Kepler Quotes

I much prefer the sharpest criticism of a single intelligent man to the thoughtless approval of the masses.

My dear Kepler, what would you say of the learned here, who, replete with the pertinacity of the asp, have steadfastly refused to cast a glance through the telescope? What shall we make of this? Shall we laugh, or shall we cry?

Why should we place Christ at the top and summit of the human race? Was he kinder, more forgiving, more self-sacrificing than Buddha? Was he wiser, did he meet death with more perfect calmness, than Socrates? Was he more patient, more charitable, than Epictetus? Was he a greater philosopher, a deeper thinker, than Epicurus? In what respect was he the superior of Zoroaster? Was he gentler than Lao-tsze, more universal than Confucius? Were his ideas of human rights and duties superior to those of Zeno? Did he express grander truths than Cicero? Was his mind subtler than Spinoza’s? Was his brain equal to Kepler’s or Newton’s? Was he grander in death – a sublimer martyr than Bruno? Was he in intelligence, in the force and beauty of expression, in breadth and scope of thought, in wealth of illustration, in aptness of comparison, in knowledge of the human brain and heart, of all passions, hopes and fears, the equal of Shakespeare, the greatest of the human race?

Copernicus, Galileo, and Kepler did not solve an old problem, they asked a new question, and in doing so they changed the whole basis on which the old questions had been framed.

Reading list (1972 edition)[edit] 1. Homer – Iliad, Odyssey 2. The Old Testament 3. Aeschylus – Tragedies 4. Sophocles – Tragedies 5. Herodotus – Histories 6. Euripides – Tragedies 7. Thucydides – History of the Peloponnesian War 8. Hippocrates – Medical Writings 9. Aristophanes – Comedies 10. Plato – Dialogues 11. Aristotle – Works 12. Epicurus – Letter to Herodotus; Letter to Menoecus 13. Euclid – Elements 14. Archimedes – Works 15. Apollonius of Perga – Conic Sections 16. Cicero – Works 17. Lucretius – On the Nature of Things 18. Virgil – Works 19. Horace – Works 20. Livy – History of Rome 21. Ovid – Works 22. Plutarch – Parallel Lives; Moralia 23. Tacitus – Histories; Annals; Agricola Germania 24. Nicomachus of Gerasa – Introduction to Arithmetic 25. Epictetus – Discourses; Encheiridion 26. Ptolemy – Almagest 27. Lucian – Works 28. Marcus Aurelius – Meditations 29. Galen – On the Natural Faculties 30. The New Testament 31. Plotinus – The Enneads 32. St. Augustine – On the Teacher; Confessions; City of God; On Christian Doctrine 33. The Song of Roland 34. The Nibelungenlied 35. The Saga of Burnt Njál 36. St. Thomas Aquinas – Summa Theologica 37. Dante Alighieri – The Divine Comedy;The New Life; On Monarchy 38. Geoffrey Chaucer – Troilus and Criseyde; The Canterbury Tales 39. Leonardo da Vinci – Notebooks 40. Niccolò Machiavelli – The Prince; Discourses on the First Ten Books of Livy 41. Desiderius Erasmus – The Praise of Folly 42. Nicolaus Copernicus – On the Revolutions of the Heavenly Spheres 43. Thomas More – Utopia 44. Martin Luther – Table Talk; Three Treatises 45. François Rabelais – Gargantua and Pantagruel 46. John Calvin – Institutes of the Christian Religion 47. Michel de Montaigne – Essays 48. William Gilbert – On the Loadstone and Magnetic Bodies 49. Miguel de Cervantes – Don Quixote 50. Edmund Spenser – Prothalamion; The Faerie Queene 51. Francis Bacon – Essays; Advancement of Learning; Novum Organum, New Atlantis 52. William Shakespeare – Poetry and Plays 53. Galileo Galilei – Starry Messenger; Dialogues Concerning Two New Sciences 54. Johannes Kepler – Epitome of Copernican Astronomy; Concerning the Harmonies of the World 55. William Harvey – On the Motion of the Heart and Blood in Animals; On the Circulation of the Blood; On the Generation of Animals 56. Thomas Hobbes – Leviathan 57. René Descartes – Rules for the Direction of the Mind; Discourse on the Method; Geometry; Meditations on First Philosophy 58. John Milton – Works 59. Molière – Comedies 60. Blaise Pascal – The Provincial Letters; Pensees; Scientific Treatises 61. Christiaan Huygens – Treatise on Light 62. Benedict de Spinoza – Ethics 63. John Locke – Letter Concerning Toleration; Of Civil Government; Essay Concerning Human Understanding;Thoughts Concerning Education 64. Jean Baptiste Racine – Tragedies 65. Isaac Newton – Mathematical Principles of Natural Philosophy; Optics 66. Gottfried Wilhelm Leibniz – Discourse on Metaphysics; New Essays Concerning Human Understanding;Monadology 67. Daniel Defoe – Robinson Crusoe 68. Jonathan Swift – A Tale of a Tub; Journal to Stella; Gulliver's Travels; A Modest Proposal 69. William Congreve – The Way of the World 70. George Berkeley – Principles of Human Knowledge 71. Alexander Pope – Essay on Criticism; Rape of the Lock; Essay on Man 72. Charles de Secondat, baron de Montesquieu – Persian Letters; Spirit of Laws 73. Voltaire – Letters on the English; Candide; Philosophical Dictionary 74. Henry Fielding – Joseph Andrews; Tom Jones 75. Samuel Johnson – The Vanity of Human Wishes; Dictionary; Rasselas; The Lives of the Poets

