Astrologers

"Roger Bacon expressed a feeling which afterwards moved many minds, when he said that if he had the power he would burn all the works of the Stagirite, since the study of them was not simply loss of time, but multiplication of ignorance. Yet in spite of this outbreak every page is studded with citations from Aristotle, of whom he everywhere speaks in the highest admiration."

"To be able to speak the language of the schools with authority was the first condition of obtaining a hearing. But he was not slow to perceive that the men who taught this philosophy were, for the most part, wholly destitute of positive knowledge. They knew no language but Latin. Beyond the shreds of arithmetic, mensuration, and astronomy taught in the manuals of the Quadrivium, they were ignorant of mathematics. Of the possibility of applying mathematical knowledge to the facts of nature they had formed no conception whatever. Their philosophy was a tangle of barren controversies reducible, for the most part, to verbal disputes. It bore no relation to the facts of real life. It held out no hope of raising the Catholic Church to the position of intellectual domination needed for establishing her authority over the Asiatic world, from which dangers were looming of appalling magnitude."

"All these foregoing sciences are, properly speaking, speculative. There is indeed in every science a practical side, as Avicenna teaches in the first book of his Art of Medicine. Nevertheless, of Moral Philosophy alone can it be said that it is in the special and autonomatic sense practical, dealing as it does with human conduct with reference to virtue and vice, beatitude and misery. All other sciences are called speculative: they are not concerned with the deeds of the present or future life affecting man's salvation or damnation. All procedures of art and of nature are directed to these moral actions, and exist on account of them. They are of no account except in that they help forward right action. Thus practical and operative sciences, as experimental alchemy and the rest, are regarded as speculative in reference to the operations with which moral or political science is concerned. This science is the mistress of every department of philosophy. It employs and controls them for the advantage of states and kingdoms. It directs the choice of men who are to study in sciences and arts for the common good. It orders all members of the state or kingdom so that none shall remain without his proper work."

"Many of these mystics, by following what they were taught by some treatises, secretly preserved from one generation to another, achieved discoveries which would not be despised even in our modern days of exact sciences. Roger Bacon, the friar, was laughed at as a quack, and is now generally numbered among "pretenders" to magic art; but his discoveries were nevertheless accepted, and are now used by those who ridicule him the most... Roger Bacon belonged by right if not by fact to that Brotherhood which includes all those who study the occult sciences. Living in the thirteenth century, almost a contemporary, therefore, of Albertus Magnus and Thomas Aquinas, his discoveries — such as gunpowder and optical glasses, and his mechanical achievements — were considered by everyone as so many miracles. He was accused of having made a compact with the Evil One... It is recounted, that, having been summoned before the king, the friar was induced to show "some of his skill before her majesty the queen. So he waved his hand... and "presently was heard such excellent music, that they all said they had never heard the like."... Then he waved his wand again,and suddenly there was such a smell "as if all the rich perfumes in the whole world had been there prepared in the best manner that art could set them out." Thephenomena of the mystic odors and music, exhibited by Roger Bacon, have been often observed in our own time."

"Roger Bacon, a disciple of the Arabs, also insisted on the primary necessity of Mathematics, without which no other science can be known; yet by Mathematics it is clear that he meant something very different from what we mean, including under that head even dancing, singing, gesticulation, and performance on musical instruments."

"Throughout the Opus Majus there is an orderly arrangement of the subject-matter formed with a definite purpose, and leading up to a central theme, the consolidation of the Catholic faith as the supreme agency for the civilization and ennoblement of mankind. For this end a complete renovation and reorganization of man's intellectual forces was needed. After a brief exposition of the four principal impediments to wisdom—authority, habit, prejudice, and false conceit of knowledge—Bacon proceeds in his second part to explain the inseparable connexion of philosophy with the highest truths of religion. ...The first condition ...of a renovation of learning is the systematic study of at least three languages besides Latin, namely Hebrew, Greek, and Arabic. The second condition was the application of mathematical method to all objects of study, whether in the world or in the Church. ...it [mathematics] raises the understanding to the plane at which knowledge can be distinguished from ignorance. Without it other sciences are unintelligible. It reveals to us the motions of the heavenly bodies, and the laws of the propagation of force in things terrestrial, of which the propagation of light may be taken as a type; without it we are incapable of regulating the festivals of the Church; we remain in ignorance of the influences of climate upon character; of the position of cities and of the boundaries of nations whom it is the function of the Catholic Church to bring within her pale, and to control spiritually. ...But mathematical method, though essential, is insufficient. It must be supplemented by the method of experiment. Experimental science governs all the preceding sciences ('domina est omnium scientiarum praecedentium' [she is the matron of all previous sciences]), it controls their methods; in prosecuting its own special researches it makes use of their results."

