The Danish Peace Academy

SCIENCE AND SOCIETY

John Avery
H.C. Ørsted Institute, University of Copenhagen

Chapter 5 SCIENCE IN THE RENAISSANCE

East-west contacts

Towards the end of the middle ages, Europe began to be influenced by the advanced Islamic civilization. European scholars were anxious to learn, but there was an “iron curtain” of religious intolerance which made travel in the Islamic countries difficult and dangerous for Christians.

However, in the 12th century, parts of Spain, including the city of Toledo, were reconquered by the Christians. Toledo had been an Islamic cultural center, and many Moslem scholars, together with their manuscripts, remained in the city when it passed into the hands of the Christians. Thus Toledo became a center for the exchange of ideas between east and west; and it was in this city that many of the books of the classical Greek and Hellenistic philosophers were translated from Arabic into Latin.

In the 12th century, the translation was confined to books of science and philosophy. Classical Greek literature was forbidden by both the Christian and Moslem religions; and the beautiful poems and dramas of Homer, Sophocles and Euripides were not translated into Latin until the time of the Renaissance Humanists.

During the Mongol period (1279-1328), direct contact between Europe and China was possible because the Mongols controlled the entire route across central Asia; and during this period Europe received from China three revolutionary inventions: printing, gunpowder and the magnetic compass.

Another bridge between east and west was established by the crusades. In 1099, taking advantage of political divisions in the Moslem world, the Christians conquered Jerusalem and Palestine, which they held until 1187. This was the first of a series of crusades, the last of which took place in 1270. European armies, returning from the Middle East, brought with them a taste for the luxurious spices, textiles, jewelry, leatherwork and fine steel weapons of the orient; and their control of the Mediterranian sea routes made trade with the east both safe and profitable. Most of the profit from this trade went to a few cities, particularly to Venice and Florence.

At the height of its glory as a trading power, the Venetian Republic maintained six fleets of nationally owned ships, which could be chartered by private enterprise. All the ships of this fleet were of identical construction and rigged with identical components, so that parts could be replaced with ease at depots of the Venetian consular service abroad. The ships of these fleets could either serve as merchant ships, or be converted into warships by the addition of guns. Protected by a guard of such warships, large convoys of Venetian merchant ships could sail without fear of plunder by pirates.

In 1420, at the time of Venice’s greatest commercial expansion, the doge, Tommaso Mocenigo, estimated the annual turnover of Venetian commerce to be ten million ducats, of which two million was profit. With this enormous income to spend, the Venetians built a city of splendid palaces, which rose like a shimmering vision above the waters of the lagoon.

The Venetians were passionately fond of pleasure, pagentry and art. The cross-shaped church of Saint Mark rang with the music of great composers, such as Gabrieli and Palestrina; and elegant triumphal music accompanied the doge as he went each year to throw a golden ring into the waters of the lagoon, an act which symbolized the marriage of Venice to the sea.

Like the Athenians after their victory in the Persian war, the Venetians were both rich and confident. Their enormous wealth allowed them to sponsor music, art, literature and science. The painters Titian, Veronese, Giorgione and Tintoretto, the sculptor Verrochio and the architect Palladio all worked in Venice at the height of the city’s prosperity. The self-confidence of the Venetians produced a degree of intellectual freedom which was not found elsewhere in Europe at that time, except in Florence. At the University of Padua, which was supported by Venetian funds, students from all countries were allowed to study regardless of their religious beliefs. It was at Padua that Copernicus studied, and there Andreas Vesalius began the research which led to his great book on anatomy. At one point in his career, Galileo also worked at the University of Padua.

The prosperity of 15th century Florence, like that of Venice, was based on commerce. In the case of Florence, the trade was not by sea, but along the main north-south road of Italy, which crossed the Arno at Florence. In addition to this trade, Florence also had an important textile industry. The Florentines imported wool from France, Flanders, Holland and England. They wove the wool into cloth and dyed it, using superior techniques, many of which had come to them from India by way of the Islamic civilization. Later, silk weaving (again using eastern techniques) became important. Florentine banking was also highly developed, and our present banking system is derived from Florentine commercial practices.

Humanism

In the 15th and 16th centuries, Florence was ruled by a syndicate of wealthy merchant families, the greatest of whom were the Medicis. Cosimo de’ Medici, the unofficial ruler of Florence from 1429 to 1464, was a banker whose personal wealth exceeded that of most contemporary kings. In spite of his great fortune, Cosimo lived in a relatively modest style, not wishing to attract attention or envy; and in general, the Medici influence tended to make life in Florence more modest than life in Venice.