Temporis filia veritas; cui me obstetricari non pudet. Truth is the daughter of time, and I feel no shame in being her midwife.

I used to measure the skies, now I measure the shadows of Earth. Although my mind was sky-bound, the shadow of my body lies here. [Epitaph he composed for himself a few months before he died]

We ought not to ask why the human mind troubles to fathom the secrets of the universe. The diversity of the phenomena of nature is so great, and the treasures hidden in the skies so rich, precisely in order that the human mind shall never be lacking in fresh nourishment.

Geometry has two great treasures; one is the Theorem of Pythagoras; the other, the division of a line into extreme and mean ratio. The first we may compare to a measure of gold; the second we may name a precious jewel.

Kepler knew what we habitually forget—that the locus of possibility expands when the unimaginable is imagined and then made real through systematic effort.

When ships to sail the void between the stars have been built, there will step forth men to sail these ships.

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). {Letter to fellow revolutionary astronomer Johannes Kepelr}

Mortui vivis docent - the dead teach the living.

Nature uses as little as possible of anything.

In my opinion, if, as the result of certain combinations, Kepler's or Newton's discoveries could become known to people in no other way than by sacrificing the lives of one, or ten, or a hundred or more people who were hindering the discovery, or standing as an obstacle in its path, then Newton would have the right, and it would even be his duty... to remove those ten or a hundred people, in order to make his discoveries known to mankind. It by no means follows from this, incidentally, that Newton should have the right to kill anyone he pleases, whomever happens along, or to steal from the market every day. Further, I recall developing in my article the idea that all... well, let's say, the lawgivers and founders of mankind, starting from the most ancient and going on to the Lycurguses, the Solons, the Muhammads, the Napoleons, and so forth, that all of them to a man were criminals, from the fact alone that in giving a new law, they thereby violated the old one, held sacred by society and passed down from their fathers, and they certainly did not stop at shedding blood either, if it happened that blood (sometimes quite innocent and shed valiantly for the ancient law) could help them.

Discover the force of the skies O Men: once recognised it can be put to use.

The soul of the newly born baby is marked for life by the pattern of the stars at the moment it comes into the world, unconsciously remembers it, and remains sensitive to the return of configurations of a similar kind.

