Post-classical history

Humanist Astronomy and Nicolaus Copernicus

There was nothing that humanists enjoyed more than a good squabble. They accused each other not of heresy but of scholarly incompetence, which was much worse. Valuable patronage was at stake and if a humanist could not gain a position at court, he could at least besmirch the reputations of those who had.

One of the most fearsome debates took place between George of Trebizond (1395–1486) and John Bessarion (1403–72) over the question of whether Plato or Aristotle represented the peak of Greek philosophy. Both men were native Greeks who made their living in Italy in the mid-fifteenth century. George of Trebizond, often known by his Latin name of Trapezuntius, actually came from Crete1 but Bessarion really was from Trebizond, a Greek enclave on the southeastern shore of the Black Sea.2 Today, he is best known as a collector of manuscripts. The San Marco Library in Venice holds over 1,000 books which he donated to the city on his death.3

Italians were clamouring for translations from ancient Greek and Trapezuntius supplied a steady stream of them. He worked quickly but carelessly, confident that few would have the necessary language skills to catch him out. Bessarion was one man who did. Although the root of their disagreement was over philosophy, Bessarion took great pleasure in compiling long lists of the errors made by his rival. Trapezuntius’s shame was compounded by his inability to be diplomatic or admit he had made mistakes. While Bessarion’s charm and easy manner saw him raised to the rank of cardinal, Trapezuntius had to flee to Naples to escape the scandal.

The New Astronomy of George Peurbach

When Constantinople fell to the Turks in 1453, Bessarion, who regarded the city as his home, devoted himself to trying to begin a crusade to liberate it. To do this, he needed the support of the Holy Roman Emperor and so travelled to Vienna in 1460 to meet him. To his disappointment, the mission was not particularly successful and no crusade resulted.

However, while he was in Vienna, Bessarion introduced himself to George Peurbach (1423–61), a friend of Nicholas of Cusa and the Emperor’s court astrologer. Peurbach was a rare example of a humanist who was actively interested in mathematics.4 The cardinal’s mind was still on the battle with Trapezuntius and he thought that Peurbach’s astronomical and literary expertise would allow him to open a second flank in his struggle. In 1450, Trapezuntius had published a new translation of Ptolemy’s Almagestdirectly from the original Greek into Latin. It was supposed to supersede the medieval version that had been rendered from Arabic back in the twelfth century. As usual, Trapezuntius’s slapdash approach let him down. The Almagest is a fearsomely complicated treatise that requires an accurate translation to be of any use at all. Demonstrating neither precision nor mathematical skill, the new version was derided a failure.5 Bessarion decided to compound Trapezuntius’s embarrassment by asking Peurbach, who possessed all the necessary skills in abundance, to produce his own summary of the Almagest.6 Peurbach, who had already written an updated version of the medieval Planetary Theories, set to work at once.

He proceeded quickly and had completed six of the thirteen books by the time he died the following year. On his deathbed, he handed the project over to his student and collaborator Johann Müller, better known as Regiomontanus (1437–76). Both master and pupil were Germans who had travelled to Vienna in search of an education and patronage. They shared a desire to make astronomical predictions as accurate as possible and had no trouble in reconciling that aim with being an official astrologer. After all, without accurate tables, astrology was impossible. Peurbach had already found that one lunar eclipse had occurred eight minutes earlier than the standard tables of the time predicted.7 Given that the tables in question had been prepared in 1252, their accuracy in predicting events two centuries later seems remarkable to us, but for Peurbach and Regiomontanus it was not good enough.

Regiomontanus completed the summary of the Almagest in 1463 and, with his master dead, joined the household of Cardinal Bessarion in Rome. He spent the rest of his life trying to correct Greek and Arab astronomy by making new observations and bringing to bear the most advanced mathematical techniques. There were rumours on his death that he had been poisoned by agents of Trapezuntius for his part in Bessarion’s schemes.8 If this is true, it would not be untypical of the politics of Renaissance Italy.

On Triangles, a guide to trigonometry that Regiomontanus wrote in 1464, is often held up as the origin of that discipline. In fact, Richard of Wallingford had composed a similar treatise back in the early fourteenth century drawing on Arab and Greek archetypes.9Regiomontanus may not have used Richard of Wallingford’s work directly but he certainly owned a rough copy of the Englishman’s treatise on how to make his innovative astronomical instrument the Albion, which contains plenty of material on trigonometry.10

Looking at the Sky

Ptolemy, in agreement with Aristotle and almost everyone else, thought that the earth was stationary at the centre of the universe and that the planets, including the moon and sun, orbited around the earth. No one in medieval Europe disagreed with this, Nicole Oresme’s suggestions about the rotation of the earth notwithstanding. On the other hand, the matter of exactly how the planets were arranged and in what order was open to question.