"I have labored much in sciences and languages, and I have up to now devoted forty years [to them] after I first learned the Alphabetum; and I was always studious. Apart from two of these forty years I was always [engaged] in study [or at a place of study], and I had many expenses just as others commonly have. Nevertheless, provided I had first composed a compendium, I am certain that within quarter or half a year I could directly teach a solicitous and confident person whatever I know of these sciences and languages. And it is known that no one worked in so many sciences and languages as I did, nor so much as I did. Indeed, when I was living in the other state of life [as a Magister], people marveled that I survived the abundance of my work. And still, I was just as involved in studies afterwards, as I had been before. But I did not work all that much, since in the pursuit of Wisdom this was not required."

"[H]aec vocatur scientia experimentalis, quae negligit argumenta, quoniam non certificant, quantumcunque sint fortia, nisi simul adsit experientia conclusionis. Et ideo haec docet experiri conclusiones nobiles omnium scientiarum, quae in aliis scientiis aut probantur per argumenta, aut investigantur per experientias naturales et imperfectas..."

"Et hæc scientia certificat omnia naturalia et artificialia in particulari et in propria disciplina, per experientiam perfectam; non per argumenta, ut scientiæ pure speculativae, nec per debiles et imperfecta experientias ut scientiae operativæ. Et ideo hæc est domina omnium scientiarum præcedentium, et finis totius speculationis."

"I use the example of the rainbow and of the phenomena connected with it, of which sort are the circle around the sun and the stars, likewise the rod lying at the side of the sun or of a star which appears to the eye in a straight line... called the rod by Seneca, and the circle is called the corona, which often has the colors of the rainbow. But neither Aristotle nor Avicenna, in their Natural Histories, has given us knowledge of things of this sort, nor has Seneca, who composed a special book on them. But Experimental Science makes certain of them. [The experimenter] considers rowers and he finds the same colors in the falling drops dripping from the raised oars when the solar rays penetrate drops of this sort. It is the same with waters falling from the wheels of a mill; and when a man sees the drops of dew in summer of a morning lying on the grass in the meadow or the field, he will see the colors. And in the same way when it rains, if he stands in a shady place and if the rays beyond it pass through dripping moisture, then the colors will appear in the shadow nearby; and very frequently of a night colors appear around the wax candle. Moreover, if a man in summer, when he rises from sleep and while his eyes are yet only partly opened, looks suddenly toward an aperture through which a ray of the sun enters, he will see colors. And if, while seated beyond the sun, he extend his hat before his eyes, he will see colors; and in the same way if he closes his eye, the same thing happens under the shade of the eyebrow; and again, the same phenomenon occurs through a glass vessel filled with water, placed in the rays of the sun. Or similarly if any one holding water in his mouth sprinkles it vigorously into the rays and stands to the side of the rays; and if rays in the proper position pass through an oil lamp hanging in the air, so that the light falls on the surface of the oil, colors will be produced. And so in an infinite number of ways, as well natural as artificial, colors of this sort appear, as the careful experimenter is able to discover."

"One man I know, and one only, who can be praised for his achievements in this science. Of discourses and battles of words he takes no heed: he follows the works of wisdom, and in these finds rest. What others strive to see dimly and blindly, like bats in twilight, he gazes at in the full light of day, because he is a master of experiment. Through experiment he gains knowledge of natural things, medical, chemical, indeed of everything in the heavens or earth. He is ashamed that things should be known to laymen, old women, soldiers, ploughmen, of which he is ignorant. Therefore he has looked closely into the doings of those who work in metals and minerals of all kinds; he knows everything relating to the art of war, the making of weapons, and the chase; he has looked closely into agriculture, mensuration, and farming work; he has even taken note of the remedies, lot casting, and charms used by old women and by wizards and magicians, and of the deceptions and devices of conjurors, so that nothing which deserves inquiry should escape him, and that he may be able to expose the falsehoods of magicians. If philosophy is to be carried to its perfection and is to be handled with utility and certainty, his aid is indispensable. As for reward, he neither receives nor seeks it. If he frequented kings and princes, he would easily find those who would bestow on him honours and wealth. Or, if in Paris he would display the results of his researches, the whole world would follow him. But since either of these courses would hinder him from pursuing the great experiments in which he delights, he puts honour and wealth aside, knowing well that his wisdom would secure him wealth whenever he chose. For the last three years he has been working at the production of a mirror that shall produce combustion at a fixed distance; a problem which the Latins have neither solved nor attempted, though books have been written upon the subject."