Cosimo de’ Medici is important in the history of ideas as one of the greatest patrons of the revival of Greek learning. In 1439, the Greek Patriarch and the Emperor John Palaeologus attended in Flo- rence a council for the reunification of the Greek and Latin churches. The Greek-speaking Byzantine scholars who accompanied the Patriarch brought with them a number of books by Plato which excited the intense interest and admiration of Cosimo de’ Medici.

Cosimo immediately set up a Platonic Academy in Florence, and chose a young man named Marsilio Ficino as its director. In one of his letters to Ficino, Cosimo says:

“Yesterday I came to the villa of Careggi, not to cultivate my fields, but my soul. Come to us, Marsilio, as soon as possible. Bring with you our Plato’s book De Summo Bono. This, I suppose, you have already translated from the Greek language into Latin, as you promised. I desire nothing so much as to know the road to happiness. Farewell, and do not come without the Orphian lyre!”

Cosimo’s grandson, Lorenzo the Magnificent, continued his grandfather’s policy of reviving classical Greek learning, and he became to the golden age of Florence what Pericles had been too the golden age of Athens. Among the artists whom Lorenzo sponsored were Michelangelo, Botticelli and Donatello. Lorenzo established a system of bursaries and prizes for the support of students. He also gave heavy financial support to the University of Pisa, which became a famous university under Lorenzo’s patronage. (It was later to be the university of Galileo and Fermi.)

At Florence, Greek was taught by scholars from Byzantium; and Poliziano, who translated Homer into Latin could say with justice: “Greek learning, long extinct in Greece itself, has come to life and lives again in Florence. There Greek literature is taught and studied, so that Athens, root and branch, has been transported to make her abode - not in Athens in ruins and in the hands of barbarians, but in Athens as she was, with her breathing spirit and her very soul.”

Leonardo da Vinci

Against this background, it may seem strange that Lorenzo the Magnificent did not form a closer relationship with Leonardo da Vinci, the most talented student of Verrocchio’s school in Florence. One might have expected a close friendship between the two men, since Lorenzo, only four years older than Leonardo, was always quick to recognize exceptional ability.

The explanation probably lies in Leonardo’s pride and sensitivity, and in the fact that, while both men were dedicated to knowledge, they represented different points of view. Lorenzo was full of enthusiasm for the revival of classical learning, while Leonardo had already taken the next step: Rejecting all blind obedience to authority, including the authority of the ancients, he relied on his own observations. Lorenzo was fluent in Latin and Greek, and was widely educated in Greek philosophy, while Leonardo was ignorant of both languages and was largely self-taught in philosophy and science (although he had studied mathematics at the school of Benedetto d’Abacco).

While he did not form a close friendship with Lorenzo the Magnificent, Leonardo was lucky in becoming the friend and proteg´e of the distinguished Florentine mathematician, physician, geographer and astronomer, Paolo Toscanelli, who was also the friend and advisor of Colombus. (Toscanelli furnished Colombus with maps of the world and encouraged him in his project of trying to reach India and China by sailing westward. Toscanelli’s maps mistakenly showed the Atlantic Ocean with Europe on one side, and Asia on the other!) Gradually, under Toscanelli’s influence, young Leonardo’s powerful and original mind was drawn away from the purely representational aspects of art, and he became more and more involved in trying to understand the underlying structure and mechanism of the things which he observed in nature - the bodies of men and animals, the flight of birds, the flow of fluids and the features of the earth.

Both in painting and in science, Leonardo looked directly to nature for guidence, rather than to previous masters. He wrote: “The painter will produce pictures of small merit if he takes as his standard the pictures of others; but if he will study from natural objects, he will produce good fruits... And I would say about these mathematical studies, that those who study the authorities and not the works of nature are descendents but not sons of nature.” In another place, Leonardo wrote:

“But first I will test with experiment before I proceed further, because my intention is to consult experience first, and then with reasoning to show why such experience is bound to operate in such a way.

And that is the true rule by which those who analyse the effects of nature must proceed; and although nature begins with the cause and ends with the experience, we must follow the opposite course, namely (as I said before) begin with the experience and by means of it investigate the cause.”

Lorenzo the Magnificent finally did help Leonardo in a backhanded way: In 1481, when Leonardo was 29 years old, Lorenzo sent him as an emissary with a gift to the Duke of Milan, Ludovico Sforza. Although Milan was far less culturally developed than Florence, Leonardo stayed there for eighteen years under the patronage of Sforza. He seemed to work better in isolation, without the competition and criticism of the Florentine intellectuals.

In Milan, Leonardo began a series of anatomical studies which he developed into a book, intended for publication. Leonardo’s anatomical drawings make previous work in this field seem like the work of children, and in many respects his studies were not surpassed for hundreds of years. Some of his anatomical drawings were published in a book by Fra Pacioli, and they were very influential; but most of the thousands of pages of notes which Leonardo wrote have only been published in recent years.

