HIS 332D Exam 2

Galileo and the Physics of Motion

-After he was condemned by the Church in 1633 and sentenced to house arrest, one might have expected Galileo—by then 71 and in poor health—just to give up and serve out his time. In fact this became one of the most scientifically active periods of his life, as he returned to the problems of motion that had been his main study before 1609. -While under house arrest at Arcetri near Florence, Galileo wrote up and extended his earlier studies of mechanics and motion into a book, Discourses on Two New Sciences. He could not have gotten permission to publish it in Italy, so he had the manuscript smuggled out to Leiden in Holland, where it appeared in 1638. -In The Assayer (1623), Galileo had declared that the book of nature is 'written in mathematical language,' and that 'its characters are triangles, circles, and other geometrical figures' (The Essential Galileo, p. 183). -Galileo drew an important distinction between primary qualities (the real objective properties of the physical world, which he said were limited to the size, shape, and motion of the particles that make up matter), and secondary qualities (such as color, smell, and taste) that are consequences of how these particles strike our sense organs. Secondary qualities, Galileo said, ultimately exist only in our minds. -Note that Galileo's primary qualities can all be treated mathematically.

Theme: The uses of mathematics

-As the key to hidden harmonies (Kepler) -As a descriptive tool (Galileo) -As a model of rigorous reasoning (Descartes)

Science, Scripture, and Truth: Galileo's Letters to Castelli and Christina

-Benedetto Castelli (1578-1643) had been Galileo's student at Padua and later became his close friend and supporter. Castelli taught mathematics at the University of Pisa and in Dec. 1613 had an important meeting with Grand Duke Cosimo II and his mother Grand Duchess Christina at which they asked Castelli how Galileo's views on Copernicanism could be squared with passages in the Bible that seemed to indicate that the Sun moves and the Earth stands still. -Grand Duchess Christina (1565-1637) remained a powerful figure in the Tuscan court after her husband Ferdinando died in 1609 and her son Cosimo became Grand Duke. She was known for her great piety; Galileo was very intent on reassuring her that his scientific views did not contradict scripture, when it was properly interpreted. -Toward the end of his letter to Castelli, and again in his Letter to Christina, Galileo gave an interpretation the 'Joshua miracle' (in which Joshua had said 'Sun, stand thou still' so that he could have more daylight to defeat his enemies) that was, he said, entirely compatible with Copernicanism. The key was Galileo's claim that the motion of sunspots showed that the Sun spins on its axis, and his suggestion that this spinning drove all other motion in the Solar System, including the rotation of the Earth. On this reading, Joshua was really telling the Sun to stop spinning on its axis, and this caused the Earth, too, to stop spinning, thus lengthening the day. -Galileo had written his letter to Castelli very hurriedly in Dec. 1613. In 1615 he wrote a more extended account of his views 'Concerning the use of Biblical Quotations in Matters of Science,' casting it as a letter to Christina, though in fact he intended to publish it as a small book. By the time he had finished it, however, the situation had changed and it would have been unwise, if not impossible, for him to publish such a book in Italy. Galileo's Letter to the Grand Duchess Christina did not appear in print until 1636, when it was finally published in Strasbourg.

Patronage, Symbolism, and Religion

-Besides simple curiosity and the desire to find new foods and medicines, work in natural history was also shaped in important ways by the pursuit of patronage and the use of plants and animals as symbols and metaphors. -Religious motivations also played a part in work in natural history, particularly in driving efforts to understand the wonders of God's creation. -On the title page of the Tesoro Messicano, Stelluti emphasized its patrons and the role the Lincean Academy had played in its production. -The Barberini bees on the frontispiece of Galileo's book The Assayer (1623) and on a column in Rome. -In 1625 Federico Cesi and Francesco Stelluti of the Lincean Academy presented Pope Urban VIII (Maffeo Barberini) with their Melissographia, a large printed sheet illustrated with images of bees as seen through a microscope. -This was the first time images of living things based on observations through a microscope had appeared in print. -Melissographia was an important contribution to natural history and also a bid for Urban's patronage. -Along with Melissographia, Cesi issued his Apiarium, a very large printed sheet laying out a mix of scientific information about bees and a celebration of Pope Urban's power and benevolence. -In 1594 Clusius founded the botanical garden at the University of Leiden in Holland. -The garden was intended to provide both a useful collection of medicinal plants and a microcosm of God's creation.

Blaise Pascal and the Weight of the Air, Experiments 'Touching the Void'

-Blaise Pascal (French, 1623-1662) performed some the most important pneumatic experiments of the 1640s, exploring the properties of the 'Torricellian space' and strengthening the evidence that the column of mercury in a barometer was held up by the weight of the air. -When he was 19, Pascal invented a mechanical calculator, later known as the Pascaline. -After hearing of Torricelli's experiments, Pascal repeated and extended them in the mid-1640s. He showed that the mercury stood at the same height whatever the shape or size of the space above it, and that the space could be made to disappear and reappear by tilting the tube. -In 1647 Pascal published New Experiments (or Experiences) Touching the Void; this was followed after his death by Treatises on the Equilibrium of Liquids and on the Weight of the Mass of the Air (1663). -In his books, Pascal did not give detailed accounts of particular experiments, but instead described what would happen under various circumstances. Rather than recounting specific events, he sought to describe the general course of nature—not 'I did so and so, and this happened,' but 'If one does so and so, this happens.' -Some of Pascal's 'experiments' are clearly impossible to perform as described: he didn't really hold a long glass tube against his skin while sitting deep under water. These instead represent simpler or more general cases of results Pascal had established to his own satisfaction by other experiments he does not describe. -For Pascal as for Galileo before him, experiments were important, but the line between 'thought experiments' and particular events was not yet clear.

Tycho Brache (1546-1601, Danish)

-Came from a very high-ranking noble family in Denmark -The greatest pre-telescopic observational astronomer -His very precise observations of the stars and planets established that the heavens are not unchanging -Tycho did not endorse Copernicanism, however, but proposed his own geo-heliocentric system, in which the planets circle the Sun which in turn circles a central stationary Earth -After a falling out with the new king of Denmark, Tycho left Hven in 1597. He was then appointed astronomer to the Holy Roman Emperor at Prague and built a new observatory near there. Tycho died in 1601 and is buried in Prague.

