Nicholas believed the human mind had innate power to know things and to acquire knowledge, and, like Aristotle, he thought that knowledge had to be acquired directly from nature and experience. He also believed that learning about nature and the universe required the use of numbers and the study of numerical proportion and ratios. He was fond of the Pythagorean practice of applying numbers to many aspects of life. In his treatise ‘On Catholic Concordance’ he used the order of the heavens as a model for harmony in the church; and in his book Of Learned Ignorance he drew a parallel between the search for truth and converting a square to a circle.
Nicholas, like Alberti, was a Renaissance man. He drew up a map of Europe and was the first to prove that air has weight. He apparently never worried whether his ideas about the arrangement of the cosmos might conflict with church doctrine. It seems he had no reason for concern. The church never condemned or criticised him.
Astronomy was about to take an even more decidedly Pythagorean turn. In 1495, twenty-two-year-old Nicolaus Copernicus and his older brother Andreas journeyed south from their native Poland and ‘walked across the Alps’ – their destination Bologna, seat of Italy’s oldest university. Nicolaus had completed four years at the Jagiellonian University in Kraków, which was renowned for its astronomy. If a student intended to continue his education after he had finished the quadrivium and the trivium, he chose an area of study and went to a university that specialised in that. Nicolaus’ uncle and guardian, an influential man who became bishop of Warmia, was apparently worried that his nephew was developing a keen interest in astronomy. Hoping that the Italian sunshine and the stimulating intellectual community of the University of Bologna would turn the young man’s interest in a better direction, he insisted Nicolaus go to Bologna, famous for its law faculty. (Copernicus did eventually receive a doctorate in canon law, the law of the church, although not from Bologna.)
While studying in Bologna, Copernicus met the university’s leading scholars and teachers of astronomy and astrology, and also a mathematician named Maria de Novara, whose influence was probably the most valuable of all that Copernicus carried away with him from these years. Novara was a neo-Platonist and a close younger associate of the men of Ficino’s academy in Florence. His neo-Platonism was decidedly Pythagorean. He fervently believed in the need to uncover the simple mathematical and geometric reality that underlies the apparent complexity of nature, and he insisted that nothing so complicated and cumbersome as Ptolemaic astronomy could possibly be a correct representation of the cosmos. His young friend Copernicus came to agree.
No new astronomical discovery, nor any better or more accurate observations of the heavens, caused Copernicus to discard Ptolemaic Earth-centred astronomy and replace it with a system in which the Sun was at the centre. Though over the long passage of years the errors produced by the Ptolemaic system had made it less and less accurate in predicting planetary positions, no observational instrument during Copernicus’ lifetime was accurate enough to show whether the Copernican system solved this problem. The telescope would not appear until early in the seventeenth century, and the astronomical observations that Copernicus made himself were often less accurate than those of Hellenistic and Islamic astronomers centuries before him.
The early Pythagoreans, in the wake of their discovery of the ratios of musical harmony, had gone off in wild and misguided directions to decide there had to be ten bodies in the cosmos, disregarding the fact that there was no evidence of that number’s correctness, running ahead of nature, and arriving at the wrong conclusions. And here was Copernicus, doing something of the same kind, for when he decided that Ptolemaic astronomy could not be correct, he did so largely for reasons other than physical evidence. The beginning of the scientific revolution was perhaps not so scientific – not in the way we most commonly think of ‘scientific’.
Copernicus translated at least two Greek texts into Latin, unaware that one of them, Lysis’ Letter to Hipparchus, was a forgery. That he knew of the Letter at all was symptomatic of his intense interest in Pythagoras and the Pythagoreans. He even originally named his new system not the ‘Copernican system’, but the Astronomia Pythagorica or Astronomia Philolaica, and he considered adopting the Pythagorean practice of secrecy. In the prefatory letter dedicating his De revolutionibus to Pope Paul III, he defended his long delay in publishing this masterwork by pointing to the example of Pythagoras and the Pythagoreans.