"Mathematics is the gate and key of the sciences. ... Neglect of mathematics works injury to all knowledge, since he who is ignorant of it cannot know the other sciences or the things of this world. And what is worse, men who are thus Ignorant are unable to perceive their own ignorance and so do not seek a remedy."

"Contemporary with Vitellio and Peccam was... Roger Bacon, a man of almost universal genius, and who wrote on almost every branch of science. He frequently quotes Alhazen on the subject of optics, and seems to have carefully studied his writings, as well as those of other Arabians, which were the fountains of natural knowledge in those days, and which had been introduced into Europe by means of the Moors in Spain. Notwithstanding the pains this great man took with the subject of opticks, it does not appear that, with respect to theory, he made any considerable advance upon what Alhazen had done before him."

"And because this Experimental Science is wholly ignored by the general run of students, for that reason I can not convince people of its utility unless I show at the same time its excellence and its property. This science alone, then, knows how to test perfectly by experience what can be done by nature, what by the industry of art, what by imposture; what the incantations, conjurations, invocations, deprecations, sacrifices (which are magical devices) seek and dream of; and what is done in them, so that all falsity may be removed and that only the truth of art and nature be retained. This science alone teaches one to consider all the insanities of magicians, not that they may be confirmed but that they may be avoided, just as logic considers sophistical argument."

"I shall draw... a figure (which all these matters are made clear as far as possible on a surface, but the full demonstration would require a body like the eye... The eye of a cow, pig, and other animals can be used for illustration, if anyone wishes to experiment."

"Everything in nature completes its action through its own force and species alone... as, for example, fire by its own force dries and consumes and does many things. Therefore vision must perform the act of seeing by its own force. But the act of seeing is the perception of a visible object at a distance, and therefore vision perceives what is visible by its own force multiplied to the object. Moreover, the species of the things of world are not fitted by nature to effect the complete act of vision at once, because of its nobleness. Hence these must be aided by the species of the eye, which travels in the locality of the visual pyramid, and changes the medium and ennobles it, and renders it analogous to vision, and so prepares the passage of the species itself of the visible object... Concerning the multiplication of this species, moreover, we are to understand that it lies in the same place as the species of the thing seen, between the sight and the thing seen, and takes place along the pyramid whose vertex is in the eye and base in the thing seen. And as the species of an object in the same medium travels in a straight path and is refracted in different ways when it meets a medium of another transparency, and is reflected when it meets the obstacles of a dense body; so is it also true of the species of vision that it travels altogether along the path of the species itself of the visible object."

"Great as Bacon was, he was far from being free from the mistakes and prejudices of those who went before him. Even some of the most wild and absurd opinions of the antients have the sanction of his approbation and authority. He does not hesitate to assent to an opinion... that visual rays proceed from the eye; giving this reason for it, that every thing in nature is qualified to discharge its proper functions by its own powers, in the same manner as the sun, and other celestial bodies. He acknowledges, however, that the presence of light, as well as several other circumstances, is necessary to vision."

"Nearly three thousand years ago, the ancient Egyptians knew that a glass lens can make an object look bigger. Nero... is said to have looked through an emerald to watch his gladiators fighting... By the ninth century, people were using 'reading stones' to assist their failing eyesight. These were polished lumps of clear glass, rounded on one side and flat on the other; you sat them on top of the document you were trying to read... The first true spectacles were almost certainly invented in Italy between 1280 and 1300. They acted like a magnifying glass and corrected long-sightedness; it would be another 300 years before lenses able to correct short-sightedness would be developed, in part because these were much harder to make. Johannes Kepler (astronomer, astrologer and mathematician) was the first to explain how convex and concave lenses corrected eyesight. ...lenses were (and still are) made by grinding glass using various types of abrasive material, which in Kepler's time were already being used by jewellers."

