Astrologers

"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."

"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 (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."

"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."

"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."

"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."

"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."

"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."

"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."

"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'."

"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."

"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.""

"Ptolemy... against the champions of this or that cosmology of the heavens... had dared to claim that it is legitimate to interpret the facts of astronomy by the simplest geometrical scheme which will 'save the phenomena,' no matter whose metaphysics might be upset. His conception of the physical structure of the earth, however, prevented him from carrying through in earnest this principle of relativity, as his objections to the hypothesis that the earth moves amply show."

"Claudius Ptolemy's great contribution to astronomy was his famous work the Almagest, which presented formally the astronomical theories of the day that had evolved from the great debates within the different Greek philosophical schools. Claudius Ptolemy freely admitted that he had contributed little original research to the treatise but rather had based his conclusions principally on the work of Hipparchus. ...Ptolemy did not claim that his cosmological model described the actual conditions. It simply reproduced geometrically the observed motions of the known heavenly bodies and enabled their positions to be easily predicted for any particular time. … Ironically, even when Copernicus' heliocentric theory had replaced the Ptolemaic system, many astronomers used Ptolemy's model to predict the motion of the planets, since its intricate calculations produced more accurate values."

"To give here an elaborate account of Pappus would be to create a false impression. His work is only the last convulsive effort of Greek geometry which was now nearly dead and was never effectually revived. It is not so with Ptolemy or Diophantus. The trigonometry of the former is the foundation of a new study which was handed on to other nations indeed but which has thenceforth a continuous history of progress."

"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)."

"I know that I am mortal by nature and ephemeral, but when I trace at my pleasure the windings to and fro of the heavenly bodies, I no longer touch earth with my feet. I stand in the presence of Zeus himself and take my fill of ambrosia."

"We consider it a good principle to explain the phenomena by the simplest hypothesis possible."

"πᾶν μὲν τὸ δυσέφικτον παρὰ τοῖς πολλοῖς εὐδιάβλητον ἔχει φύσιν"

"The length of lifetakes the leading place among inquiries about events following birth."

"As material fortune is associated with the properties of the body, so honor belongs to those of the soul."

"There are three classes of friendship and enmity, since men are so disposed to one another either by preference or by need or through pleasure and pain."

"Ptolemy's Geography is the only book on cartography to have survived from the classical period and one of the most influential scientific works of all time."

"He left in his Optics, the earliest surviving table of angles of refraction from air to water. ...This table, quoted and requoted until modern times, has been admired... A closer glance at it, however, suggests that there was less experimentation involved in it than originally was thought, for the values of the angles of refraction form an arithmetic progression of second order... As in other portions of Greek Science, confidence in mathematics was here greater than that in the evidence of the senses, although the value corresponding to 60° agrees remarkably well with experience."

"I had determined to go as far as declaring in abstruse and puzzling utterances the future causes of the "common advent", even those truly cogent ones that I have foreseen. Yet lest whatever human changes may be to come should scandalise delicate ears, the whole thing is written in nebulous form, rather than as a clear prophecy of any kind."

"Estant assis de nuit secret estude, Seul repousé sur la selle d'ærain, Flambe exigue sortant de solitude, Fait prosperer qui n'est à croire vain."

"When twenty years of the Moon's reign have passed another will take up his reign for seven thousand years. When the exhausted Sun takes up his cycle then my prophecy and threats will be accomplished."

"Were we to record the failures and ridiculous blunders of astronomers, we are afraid they would outnumber by far those of the astrologers. Present events fully vindicate Nostradamus, who has been so much ridiculed by our skeptics."

"If I have eschewed the word prophet, I do not wish to attribute to myself such lofty title at the present time, for whoever is called a prophet now was once called a seer; since a prophet, my son, is properly speaking one who sees distant things through a natural knowledge of all creatures. And it can happen that the prophet bringing about the perfect light of prophecy may make manifest things both human and divine, because this cannot be done otherwise, given that the effects of predicting the future extend far off into time."

"Tomorrow, I shall no longer be here."

"Perfect knowledge of such things cannot be acquired without divine inspiration, given that all prophetic inspiration derives its initial origin from God Almighty, then from chance and nature. Since all these portents are produced impartially, prophecy comes to pass partly as predicted. For understanding created by the intellect cannot be acquired by means of the occult, only by the aid of the zodiac, bringing forth that small flame by whose light part of the future may be discerned. We need god to prosper those without him will not."

"The man who realizes his ignorance has taken the first step toward knowledge."