Thinking therefore within myself that to ascribe movement to the Earth must indeed seem an absurd performance on my part to those who know that many centuries have consented to the establishment of the contrary judgement, namely that the Earth is placed immovably as the central point in the middle of the Universe, I hesitated long whether, on the one hand, I should give to the light these my Commentaries written to prove the Earth’s motion, or whether, on the other hand, it were better to follow the example of the Pythagoreans and others who were wont to impart their philosophic mysteries only to intimates and friends, and then not in writing but by word of mouth, as the letter of Lysis to Hipparchus witnesses.12
Nicolaus Copernicus
Copernicus had thought of including the Letter in De revolutionibus, but decided not to. Having defended his long period of secrecy, however, he went on in the same preface letter to point to the Pythagoreans as an ancient precedent for his own ideas. Because of his dissatisfaction with the Ptolemaic accounts of the heaven’s motions, he said, he had begun to search in ‘the works of all the philosophers on whom I could lay hand’. He had discovered some influential figures who had not, after all, agreed with the overwhelming consensus. Aristarchus in the third century B.C. had moved the Sun to the centre in his remarkable cosmology. Cicero had mentioned Hicetas’ suggestion that the Earth moved. Even better, Plutarch had written in his Placita (Copernicus quoted in Greek),
The rest hold the Earth to be stationary, but Philolaus the Pythagorean says that she moves around the fire on an oblique circle like the Sun and Moon. Heraclides of Pontus and Ecphantus the Pythagorean also make the Earth to move, not indeed through space but by rotating round her own centre as a wheel on an axle, from West to East.13 [5]
The philosopher Paul Feyerabend observed that when Copernicus decided to order the heavens he did not consult his ‘scientific forebears’, but instead cited a ‘crazy Pythagorean’.14
In Chapter 10 of Book One of De revolutionibus, Copernicus illustrated most fully the new and aesthetically beautiful harmony of his system, revealing in the process how well he knew his Plato, a wealth of other classical literature, and even the work of the Islamic astronomers. Calling attention to the simplicity of the new system, he wrote:
I think it easier to believe this than to confuse the issue by assuming a vast number of spheres, which those who keep Earth at the centre must do. We thus rather follow Nature, who, producing nothing vain or superfluous, often prefers to endow one cause with many effects. . . . So we find underlying this ordination an admirable symmetry in the universe, and a clear bond of harmony in the motion and magnitude of the spheres such as can be discovered in no other wise.15
The Pythagorean insight, from the sixth century B.C., that harmony and simple pattern expressed in numbers underlie nature clearly was for Copernicus a persuasively strong point in favour of his rearrangement of the cosmos. The potential of numbers, in combination with a preference for harmony and simplicity, to lead to a truer understanding of the universe – a potential that had been poorly exploited by the early Pythagoreans and reinterpreted in many ways, some of them admittedly quite strange, by a great many people since – was finally about to be realised.
Copernicus would not live to see the result of his own Pythagorean dream in print. If he saw a printed copy of De revolutionibus at all it was on his deathbed, for he had followed the Pythagorean example of secrecy for years before deciding, finally, to publish. The astronomy he was able to devise in the book turned out to be, i
n its details, almost as complicated as Ptolemy’s, but those few who read it carefully and recognised that Copernicus meant his revolutionary Sun-centred suggestion to be taken seriously, found their minds set on a fresh path indeed. The great Pythagorean insight that had led Copernicus was about to lead younger men out of the Middle Ages and into the modern world.
Others in the sixteenth century were captivated by the ideas of the Pythagoreans for what might on the surface seem to be entirely different reasons. However, there were deep connections having to do with harmony and numbers.