The notebooks of Leonardo da Vinci cover an astonishing range of topics: mathematics, physics, astronomy, optics, engineering, architecture, city planing, geology, hydrodynamics and aerodynamics, anatomy, painting and perspective, in addition to purely literary works. He was particularly interested in the problem of flight, and he made many studies of the flight of birds and bats in order to design a flying machine. Among his notes are designs for a helicopter and a parachute, as well as for a propellor-driven flying machine.

In astronomy, Leonardo knew that the earth rotates about its axis once every day, and he understood the physical law of inertia which makes this motion imperceptible to us except through the apparent motion of the stars. In one of his notebooks, Leonardo wrote: “The sun does not move.” However, he did not publish his ideas concerning astronomy. Leonardo was always planning to organize and publish his notes, but he was so busy with his many projects that he never finished the task. At one point, he wrote what sounds like a cry of despair: “Tell me, tell me if anything ever was finished!”

Leonardo ended his life in the court of the king of France, Francis I. The king gave him a charming chateau in which to live, and treated him with great respect. Francis I visited Leonardo frequently in order to discuss philosophy, science and art; and when Leonardo died, the king is said to have wept openly.

Copernicus

The career of Leonardo da Vinci illustrates the first phase of the “information explosion” which has produced the modern world: Inexpensive paper was being manufactured in Europe, and it formed the medium for Leonardo’s thousands of pages of notes. His notes and sketches would never have been possible if he had been forced to use expensive parchment as a medium. On the other hand, the full force of Leonardo’s genius and diligence was never felt because his notes were not printed. Copernicus, who was a younger contemporary of Leonardo, had a much greater effect on the history of ideas, because his work was published. Thus, while paper alone made a large contribution to the information explosion, it was printing combined with paper which had an absolutely decisive and revolutionary impact: The modern scientific era began with the introduction of printing.

Nicolas Copernicus (1473-1543) was orphaned at the age of ten, but fortunately for science he was adopted by his uncle, Lucas Watzelrode, the Prince-Bishop of Ermland (a small semi-independent state which is now part of Poland). Through his uncle’s influence, Copernicus was made a Canon of the Cathedral of Frauenberg in Ermland at the age of twenty-three. He had already spent four years at the University of Krakow, but his first act as Canon was to apply for leave of absence to study in Italy.

At that time, Italy was very much the center of European intellectual activity. Copernicus stayed there for ten years, drawing a comfortable salary from his cathedral, and wandering from one Italian University to another. He studied medicine and church law at Padua and Bologna, and was made a Doctor of Law at the University of Ferrara. Thus, thanks to the influence of his uncle, Copernicus had an education which few men of his time could match. He spent altogether fourteen years as a student at various universities, and he experienced the bracing intellectual atmosphere of Italy at the height of the Renaissance. In 1506, Bishop Lucas recalled Copernicus to Ermland, where the young Canon spent the next six years as his uncle’s personal physician and administrative assistant. After his uncle’s death, Copernicus finally took up his duties as Canon at the cathedral-fortress of Frauenberg on the Baltic coast of Ermland; and he remained there for the rest of his life, administering the estates of the cathedral, acting as a physician to the people of Ermland, and working in secret on his sun-centered cosmology.

Even as a student in Krakow, Copernicus had thought about the problem of removing the defects in the Ptolomeic system. In Italy, where the books of the ancient philosophers had just become available in the original Greek, Copernicus was able to search among their writings for alternative proposals. In Ptolemy’s system, not all the “wheels within wheels” turn with a uniform velocity, although it is possible to find a point of observation called the “punctum equans” from which the motion seems to be uniform. Concerning this, Copernicus wrote: “A system of this sort seems neither sufficiently absolute, nor suffi- ciently pleasing to the mind... Having become aware of these defects, I often considered whether there could be found a more reasonable arrangement of circles, in which everything would move uniformly about its proper center, as the rule of absolute motion requires..” While trying to remove what he regarded as a defect in the Ptolemeic system by rearranging the wheels, Copernicus rediscovered the sun-centered cosmology of Aristarchus. However, he took a crucial step which went beyond Aristarchus: What Copernicus did during the thirty-one years which he spent in his isolated outpost on the Baltic was to develop the heliocentric model into a complete system, from which he calculated tables of planetary positions.