Theme: Debate over method

-Deductive rationalism (Descartes, Hobbes) vs. inductive empiricism (Bacon) -Use of experiments by Galileo, Harvey, Torricelli, and Pascal

Galileo's First Telescopic Discoveries: Sidereus Nuncius

-Galileo included woodblock prints of the Moon in Sidereus Nuncius. These are not absolutely accurate representations of the face of the Moon, but illustrate Galileo's points about the mountains and craters revealed along the line between the illuminated and dark parts of the Moon. -The Milky Way, which appears to the naked eye to be a faint glow in the sky, was revealed by Galileo's telescope to be huge mass of faint stars. -Galileo's most spectacular discovery came in January 1610, when he turned his telescope on Jupiter and spotted three little stars that seemed to line up next to it. As he watched on successive nights, the three stars—joined by a fourth—moved along with Jupiter through the sky, appearing sometimes on one side of it and sometimes the other. Galileo realized that they were moons orbiting around the planet. He had discovered new worlds in the heavens. -The moons of Jupiter were potentially of practical use. They provided what amounted to a giant clock in the sky, and Galileo showed how they could be used to find longitude by comparing the time of the moons' eclipses with the local solar time.

Galileo Galilei (1564-1642)

-Galileo was a famous figure in his own time, celebrated as a 'new Columbus' for discovering new worlds in the heavens. -Galileo's telescopes, these were among the first scientific instruments effectively to extend the human senses. -Galileo did not invent the telescope, but on hearing reports in 1609 of the new Dutch invention, he soon designed and made ones of his own that were substantially better. The Dutch spyglasses had a magnifying power of about 3; Galileo's had a power of about 20 or even 30. Galileo combined a convex objective lens with a concave eyepiece; the resulting 'Galilean' telescopes gave an upright image with a small field of view.

Galileo and the Laws of Motion

-Galileo's principle of relative motion, illustrated by a ball shot straight up from a moving toy locomotive. From the point of view of the locomotive, the ball just goes straight up and comes straight back down. From the point of view of a stationary observer, however, the ball follows a parabolic trajectory as it rises up and then falls back down to strike the locomotive. -The dialogues in Two New Sciences were set in the Arsenal, the great naval shipyard of the Venetian Republic. Galileo said he learned much by watching how the artisans at the Arsenal went about their work; they were 'truly expert,' he said, and their 'reasoning is of the finest.' -Much of Two New Sciences consists of a formal geometrical text, written in Latin by 'the Academician' (Galileo) and illustrated with diagrams, interspersed with discussions in Italian by Salviati, Sagredo, and Simplicio. -Galileo said that a body in free fall (or a ball rolling down a track) will undergo constant acceleration; its velocity will thus increase in direct proportion to the elapsed time (v = at), and the distance it falls will increase with the square of the elapsed time (d = ½ at2). -Galileo's experiments with balls rolling down tracks confirmed this law with high precision—but such experiments could never yield exact confirmation, any more than a diagram on paper can exactly match a geometrical theorem. -Galileo next combined his principle of inertial motion with his law of falling bodies to show that a ball rolling off a table will follow a parabolic trajectory. He then quickly extended this to projectile motion in general: the path of any projectile will form a parabola. -At the end of Two New Sciences, Galileo used his laws of motion to tackle a long-standing practical problem: calculating range tables for artillery. -According to the range tables in Galileo's Two New Sciences, the greatest range for any given initial velocity occurs at a launch angle of 45 degrees. Note, however, that in deriving this, Galileo ignored air resistance; his laws are idealizations and must be adjusted to apply accurately to 'real world' cases.

William Harvey and the Circulation of the Blood, Experiments and Facts

-Harvey based his theory of the circulation of the blood on many dissections of humans and animals, as well as experiments on himself and others. He focused on establishing the circulation of the blood as an experimental fact, leaving any explanation of its ultimate purpose for later. Although it was not his intention, Harvey's treatment of the heart as a pump also contributed to the mechanical program, which sought to treat everything in nature in essentially mechanical terms, as simply matter in motion. -Harvey performed many dissections of both humans and animals, as well as vivisections of living animals—including deer hunted by King Charles I. -The Royal College of Physicians made a film recreating Harvey's experiments in 1927 (remade in color in 1957 and 1972); you can find a link to it on our Canvas page under 'Supplementary Documents and Links.' Be warned, however: it is quite bloody and not for the squeamish. -Harvey showed the action of the one-way valves in the veins of his arm by tying a tourniquet to make the veins stand out. When he then ran his finger along the vein, pressing the blood toward his hand (away from his heart), the vein remained empty, since the valve in it only allowed blood to flow inward, toward the heart. -Like Vesalius before him, Harvey could find no holes in the septum of the heart. He concluded, as Colombo had, that blood was not passing from the right ventricle to the left one through the septum, but instead was being pumped through the lungs. -Harvey thus arrived at his model of the circulatory system: the heart pumps venous blood (blue) through the lungs, exposing it to air and transforming it into arterial blood (red). The heart then pumps the arterial blood out through body, where is converted back into venous blood and then returns to the heart for another cycle. -Harvey could not see the tiny blood vessels in which venous blood was transformed into arterial blood in the lungs, and arterial blood into venous blood in the extremities, but he was sure they must exist. Marcello Malpighi finally observed these capillaries through a microscope in 1661. -Harvey's claims about the circulation of the blood were criticized by more conservative physicians, but the evidence eventually proved overwhelming and within a couple of decades his theory was generally accepted. -During the English Civil War of the 1640s, Harvey's ties to King Charles led to him being harassed by mobs, but he remained a royalist. He attracted a circle of younger experimentalists at Oxford, including Robert Boyle, and later retired to London, where he died in 1657. -Harvey was an important figure in the rise of experimental methods in science and medicine, and also in the emergence of England as a major center of the new science in the 17th century.

Galileo: Fame and Patronage

-He was named Philosopher and Mathematician to the Grand Duke of Tuscany. -Galileo emphasized that he had named the newly-discovered moons of Jupiter the 'Medicean Stars' ('Medicea Sidera') for his prospective patron, Cosimo de Medici. -Galileo's Sidereus Nuncius received the required 'imprimatur' from Church officials, attesting that it contained nothing objectionable. -Galileo published an account of his new discoveries in his Letters on Sunspots (1613). -Besides its description of his observations of sunspots and the phases of Venus, Galileo's Letters on Sunspots (1613) had several notable features: Galileo wrote it in Italian to reach a wider audience beyond the university-trained elite, he emphasized his status as 'Philosopher and Mathematician to the Grand Duke of Tuscany', it was published by the recently-founded 'Lincean Academy,' led by Prince Federico Cesi, which promoted the new science, and it was Galileo's first overtly pro-Copernican work.