"Kepler states expressly that he gave the name Foci to certain points related to the conic sections which had previously "no name." With their new name he associated his new views about the points themselves, and his doctrines of Continuity (under the name Analogy) and Parallelism, which would soon have become known, and would after a time have been taken up by competent mathematicians.... A letter of Henry Briggs to Kepler [dated Mar 10, 1625] suggest improvements in the Paralipomena ad Vitellionem. In this letter Briggs... comprehended and accepted Kepler's way of looking at parallels as lines to or from a point at infinity in one direction or its opposite."

"Kepler's project in was to give 'true and perfect reasons for the numbers, quantities, and periodic motions of celestial orbits.' The perfect reasons must be based on the simple mathematical principles, which had been discovered by Kepler in the solar system, by using geometric demonstrations. The general scheme of his model was borrowed... from Plato's 'Timaeus', but the mathematical relations for the s (pyramid, cube, , , ) were taken by Kepler from the works of Euclid and Ptolemy. Kepler followed Proclus and believed that 'the main goal of Euclid was to build a geometric theory of the so-called Platonic solids.' Kepler was fascinated by Proclus and often quotes him calling him a 'Pythagorean'."

"Kepler also thought of the Inverse Square Law; he thought of it first. ...Kepler regarded gravitational attraction as analogous to propagation of light... Consider now the intensity of light falling on a planet P at a distance R from the Sun. Let S be the total amount if light emitted by the Sun. ...the intensity will be the same at all points distance R from the Sun. But these points constitute a spherical sheet (with center the Sun) whose radius is R and whose surface area, therefore, is 4πR2. Consequently, intensity of radiation =\frac {S}{4\pi}\cdot\frac {1}{R^2}i.e., the intensity is inversely proportional to the square of the distance between the planet P and the Sun. ...Kepler thought carefully about the possibility, but was dubious... to his credit; he mistrusted the idea for a very good reason. ...although during a solar eclipse the Moon blocks the Sun's radiation to part of the Earth, there is no discontinuity in the Earth's motion. If gravitational attraction were radiated as light is radiated, this too would be temporarily blocked by the Moon, so that during the eclipse it would discontinue its eliptical orbit..."

"Kepler was a brilliant thinker and a lucid writer, but he was a disaster as a classroom teacher. He mumbled. He digressed. He was at times utterly incomprehensible. He drew only a handful of students his first year at Graz; the next year there were none. He was distracted by an incessant interior clamour of associations and speculations vying for his attention. And one pleasant summer afternoon, deep in the interstices of one of his interminable lectures, he was visited by a revelation that was to alter radically the future of astronomy. Perhaps he stopped in mid-sentence. His inattentive students, longing for the end of the day, took little notice, I suspect, of the historic moment."

"As living bodies have hair, so does the earth have grass and trees, the cicadas being its dandruff; as living creatures secrete urine in a bladder, so do the mountains make springs; sulphur and volcanic products correspond to excrement, metals and rainwater to blood and sweat; the sea water is the earth's nourishment … At the same time the anima terrae [soul of the earth] is also a formative power (facultas formatrix) in the earth's interior and expresses, for example, the five regular bodies in precious stones and fossils ..... It is important that in Kepler's view the anima terrae is responsible for the weather and also for meteoric phenomena. Too much rain, for instance, is an illness of the earth."

"It was only the third new set of planetary tables in European history. And whereas Copernicus's and Ptolemy's tables were more or less equally accurate, Kepler's were some 50 times more so. Within a few years, it was possible to pinpoint the time of transit of Mercury across the face of the sun so that it was possible to observe it in transit for the first time in human history. Of course, Kepler's theories were more difficult, especially since he had incorporated logarithms, which had only been invented a few years earlier. Much of the book, therefore, was made up of explanatory text that told the reader how to use the tables. ...The printing ...was finished on time in September 1627 ...but he was not optimistic ...noting, "There will be few purchasers, as is always the case with mathematical works, especially in the present chaos.""

"Kepler made free use if indivisibles in both astronomical work and a treatise on measuring volumes of wine casks. He went far beyond the practical needs... and wrote an extensive tract on indivisible methods. Two illustrative examples are his approaches to the areas of a circle and an ellipse."