The accuracy of Copernicus’ tables was a great improvement on those calculated from the Ptolemeic system, and the motions of the planets followed in a much more natural way. The inner planets, Mercury and Venus, stayed close to the sun because of the smallness of their orbits, while the occasional apparently retrograde motion of the outer planets could be explained in a very natural way by the fact that the more rapidly-moving earth sometimes overtook and passed one of the outer planets. Furthermore, the speed of the planets diminished in a perfectly regular way according to their distances from the sun. In spite of these successes, Copernicus hesitated to publish the book which he had written outlining his theory. He feared ridicule, and he feared that his position in the church hierarchy would be endangered if he put forward such unorthodox and possibly heretical ideas. In his youth, he had participated in the Italian Renaissance, and he had even translated a book of Greek poems into Latin, thus declaring himself to be on the side of the humanists in the controversy over whether pagan Greek literature ought to be revived. However, old age and isolation in medieval Ermland had turned him into a thoroughly conservative churchman.

The intellectual freedom of the early 15th century had begun to disappear because of the increasingly bitter controversy between Martin Luther and the established church. As a result of the attacks of Luther, the Roman church had become more strict. Following the edict of his bishop, Copernicus was forced to send away his housekeeper of many years, a woman who was probably his unofficial wife. Against the background of this atmosphere of intolerance, it is easy to understand why Copernicus hesitated to publish his unorthodox theory. Probably he would never have done so had it not been for the arrival at Frauenberg of an ardent young disciple, Georg Joachim Rheticus, a professor of mathematics and astronomy from the University of Wittenberg.

Rheticus had heard rumors about the sun-centered cosmology of Copernicus, and he arrived at Frauenberg “at the extreme outskirts of the earth” full of enthusiasm and hero worship, determined to learn from Copernicus the details of his heliocentric system. He brought with him as gifts the first printed editions of Euclid and Ptolemy in the original Greek.

Copernicus could not resist the flattering admiration and enthusiasm of Rheticus, but he was much embarrassed to have a visitor from Wittenberg, the very center of the Lutheran heresy. Therefore he hastily packed Rheticus off to Loebau Castle in Kulm. Tiedimann Geise, the closest friend of Copernicus, had been made Bishop of Kulm, and Loebau Castle was his official residence. Rheticus and Bishop Geise worked together at Loebau Castle, trying in every way they could think of to persuade Copernicus to publish his great book, De Revolutionibus Orbium Coelestium; but the cautious old Canon resisted all their arguments. Finally they hammered out a compromise: Rheticus was to take a short course on the sun-centered system from Copernicus. Then he would write a little book which would be a Preliminary Account of Copernicus’ great work; and the name of Copernicus would not be mentioned in the Preliminary Account except in a very oblique way.

In other words, Rheticus agreed to stick his neck out, and if it was not chopped off, then Copernicus might possibly agree to publish his book. This was done, and Rheticus seemed to survive the publication of his little book. In fact the Preliminary Account was quite well received. Copernicus could no longer resist the combined forces of Rheticus and Geise. He handed over his precious manuscript to Rheticus, who left triumphantly for N¨urnberg to have it printed. (At that time, printing was most advanced in the Protestant parts of Germany. Like the Buddhist monks of China, the Lutherans had strong religious motives for promoting the development of printing. They believed that the Bible ought to be read by ordinary people. Also, Luther’s battle against the established church was being fought by means of printed pamphlets.)

His great Revolutionibus was finally being printed, but in 1512, Copernicus himself fell mortally ill with a cerebral hemmorhage. His faithful friend, Bishop Geise, recorded that “For many days he had been deprived of his memory and his mental vigour; he only saw his completed book at the last moment, on the day that he died.” The publication of the Revolutionibus did not cause an immediate stir; nor was Copernicus himself the sort of person who might have been expected to overthrow the established patterns of human thought. He was an extremely learned man, but his outlook was distinctly conservative. Nevertheless, hidden in the Copernican cosmology, there were implications which caused an intellectual revolution once they were understood. The earth was dethroned from its position as the center of the universe. Also, if Copernicus was right, the universe had to be almost unimaginably enormous.

According the the Copernican cosmology, the earth moves around the sun in an orbit whose radius is ninety-three million miles. As the earth moves in its enormous orbit, it is sometimes closer to a particular star, and sometimes farther away. Therefore the observed positions of the stars relative to each other ought to change as the earth moves around its orbit. This effect, called “stellar parallax”, could not be observed with the instruments which were available in the 16th century. The explanation which Copernicus gave for the absence of stellar parallax was that “Compared to the distance of the fixed stars, the earth’s distance from the sun is neglegably small!” If this is true for the nearest stars, then what about the distance to the farthest stars? Vast and frightening chasms of infinity seemed to open under the feet of those who understood the implications of the Copernican cosmology.

Humans were no longer rulers of a small, tidy universe especially created for themselves. They were suddenly “lost in the stars”, drifting on a tiny speck of earth through unimaginably vast depths of space. Hence the cry of Blaise Pascal: “Le silence eternal de ce ´espaces infinis m’effraie!”, “The eternal silence of these infinite spaces terrifies me!”