Tesoro Messicano (1651): Treasures from the New World

-In 1571 King Philip II of Spain commissioned Francisco Hernández to gather medically useful plants in New Spain (Mexico). Drawing on local Nahuatl-speaking experts and artists, Hernandez compiled a vast collection of images and specimens. -Hernández sent this material to Spain in 1576, but organizing it took decades; much of the work was done in Italy by Federico Cesi and his Lincean Academy, culminating in Francesco Stelluti's publication of the Tesoro Messicano (1651). -Title page of Francesco Stelluti's Tesoro Messicano (Rome, 1651), more formally titled Rerum Medicarum Novae Hispaniae Thesaurus, seu Plantarum, Animalium, Mineralium Mexicanorum ('Inventory of Medical Items from New Spain, or, History of Mexican Plants, Animals, and Minerals'), based on the collections gathered by Francisco Hernández. -The Latin text and careful engravings helped to disseminate among Europeans knowledge of New World plants and animals. -A tobacco plant and a workman crushing its leaves, from 'La Historia Universal de las Cosas de Nueva España' ('The Universal History of the Things of New Spain'), a manuscript compiled between 1545 and 1590 by Bernardino de Sahagún and his Nahua collaborators; it is now generally known as the Florentine Codex. -Tobacco plant, from Nicolas Monardes's account of medicinal plants of the West Indies, published in Spain in parts between 1565 and 1574. -John Frampton called his English translation of Monardes's book Joyfull Newes out of the Newe Founde Worlde (1577). Like Monardes, he praised the health-giving virtues of tobacco. -The Dutch physician Giles Everard went further: in his 1587 book De Herba Panacea, he proclaimed that tobacco could cure almost any disease. Such ideas long remained in circulation; this English translation of Everard's book appeared in 1659. -Philippe Sylvestre Dufour's Treatise on the Novelties and Curiosities of Coffee, Tea, and Chocolate (Lyon, 1671) promoted these exotic drinks from Arabia, China, and the Americas.

Uraniborg: Tycho's Castle-Observatory

-In 1576, King Frederick II of Denmark gave Tycho control of the island of Hven near Copenhagen, making him feudal lord over the island and the peasants living there. Tycho built there a castle-observatory which he called Uraniborg, or 'castle of Urania,' dedicated to the muse of astronomy. Over the next twenty years Tycho turned Hven into a great center of astronomical research. -Tycho believed there were deep connections between the Heavens and the Earth, and he had a strong interest in alchemy as well as astronomy. He built a large alchemical laboratory in the basement of Uraniborg, equipped with furnaces and other apparatus. -The observing towers at Uraniborg were exposed to the wind, making them too unstable for highly precise observations. Tycho thereforce built Stjerneborg nearby, with instruments like this sextant mainly mounted in underground structures.

The Tychonic System

-In 1577, just before completing his move to Hven, Tycho made observations of a comet that established that its orbit must cross those the planets. This showed that there could not be real solid crystalline spheres in the Heavens. -Having rejected the crystalline spheres, Tycho suggested around 1580 that the planets circle the Sun, which in turn circles the stationary Earth. This geo-heliocentric system made better sense of the pattern of the planets' motions than Ptolemy's purely geocentric system did, while not involving the apparent absurdities of Copernicus's moving Earth.

Science and Ideology in the English Civil War: Thomas Hobbes

-In January 1649, the English Parliament put King Charles I on trial for treason. Claiming he ruled by divine right, Charles refused to recognize the legitimacy of the trial. Not surprisingly, he was convicted and sentenced to death. -On 30 January 1649, King Charles I was beheaded in London in front of a large crowd. -After Charles was beheaded, Parliament abolished the monarchy. In 1653 Oliver Cromwell dismissed Parliament and installed himself as 'Lord Protector.' But what was the proper basis of Cromwell's authority? -The 1640s and 1650s were a great period for political philosophy in England, as theorists wrestled with deep questions about how society should be organized.

William Harvey and the Circulation of the Blood, Early Theories of the Heart and Blood

-In his 1628 book De Motu Cordis et Sanguinis ('On the Motion of the Heart and Blood'), the English anatomist and physician William Harvey (1578-1657) presented compelling evidence that the heart acts as a pump to circulate blood through the body. Harvey's discovery marked a major break with earlier Galenic theories of the heart and blood; even more importantly, it introduced experimental methods into medicine and physiology. Harvey's work also provides illuminating examples of the ways patronage could contribute to the credibility of scientific claims. -In Galen's humoral theory, the veins distribute nutriment to feed the body, while the arteries distribute 'pneuma' or vital spirit to vivify the body, keeping it warm and active. -Galen said fresh air is drawn through the lungs right into the left ventricle of the heart, where it vivifies the arterial blood. -Galen saw the venous and arterial systems as largely separate, with the contractions of the heart making both kinds of blood slosh back and forth through the body. -According to Galen, a small amount of venous blood passes through small holes in the septum of the heart to feed and replenish the arterial blood. -Vesalius could not detect the holes Galen said must exist in the septum of the heart. In the first edition of his De Fabrica (1543), Vesalius said it was marvellous that venous blood could pass through seemingly impermeable septum. In the second edition (1555), Vesalius just said no blood could get through it and presumably Galenic theories would have to be adjusted. -In the second half of the 16th century, anatomists at the University of Padua made other discoveries that were hard to reconcile with Galenic theory. For instance, they found that valves in blood vessels allowed the blood to flow in only one direction—out from the heart in arteries, back toward the heart in veins. Their studies of the pulmonary vein also made it hard to believe it carried air into the heart: it was always filled with blood, not air, and it structurally it was much more like a vein than a windpipe. -The Padua anatomist Realdo Colombo (c. 1510-1559) introduced the idea of pulmonary circulation in his De Re Anatomica, published just after his death in 1559. -Several physicians, including Ibn Al-Nafis in 13th century Syria, had hit on similar ideas before Colombo, but their theories remained unknown until much later. -Galen's system is basically open-ended; venous blood (blue) and arterial blood (red) both slosh back and forth rather than circulating in a closed loop. -Colombo's pulmonary circulation partially closed the loop by showing how venous blood is converted into arterial blood in the lungs. But the venous and arterial systems were still left unconnected at the other end; the two kinds of blood just sloshed back and forth.

Descartes and His Method, 'Cogito ergo sum'

-In his Discourse on Method, Descartes famously declared 'Cogito ergo sum' ('I think, therefore I am'). This statement, on the surface a product of extreme skepticism, provided the foundation on which Descartes sought to overcome skepticism and build his new philosophy. -Descartes lived in a time of religious and intellectual upheaval, in which the traditional foundations of belief were being called into question. -Descartes's Discourse on Method offered, its subtitle said, a means to 'the well-guiding of REASON,' and to the 'the Discovery of Truth in the Sciences.' This was especially attractive in the mid-17th century, as many Europeans were searching for a new and better way forward. -Taking mathematics as his model of rigorous reasoning, Descartes sought to isolate the rules of reason that made mathematical conclusions so certain. He said we should rely only on ideas that are 'clear and distinct' in our minds; we should analyze problems into their simplest elements; and we should advance to our conclusions only by clear and secure steps. -He then set out to doubt any claim or belief that did not meet these criteria. -As he engaged in systematic doubt, Descartes called into question all past authority and tradition, all sense experience, his own memory, and even his usual course of reasoning. But he found he could not doubt his own existence: even to formulate such a doubt was to prove his own existence.