Your favourite virtue ... Simplicity Your favourite virtue in man ... Strength Your favourite virtue in woman ... Weakness Your chief characteristic ... Singleness of purpose Your idea of happiness ... To fight Your idea of misery ... Submission The vice you excuse most ... Gullibility The vice you detest most ... Servility Your aversion ... Martin Tupper Favourite occupation ... Book-worming Favourite poet ... Shakespeare, Aeschylus, Goethe Favourite prose-writer ... Diderot Favourite hero ... Spartacus, Kepler Favourite heroine ... Gretchen [Heroine of Goethe's Faust] Favourite flower ... Daphne Favourite colour ... Red Favourite name ... Laura, Jenny Favourite dish ... Fish Favourite maxim ... Nihil humani a me alienum puto [Nothing human is alien to me] Favourite motto ... De omnibus dubitandum [Everything must be doubted].

The treasures hidden in the heavens are so rich that the human mind shall never be lacking in fresh nourishment.

The Earth is round, and is inhabited on all sides, is insignificantly small, and is borne through the stars.

i was accused of being against civilization, against science, against humanity. naturally, i was flattered and at the same time surprised, hurt, a little shocked. he repeated the charge. but how, i replied, being myself a member of humanity (albeit involuntarily, without prior consultation), could i be against humanity without being against myself, whom i love - though not very much; how can i be against science, when i gratefully admire, as much as i can, thales, democritus, aristarchus, faustus, paracelsus, copernicus, galiley, kepler, newton, darwin and einstien; and finally, how could i be against civilization when all which i most willingly defend and venerate - including the love of wilderness - is comprehended by the term

Lest we forget, the birth of modern physics and cosmology was achieved by Galileo, Kepler and Newton breaking free not from the close confining prison of faith (all three were believing Christians, of one sort or another) but from the enormous burden of the millennial authority of Aristotelian science. The scientific revolution of the sixteenth and seventeenth centuries was not a revival of Hellenistic science but its final defeat.

Sky-bound was the mind, Earth-bound the body rests

What a deep [trust] in the rationality of the structure of the world and what a longing to understand even a small glimpse of the reason revealed in the world there must have been in Kepler and Newton to enable them to unravel the mechanism of the heavens in long years of lonely work!

Galileo and Kepler had "dangerous thoughts" (as they are called in Japan), and so have the most intelligent men of our own day.

If the people of Europe had known as much of astronomy and geology when the bible was introduced among them, as they do now, there never could have been one believer in the doctrine of inspiration. If the writers of the various parts of the bible had known as much about the sciences as is now known by every intelligent man, the book never could have been written. It was produced by ignorance, and has been believed and defended by its author. It has lost power in the proportion that man has gained knowledge. A few years ago, this book was appealed to in the settlement of all scientific questions; but now, even the clergy confess that in such matters, it has ceased to speak with the voice of authority. For the establishment of facts, the word of man is now considered far better than the word of God. In the world of science, Jehovah was superseded by Copernicus, Galileo, and Kepler. All that God told Moses, admitting the entire account to be true, is dust and ashes compared to the discoveries of Descartes, Laplace, and Humboldt. In matters of fact, the bible has ceased to be regarded as a standard. Science has succeeded in breaking the chains of theology. A few years ago, Science endeavored to show that it was not inconsistent with the bible. The tables have been turned, and now, Religion is endeavoring to prove that the bible is not inconsistent with Science. The standard has been changed.

I too play with symbols... but I play in such a way that I do not forget that I am playing. For nothing is proved by symbols... unless by sure reasons it can be demonstrated that they are not merely symbolic but are descriptions of the ways in which the two things are connected and of the causes of this connection.

But who shall dwell in these worlds if they be inhabited? . . . Are we or they Lords of the World? . . . And how are all things made for man?-- KEPLER (quoted in The Anatomy of Melancholy)

Kepler’s second law: A planet sweeps out equal areas in equal times. It takes as long to travel from B to A as from F to E as from D to C; and the shaded areas BSA, FSE and DSC are all equal.

Priusquam autem ad creationem, hoc est ad finem omnis disputationis, veniamus: tentanda omnia existimo. However, before we come to [special] creation, which puts an end to all discussion: I think we should try everything else.