Tycho Brahe

The next step in the Copernican revolution was taken by two men who presented a striking contrast to one another. Tycho Brahe (1546-1601) was a wealthy and autocratic Danish nobleman, while Johannes Kepler (1571-1630) was a neurotic and poverty-stricken teacher in a provincial German school. Nevertheless, in spite of these differences, the two men collaborated for a time, and Johannes Kepler completed the work of Tycho Brahe.

At the time when Tycho was born, Denmark included southern Sweden; and ships sailing to and from the Baltic had to pay a toll as they passed through the narrow sound between Helsingør (Elsinore) in Denmark, and Helsingborg in what is now Sweden. On each side of the sound was a castle, with guns to control the sea passage. Tycho Brahe’s father, a Danish nobleman, was Governor of Helsingborg Castle. Tycho’s uncle was also a military man, a Vice-Admiral in the navy of the Danish king, Frederik II. This uncle was childless, and Tycho’s father promised that the Vice-Admiral could adopt one of his own children. By a fortunate coincidence, twins were born to the Governor’s wife. However, when one of the twins died, Tycho’s father was unwilling to part with the survivor (Tycho). The result was that, in the typically high-handed style of the Brahe family, the Vice-Admiral kidnapped Tycho. The Governor at first threatened murder, but soon calmed down and accepted the situation with good grace.

The adoption of Tycho Brahe by his uncle was as fortunate for science as the adoption of Copernicus by Bishop Watzelrode, because the Vice-Admiral soon met his death in an heroic manner which won the particular gratitude of the Danish Royal Family:

Admiral Brahe, returning from a battle against the Swedes, was crossing a bridge in the company of King Frederik II. As the king rode across the bridge, his horse reared suddenly, throwing him into the icy water below. The king would have drowned if Admiral Brahe had not leaped into the water and saved him. However, the Admiral saved the king’s life at the cost of his own. He caught pneumonia and died from it. The king’s gratitude to Admiral Brahe was expressed in the form of special favor shown to his adopted son, Tycho, who had in the meantime become an astronomer (against the wishes of his family). As a boy of fourteen, Tycho Brahe had witnessed a partial eclipse of the sun, which had been predicted in advance. It struck him as “something divine that men could know the motions of the stars so accurately that they were able a long time beforehand to predict their places and relative positions”. Nothing that his family could say would dissuade him from studying astronomy, and he did so not only at the University of Copenhagen, but also at Leipzig, Wittenberg, Rostock, Basel and Augsberg.

During this period of study, Tycho began collecting astronomical instruments. His lifelong quest for precision in astronomical observation dated from his seventeenth year, when he observed a conjunction of Saturn and Jupiter. He found that the best tables available were a month in error in predicting this event. Tycho had been greatly struck by the fact that (at least as far as the celestial bodies were concerned), it was possible to predict the future; but here the prediction was in error by a full month! He resolved to do better.

Tycho first became famous among astronomers through his observations on a new star, which suddenly appeared in the sky in 1572. He used the splendid instruments in his collection to show that the new star was very distant from the earth - certainly beyond the sphere of the moon - and that it definitely did not move with respect to the fixed stars. This was, at the time, a very revolutionary conclusion. According to Aristotle, (who was still regarded as the greatest authority on matters of natural philosophy), all generation and decay should be confined to the region beneath the sphere of the moon. Tycho’s result meant that Aristotle could be wrong!

Tycho thought of moving to Basel. He was attracted by the beauty of the town, and he wanted to be nearer to the southern centers of culture. However, in 1576 he was summoned to appear before Frederik II. Partly in recognition of Tycho’s growing fame as an astronomer, and partly to repay the debt of gratitude which he owed to Admiral Brahe, the king made Tycho the ruler of Hven, an island in the sound between Helsingborg and Helsingør. Furthermore, Frederik granted Tycho generous funds from his treasury to construct an observatory on Hven.

With these copious funds, Tycho Brahe constructed a fantastic castle-observatory which he called Uraniborg. It was equipped not only with the most precise astronomical instruments the world had ever seen, but also with a chemical laboratory, a paper mill, a printing press and a dungeon for imprisoning unruly tenants.

Tycho moved in with a retinue of scientific assistants and servants. The only thing which he lacked was his pet elk. This beast had been transported from the Brahe estate at Knudstrup to Landskrona Castle on the Sound, and it was due to be brought on a boat to the island of Hven. However, during the night, the elk wandered up a stairway in Landskrona Castle and found a large bowl of beer in an unoccupied room. Like its master, the elk was excessively fond of beer, and it drank so much that, returning down the stairway, it fell, broke its leg, and had to be shot.