Blaise Pascal and the Weight of the Air, Pumps, Siphons, and Barometers

-In the 1630s and 1640s, the study of pneumatics—the effects of air pressure—became an active area of experimental science. It had close ties to the practical technologies of pumps and siphons, and also to fundamental questions about the nature and structure of matter, the possible existence of a true vacuum, and proper methods of experimentation. -By 1600, practical experience with suction pumps had established that they could raise water no more than about 30 feet. -A siphon: once the flow is started, it will continue until either the upper vessel is emptied or the level in the lower vessel rises to equal that in the upper one. -In 1630 Giovanni Baliani wrote to tell Galileo of a curious experience with a siphon that was designed to carry water over a rise of about 70 feet. Once the pipe was completed and filled, the water did not flow evenly to the lower elevation, but settled in the pipe at about 34 feet above the level at either end. It was hard to open a plug at the top, but when Baliani did, air rushed into the pipe and the water drained completely from both sides. -Around 1643, Gasparo Berti performed an experiment in Rome to what would happen if he filled a long pipe with water, sealed it at the top end with a glass bulb, and inverted it into a bucket. He found that the water in the pipe fell to a level about 34 feet above the surface of the water in the bucket, and that the space in the glass bulb appeared to be completely empty. -In 1644 Evangelista Torricelli (1608-1647) repeated Berti's experiment using mercury in place of water, producing the first real barometer. -Torricelli argued that his barometer was in effect a balance, in which the weight of the mercury in the tube was balanced by the weight of the air bearing down on the mercury in the dish. -Torricelli declared that 'we live submerged at the bottom of an ocean of air.' -Torricelli believed the space at the top of his barometer to be a true vacuum, devoid of all matter—but he could not prove this. Whatever they thought of its real nature, however, experimenters could now study the properties of this 'Torricellian space.'

Kepler's Laws of Planetary Motion: Equal Areas and Elliptical Orbits

-Kepler found that as Mars went around the Sun, it moved more quickly when it was closer and more slowly when it was farther away. He soon refined this to show that the line from the Sun to Mars sweeps out equal areas in equal times. -Kepler next sought to determine the exact shape of Mars's orbit (and presumably the other planets' as well). After great struggles, he found it to be an ellipse, though one that is very close to a perfect circle.

Johannes Kepler and God's Geometry

-Kepler saw mathematics as the key to a deeper level of reality—in a sense, to reading God's thoughts. -Kepler's views on the centrality of mathematics appear in almost all of his works, but especially in his Harmonices Mundi ('Harmonies of the Worlds') of 1619. There he asserted that geometry was 'co-eternal with the mind of God' and 'provided God with a model for the Creation.' By finding those mathematical patterns, we are sharing God's thoughts. -Pythagoreans/Platonists say yes, the natural world is intelligible to our minds, because God built the world on mathematical patterns and gave us minds capable of grasping those patterns, and thus of sharing God's thoughts. -Kepler believed these divine mathematical patterns must also be reflected in the observable world, and he was strongly committed to checking his theories against empirical measurements. In that respect his nested polyhedra didn't quite work; though some of the ratios fit observations quite well, others didn't. Nonetheless he remained hopeful that it would be found to contain a seed of truth, and in 1621 he brought out a second edition of his Mysterium Cosmographicum. -Kepler's theory of nested polyhedra solidified his commitment to Copernican heliocentrism and also drove him to seek better data on planetary distances. He thus turned to Tycho, the great authority on astronomical measurements and in 1599 applied for job as one of his assistants. By then Tycho had left Hven and settled at Benatky Castle, near Prague, where he became the astronomer and astrologer to the Holy Roman Emperor, Rudolph II. -Tycho died not long after Kepler went to work for him, but their collaboration had enormous consequences for Kepler's later work. It was in the confrontation of Kepler's mathematical vision with Tycho's observational data that modern astronomy really began.

Kepler's Laws of Planetary Motion: Plotting Planets' Orbits

-Kepler sought to construct an account of the motions of the planets that would be both mathematical and physical. To do that, he drew on Tycho's highly precise observational data, and in the early 1600s these led him to formulate three laws of planetary motion that he believed reflected God's plan and handiwork. -Kepler was a firm Copernican and wanted to use Tycho's data to improve and extend the heliocentric theory. -Kepler was given the job of solving the motion of Mars. Kepler started by charting the actual path Mars followed through space, according to the Ptolemaic and Tychonic theories. -Kepler eventually published his results in his Astronomia Nova (1609), one of the most important books of the Scientific Revolution. -Kepler wanted not just an 'Alexandrian' account of mathematical methods that would predict appearances, but a physical theory that could explain the motions of the planets by forces acting on them. -Kepler believed these physical causes would also follow mathematical rules, and that the motions of the planets could thus be described mathematically. He tried various ways to model the motion of Mars around the Sun, including using an equant to account for its changing speed.

Kepler's Laws of Planetary Motion: The Harmonies of the Worlds

-Kepler's patron Emperor Rudolf II was deposed in 1611. -Kepler sought harmonies in the skies, and in 1619 published his Harmonices Mundi ('Harmonies of the Worlds') in which, amid much else, he stated the third of his Laws of Planetary Motion. -Kepler applied music theory to the motions of the planets and, by assigning musical tones to their changing speeds, claimed to find a literal 'harmony' in their motions around the Sun. -In Harmonices Mundi, Kepler also laid out a mathematical relationship between the periods of the planets and the sizes of their orbits. He found that the square of the period divided by the cube of the orbital radius was the same for all of the planets—thus firmly uniting the Copernican planetary system. -Kepler summarized his various results in his Epitome of Copernican Astronomy (1621). -Kepler finally published his Rudolphine Tables in 1627. Based on his most advanced theories and the best observations (mainly from Tycho), it marked an enormous improvement over all earlier astronomical tables. -Kepler's Rudolphine Tables gave far more accurate predictions of the positions of the planets than did tables based either on Ptolemy's theory or the original version of Copernicus's theory. In Kepler's hands, heliocentrism finally had a clear empirical advantage over geocentric theories.