If there is anything that can bind the mind of man to this dreary exile of our earthly home and can reconcile us with our fate so that one can enjoy living,—then it is verily the enjoyment of the mathematical sciences and astronomy.

After the birth of printing books became widespread. Hence everyone throughout Europe devoted himself to the study of literature... Every year, especially since 1563, the number of writings published in every field is greater than all those produced in the past thousand years. The Paracelsians have created medicine anew and the Copernicans have created astronomy anew. I really believe that at last the world is alive, indeed seething, and that the stimuli of these remarkable conjunctions did not act in vain.

«Porque o passado não está morto. O passado nem sequer passou» - William Faulkner. Referia-me a que cada pequena coisa que acontece a um ser humano o acompanha até ao presente. Todas as suas vivências influenciam cada uma das suas opções e, tratando-se de experiências traumaticas, o passado passa a ocupar todo o espaço do presente.

It is to these two discoveries by Bradley that we owe the exactness of modern astronomy. .... This double service assures to their discoverer the most distinguished place (after Hipparchus and Kepler) above the greatest astronomers of all ages and all countries.

Kepler's laws, although not rigidly true, are sufficiently near to the truth to have led to the discovery of the law of attraction of the bodies of the solar system. The deviation from complete accuracy is due to the facts, that the planets are not of inappreciable mass, that, in consequence, they disturb each other's orbits about the Sun, and, by their action on the Sun itself, cause the periodic time of each to be shorter than if the Sun were a fixed body, in the subduplicate ratio of the mass of the Sun to the sum of the masses of the Sun and Planet; these errors are appreciable although very small, since the mass of the largest of the planets, Jupiter, is less than 1/1000th of the Sun's mass.

But before the grandeur and intricacy of Nature, he was, like Ptolemy and Kepler, exhilarated as well as disarmingly modest. Just before his death he wrote: “I do not know what I may appear to the world; but to myself I seem to have been only like a boy, playing on the seashore, and diverting myself, in now and then finding a smoother pebble or a prettier shell than ordinary, while the great ocean of truth lay all undiscovered before me.

Thus far our meditation on quantum reality has revealed that the world of everyday matter, when properly understood, embodies concepts of extraordinary beauty. Indeed, ordinary matter is built up from atoms that are, in a rich and precise sense, tiny musical instruments. In their interplay with light, they realize a mathematical Music of the Spheres that surpasses the visions of Pythagoras, Plato, and Kepler. In molecules and ordered materials, those atomic instruments play together as harmonious ensembles and synchronized orchestras.

before the origin of things, geometry was coeternal with the Divine Mind

I used to measure the heavens Now the Earth's shadows I measure My mind was in the heavens, Now the shadow of my body rests here

The orbit of every planet is an ellipse with the sun at one of the two foci.

I used to measure the skies, now I measure the shadows of Earth. Sky-bound was the mind, earthbound the body rests.

In the century of Kepler, Galileo, Descartes, Pascal, and Newton,” one historian wrote, “the most versatile genius of all was Gottfried Wilhelm Leibniz.

Now because 18 months ago the first dawn, 3 months ago broad daylight but a very few days ago the full sun of the most highly remarkable spectacle has risen — nothing holds me back. I can give myself up to the sacred frenzy, I can have the insolence to make a full confession to mortal men that I have stolen the golden vessel of the Egyptians to make from them a tabernacle for my God far from the confines of the land of Egypt. If you forgive me I shall rejoice; if you are angry, I shall bear it; I am indeed casting the die and writing the book, either for my contemporaries or for posterity to read, it matters not which: let the book await its reader for a hundred years; God himself has waited six thousand years for his work to be seen.

I have consummated the work to which I pledged myself, using all the abilities that You (God) gave me; I have shown the glory of Your works to men, but if I have pursued my own glory among men while engaged in a work intended for Your glory, be merciful, be compassionate, and forgive.