Today, many people would be hard pressed to identify a planet in the night sky. When it is close to the earth, the easiest to spot is Mars because it is bright and clearly red in colour. Venus is even brighter but keeps lower in the sky and so is often more difficult to find. It appears just after sunset or just before sunrise, giving it the title of the morning or evening star. Jupiter and Saturn are both often visible, although the latter is hard to differentiate from a normal star unless you know what you are looking for. Mercury is quite dim and stays even closer to the horizon than Venus. Until the eighteenth century, these five were the only known planets.

We now know that the reason why Mercury and Venus are only visible around sunrise or sunset is that both planets orbit closer to the sun than the earth does. This means we only see them when we are looking in the direction of the sun, but obviously they are invisible when the sun is actually in the sky. In the ancient and medieval worlds, the way that these two planets were tied to the sun was a mystery. A few people suggested that they did orbit the sun rather than the earth, although this was not a popular view. The perturbations of the outer planets – Mars, Jupiter and Saturn – also share the same duration as the sun’s orbit and there seemed to be no reason why this should be so.

Since Pythagoras, the ancient Greeks had believed that the planets moved with an unchanging and uniform circular motion.11 According to their worldview the heavens were perfect and so the motion of the planets had to reflect this. The planets themselves, oblivious to this theory, did not behave themselves. While they supposedly orbited the earth in circles, they did not travel across the sky with a uniform speed. Worse still, they could clearly be observed to move backwards from time to time. Finally, the brightness of the planets (and the moon’s size) varied over the course of months or years. This should not happen if they stayed the same distance away from the earth.

Ptolemy had presented answers to these problems but his solutions were very convoluted. The idea of the planets sailing serenely through the heavens was lost in a fog of fiendish geometry. In essence, his method was to assign to each planet several different uniform circular motions that, when added together, gave a very close approximation to the observed movements. His two principal mechanisms were eccentrics and epicycles. An eccentric orbit was one that did not centre on the earth, meaning that the planet was not always the same distance away from it. An epicycle was a smaller circle about which the planet orbited that was, in turn, carried around the larger eccentric orbit. By manipulating the speeds at which the various circles rotated, Ptolemy was able to model the movements that he observed in the sky, including the backwards motion and changes of speed. He could also explain the differing brightness of the planets and size of the moon by the fact that the eccentrics and epicycles carried the planets closer and further away from the earth. To get a really exact fit between these models and his observations he also had to use a device called an equant which is simply too complex to describe and explain here.12

Many natural philosophers hated Ptolemy’s system because it made the heavens such a muddle. The original principle of uniform motion in circles disappeared in a blizzard of geometrical constructions. This was a particular embarrassment for Jews, Christians and Muslims because they believed that God had created the world as perfect. How could he have made the heavens when they were in such a jumble?

In Muslim Egypt the Jewish philosopher Moses Maimonides, who would later inspire Thomas Aquinas, wrestled with this matter in his influential Guide for the Perplexed. He eventually conceded that astronomers could do no more than find a hypothesis that fits the observed motions of heavenly bodies. He hoped that someone would come after him who could show how the planets actually moved.13 John Buridan rejected epicycles as physically ridiculous but found eccentric orbits acceptable.14 Still, this left him unable to reconcile observation with theory. Sadly, no one else could come up with an alternative that did away with Ptolemy’s constructions and still reproduced the observed path of the planets in the sky.

The physical construction of the heavens was also a source of debate. The ancient Greeks envisaged a series of shells into each of which a planet was embedded. Peurbach combined this proposal with Ptolemy’s epicycles to postulate a universe of solid crystalline spheres. Each sphere had to be thick enough to accommodate its planet at both its minimum and maximum distance from the earth. Assuming no space in between the spheres, Arab astronomers had calculated the total radius of the universe from the centre of the earth to the fixed stars to be 90 million miles (roughly the distance we measure between the sun and the earth today).15 Figures of around this order of magnitude had been determined in antiquity and were well known in the Middle Ages.16 This was merely the minimum size of the universe assuming that there were no gaps between the planetary spheres. No one can call the medieval universe small, even if our own is vastly larger.