Descartes and the Mechanical Philosophy, The Laws of Motion and Impact

-Laws of motion, particularly laws of impact, lay at the foundation of Descartes's mechanical philosophy. Though he made fundamental contributions, particularly in clarifying the principle of inertial motion, Descartes's laws of impact were deeply flawed and later had to be corrected. -Because Descartes had completely separated mind from matter, he held that a particle of matter cannot 'know' anything—it can't know where it is, where it has been, or where it ought to go next. It thus cannot have any 'natural motion' toward the center of the universe or anywhere else. All it can do, Descartes said, is keep doing what it is doing: it can only remain in the state of motion is already in, moving in a straight line at a steady speed, unless and until something else acts on it. This was Descartes's principle of inertial motion, and was a substantial step from Galileo's earlier version of it. -What can act on a body to change its state of motion? According to Descartes, only one thing: a collision with another body. The only thing a body can ever 'know' is that it just got hit. Everything in Descartes's universe happens by direct contact action; there are no 'sympathies' and no action at a distance. -When one body strikes another, they bounce off. Descartes said motion itself is indestructible, so that the total quantity of motion (size times speed) is the same after the collision as before. -Thus when two equal bodies strike each other, they must bounce off with the same speeds they came in with. -Note, too, that by the principle of the relativity of motion, which Descartes borrowed from Galileo, we can treat either body as at rest or in motion; only their relative motions count. -Descartes had more trouble with the case of a smaller body colliding with a larger one. He laid down as a necessary principle that "a body upon coming in contact with a stronger one, loses none of its motion; but that, upon coming in contact with a weaker one, it loses as much as it transfers to that weaker body." This contradicts experience and is inconsistent with Galileo's principle of the relativity of motion (which Descartes accepted). Descartes's laws of impact were a mess and had to be cleaned up later, mainly by Christiaan Huygens in the 1660s.

Descartes and His Method, Mind and Matter

-Look closely at the 'I' in Descartes's 'I think, therefore I am': it is not the physical René Descartes, a Frenchman with arms and legs, but only his conscious mind. His great challenge would be to go beyond this and try to establish the existence and properties of the material world. -To this point Descartes had established only the existence of 'that which thinks': res cogitans. His next step would be to establish the existence and properties of the material world, what he came to call 'that which is extended': res extensa. Pure reason led him to conclude that the physical world is purely mechanical, consisting solely of particles whose only properties are size, shape, and motion. Having drawn such a strict line between mind and matter (mind-body dualism), Descartes had a hard time connecting them back up. -The last part of the Discourse on Method is basically a come-on for the still-unpublished Le Monde, with examples of the power and utility of Descartes's approach. Descartes said that by following his method, we can become the 'masters and possessors of Nature.' -Descartes extended his mechanical program even to animals and human bodies, which he said are essentially machines. But humans, he said, have something extra: conscious minds and immortal souls. But how are our minds and bodies connected? Descartes fell back on the 'pineal body,' a small organ in the center of the brain that he said was the connecting link between mind and body. -Descartes was intensely interested in anatomy and physiology and developed elaborate explanations of the nervous and muscular systems and of the organs of perception. He said all of these were connected to the mind through the pineal body, but he could never explain exactly how this worked. Descartes had split mind so completely from matter that he was left with no convincing way to connect them back up. -Many later Cartesians left aside his ideas about mind and focused on devising hypothetical mechanisms to explain physical phenomena.

Galileo and the Church: Background and Context

-Much of the context for Galileo's troubles with the Church lay in the Counter-Reformation of the late 16th and early 17th centuries, as the Catholic Church responded to the Protestant Reformation by tightening up its internal discipline and sharpening its positions on many disputed points. -After 1610, Galileo used the fame his telescopic discoveries had brought him to launch a frontal attack on Aristotelian natural philosophy. His public advocacy of Copernicanism was an important part of this broader intellectual campaign. -Between 1610 and 1616, Galileo engaged in a series of disputes over many scientific and philosophical issues. Most of his opponents were Aristotelian philosophers seeking to defend established scholastic doctrines and methods. -Galileo's Letters on Sunspots (1613) reflects his approach: it was overtly pro-Copernican, it was written in Italian to reach a new audience outside the universities, and it was sponsored by the Lincean Academy, strong supporters of the new science. -Galileo was not seeking a confrontation with the Church, but Aristotelian scholasticism had been so tightly woven into the fabric of the Church's doctrines that it was difficult for him to avoid a conflict of some kind.

New Worlds of Natural History

-Natural history focuses on the collection, description, and classification of animals, plants, and minerals. It seeks to find order in nature and patterns within diversity. Much work in natural history also aims at gathering useful information, especially concerning foods and medicines. -All cultures have their own systems of natural history to organize their knowledge of the natural world. European work in natural history had ancient roots (Aristotle, Theophrastus, Dioscorides), but it took on a new global dimension between about 1450 and 1650. This period was also marked by new emphasis on illustrations, especially after the introduction of printing. -Voyages in the late 15th and early 16th centuries, especially by the Portuguese along the coast of Africa and to the Indian Ocean and by the Spanish to the Americas, exposed Europeans to a flood of new descriptions, drawings, and specimens of plants and animals that were previously unknown to them. -Working from fragmentary descriptions, Europeans sometimes produced rather fanciful depictions of plants and animals from far-off lands, as in Albrecht Dürer's famous woodcut of a rhinoceros (1515). -Later images of rhinoceroses were based more on Dürer's woodcut than on observations of actual rhinos. -Botanical books such as Leonhart Fuchs's History of Plants (1542) included images of many plants from the Americas that were new to Europeans, such as the capsicum peppers shown on the left. Fuchs was sometimes confused about where these new plants really came from, as when he identified corn (maize) as coming from Turkey, rather than the Americas.

Johannes Kepler (1571-1630)

-One of the key figures of the Scientific Revolution -Driven by a strong belief that the universe must be mathematically beautiful, and an equally strong belief that our theories must fit with the empirical evidence, he took Copernicus's idea that the Earth goes around the Sun and turned it into a solid and accurate theory in which the motions of the planets were governed by physical and mathematical laws. -At the University of Tübingen, Kepler studied mathematics and astronomy under Michael Maestlin (1550-1631), who became his lifelong mentor. Maestlin was one of the few true Copernicans of the time, and through him Kepler soon became an enthusiastic adherent of the heliocentric theory. -In 1594, Kepler took a job teaching mathematics in Graz, Austria and while there he hit on an idea that would obsess him for years to come: that the five 'Platonic solids' might hold the key to the architecture of the universe.

Blaise Pascal and the Weight of the Air, The Puy de Dôme Experiment

-Pascal published a revealing account of a specific experiment—one that was actually performed by his brother-in-law, Florin Perier, who in 1648 carried a barometer up the Puy de Dôme in central France. This experiment showed very clearly that the mercury in the barometer was held up by the weight of the air bearing down on it. But it did not—and really could not—prove that the 'Torricellian space' was a true vacuum. Experiments are about finding properties, not essences. -Pascal's 'vacuum-in-a-vacuum' experiment, in which he in effect set up a barometer in the 'Torricellian space' atop another barometer. When Pascal let air into the space of the lower barometer, the fall of the mercury in the lower barometer and its rise in the upper one showed that it was being held up by the weight of the air, not the 'strength of the vacuum.' -Pascal next sought to show this effect more directly by somehow varying the weight of the air bearing down on the mercury. -A 19th-century print depicting Pascal's brother-in-law Florin Perier taking a barometer up the Puy de Dôme in September 1648. -Pascal later published a very full 'history' of this event, treating it as specific evidence of what happened on a particular occasion, as well as of what happens under any such circumstances.