Is it possible that the Pentateuch could not have been written by uninspired men? that the assistance of God was necessary to produce these books? Is it possible that Galilei ascertained the mechanical principles of 'Virtual Velocity,' the laws of falling bodies and of all motion; that Copernicus ascertained the true position of the earth and accounted for all celestial phenomena; that Kepler discovered his three laws—discoveries of such importance that the 8th of May, 1618, may be called the birth-day of modern science; that Newton gave to the world the Method of Fluxions, the Theory of Universal Gravitation, and the Decomposition of Light; that Euclid, Cavalieri, Descartes, and Leibniz, almost completed the science of mathematics; that all the discoveries in optics, hydrostatics, pneumatics and chemistry, the experiments, discoveries, and inventions of Galvani, Volta, Franklin and Morse, of Trevithick, Watt and Fulton and of all the pioneers of progress—that all this was accomplished by uninspired men, while the writer of the Pentateuch was directed and inspired by an infinite God? Is it possible that the codes of China, India, Egypt, Greece and Rome were made by man, and that the laws recorded in the Pentateuch were alone given by God? Is it possible that Æschylus and Shakespeare, Burns, and Beranger, Goethe and Schiller, and all the poets of the world, and all their wondrous tragedies and songs are but the work of men, while no intelligence except the infinite God could be the author of the Pentateuch? Is it possible that of all the books that crowd the libraries of the world, the books of science, fiction, history and song, that all save only one, have been produced by man? Is it possible that of all these, the bible only is the work of God?

For Pythagoras as for Kepler, the two kinds of contemplation were twins; for them philosophy and religion were motivated by the same longing : to catch glimpses of eternity through the window of time.

To Plato, God was a mathematician. To Kepler, too, and to Biehl and Fredhoj. I do not believe it was a coincidence that their main subjects were biology and mathematics. A purpose behind them, the purpose that steered both them and the school, had caused them to align their own fates as closely as possible with God.

My dear Kepler, I wish that we might laugh at the stupidity of the human herd. What do you have to say about the principal philosophers of this academy who are filled with the stubbornness of an asp and do not want to look at either the planets, the moon or the telescope, even though I have freely and deliberately offered them the opportunity a thousand times? Truly, just as the asp stops its ears, so do these philosophers shut their eyes to the light of truth.

.... it wasn´t the people who were buried who were being punished, but those left behind.

I measured the skies, now the shadows I measure. Sky-bound was the mind, Earth-bound the body rests.

And I cherish more than anything else the Analogies, my most trustworthy masters. They know all the secrets of Nature, and they ought to be least neglected in Geometry.

Johannes Kepler described his motivation thus: ‘The chief aim of all investigations of the external world should be to discover the rational order which has been imposed on it by God, and which he revealed to us in the language of mathematics.

Meanwhile, someplace in the world, somebody is making love and another a poem. Elsewhere in the universe, a star manyfold the mass of our third-rate sun is living out its final moments in a wild spin before collapsing into a black hole, its exhale bending spacetime itself into a well of nothingness that can swallow every atom that ever touched us and every datum we ever produced, every poem and statue and symphony we’ve ever known—an entropic spectacle insentient to questions of blame and mercy, devoid of why. “In four billion years, our own star will follow its fate, collapsing into a white dwarf. We exist only by chance, after all. The Voyager will still be sailing into the interstellar shorelessness on the wings of the “heavenly breezes” Kepler had once imagined, carrying Beethoven on a golden disc crafted by a symphonic civilization that long ago made love and war and mathematics on a distant blue dot. But until that day comes, nothing once created ever fully leaves us. Seeds are planted and come abloom generations, centuries, civilizations later, migrating across coteries and countries and continents. Meanwhile, people live and people die—in peace as war rages on, in poverty and disrepute as latent fame awaits, with much that never meets its more, in shipwrecked love. I will die. You will die. The atoms that huddled for a cosmic blink around the shadow of a self will return to the seas that made us. What will survive of us are shoreless seeds and stardust.