"But to return to Kepler, his great sagacity, and continual meditation on the planetary motions, suggested to him some views of the true principles from which these motions flow. In his preface to the commentaries concerning the planet Mars, he speaks of gravity as of a power that was mutual betwixt bodies, and tells us that the earth and moon tend towards each other, and would meet in a point so many times nearer to the earth than to the moon, as the earth is greater than the moon, if their motions did not hinder it. He adds that the tides arise from the gravity of the waters towards the moon. But not having just enough notions of the laws of motion, he does not seem to have been able to make the best use of these thoughts; nor does he appear to have adhered to them steadily, since in his epitome of astronomy, published eleven years after, he proposes a physical account of the planetary motions, derived from different principles."

"The Harmony of the World is the continuation of the Cosmic Mystery, and the climax of his lifelong obsession. What Kepler attempted here is, simply, to bare the ultimate secret of the universe in an all-embracing synthesis of geometry, music, astrology, astronomy and epistemology. It was the first attempt of this kind since Plato, and it is the last to our day. After Kepler, fragmentation of experience sets in again, science is divorced from religion, religion from art, substance from form, matter from wind."

"Over and above the specific theorems created by men such as Desargues, Pascal and La Hire, several new ideas and outlooks were beginning to appear. The first is the idea of continuous change of a mathematical entity from one state to another... [i.e., of a] a geometrical figure. It was Kepler, in his Astronomiae Optica of 1604, who first seemed to grasp the fact that parabola, ellipse, hyperbola, circle, and the degenerate conic consisting of a pair of lines are continuously derivable from each other. ...The notion of a continuous change in a figure was also employed by Pascal. He allowed two consecutive vertices of his hexagon to approach each other so that the figure became a pentagon. In the same manner he passed from pentagons to quadrilaterals. The second idea to emerge from the work of the projective geometers is that of transformation and invariance."

"The Pythagorean dream of musical harmony governing the motion of the stars never lost its mysterious impact, its power to call forth responses from the depth of the unconscious mind. ...But, one might ask, was the "Harmony of the Spheres" a poetic conceit or a scientific concept. A working hypothesis or a dream dreamt through a mystic's ear? ...Even Aristotle laughed "harmony, heavenly harmony" out of the courts of earnest, exact science. Yet... Johannes Kepler became enamoured with the Pythagorean dream, and on this foundation of fantasy, by methods of reasoning equally unsound, built the solid edifice of modern astronomy. It is one of the most astonishing episodes in the history of thought, and an antidote to the pious belief that the Progress of Science is governed by logic."

"Kepler (and Desargues) regarded the two "ends" of the ["straight"] line as meeting at "infinity" so that the line has the structure of a circle. In fact, Kepler actually thought of a line as a circle with its center at infinity."

"He [Kepler] supposes, in that treatise [epitome of astronomy], that the motion of the sun on his axis is preserved by some inherent vital principle; that a certain virtue, or immaterial image of the sun, is diffused with his rays into the ambient spaces, and, revolving with the body of the sun on his axis, takes hold of the planets and carries them along with it in the same direction; as a load-stone turned round in the neighborhood of a magnetic needle makes it turn round at the same time. The planet, according to him, by its inertia endeavors to continue in its place, and the action of the sun's image and this inertia are in a perpetual struggle. He adds, that this action of the sun, like to his light, decreases as the distance increases; and therefore moves the same planet with greater celerity when nearer the sun, than at a greater distance. To account for the planet's approaching towards the sun as it descends from the aphelium to the perihelium, and receding from the sun while it ascends to the aphelium again, he supposes that the sun attracts one part of each planet, and repels the opposite part; and that the part which is attracted is turned towards the sun in the descent, and that the other part is towards the sun in the ascent. By suppositions of this kind he endeavored to account for all the other varieties of the celestial motions."

"One wonders how many modern scientists faced by a similar situation in their work would fail to be impressed by such remarkable numerical coincidences."

"If Kepler had been a mathematician of the twentieth century, he would have stopped his laborious observational inductions after noting his first law, and deduced the other two analytically."

"Galileo argued that nature, God's second book, is written in mathematical letters... Kepler is even more explicit in his work on world harmony; he says: God created the world in accordance with his ideas of creation. These ideas are the pure archetypal forms which Plato termed Ideas, and they can be understood by man as mathematical constructs. They can be understood by Man, because Man was created in the spiritual image of God. Physics is reflection on the divine Ideas of Creation, therefore physics is divine service."