Theme: The mechanical philosophy

-Regarded matter as just 'dead rocks' with only size, shape and motion (primary qualities) -Invented detailed mechanisms to account for natural phenomena

Descartes and the Mechanical Philosophy

-René Descartes (1596-1650) was one of the main proponents of the mechanical philosophy: the belief that the material universe consists solely of particles ('dead rocks') whose only qualities are size, shape, and motion. The mechanical philosophy became very influential in the 17th century and was widely seen as providing a new and comprehensive basis for understanding all of the workings of the natural world. -According to Descartes, the physical world is entirely intelligible because it is fundamentally very simple: it is just bits of matter in motion, as transparent to reason as a piece of clockwork. -Moreover, Descartes believed that everything in the physical world could in principle be fully understood simply by thinking hard about how it must be. -Descartes's hypothetical model of a magnet. Rather than falling back on mysterious 'principles' or 'sympathies,' Descartes claimed he could explain magnetic attraction and similar phenomena simply by the motion of invisible particles of matter. -The foundation of Descartes's mechanical philosophy was his belief that everything could be reduced simply to matter in motion. He thus needed some laws of motion, and he set out to provide them in his Principles of Philosophy (1644). -For Descartes, the fundamental laws of nature were not to be found empirically, by experiment and measurement, but deductively, from necessary first principles. These must then lead to results, as in his law of refraction and his explanation of the rainbow, that would match observations, but as in geometry, the laws and principles came first and were not derived from the observations.

Descartes and His Method

-René Descartes (1596-1650) was one of the most important figures in the history of philosophy. His ideas had a great impact on science as well. He made major contributions to mathematics (Cartesian coordinates), optics, and mechanics, but his greatest effect came through his underlying method and the theories of matter and mind to which it led. -He aimed to overturn what was left of Aristotelian scholasticism and replace it with a new philosophical system of his own devising. -He also sought to combat a rising tide of skepticism and provide a new and solid foundation on which human knowledge could be built. He would do this by using the tools of skepticism to defeat skepticism. -Descartes was born in 1596 in the town of La Haye in west central France. The town was later renamed Descartes in his honor. -When he was 10, Descartes was sent off to the Jesuit school at La Fleche. He did very well there, though he later said he found much of what he was taught to be empty and unsatisfying. -After a few years studying law, Descartes took up a career as a professional soldier during the Thirty Years War. He wasn't involved in much fighting, but he learned military engineering and began to study with the Dutch philosopher and mathematician Isaac Beeckman. -Descartes was impressed by the conclusiveness of mathematical proofs and sought to bring the same rigor to all other areas of thought. -Descartes spent much of the 1620s in Paris, working on mathematics and developing his philosophical ideas. In 1628 he moved back to the Netherlands, where he would spend most of the rest of his life, and began writing what he regarded as his great work, Le Monde ('The World'), in which he laid out his mechanical theory of light and matter, including his vortex theory of the solar system. Descartes's theory was strongly Copernican, and when he learned in 1633 that Galileo had been condemned by the Church, he withdrew Le Monde from publication—Descartes did not want to confront the Church, but rather to win it over to his new philosophy. Le Monde was not finally published until 1664, after Descartes's death. -After putting Le Monde aside, Descartes tried a new tack that downplayed his Copernicanism and focused on his underlying method. -Descartes's short Discourse on Method appeared in 1637 along with three treatises meant to show the power of his approach: on Dioptrics (reflection and refraction of light), on Meteorology (atmospheric phenomena, including rain, wind, and rainbows), and on Geometry (in which he introduced Cartesian coordinates, expressing curves as equations). -Descartes followed his Discourse on Method with Meditations on First Philosophy (1641) and Principles of Philosophy (1644). He soon became well known throughout Europe, though his ideas remained controversial. -In 1649, Queen Christina of Sweden invited Descartes to come to Stockholm to tutor her in philosophy, but neither the queen nor the Swedish climate suited Descartes; on 11 February 1650 he died of pneumonia.

Theme: Belief and authority

-The Galileo affair -Hobbes on science, religion and the state

Theme: Response to Copernicanism

-The new astronomy (Copernicus, Kepler) requires new physics (Galileo)

Science and Ideology in the English Civil War: Thomas Hobbes, cont.

-Thomas Hobbes's Leviathan (1651) gave the fullest and most influential account of his social and political ideas. It aroused enormous controversy, which extended to the scientific and philosophical principles on which he said it was based. The reaction against Hobbes later strongly affected attitudes in England toward his form of the mechanical philosophy. -From one angle, Hobbes's Leviathan was about the social and political implications of his form of the mechanical philosophy; from another, it was about how authority could properly be constituted in a society and civil war and anarchy avoided. -The frontispiece of Hobbes's Leviathan famously depicts a sovereign whose body is made up of many little people. Hobbes emphasized that the state itself—the 'Leviathan'—is a human construction, and said we can understand it by mentally taking it to pieces and seeing how its parts interact. This was a kind of social atomism. -According to Hobbes, individuals are driven by appetites and aversions; left to themselves they would engage in a constant 'war of each against all,' rendering their lives 'solitary, poor, nasty, brutish, and short.' To avoid this, individuals must in effect sign their freedom of action over to a sovereign in return for protection: 'law and order.' -Hobbes's mechanical philosophy thus led him to advocate a strongly authoritarian political system. -For Hobbes, the authority of the sovereign must be absolute, not just in 'political' matters but also in religion—thus his sovereign holds not just the sword of state power but the also the crosier of religious authority. This, he said, was the only way to avoid division, anarchy, and civil war. The authority of the sovereign must extend even to control over the teaching of philosophy and mathematics; Hobbes also objected to scientific experimentation, since it would lead to claims of access to truth independently of the sovereign. -The sovereign could be a king, and Hobbes usually claimed to be a good royalist; in the 1640s he had been part of the English royal court in exile in Paris and had even been the mathematics tutor to the young Prince of Wales, the future King Charles II. But Hobbes's reasoning could be applied to any sovereign that was able to provide 'law and order,' including Parliament or Cromwell. This (along with Hobbes's conflicts with the clergy) led to a break with the English court in exile; late in 1651 he left Paris and returned to England. -For the rest of his long life, until his death in 1679, Hobbes was denounced as a wicked atheist and threatened with prosecution for blasphemy. His patrons, the Cavendish family, protected him, as did King Charles II after the restoration of the monarchy in 1660, but more out of personal regard than agreement with his views. -Hobbes got in many fights in this period, including acrimonious disputes with mathematicians about his mistaken claims to have 'squared the circle.' -Hobbes's objections to experimentation as a path to real knowledge led him into disputes in the 1660s with Robert Boyle and other founders of the Royal Society of London, particularly over Boyle's experiments with the air-pump. -More broadly, in the later 17th century many English thinkers came to see Hobbes as an example of the dangerous and mistaken consequences of following a strict form of the mechanical philosophy. After about 1650 they increasingly turned away from Descartes's and Hobbes's deductive approach and developed more modest empirical methods, as we'll see when we take up Boyle, Locke, and Newton.