Architectural trends begun by Vitruvius in antiquity and continued by Alberti in the fifteenth century were brought to their zenith in the sixteenth in the work of one of the most gifted architectural geniuses of all time, Andrea Palladio, whose rise from stonemason to educated architect occurred thanks to an ‘academy’ like the one that Marsilio Ficino had established and Lorenzo de Medici had patronised in the fifteenth century at Ficino’s villa near Florence. Following Ficino’s model, academies had become a part of life in northern Italy; nearly every important town had one. Conscious attempts to re-create Plato’s original, they were a combination of boarding school, lecture centre, and attractive location for scholars, intellectuals, and lovers of learning to meet and discuss literature, philosophy, mathematics, and music. The activities often included physical exercise and musical performances. To a surprising extent, social rank was disregarded and talented or clever men of no social standing rubbed shoulders with wealthy aristocrats.
When Palladio was in his early twenties, in the early 1530s, he was hired as a stonemason for a building project near Vicenza. Count Gian Giorgio Trissino, a wealthy humanist scholar and poet, was rebuilding his villa in the classical style to house an academy. Trissino had designed the new buildings himself, and he thought of his design as an interpretation of the work of Vitruvius. Keeping an eye on the progress of the construction, Trissino watched Palladio at work, made a point of getting to know him, and decided that the young man deserved to have a humanist education.
In his famous I quattro libri dell’ architettura, published in 1570, Palladio would make a deliberate connection with the Pythagorean discovery that certain ratios in music produced sounds that were pleasant to human ears regardless of whether the hearer knew the underlying numbers. ‘Just as the proportions of voices are harmony to the ears,’ he wrote, ‘so those of measurement are harmony to the eyes, which according to their habit delight in them to a great degree, without it being known why, save by those who study to know the reasons of things.’16 For him, the ‘preferred’ numbers that would produce such spontaneous delight for the beholder of a building were those based on the same sequences the Pythagoreans had discovered in the ratios of musical harmony: 1 to 2, 2 to 3, and 3 to 4.
In Book I of I quattro libri, Palladio chose ‘seven sets of the most beautiful and harmonious proportions to be used in the construction of rooms’. Of course the circle and square were among them. Four others were derived from the Pythagorean musical ratios, and the remaining one was the same room Vitruvius had designed based on Socrates’ lesson in Plato’s Meno, with one dimension of the room being incommensurable. Palladio’s seven shapes and proportions were a circle, a square (1:1), a room whose length was the same as the diagonal of the square (1:1.414 . . . etc.), a square plus a third (3:4), a square plus a half (2:3), a square plus two thirds, and a double square (1:2).
Though Palladio devoted only one chapter in the second book of I quattro libri to harmonic proportions, and other authors who wrote about him later were more concerned than he, the craftsman, for the theoretical aspects of his work, these Pythagorean proportions were abundantly evident in his drawings.17 It seemed not to bother Palladio that there were differences between the drawings of buildings and the actual buildings that resulted. If one believed Plato, the Forms were never perfectly realised in the material world.
Andrea Palladio
I quattro libri was probably the most influential book ever written about architecture. Palladio wrote it in Italian for a lay audience, and Daniele Barbaro, an architectural expert in his own right, for whom Palladio designed the Villa Barbaro in the Veneto near Venice, aptly described it as a complete guide to building from the foundation to the roof. Soon after publication in 1570, the book and its drawings became the rage throughout mainland Europe and, early in the next century, Inigo Jones returned from a trip to Italy and introduced Palladian design to England. Following this ‘first great English Palladian’, whose surviving buildings include the Queen’s Chapel at St. James’s Palace and the Banqueting House at Whitehall, many of England’s large country houses were soon being built, or rebuilt, along Palladian lines. Lord Burlington constructed the Assembly Rooms at York on Palladio’s designs and fashioned his own home, Chiswick House, after Palladio’s Villa Rotonda. Around 1800, Thomas Jefferson designed his Palladian Monticello in Virginia, and numerous American churches of many denominations, university buildings, and official structures and memorials and monuments in Washington, D.C., were following suit, for the feeling was that there was a link between Palladian principles of architecture, with their Pythagorean proportions, and the education, enhancement, and wise governance of society. Palladian design spread to Germany, Russia, Poland, back to Italy, and to Scandinavia.
