available, short of telescopes (which had yet to be invented).4 The basement held an alchemical laboratory, in case Tycho needed a break from the stars. There were servants’ quarters, a cell for any tenants who caused trouble, and a printing press, which was used for publishing both scientific works and his poetry. It was all set in a garden arranged on the classical forms of circles and squares. He soon established a reputation as a mediocre poet but the best naked-eye astronomer in Europe; he was able to plot the positions of celestial objects to better than two minutes (sixtieths of a degree). The stars had never before been pursued with such rigour, precision, equipment, and ambition. As one of his elegies read:
Like blind moles, lethargic mobs see
No more than earthly, perishable things.
So very few Apollo grants to see
The riches which Olympus hides away . . .
More beautiful by far the goal they seek,
For it is not a goal unknown to gods:
Through mental force control the heaven’s stars,
Subject the ether to his conquering spirit.5
FIGURE 2.2. The observatory of Tycho Brahe at Uraniborg.6 The main observatory building is at the centre.
Tycho knew of Copernicus’s theory and was sufficiently curious to check it with observations. If the sun-centred model was true, then the position of the stars should change as the earth rotates around the sun. However, even with his best tools, Tycho could detect no such parallax shift. Either the earth was fixed or the universe was so incredibly large that the earth’s motion around the sun was minor in scale. Finding this too hard to accept, he came up with a hybrid model that had the planets rotating around the sun, but the sun and the moon rotating around the earth, so the earth was still the centre of the universe.
Actually, Tycho came to think that he was at the centre of the universe. Scientists are often perceived publicly as being a humble group of truth-seekers, but the reality is sometimes different. As Iamblichus wrote, humility was not a virtue for the Pythagoreans, or for Aristotle. Pythagoras believed that he was the reincarnation of Euphorbus, a famous warrior, and “frequently sang the Homeric verses pertaining to himself, to the music of his lyre.”7
One indicator that things were getting out of hand with Tycho came when he covered a wall of his study with a giant mural of himself. He began to view himself as a kind of successor to Ptolemy, which in his eyes at least made him better than royalty.8 After King Frederick died, Tycho’s relationship with the new king deteriorated when he refused to tend to Frederick’s burial site, which was on his land. He closed down his laboratory in 1597 and moved first to Copenhagen, then to Prague to take a position as imperial mathematician to the Holy Roman emperor, Rudolph II.
Rudolph II was a reclusive and somewhat eccentric ruler who had a fascination with both science of the sort practised by Tycho and the occult. He also loved any kind of machine or gadget. When Tycho showed up in a carriage that featured an odometer, a novel device that signalled the distance travelled by ringing two small bells, he immediately got the job. He hired as his assistant a young astronomer by the name of Johannes Kepler.
THE THEORIST
Kepler’s father was a mercenary soldier, his mother an innkeeper’s daughter. Weak and sickly as a child, Kepler got his education in his grandmother’s pub in Leonberg (now in Germany), then at a nearby semina
ry, then at the university of Tübingen, where he learned astronomy, mathematics, theology, and philosophy. His first job was at a new Lutheran high school in Graz, where he also served as district mathematician for the surrounding region. This meant preparing astrological calendars, along with forecasts of weather, crops, politics, and so on. In 1595, for example, he made three predictions: for a freezing cold winter, an attack by the Turks, and a peasant uprising.9 Everyone was impressed, if a little inconvenienced, when all three came true. Six months on, he wrote to a friend: “By the way, so far the calendar’s predictions are proving correct. There is an unheard-of cold in our land. In the Alpine farms people die of the cold. It is reliably reported that when they arrive home and blow their noses, the noses fall off. . . . As for the Turks, on January 1 they devastated the whole country from Vienna to Neustadt, setting everything on fire and carrying off men and plunder.”10
Just as the Greeks had consulted with the oracles, the nobles and peasants of Europe ordered their world astrologically. The slow, ordered dance of the moon and the planets around the sky was a window into the mind of God, and a signal for success or disaster. Europe at the time was enveloped in the Little Ice Age, with unusually bad winters, a high risk of crop failure, and a population susceptible to the spread of epidemics (see boxed text on pages 68–69). Farmers and merchants used astrological clocks, like the one in Prague’s Old Town Square, to aid their decision-making, and prognostication was a lucrative business. The arrival of a comet could even have implications for national security. Rudolph II employed scientists like Tycho and Kepler less for their scientific theories than for their usefulness at making astrological forecasts. He also hired savants such as the Englishmen Edward Kelley and John Dee, who obtained their visions of the future from crystal balls, mirrors, occult manuscripts, and angels.11
By the time he took the job with Tycho, Kepler already had his own ideas about the way the world worked. These were an intriguing mix of the old and the new. Rather than just try to produce a model that fitted the data, he wanted to know why things were the way they were. He was in search of a dynamic, a causative principle. Like Pythagoras, Kepler wanted to “perceive the true principles and causes of the Universe.”12 He believed that the universe was based on geometry, and that understanding geometry was the key to unlocking the workings of the universe. The Copernican heliocentric model had a simplicity and elegance, it seemed to Kepler, which was indicative of God’s plan.
FIGURE 2.3 Kepler’s model, based on Platonic solids.13
If Copernicus was right, his model could be used to estimate the relative sizes of the planetary orbits. It turned out that these were very different, so there were enormous distances between the planets. If this was part of God’s plan, then what was the reason? Kepler was convinced that the answer lay in the Platonic solids, to which Pythagoras had attached great importance. Rather like Vitruvius, who stretched a man to fit a geometric pattern, Kepler believed that the relative sizes of the planets’ orbits (only six were known at the time) could be accounted for by a nested sequence of spheres, each separated from the next by one of the Platonic solids (as shown in figure 2.3). Kepler published his theory, which the physicist B. K. Ridley describes as “pure Pythagoreanism,” in his modestly titled Mysterium Cosmographicum, or Mysteries of the Cosmos.14 Since Kepler’s book supported Copernicus’s heliocentric model, his position was unpopular, for religious and scientific reasons. To comprehensively prove his theory, he needed better data. Which is how he found himself applying for the job with Tycho.