Galileo's 'First Trial': The Church Condemns Copernicanism (1616)

-Though he faced criticism, Galileo had important supporters within the Church, notably Cardinal Maffeo Barberini. -Barberini advised Galileo not to confront the theologians directly but just to argue that the motion of the Earth was an interesting hypothesis, even if not literally true. Galileo, however, was reluctant to compromise in this way. -Paolo Antonio Foscarini was a Carmelite monk and professor of theology in southern Italy. Early in 1615 he published a little book defending Galileo and arguing that any apparent conflict between Copernicanism and scripture could be readily resolved. -At first Galileo and his friends welcomed this support, until they realized that Foscarini's book would give Galileo's opponents a convenient and relatively safe target—they could strike against Galileo's ideas without having engage with Galileo himself. -Foscarini sent a copy of his little book to Cardinal Robert Bellarmine (1542-1621), a Jesuit scholar who was the leading Catholic theologian of the time. Bellarmine's reply is one of the most important documents of the whole Galileo affair. Bellarmine rejected Foscarini's position (and by implication, Galileo's) and laid out very concisely the orthodox position: in cases of apparent conflict, the accepted interpretation of the Bible must prevail over any scientific results. -Late in 1614, a Dominican monk in Florence, Niccolo Lorini, had obtained a copy of Galileo's letter to Castelli. Believing Galileo's views on the interpretation of scripture to be heretical, Lorini sent the letter to the Inquisition in Rome, which launched a formal investigation. In February 1616 a board of theologians in Rome declared the propositions that the Earth moves and the Sun stands still be to be 'philosophically absurd' and 'theologically erroneous'—even heretical, in that they contradict the accepted interpretation of several Biblical passages. The next month Foscarini's book was put on the Index of books banned by the Church, as was Copernicus's De Revolutionibus until various offending passages could be censored. -None of Galileo's books were banned in 1616, but Pope Paul V ordered Cardinal Bellarmine to give Galileo a personal warning not to teach or defend Copernicanism any longer. Galileo obeyed, at least for a while.

Descartes and the Mechanical Philosophy, cont.

-Though his laws of impact were flawed, Descartes set about devising hypothetical mechanisms with which to explain a wide range of physical phenomena—indeed, he sought to provide a theory of everything. Although most of Descartes's detailed mechanisms were later rejected, his goal of providing purely mechanical explanations proved widely influential. -Descartes's vortex theory of the Solar System proved especially influential. It pictured the Earth and planets being carried around the Sun in a swirling whirlpool of invisibly small particles, and promised to explain not just why the planets go around the Sun but how and why the Sun gives off heat and light, why comets sometimes come sweeping toward the Sun, and everything else about the workings of the heavens. -Descartes said his vortex theory could also explain why objects fall to the ground: it is not their 'natural motion' toward a 'natural place,' nor is it an 'attractive force' that acts across space from one body to another, but instead is simply the result of a difference in pressure set up as invisible particles of matter swirl around in the Earth's vortex. -Magnetic phenomena, particularly the way a compass needle points toward the North Star, had long been taken as the classic example of immaterial 'sympathies' acting on matter. This posed a special challenge for Descartes. He responded by devising an elaborate hypothetical model, shown here, in which magnetic bodies, including the entire Earth, are penetrated by spiral threaded channels through which screw-shaped particles continually pass. The motion of these particles causes magnetic needles to align with the poles of the Earth, Descartes said, and their pressure pushes together magnets and bits of iron. Descartes's mechanism was entirely hypothetical, but it made his point that even magnets could be explained purely mechanically. -Descartes and later Cartesians tended to treat experiments less as sources of new knowledge than as illustrations of phenomena that they would then claim to explain mechanically. In his Principles of Philosophy and other writings, Descartes included a number of physical analogies, like this stone in a sling, to illustrate his ideas and try to make them more credible. -Descartes's extremely ambitious intellectual and scientific program did not prove entirely successful; in the end he was not the 'winner' of the Scientific Revolution. -But Descartes's ideas, particularly his form of the mechanical philosophy, would have a strong influence in the 17th century, and the response to them, above all by Isaac Newton, eventually set science on a new and very productive course.

Galileo's 'Second Trial': Galileo is Forced to Recant (1633)

-Three prominent comets appeared in the sky in 1618, and though health problems prevented Galileo from observing them himself, he engaged in a heated exchange about them with a Jesuit astronomer, Orazio Grassi, culminating in Galileo's book The Assayer (1623). -Although he was mostly wrong about the comets themselves, Galileo made some good points in The Assayer about proper method, the uses of mathematics, and the nature of matter. The book came out just as Galileo's friend Maffeo Barberini was being elected Pope Urban VIII, and Galileo and other members of the Lincean Academy hoped they would now be able again to promote the new science, including Copernicanism. -Galileo's Dialogue required an 'imprimatur' from Church officials attesting that it did not contain anything objectionable. After many delays, Galileo secured a preliminary imprimatur in Rome; when various complications, including an outbreak of the plague, forced him to have the book printed in Florence instead, he secured a second imprimatur from Church officials there. He included both imprimaturs when the book was finally published, a move that irritated officials in Rome. -In June 1633 he was forced to recant his belief in the Earth's motion. He thought he had worked out a plea bargain and would be given only a light reprimand; he was surprised when he was in fact sentenced to house arrest for the rest of his life.

Theme: Patronage

-Tycho and the king -Kepler and the emperor -Galileo and the Medici -Harvey and the king

Tycho and Observational Astronomy

-Tycho used a variety of astronomical instruments to measure the positions of stars and planets, including the quadrant and the cross-staff -In 1572, Tycho spotted a bright new star in the constellation Cassiopeia. His careful measurements showed that it must be above the orbit of the Moon—proving that Heavens were not wholly unchanging. Tycho recounted his observations in his book De Stella Nova ('On the New Star'); the star became known as 'Tycho's star.' -'Tycho's star' was what we now call a supernova, an exploding star. By 1574 it had faded and was no longer visible to the naked eye. -Tycho's work on his 'new star' made him famous throughout Europe. He soon attracted offers of patronage, first from a duke in Germany and then from King Frederick II of Denmark, with whom he had family connections.

Science and Ideology in the English Civil War: Thomas Hobbes, cont.