Peurbach and Regiomontanus revealed the problems with Ptolemy’s system but did not suggest an alternative. Peurbach also realised that the differences in the apparent size of the moon were not as great as Ptolemy’s model predicted. As thousands of their printed books were sold to students at universities throughout Europe, the insights of Peurbach and Regiomontanus spread. Their summary of the Almagest might have had its genesis in a literary dispute and astrologers’ need for accurate planetary tables, but that did not stop it being the cutting edge of astronomical theory. The shortcomings of Ptolemy, long recognised, were now clear for all to see and several astronomers began work on alternatives.

The Life of Copernicus

In 1543 Nicolaus Copernicus, a Polish clergyman nearing the end of his life, finally allowed his contribution to the astronomical debate to be published. It was a book called Revolutions of the Heavenly Spheres. In it, Copernicus claimed to have demonstrated that the sun was the centre of the universe and the earth orbited around it along with the other planets. The impact of this radical idea was softened slightly by the fact of his friend, Andreas Osiander (1498–1552), adding a foreword that explained the theory was only meant to be a hypothesis and was not presented as a fact.17 What Copernicus thought about this late addition is not recorded, since he died as his book came off the press. Osiander had penned his preface because he found the idea of the earth rushing though space at high speed while simultaneously spinning on its axis ridiculous and he knew Europe’s intellectual elite would agree. There was no question of ecclesiastical pressure being brought to bear and no chance that the church would seek to suppress the book. After all, it was dedicated to Pope Paul III (1468–1549) himself. This was the done thing at the time when all scholars needed patronage, and a great number of books were presented to princes and kings complete with gushing pronouncements on the royal virtues. Paul III had been the dedicatee of another book presenting a reformed model of astronomy five years before Copernicus’s.18 All the signs are that the Pope appreciated the flattery and read neither of them.

The real problem with stating that the earth is moving was that almost all of the available evidence and all expert opinion was against it. We saw in chapter 12 how John Buridan and Nicole Oresme had suggested a rotating earth in the fourteenth century. Oresme had concluded that there was no physical reason to reject the hypothesis, but no positive confirmation for it either. On the other hand, physical evidence against the earth orbiting the sun did exist. When we look up at stars each night, we see that they are fixed in the same patterns, called constellations. If the earth were in motion, we should expect the stars would change their relative positions as the earth followed its orbit. For example, a star that was directly overhead at midwinter should be off to one side at midsummer.

To grasp this phenomenon, called stellar parallax, a bit better, remember how many children are convinced that the moon is following them when they are travelling by car. This is because, however far the car moves, the direction and size of the moon do not change at all. In comparison, all nearby everyday objects move across our field of vision as we approach and then pass them. The only exception to this rule is another car that is following our own. So it seems to a child that the moon is tracking his or her own motion. Of course, the real reason the moon’s size and direction appear fixed is that it is an immense distance away compared to the everyday scale of road journeys.

Substituting the moving earth for a moving car, we note that even as we travel over the entire distance of the earth’s orbit, the direction and brightness of the stars remain the same. This must mean that either they are preposterously far away, or else, as everyone in the Middle Ages thought, the earth is not moving after all.19

People often imagine Copernicus as a lone revolutionary genius working at the fringes of Europe. Poland, however, was not a backwater at the time but part of a vast commonwealth whose king, Sigismund I (1467–1548), was one of the most powerful monarchs of Europe, a correspondent of Erasmus and patron of the arts. Born Nikolaj Kopernik, Copernicus adopted the common habit of taking a Latin name to emphasise his links with the cosmopolitan and international elite. He was brought up in the house of his uncle, the bishop of Ermeland, before studying at the university of Cracow from 1491. Then, five years later, he travelled to Italy to continue his education. He spent time at the ancient universities of Bologna and Padua before receiving a degree in canon law at Ferrara.20In all, he spent ten years in Italy when he would have been exposed to the fashionable Platonic works of Marsilio Ficino. At the same time, the books of the medieval natural philosophers were pouring off the presses in Venice for use at the nearby universities. Copernicus would also have been taught astronomy from Peurbach’s textbooks, as well as geometry from Euclid’s Elements.

On his return to Poland, Copernicus embarked on the comfortable and leisurely life marked out for a well-educated man of his class. His uncle had presented him with a canonry at Frombork Cathedral for which he was paid a substantial stipend and not required to do very much work. These canonries were extremely popular with scholars because they provided a steady income without onerous duties attached. You may recall that Peter Abelard had had one back in the twelfth century. So did Nicole Oresme and Nicholas of Autrecourt 200 years later. Copernicus had the necessary family connections to expect a post of this kind, and it meant he had plenty of time to indulge in his full-time hobby of astronomy.