SQUARE VS OBLONG
According to the scientific method first proposed by Aristotle and later developed by Sir Francis Bacon, scientists come to their conclusions by making careful observations, then forming a hypothesis, and then testing the hypothesis with experiments. If the theoretical predictions match reality, then the theory is confirmed, at least for the time being; otherwise, the theory must be changed. A type of conflict, between theory and experiment, is therefore built into the scientific process; but the aim is always to resolve it by coming up with a single model that satisfies these dual aspects.
To be a good observer requires patience, a mind for detail, the will to grapple with physical equipment. The ability to theorize often requires the opposite: a willingness to focus on abstract problems, a certain detachment from the everyday distractions of the real world. Plato told a story of the mathematician Thales, who one night was gazing at the sky as he walked and fell into a ditch. A servant girl helped him up and said, “How do you expect to understand what is going on up in the sky if you do not even see what is at your feet?”
If Tycho was the consummate observer, then Kepler was the ideal theorizer. The two had completely different personalities. The twenty-nine-year-old Kepler was a devout Lutheran who just wanted the peace and quiet to get on with his work, while Tycho, at fifty-three, was a rowdy, pugnacious, extroverted nobleman. His nose had been rebuilt from silver and gold after he’d had a fight as a student, and he maintained a dwarf named Jepp as court fool. But Kepler needed detailed observations if he was going to confirm his model of the universe. Even if he’d had the aptitude and the equipment, he had bad eyesight from an early bout with smallpox. Tycho had the observations, but he didn’t have the theoretical ability to piece them together into a convincing model.
To Kepler, the problem with both the Greek Circle Model and Tycho’s hybrid version was not that they didn’t work, but that they were ugly. To match observations of the planets, they both had to introduce highly complex epicycles, circles within circles. A kind of corollary to the scientific method, known as Ockham’s Razor, is that a theory should be no more complicated than necessary: that which is not needed should be cut away. It has since been restated in various forms. Newton wrote, “We are to admit no more causes of natural things than such as are both true and sufficient to explain their appearances.” Einstein is supposed to have said, “Theories should be as simple as possible, but no simpler.”
The desire for simplicity is married to a love of elegance, a kind of mathematical aesthetics. For Kepler, it was also a religious impulse. He believed that the motion of the planets reveals a kind of cosmic harmony. As Iamblichus wrote of Pythagoras, he “extended his ears and fixed his attention, his intellect, in the sublime symphonies of the world, hearing and understanding the universal harmony and consonance of the spheres and the stars that are moved through them, which produce a fuller and more intense melody than anything effected by mortal sounds.”15 God had given us the gift of mathematics so that we could understand and participate in this celestial music. So that we could join the dance.
Tycho and Kepler worked together for a year and a half. It was a battle between two scientific egos. Tycho was stingy with his data and released it to Kepler only in small doses, all the time trying to convert him to his hybrid model. Kepler, meanwhile, was trying to obtain enough data to verify his own model, and trying to get his salary improved so he could provide adequately for his wife and family. On October 24, 1601, the battle ended when Tycho passed away from complications after a urinary infection, which might have been induced when he tried to self-medicate with mercury (like many astronomers at the time, he was also a dabbler in medicine). On his deathbed, he pleaded to Kepler, “Let me not seem to have lived in vain.”
Kepler inherited both Tycho’s position as imperial mathematician and access to all of his data. Eventually, the data revealed to him that not only was Tycho’s model wrong, but so was his own. At first, Kepler tried to adjust both to fit Tycho’s observations. But after months of analysis, he realized that although planetary motion was nearly circular, it was better described by an ellipse, with the sun at one of the foci. The calculations were incredibly arduous; Kepler had at his disposal only primitive tools, such as basic geometry and trigonometry.
While Kepler is today best known for his discovery that the planets follow elliptical orbits, he seems to have taken far more delight in his earlier “discovery” tha
t the universe is based on Platonic solids. In his notes to the second edition of Mysteries of the Cosmos, written twenty-five years later, ellipses are not even mentioned. As Arthur Koestler writes: “Kepler set out to prove that the solar system was built like a perfect crystal around the five divine solids, and discovered, to his chagrin, that it was dominated by lopsided and undistinguished curves; hence his unconscious taboo on the word ‘ellipse.’”16 He spent a full year trying to express the ellipse in terms of symmetrical circular motion, or as he put it, “squaring my oval.”17 A circle or square can be described by a single parameter, the diameter or diagonal, while an ellipse or rectangle seems arbitrary. To conclude that the universe was built on such figures was like suggesting to Brahe that he remodel his observatory garden after a randomly shaped oblong.
ODD VS EVEN
The culmination of Kepler’s work was his book Harmony of the World. The title might have been inspired by a book by an Italian musician called Vincenzo Galilei, who believed that the music of the time could be revitalized by a return to the Pythagorean theory of harmony.18 Kepler’s book attempted to do the same for astrology, meteorology, and astronomy, by showing how they could be understood in terms of Pythagorean geometry. Pythagoras had claimed to be able to hear the celestial music of the planets as they orbited the earth; Kepler went further and figured out the notes. He said that “the Earth sings Mi-Fa-Mi, so we can gather even from this that Misery and Famine reign on our habitat.”19