Tycho ruled his island in a thoroughly autocratic and grandiose style, the effect of which was heightened by his remarkable nose. In his younger days, Tycho had fought a duel with another student over the question of who was the better mathematician. During the duel, the bridge of Tycho’s nose had been sliced off. He had replaced the missing piece by an artificial bridge which he had made of gold and silver alloy, and this was held in place by means of a sticky ointment which he always carried with him in a snuff box.

Tycho entertained in the grandest possible manner the stream of scholars who came to Hven to see the wonders of Uraniborg. Among his visitors were King James VI of Scotland (who later ascended the English throne as James I), and the young prince who later became Christian IV of Denmark.

With the help of his numerous assistants, Tycho observed and recorded the positions of the sun, moon, planets and stars with an accuracy entirely unprecedented in the history of astronomy. He corrected both for atmospheric refraction and for instrumental errors, with the result that his observations were accurate to within two minutes of arc. This corresponds to the absolute limit of what can be achieved without the help of a telescope.

Not only were Tycho’s observations made with unprecedented accuracy - they were also made continuously over a period of 35 years. Before Tycho’s time, astronomers had haphazardly recorded an observation every now and then, but no one had thought of making systematic daily records of the positions of each of the celestial bodies. Tycho was able to make a “motion picture” record of the positions of the planets because he could divide the work among his numerous assistants.

In 1577, a spectacular comet appeared in the sky. Tycho treated it in the same way that he treated the planets, making scrupulously careful and continuous records of its position. He showed by parallax studies that the comet had to be farther away from the earth than the orbit of the moon. Again Aristotle was shown to be wrong! Aristotle had recognized that comets violated the rules which he had set down for celestial motion, but he believed comets to be atmospheric phenomena. In a book which he wrote about the comet in 1577, Tycho proposed his own cosmology. It was halfway between Ptolemy and Copernicus, and was designed to eliminate the shocking idea of a moving earth. In Tycho’s system, Mercury, Venus, Mars, Jupiter and Saturn all moved in orbits around the sun, but the sun moved in an orbit around the earth, which remained stationary at the center of the universe.

Tycho believed his system to be true because, even though he tried very hard with his superb instruments, he could not observe the stellar parallax which must exist if the earth really moves in an orbit around the sun. The parallax does in fact exist, but because the distance to the nearest stars is so immense, it cannot be observed without the use of a large telescope. It was finally observed in the 19th century by the German astronomer, F.W. Bessel (the inventor of Bessel functions). All went well with Tycho on the island of Hven for twelve years. Then, in 1588, Frederik II died (of alcoholism), and his son ascended the throne as Christian IV. Frederik II had been especially grateful to Admiral Brahe for saving his life, and he treated the Admiral’s adopted son, Tycho, with great indulgence. However, Christian IV was unwilling to overlook the increasingly scandalous and despotic way in which Tycho was ruling Hven; and he reduced the subsidies which Tycho Brahe had been receiving from the royal treasury. The result was that Tycho, feeling greatly insulted, dismantled his instruments and moved them to Prague, together with his retinue of family, scientific assistants, servants and jester.

In Prague, Tycho became the Imperial Mathematician of the Holy Roman Emperor, Rudolph II. (We should mention in passing that royal patrons such as Rudolph were more interested in astrology than in astronomy: The chief duty of the Imperial Mathematician was to cast horoscopes for the court!) After the move to Prague, one of Tycho’s senior scientific assistants became dissatisfied and left. To replace him, Tycho recruited a young German mathematician named Johannes Kepler. Johannes Kepler

Two thousand years before the time of Kepler, Pythagoras had dreamed of finding mathematical harmony in the motions of the planets. Kepler and Newton were destined to fulfil his dream. Kepler was also a true follower of Pythagoras in another sense: Through his devotion to philosophy, he transcended the personal sufferings of a tortured childhood and adolescence. He came from a family of misfits whose neurotic quarrelsomeness was such that Kepler’s father narrowly escaped being hanged, and his mother was accused of witchcraft by her neighbors. She was imprisoned, and came close to being burned.

At the age of 4, Kepler almost died of smallpox, and his hands were badly crippled. Concerning his adolescence, Kepler wrote: “I suffered continually from skin ailments, often severe sores, often from the scabs of chronic putrid wounds in my feet, which healed badly and kept breaking out again. On the middle finger of my right hand, I had a worm, and on the left, a huge sore.”

Kepler’s mental strength compensated for his bodily weakness. His brilliance as a student was quickly recognized, and he was given a scholarship to study theology at the University of T¨ubingen. He was agonizingly lonely and unpopular among his classmates.