Copernicus first circulated some ideas about a heliocentric universe in manuscript form some time after 1507.21 His contemporaries looked upon his proposals as interesting but certainly wrong. After this failure, he went back to the drawing board and tried to produce a viable cosmology that would withstand the scrutiny of his peers. He read a copy of Regiomontanus’s treatise on trigonometry and found it contained the mathematical techniques that he needed to perfect his work.22 The result was Revolutions of the Heavenly Spheres which remains one of the great triumphs of human genius.

Unlike some of the famous books in the history of science, this is not one that most people can just pick up and read. The bulk of the book contains a complete reworking of Ptolemy’s system using the cutting-edge geometry of its day. Even though geometry was part of the basic university education given to all candidates for Master of Arts degrees, Copernicus’s book was still very advanced.

The heliocentric system proposed by Copernicus, despite all his years of effort, was not very much simpler than Ptolemy’s had been. Copernicus managed to cut down the number of epicycles, and the heliocentric system also explained why Mercury and Venus always stay close to the sun. As we have seen, they must appear to do so because they are orbiting the sun more closely than we are.

Unfortunately, Copernicus could not provide any direct demonstration that the earth orbited the sun and not vice versa. Conversely, the evidence against the earth moving still seemed strong. The stars remained obstinately stationary. This lack of stellar parallax meant that the universe was either much, much larger than anyone had previously thought (and they already thought it was extremely big), or Copernicus was wrong. He resolved the problem with some intellectual sleight of hand. It was recognised that because the universe was so large, it appeared the same from wherever on earth you looked at it. Copernicus simply said that it was actually so indescribably huge that it appeared the same from wherever in the earth’s orbit you looked at it.23 To do this he had to increase the size of the universe by about a factor of a billion. This explanation offended the principle of parsimony – the idea that nature does nothing unnecessarily. Copernicus was making the universe far bigger than it needed to be just so that it would fit with his theory. We know today that he was right, but his reasons were not convincing.

The Sources for Revolutions of the Heavenly Spheres

Where did Copernicus find the idea that the earth orbits the sun? And why was he willing to entertain such an absurd suggestion in the first place? He explained in the preface to his book that he was as dissatisfied with the then-current models of the universe as many of his contemporaries. He wanted a model of the world machine worthy of its Creator whom he called ‘the best and most orderly workman of all.’24 As far as Copernicus was concerned, Ptolemy’s system was too messy to have been designed by God. So, he claimed, he read all the books of philosophy that he could lay his hands on in search of an alternative.

One obscure Greek astronomer, Aristarchus of Samos (c.310– 230BC), had believed that the earth orbits the sun. It would seem obvious that Aristarchus represented the best chance to impart some ancient legitimacy to Copernicus’s ideas. But instead he excised all mention of him from the final version of Revolutions of the Heavenly Spheres.25 Rather, he quoted from various followers of Pythagoras, even though they did not actually support his theory. This was because it was the neo-Platonism of Marsilio Ficino that most strongly influenced him. Platonists looked back to Pythagoras as the font of wisdom, and so Copernicus quoted from his followers rather than from Aristarchus of Samos. Ficino was aware that the sun was a great deal larger than the earth or any of the other planets, 160 times larger by his reckoning. ‘All celestial things appear by divine law to lead back to the one Sun, the Lord and regulator of the heavens’, he wrote.26 Besides Ficino, Italy was awash with occult theories about the sun, placing it figuratively, if not literally, at the centre of the universe. One neo-Platonic sage, Francisco Giorgi (1466–1540), referred to the sun as the ‘heart of the heavens’ in a book published in 1525.27 This is too late to have stimulated Copernicus directly, but it is indicative of the zeitgeist in which he was educated. We even find the Pole citing Hermes Trismegistus, who wrote that the sun was a visible god.28

As for his technical arguments for the rotation of the earth, Copernicus appears to have lifted them straight out of the work of John Buridan. They both suggested that the rotation of the earth is more parsimonious than the rotation of the entire universe. And compare these two passages – here is Buridan writing in about 1350:

If anyone is in a moving ship and imagines that he is at rest, then should he see another ship, which is truly at rest, it will appear to him that the other ship is moved … And so, we also posit that the sphere of the sun is everywhere at rest and the earth in carrying us would be rotated. Since, however, we imagine we are at rest … the sun would appear to us to rise and then to set, just as it does when it is moved and we are at rest.29

Copernicus wrote 200 years later:

When a ship sails on a tranquil sea, all the things outside seem to the voyagers to be moving in a pattern that is an image of their own. They think, on the contrary, that they are themselves and all the things with them are at rest. So, it can easily happen in the case of the earth that the whole universe should be believed to be moving in a circle [while the earth is at rest].30

As late as 1516, Buridan ‘still ruled the subject of physics at the university of Paris.’31 And commentaries on his work were produced by several of the masters at the university of Cracow at the time that Copernicus was studying there.32 True, Buridan and Oresme had only discussed the rotation of the earth, but their reasoning stood just as well to justify the earth orbiting the sun. Even if Copernicus did not have direct access to Buridan’s work, exactly the same argument appears in Nicholas of Cusa’s On Learned Ignorance.33 Nicholas of Cusa even studied at Padua in the century before Copernicus arrived there.