One of the most unusual houses built using Palladian proportions was the palace-observatory that Tycho Brahe, the finest pre-telescope astronomer, constructed in the latter part of the sixteenth century on the island of Hven in Denmark. As a young aristocrat travelling in Europe, Tycho had visited Venice and the Veneto during the years when Palladio himself was building there, and had probably also seen I quattro libri, for he had a connoiseur’s appreciation of fine books. Perhaps Tycho was also aware of Palladio’s humble origins as a stonemason because, for his own project, he hired a stonemason named Hans van Steenwinkel and raised him to the rank of master builder.
Not everyone who would build in the ‘Palladian’ style would pay mind to Pythagorean or Palladian proportions, but Tycho Brahe did. When his ‘Uraniborg’ was finished, although it looked at first glance anything but Palladian, the Pythagorean musical ratios were all there and the symmetry extended into the landscape, just as Palladio advised. The portal towers on the east and west sides of the house were each fifteen Danish feet wide and fifteen feet long; the height of the façade was thirty feet, the peak of the roof forty-five feet, the side of the central block sixty feet, giving the ratio 1:2:3:4. The same ratios underlay the dimensions of Tycho’s rooms and other elements of the structure. The perimeter wall around Tycho’s garden enclosed a square divided by avenues on the diagonal, just as Socrates had divided the squares in Plato’s Meno. Someone unaware of Tycho’s intentions, and not steeped in the architecture of Palladio or on the lookout for Pythagorean ratios, would not have noticed these mathematical and musical subtleties, but Tycho was sure this harmony would make his home and gardens satisfying to the eye and soul, encouraging peaceful, intelligent work and inspiring any sensitive person. Tycho designed and built Uraniborg to be both a palace home and an observatory, all for the purpose of better scrutinising the heavens where the Pythagorean harmony of the spheres – the musical ratios, or perhaps even some deeper harmony – might be discovered. Nowhere else was the Pythagorean and Palladian ideal of proportion so literally, and so idiosyncratically, realised, as in Uraniborg.18
For complicated reasons involving Danish politics and personal issues, Tycho Brahe eventually abandoned this remarkable, beloved palace, and Denmark, and went into exile – the exile that made it possible for him to meet Johannes Kepler.
[1]The ‘Chaldean Oracles’, written in verse in the second century A.D. by a man named Julianus the Theurgist and his son, combined Babylonian and Persian beliefs with Platonic and neo-Platonic philosophy and became an important religious book for neo-Platonists.
[2]‘Chaldean’ in this case meaning
Babylonian.
[3]The great Andrea Palladio was to write four.
[4]Alberti’s most important buildings included, in Florence, the Palazzo Rucellai, the Rucellai Chapel, the Annunziata, and the façade of the Maria Novella church; in Rimini, the Tempio Malatestiano; and in Mantua, the churches of San Sebastiano and San Andrea.
[5]Ecphantus the Pythagorean lived in the fourth century B.C. There is some suspicion that he may have been only a fictional character in one of Heracleides’ dialogues, but Copernicus thought he was a historical person, and most modern scholars tend to agree.
CHAPTER 16
‘While the morning stars sang together’: Johannes Kepler
Sixteenth and Seventeenth Centuries
As the last decade of the sixteenth century began, the two-thousand-year-old Pythagorean dream of rationality, unity, and the power of numbers was about to be given a serious test. Pythagoras and his followers had been sure they had caught a glimpse, as through a crack or a keyhole, of truth based on numbers that lay beyond the façade of nature. Johannes Kepler would force the door wide open, once and for all. After him, ironically, and though Kepler did not intend it to be so, the Pythagorean concept of the music of the spheres would survive only in poetic imagery. Yet in a profound and magnificent way, the faith embodied in that concept – faith in a wondrously rational and ordered universe – tempered by Kepler’s imaginative genius and rigorous mathematics, would finally place real examples of that music under the feet of science.
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