Kepler distinguished himself as a student at Tübingen, and shortly before his graduation, he was offered a post as a teacher of mathematics and astronomy at the Protestant School in Graz. With the post went the title of “Mathematician of the Provence of Styria”. (Gratz was the capital of Styria, a province of Austria).

Johannes Kepler was already an ardent follower of Copernicus; and during the summer of his first year in Graz, he began to wonder why the speed of the planets decreased in a regular way according to their distances from the sun, and why the planetary orbits had the particular sizes which Copernicus assigned to them.

On July 9, 1595, in the middle of a lecture which he was giving to his class, Kepler was electrified by an idea which changed the entire course of his life. In fact, the idea was totally wrong, but it struck Kepler with such force that he thought he had solved the riddle of the universe with a single stroke!

Kepler had drawn for his class an equilateral triangle with a circle circumscribed about it, so that the circle passed through all three corners of the triangle. Inside, another circle was inscribed, so that it touched each side of the triangle. It suddenly struck Kepler that the ratio between the sizes of the two circles resembled the ratio between the orbits of Jupiter and Saturn. His mercurial mind immediately leaped from the two-dimensional figure which he had drawn to the five regular solids of Pythagoras and Plato.

In three dimensions, only five different completely symmetrical many- sided figures are possible: the tetrahedron, cube, octahedron, icosohedron and the dodecahedron. There the list stops. As Euclid proved, it is a peculiarity of three-dimensional space that there are only five possible regular polyhedra. These five had been discovered by Pythagoras, and they had been popularized by Plato, the most famous of the Pythagorean philosophers. Because Plato made so much of the five regular solids in his dialogue Timaeus, they became known as the “Platonic solids”.

In a flash of (completely false) intuition, Kepler saw why there had to be exactly six planets: The six spheres of the planetary orbits were separated by the five Platonic solids! This explained the sizes of the orbits too: Each sphere except the innermost and the outermost was inscribed in one solid and circumscribed about another!

Kepler, who was then twenty-three years old, was carried away with enthusiasm. He immediately wrote a book about his discovery and called it Mysterium Cosmigraphicum, “The Celestial Mystery”. The book begins with an introduction strongly supporting the Copernican cosmology. After that comes the revelation of Kepler’s marvelous (and false) solution to the cosmic mystery by means of the five Platonic solids. Kepler was unable to make the orbit of Jupiter fit his model, but he explains naively that “nobody will wonder at it, considering the great distance”. The figures for the other planets did not quite fit either, but Kepler believed that the distances given by Copernicus were inaccurate.

Finally, after the mistaken ideas of the book, comes another idea, which comes close to the true picture of gravitation. Kepler tries to solve the problem of why the outer planets move more slowly than the inner ones, and he says:

“If we want to get closer to the truth and establish some correspondence in the proportions, then we must choose between these two assumptions: Either the souls of the planets are less active the farther they are from the sun, or there exists only one moving soul in the center of the orbits, that is the sun, which drives the planets the more vigorously the closer the planet is, but whose force is quasi-exhausted when acting on the outer planets, because of the long distance and the weakening of the force which it entails.”

In Mysterium Cosmographicum, Kepler tried to find an exact mathematical relationship between the speeds of the planets and the sizes of their orbits; but he did not succeed in this first attempt. He finally solved this problem many years later, towards the end of his life. Kepler sent a copy of his book to Tycho Brahe with a letter in which he called Tycho “the prince of mathematicians, not only of our time, but of all time”. Tycho was pleased with this “fan letter”; and he recognized the originality of Kepler’s book, although he had reservations about its main thesis.

Meanwhile, religious hatred had been deepening and Kepler, like all other Protestants, was about to be expelled from Catholic Austria. He appealed to Tycho for help, and Tycho, who was in need of a scientific assistant, wrote to Kepler from the castle of Benatek near Prague: “You have no doubt already been told that I have most graciously been called here by his Imperial Majesty and that I have been received in a most friendly and benevolent manner. I wish that you would come here, not forced by the adversity of fate, but rather of your own will and desire for common study. But whatever your reason, you will find in me your friend, who will not deny you his advice and help in adversity” To say that Kepler was glad for this opportunity to work with Tycho Brahe is to put the matter very mildly. The figures of Copernicus did not really fit Kepler’s model, and his great hope was that Tycho’s more accurate observations would give a better fit. In his less manic moments, Kepler also recognized that his model might not be correct after all, but he hoped that Tycho’s data would allow him to find the true solution.