Theorems developed by earlier Muslim astronomers are also included in Revolutions. For example, a geometrical construction of a Persian astronomer, Nasir al-Din al-Tusi (1201–74), which has been dubbed the Tusi couple by historians, was used to generate a linear motion from two circles. Copernicus’s diagram of the couple bears a remarkable resemblance to Arabic manuscripts, quite apart from his use of the same theorem.34 Furthermore, his model for the moon is exactly the same as that developed by the Syrian Ibn al-Shatir (d.1375).35

Copernicus may have learnt about these ideas while he was travelling in Italy. Unfortunately, historians have not been able to determine exactly where he came across them. It is unlikely that he actually read the Arabic treatises containing the theorems, because he could not understand the language and there is no record of them being translated. So the route by which Muslim astronomy found its way into this seminal work of western science remains a mystery.36

Thus, Copernicus was not a lone genius who rediscovered ancient wisdom. He was part of the long-running European school of natural philosophy that went back to William of Conches and Adelard of Bath, cross-fertilised by the parallel occult and Arabic traditions. That is not to say that heliocentricism was not radical and new, but Revolutions of the Heavenly Spheres is written in the language of medieval thinkers and uses their arguments. If John Buridan had picked it up, it would have made perfect sense to him, far more than it does to us today, even though he probably would have respectfully disagreed with its thesis.

The Impact of Copernicus

The reaction to Copernicus’s work was initially muted. Its difficult mathematical content meant that not many people read it, and his ideas appeared at first glance to be absurd. Martin Luther, over dinner one day, said he thought Copernicus’s idea was just a newfangled theory designed to attract attention.37 Astronomers were more impressed. Although they rejected the movement of the earth, they realised that Copernicus’s system was easier to apply than the existing alternatives. A new set of astronomical tables was produced in 1551, calculated using the methods in Revolutions of the Heavenly Spheres, which rivalled the popular medieval version. Even the Catholic Church found that Copernicus had his uses in the area of calendar reform.

Senior churchmen had been worried about the calendar for centuries. Throughout the Middle Ages, Europe had used the 365-day year, with a leap year once every four years, as instituted by Julius Caesar (100–44BC). Unfortunately, this is not precisely correct because it makes the year, on average, about eleven minutes too long. That might not sound like much, but by 1500 the error had accumulated to almost ten days. The immediate concern of the Church was that Christian festivals were being celebrated at the wrong time, but there were other, more practical disadvantages as well. In the fifteenth century, the cardinals Pierre D’Ailly and Nicholas of Cusa had supported the call for improvement. But nothing was done until the aftermath of the Protestant Reformation, when the calendar became one of many things that were changed as the Catholic Church put its house in order.

In the 1570s, Pope Gregory XIII set up a commission to decide on the method and implementation of reform. Because his system made calculations easier, the commission used Copernicus rather than Ptolemy to determine the length of the year. After nearly ten years of consideration, a report was presented to the Pope. The month of October 1582 lost ten days and the calendar was realigned with the solar year. To prevent them drifting apart again, the new calendar omitted a leap year every three centuries out of four.38Unfortunately, by the time the Catholic Church had sorted out its calendar, Protestant countries no longer accepted papal dictate. Consequently, they only gradually came to adopt the Gregorian reckoning. Today this causes historians no end of trouble because, for several centuries, different countries used different calendars. A letter sent from Protestant England to Catholic France could arrive before the date on which it had been posted. England did not finally adopt the reformed calendar until 1752, when the month of September lost no less than twelve days. Stories that the move prompted rioters to demand the return of their lost days are, unfortunately, mythical but the change is the reason why the English tax year ends on 5 April rather than the traditional quarter day of 25 March.39

Little was heard of the central idea behind Copernicus’s book, that the earth is orbiting the sun, for the next 50 years. Astronomers were aware of it and discussed it from time to time, but very few people believed it.40 It was only when new evidence about the constitution of the heavens came to light that everyone started to talk about Copernicus.

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