"Christ said, "The Truth shall make you free," but Truth is not found once and forever. Truth is eternal, and the quest for Truth must also be eternal."

"We venture to make the assertion that there is but one sin: IGNORANCE, and but one salvation: APPLIED KNOWLEDGE."

"Peace is a matter of education, and impossible of achievement until we have learned to deal charitably, justly, and openly with one another, as nations as well as individuals. As long as we manufacture arms, peace will not become established. It should become our aim and object to do all we can toward the abolition of militarism in all countries and the establishment of the principle of arbitration of difficulties."

"... looking at woman suffrage from the larger standpoint, it would be to the advantage of the men of the present day to grant women that which is really their right--a full and complete equality in every particular. The double social standard which obtains at the present time, whereby a man may commit the social sin without being ostracized, should be done away with. Woman's work should be paid as much as man's work, ... It would be of an enormous benefit to the race if she were given an equal right with man in every particular. For not until then can we hope to see reforms brought about that will really unite humanity. ... While laws are only makeshifts to bring humanity to a higher plane where each one will be a law unto himself, doing right without coercion, it is nevertheless necessary that such reforms should be brought about at the present time by legislation."

"But there are vegetarians and vegetarians: In Europe conditions cause people now to abstain from flesh eating to a very large extent. They are not true vegetarians for they are lusting for flesh every moment of their lives, and they feel the want of it as a great hardship and sacrifice. In time they would of course grow used to is, and in many generations it would make them gentle and docile, but obviously that is not the kind of vegetarianism we need now. There are others who abstain from flesh foods for the sake of health; their motive is selfish, and many among them probably also lust after the "flesh pots of Egypt". Their attitude of mind is not such either that it would abolish ferocity very quickly. But there is a third class which realizes that all life is God's life and that to cause suffering to any sentient being is wrong, so out of pure compassion they abstain from the use of flesh foods. They are the true vegetarians, and it is obvious that a world war could never be fought by people of this turn of mind. All true Christians will also be abstainers from flesh foods for similar motives. Then peace on earth and good will among men will be an assured fact; the nations will beat their swords into plowshares and their spears into pruning hooks that they may cease to deal death, sorrow, and suffering, and become instruments to foster life, love, and happiness."

"No man loves God who hates his kind,"

"On whistling stormcloud; on Zephyrus wing,"

"Dee goes so far as to assert that, although he called the work hieroglyphic, it is endowed with a clarity and rigour almost mathematical; yet at the same time he leaves it to the reader even to guess that the subject of the elaborate display, which he is asked to view in such dim light, is the hermetic quest. The semblance of clarity is achieved by discussing the dark subject under the guise of a symbolic sign invented by Dee, which is his monad. This symbol indeed lends itself easily to digressive secondary interpretations of a numerological, cabbalistic, astrological, cosmological, or mathematical nature, all which, however, are without any doubt given so as to establish significant connexions with the all-embracing central theme, alchemy, which is barely mentioned."

"Cut that in Three, which Nature hath made One, Then strengthen hyt, even by it self alone, Wherewith then Cutte the poudred Sonne in twayne, By length of tyme, and heale the woonde againe. The self same Sunne twys yet more, ye must wounde, Still with new Knives, of the same kinde, and grounde; Our Monas trewe thus use by natures Law, Both binde and lewse, only with rype and rawe, And ay thanke God who only is our Guyde, All is ynugh, no more then at this Tyde."

"It is by the straight line and the circle that the first and most simple example and representation of all things may be demonstrated, whether such things be either non-existent or merely hidden under Nature's veils."

"Neither the circle without the line, nor the line without the point, can be artificially produced. It is, therefore, by virtue of the point and the Monad that all things commence to emerge in principle. That which is affected at the periphery, however large it may be, cannot in any way lack the support of the central point."

"Therefore, the central point which we see in the centre of the hieroglyphic Monad produces the Earth, round which the Sun, the Moon, and the other planets follow their respective paths. The Sun has the supreme dignity, and we represent him by a circle having a visible centre."

"Although the semicircle of the Moon is placed above the circle of the Sun and would appear to be superior, nevertheless we know that the Sun is ruler and King. We see that the Moon in her shape and her proximity rivals the Sun with her grandeur, which is apparent to ordinary men, yet the face, or a semi-sphere of the Moon, always reflects the light of the Sun."

"We finish the brief hieroglyphic consideration of our Monad, which we would sum up in one only hieroglyphic context: The Sun and the Moon of this Monad desire that the Elements in which the tenth proportion will flower, shall be separated, and this is done by the application of Fire."