Kepler longed to get his hands on Tycho’s treasure of accurate data, and concerning these he wrote:

“Tycho possesses the best observations, and thus so-to-speak the material for building the new edifice. He also has collaborators, and everything else he could wish for. He only lacks the architect who would put all this to use according to his own design. For although he has a happy disposition and real architectural skill, he is nevertheless obstructed in his progress by the multitude of the phenomena, and by the fact that the truth is deeply hidden in them. Now old age is creeping upon him, enfeebling his spirit and his forces” In fact, Tycho had only a short time to live. Kepler arrived in Prague in 1600, and in 1601 he wrote:

“On October 13, Tycho Brahe, in the company of Master Minkowitz, had dinner at the illustrious Rosenborg’s table, and held back his water beyond the demands of courtesy. When he drank more, he felt the tension in his bladder increase, but he put politeness before health. When he got home, he was scarcely able to urinate. After five sleepless nights, he could still only pass water with the greatest pain, and even so the passage was impeded. The insomnia continued, with internal fever gradually leading to delirium; and the food which he ate, from which he could not be kept, exacerbated the evil... On his last night, he repeated over and over again, like someone composing a poem: ‘Let me not seem to have lived in vain’.”

A few days after Tycho’s death, Kepler was appointed to succeed him as Imperial Mathematician of the Holy Roman Empire. Kepler states that the problem of analysing Tycho’s data took such a hold on him that he nearly went out of his mind. With a fanatic diligence rarely equaled in the history of science, he covered thousands of pages with calculations. Finally, after many years of struggle and many false starts, he wrung from Tycho’s data three precise laws of planetary motion:

1) The orbits of the planets are ellipses, with the sun at one focal point.

2) A line drawn from the sun to any one of the planets sweeps out equal areas in equal intervals of time.

3) The square of the period of a planet is proportional to the cube of the mean radius of its orbit.

Thanks to Kepler’s struggles, Tycho certainly had not lived in vain. Kepler’s three laws were to become the basis for Newton’s great universal laws of motion and gravitation. Kepler himself imagined a universal gravitational force holding the planets in their orbits around the sun, and he wrote:

“If two stones were placed anywhere in space, near to each other, and outside the reach of force of any other material body, then they would come together after the manner of magnetic bodies, at an intermediate point, each approaching the other in proportion to the other’s mass... ”

“If the earth ceased to attract the waters of the sea, the seas would rise up and flow to the moon... If the attractive force of the moon reaches down to the earth, it follows that the attractive force of the earth, all the more, extends to the moon, and even farther... ” “Nothing made of earthly substance is absolutely light; but matter which is less dense, either by nature or through heat, is relatively lighter... Out of the definition of lightness follows its motion; for one should not believe that when lifted up it escapes to the periphery of the world, or that it is not attracted to the earth. It is merely less attracted than heavier matter, and is therefore displaced by heavier matter.” Kepler also understood the correct explanation of the tides. He explained them as being produced primarily by the gravitational attraction of the moon, while being influenced to a lesser extent by the gravitational field of the sun.

Unfortunately, when Kepler published these revolutionary ideas, he hid them in a tangled jungle of verbiage and fantasy which repelled the most important of his readers, Galileo Galilei. In fact, the English were the first to appreciate Kepler. King James I (whom Tycho entertained on Hven) invited Kepler to move to England, but he declined the invitation. Although the skies of Europe were darkened by the Thirty Years War, Kepler could not bring himself to leave the German cultural background where he had been brought up and where he felt at home. Meanwhile, his contemporary, Galileo Galilei, who should have profited greatly from Kepler’s insights, ignored Kepler and broke off correspondence with him.

Chapter 6: GALILEO.

Suggestions for further reading

1. Irma A. Richter (editor), Selections from the Notebooks of Leonardo da Vinci, Oxford University Press (1977).
2. Lorna Lewis, Leonardo the Inventor, Heinemann Educational Books, London (1974).
3. Iris Noble, Leonardo da Vinci, Blackie, London (1968).
4. C.H. Monk, Leonardo da Vinci, Hamlyn, London (1975).
5. Thomas S. Kuhn, The Copernican Revolution, Harvard University Press (1957).
6. Angus Armitage, The World of Copernicus, The New American Library, New York (1951).
7. Arthur Koestler, The Watershed, Heinemann, London (1961).
8. D.W. Singer, Gordiano Bruno: His Life and Thought, Greenwood Press, New York (1968).
9. Edward A. Gosselin and Lawrence S. Lerner, Galileo and the Long Shadow of Bruno, Archives Internationales d’Histoire des Sciences, 25, 223 (1975).
10. Martin Olsson, Uraniborg och Stjarneborg, Almquist and Wiksell, Stockholm (1968).
11. Galileo Galilei, Dialogues Concerning Two New Sciences, Dover, New York (1954).
12. I. Bernard Cohen, The Birth of a New Physics, Heinemann, London (1960).
13. D.L. Hurd and J.J. Kipling (editors), The Origins and Growth of Physical Science, Penguin Books Ltd. (1964).

Top