"Luckily, Napier came on the scene with his logarithms just when Johannes Kepler, the discoverer of the laws of planetary motion, was deeply immersed in mind-numbing, tedious calculations, filling hundreds of folio pages with lengthy arithmetic operations, in his construction of the orbit of Mars from the observational data of Tycho Brahe. To Kepler, this discovery was a gift from heaven, for logarithms reduced considerably the time he had to spend just doing arithmetic calculations, a task which he detested."

"J. Kepler was the first (that I know of) that discover'd the true cause of the Tide, and he explains it largely in his Introduction to the Physics of the Heavens, given in his Commentaries to the Motion of the Planet Mars, where after he has shewn the Gravity or Gravitation of all Bodies towards another, he thus writes: "The Orb of the attracting Power, which is in the Moon is extended as far as the Earth, and draws the Waters under the Torrid Zone, acting upon places where it is vertical, insensibly on included Seas, but sensibly on the Ocean, whose Beds are large, and the Waters have the liberty of reciprocation, that is, of rising and falling"; and in the 70th Page of his Lunar Astronomy,—"But the cause of the Tides of the Sea appear to be the Bodies of the Sun and Moon drawing the Waters of the Sea.""

"Afterwards that incomparable Philosopher Sir Isaac Newton, improv'd the hint, and wrote so amply upon this Subject as to make the Theory of the Tides his own, by shewing that the Waters of the Sea rise under the Moon and the Place opposite to it: For Kepler believ'd "that the Impetus occasion'd by the presence of the Moon, by the absence of the Moon, occasions another Impetus; till the Moon returning, stops and moderates the Force of that Impetus, and carries it round with its motion." Therefore this Spheroidical Figure which stands out above the Sphere (like two Mountains, the one under the Moon and the other in the place opposite to it) together with the Moon (which it follows) is carried by the Diurnal Motion, (or rather, according to the truth of the matter, as the Earth turns towards the East it leaves those Eminencies of Water, which being carried by their own motion slowly towards the East, are as it were unmov'd) in its journey makes the Water swell twice and sink twice in the space of 25 Hours, in which time the Moon being gone from the Meridian of any Place, returns to it again."

"To say... that the motion of the Earth meeting with the motion of the Lunar Orb, the concurrence of them occasioneth the Ebbing and Flowing [of the seas], is an absolute vanity, not onely be­cause it is not exprest, nor seen how it should so happen, but the falsity is obvious, for that the Revolution of the Earth is not con­trary to the motion of the Moon, but is towards the same way. So that all that hath been hitherto said, and imagined by others, is, in my judgment, altogether invalid. But amongst all the famous men that have philosophated upon this admirable effect of Nature, I more wonder at Kepler than any of the rest, who being of a free and piercing wit, and having the motion ascri­bed to the Earth, before him, hath for all that given his ear and assent to the Moons predominancy over the Water, and to oc­cult properties, and such like trifles."

"Copernicus, Kepler and Galileo were ‘revisionists’ in rejecting the geocentric system of Ptolemy (which held sway for some 1500 years) and, against an oppressive and repressive mainstream opinion (and officialdom), reinstated—with improvements—the heliocentric system of Aristarchos of Samos (3rd cent BCE)."

"Kepler is the first who ventured here [into] an exact mathematical treatment of the problems (of astronomical science), the first to establish natural laws in the specific sense of the new science."

"Dumbleton was one of the first to express functional relationships in graphical form. ...Dumbleton also gave a proof of the Merton mean-speed rule... stating that "the latitude of a uniformly difform movement corresponds to the degree of the midpoint." He used the method in the Suma [Suma logicæ et philosophiæ naturalis] to study the problem of the variation in the strength of light as a function of the distance from its source. ...He realized that that the decrease in intensity of illumination was not linearly proportional to the distance... But he did not succeed in finding the exact quantitative relationship, which is that the intensity of illumination due to a luminous source is inversely proportional to the square of the distance, a law discovered by Johannes Kepler in 1604."

"When he discovered the polyhedral hypothesis soon after being sent to teach mathematics in Graz, he changed his mind [about becoming a Lutheran minister] , indicating... that he now saw his work in astronomy as an exercise of a priestly vocation. ...he claimed that, in the Harmonice mundi, he offered to the world nothing less than the plan of creation, which God himself had waited six thousand years for someone to comprehend."