-Various French philosophers, including René Descartes, had taken up questions of the nature of human beings and of human knowledge in the 1630s and 1640s, often casting their ideas in terms of the mechanical philosophy. They had, however, generally steered clear of taking up political questions. -The social and political implications of the mechanical philosophy (or at least his own version of it) were pursued most thoroughly and controversially by the English philosopher Thomas Hobbes. In his book Leviathan (1651), these principles led him to advocate authoritarianism as the only way to avoid social and political anarchy. -From 1608 into the 1630s, Hobbes served as tutor and secretary to successive members of the Cavendish family, the Dukes of Devonshire; their patronage would be important for the rest of his life. Travelling on the Continent with William Cavendish, Hobbes met important European thinkers, including Galileo, Marin Mersenne, and later Descartes. -A chance encounter with a volume of Euclid's Elements of Geometry around 1630 made a deep impression on Hobbes: he was struck by the power of geometry as demonstrative reasoning and formed the ambition to extend the same kind of reasoning to physical and even social questions. -Many of Hobbes's ideas resembled Descartes's (and he was sometimes accused of just borrowing them), but he did not share Descartes's dualism. Where Descartes had said there were separate realms of mind and matter, Hobbes said matter was all that truly existed. As a thorough-going materialist, he denied that mind, spirit, or soul existed except as products of the motions of matter. -Hobbes originally planned to write a great trilogy in which he would build up from 'Body' (physics of matter) to 'Man' (human psychology) and finally to 'State' (society). The political tensions of the late 1630s and early 1640s led him to jump ahead and write the 'State' volume (De Cive) first, publishing it in Paris in 1642. Here he argued that the original state of nature (on the right) is one of anarchy, and that only firm rule could bring order and peace. -Hobbes expressed these ideas more fully in his best-known and most controversial work, Leviathan, published in London in 1651 in the wake of the execution of King Charles I.

Galileo and the Physics of Motion: Experiments and Measurements

-While he was a professor of mathematics at Pisa (1589-92) and then Padua (1592-1610), Galileo began to criticize Aristotle's theory of motion and develop a new physics of motion based on mathematical principles. Galileo also began to perform careful experiments, particularly with balls rolling down tracks, in an effort to establish laws of free fall and projectile motion. He was on the verge of publishing his results when the telescope drew him in another direction in 1609. -Thomas Settle's reconstruction of Galileo's experiments with a ball rolling down a track. Settle showed that experiments like those Galileo described gave consistent results. -Galileo's notebooks show not only that he could have performed the experiments he described, but that he really did so. He did not yet treat these experiments as evidence, however, but mainly as sources of principles on which he could base mathematical deductions.

Johannes Kepler's Nested Polyhedra

-While teaching his geometry class at Graz, Kepler circumscribed a circle around an equilateral triangle and inscribed another circle within it—and noticed that the ratio of the radii of the two circles (2:1) was about the same as the ratio of the orbits of Jupiter and Saturn in the Copernican system. -Kepler thought that God must have used such geometry to lay out the spacing of the orbits of the planets. But then Kepler hit on what he thought was an even better idea: that the spacing was not based on two-dimensional plane geometry, but on three-dimensional solids. -It had been known since the ancient Greeks that are exactly five perfect or 'Platonic' solids, the faces and angles of each of which were all identical. -In his Timaeus, Plato had associated the four sublunary elements (earth, water, air, and fire) and the fifth heavenly element (ether) with these five perfect solids, or polyhedra. -Now Kepler suggested that these five Platonic solids were the 'spacers' between the orbits of the six planets in the Copernican system. That is why there are exactly six planets: because there are exactly five Platonic solids to fit between their orbits. And the ratios of the inscribed and circumscribed spheres uniquely determine the ratios of the planets' orbits; Kepler had only to work out the order of the five solids, starting from Saturn and working inward. Here we see a model he devised to show the 'nested polyhedra,' starting with a cube between the orbits of Saturn and Jupiter and a tetrahedron between the orbits of Jupiter and Mars. -Kepler's model of the nested polyhedra for the inner planets: a dodecahedron between the orbits of Mars and Earth, an icosahedron between those of Earth and Venus, and an octahedron between the orbits of Venus and Mercury. The Sun can be seen at the center. -In 1596 Kepler laid out his theory of nested polyhedra in a little book, published in Tübingen, that came to be know as his Mysterium Cosmographicum. -Kepler's was the first overtly pro-Copernican book to be published since Copernicus's own De Revolutionibus.

William Harvey and the Circulation of the Blood, De Motu Cordis et Sanguinis (1628)

-William Harvey (1578-1657) was educated at the University of Padua and built on earlier work there to introduce his theory of the circulation of the blood, published in his De Motu Cordis et Sanguinis (1628). He was a strong advocate of observation, experiment, and careful reasoning. -Harvey was a prominent member of the London College of Physicians and served as the royal physician to King James I and later King Charles I. The two dedications of his De Motu Cordis, to King Charles and to the president of the College of Physicians, illustrate important points about the roles different kinds of patronage could play in science and medicine. -William Harvey was born in Folkestone in southern England and studied first at Cambridge before setting off to Padua to complete his medical education. -Harvey's time at Padua (1597-1602) was a very active period there. He was exposed to the latest advances in anatomy, physiology, and experimental science more widely. -After his return to England, Harvey rose rapidly in the London College of Physicians; from 1615 he served as its lecturer on anatomy, performing many dissections and experiments. -In 1618 Harvey was appointed royal physician to King James I and in 1625 to his successor, King Charles I; Francis Bacon was also Harvey's patient. -Harvey had long been studying the heart and blood, and in 1628 he brought his results together in a small book, De Motu Cordis et Sanguinis, published in Frankfurt. -In this dedication of his book to King Charles I, Harvey compared the role of the heart in the body of an animal to the role of the king in his realm. The rule of the king over his kingdom could thus seem as right and natural as the primacy of the heart in the body. -This is the opening paragraph of Harvey's second dedication, this one to the president of the London College of Physicians. In a later paragraph Harvey says that he professes 'to learn and teach anatomy not from books but from dissections, not from the tenets of Philosophers but from the fabric of Nature.' Harvey here emphasizes the direct visual evidence he has presented to his fellow physicians and enlists their support as witnesses to the truth of his assertions.

Deriving Tycho from Ptolemy

-You can derive Tycho's system from Ptolemy's by adjusting the sizes of the deferents and epicycles. For Venus and Mercury, just expand their deferents until they equal that of the Sun; they will then simply orbit the Sun and be carried along as it orbits the Earth. For Mars, Jupiter, and Saturn, expand their deferents until their epicycles are same size as the deferent of the Sun. Remembering that the radius of each outer planet's epicycle is always parallel to the line from the Earth to the Sun, complete the parallelogram and put the planet in orbit around the Sun, eliminating the epicycle. -The relative motions of the Earth, Sun, and planets are in fact equivalent (in their main features) in the Ptolemaic, Tychonic, and Copernican systems. The question then becomes which system is more physically coherent. -In the 17th century, the contest was not between Ptolemy and Copernicus, but between Tycho and Copernicus.