"With the discovery of the law of inertia and the subsequent downfall of the Aristotelian theory of motion on which Kepler had based his work, his physical theories soon became outmoded and were then rendered obsolete by Newton's work. Yet Kepler's laws of planetary motion remained, so that Edmond Halley could write in his review of Newton's Principia that the first eleven propositions were found to agree with the phenomena of celestial motions, as discovered by the great sagacity and diligence of Kepler."

"Although the concept of heavenly harmony was a theme mentioned in the literature of the time... Kepler's world harmony had little influence on his contemporaries. ...With the rise of the experimental science advocated by Francis Bacon and greatly facilitated by the invention and development of scientific instruments, the general trend of the seventeenth century was towards a mechanical natural philosophy in which metaphysical speculation would play little part. Another factor... may possibly be recognized in the nature of developments that had taken place in mathematics during the sixteenth century, for the advances in algebra and the introduction of symbolism favored a nominalist view of mathematics in contrast to the realist Platonic view of geometry that Kepler adopted as a foundation for his theory of a world harmony."

"The effective inventor of the telescope and compound microscope was Galileo... Galileo's account of the path of the rays through the concave eye-piece and convex objective which he used was not satisfactory and was considerably improved by Kepler, who suggested the use of two convex lenses which became the basis of later instruments. Kepler had already written an important optical treatise in the form of a commentary on Witelo's Perspectiva... His improvements to the telescope may be regarded as what he had learned from the thirteenth-century writer."

"I esteem myself happy to have as great an ally as you in my search for truth. I will read your work … all the more willingly because I have for many years been a partisan of the Copernican view because it reveals to me the causes of many natural phenomena that are entirely incomprehensible in the light of the generally accepted hypothesis. To refute the latter I have collected many proofs, but I do not publish them, because I am deterred by the fate of our teacher Copernicus who, although he had won immortal fame with a few, was ridiculed and condemned by countless people (for very great is the number of the stupid)."

"A law explains a set of observations; a theory explains a set of laws. The quintessential illustration of this jump in level is the way in which Newton’s theory of mechanics explained Kepler’s law of planetary motion. Basically, a law applies to observed phenomena in one domain (e.g., planetary bodies and their movements), while a theory is intended to unify phenomena in many domains. Thus, Newton’s theory of mechanics explained not only Kepler’s laws, but also Galileo’s findings about the motion of balls rolling down an inclined plane, as well as the pattern of oceanic tides. Unlike laws, theories often postulate unobservable objects as part of their explanatory mechanism. So, for instance, Freud’s theory of mind relies upon the unobservable ego, superego, and id, and in modern physics we have theories of elementary particles that postulate various types of quarks, all of which have yet to be observed."

"In his 1619 book The Harmony of the World he tells us that he discovered a harmonic law while delivering a lecture on astronomy to his students. Kepler found that for each planet, the cube of the average distance from the sun is proportional to the square of the period of revolution. Kepler later found a similar law for the satellites of Jupiter. Today we know that such a law holds for any system of bodies that circulates around a central parent body. There are many applications of Kepler's law; for instance, half a century later it gave Isaac Newton the clue to his discovery of the law of universal gravitation."

"As I have stated the most remarkable aspect of Kepler's pursuit of science is the constancy with which he applied himself to his chosen quest. To use a phrase of Shelley's his 'was a character superior in singleness'."

"I have as yet read nothing beyond the preface of your book, from which, however, I catch a glimpse of your meaning, and feel great joy on meeting with so powerful an associate in the pursuit of truth, and consequently, such a friend to truth itself; for it is deplorable that there should be so few who care about truth, and who do not persist in their perverse mode of philosophising. But as this is not the fit time for lamenting the melancholy condition of our times, but for congratulating you on your elegant discoveries in confirmation of the truth, I shall only add a promise to peruse your book dispassionately, and with the conviction that I shall find in it much to admire. This I shall do the more willingly because many years ago I became a convert to the opinions of Copernicus, and by his theory have succeeded in explaining many phenomena which on the contrary hypothesis are altogether inexplicable. I have arranged many arguments and confutations of the opposite opinions, which, however, I have not yet dared to publish, fearing the fate of our master, Copernicus, who, although he has earned immortal fame among a few, yet by an infinite number (for so only can the number of fools be measured) is hissed and derided. If there were many such as you I would venture to publish my speculations, but since that is not so I shall take time to consider of it."