…   not my own opinion, but my wife’s: Yesterday, when weary with writing, I was called to supper, and a salad I had asked for was set before me. ‘It seems then,’ I said, ‘if pewter dishes, leaves of lettuce, grains of salt, drops of water, vinegar, oil and slices of eggs had been flying about in the air for all eternity, it might at last happen by chance that there would come a salad.’ ‘Yes,’ responded my lovely, ‘but not so nice as this one of mine.

Things that look like they were designed, probably were... If intelligence is an operative component of the universe, a science that methodologically excludes its existence will be susceptible to being trapped in an endless chase for materialistic causes that do not exist... Where there are sufficient grounds for inferring intelligent causation, based on evidence of "specified complexity," it should be considered as a component of scientific theories. Inclusion of intelligent causation in the scientific equation is not novel and has not impeded the practice of science in the past, e.g. Newton and Kepler, in an age when science was not constrained by a philosophical materialism, and by many current scientists who have remained open to following the evidence where it leads.

Kepler and Newton represent a critical transition in human history, the discovery that fairly simple mathematical laws pervade all of Nature; that the same rules apply on Earth as in the skies; and that there is a resonance between the way we think and the way the world works.

Our generation is witness to a development of physical knowledge such as has not been seen since the days of Kepler, Galileo and Newton, and mathematics has scarcely ever experienced such a stormy epoch. Mathematical thought removes the spirit from its worldly haunts to solitude and renounces the unveiling of the secrets of Nature. But as recompense, mathematics is less bound to the course of worldly events than physics.

Condon, quick on his feet, replied that the accusation was untrue. He was not a revolutionary in physics. He raised his right hand: “I believe in Archimedes’ Principle, formulated in the third century B.C. I believe in Kepler’s laws of planetary motion, discovered in the seventeenth century. I believe in Newton’s laws.…” And on he went, invoking the illustrious names of Bernoulli, Fourier, Ampère, Boltzmann, and Maxwell.

Deep analogical thinking is the practice of recognizing conceptual similarities in multiple domains or scenarios that may seem to have little in common on the surface. It is a powerful tool for solving wicked problems, and Kepler was an analogy addict, so Gentner is naturally very fond of him.

Revealing my desert thoughts to a visitor one evening, I was accused of being against civilization, against science, against humanity. Naturally I was flattered and at the same time surprised, hurt, a little shocked. He repeated the charge. But how, I replied, being myself a member of humanity (albeit involuntarily, without prior consultation), could I be against humanity without being against myself, whom I love—though not very much; how can I be against science, when I gratefully admire, as much as any man, Thales, Democritus, Aristarchus, Faustus, Paracelsus, Copernicus, Galileo, Kepler, Newton, Darwin and Einstein; and finally, how could I be against civilization when all which I most willingly defend and venerate—including the love

In the beginning of the year 1665 I found the Method of approximating series & the Rule for reducing any dignity of any Binomial into such a series. The same year in May I found the method of Tangents of Gregory & Slusius, & in November had the direct method of fluxions & the next year in January had the Theory of Colours & in May following I had entrance into ye inverse method of fluxions. And the same year I began to think of gravity extending to ye orb of the Moon & (having found out how to estimate the force with wch [a] globe revolving within a sphere presses the surface of the sphere) from Kepler's rule of the periodic times of the Planets being in sesquialterate proportion of their distances from the center of their Orbs, I deduced that the forces wch keep the Planets in their Orbs must [be] reciprocally as the squares of their distances from the centers about wch they revolve: & thereby compared the force requisite to keep the Moon in her Orb with the force of gravity at the surface of the earth, & found them answer pretty nearly. All this was in the two plague years of 1665-1666. For in those days I was in the prime of my age for invention & minded Mathematicks & Philosophy more then than at any time since.

Kepler’s third or harmonic law states that the squares of the periods of the planets (the times for them to complete one orbit) are proportional to the cubes of their average distance from the Sun; the more distant the planet, the more slowly it moves, but according to a precise mathematical law: P2 = a3, where P represents the period of revolution of the planet about the Sun, measured in years, and a the distance of the planet from the Sun measured in “astronomical units.

We do not ask for what useful purpose the birds do sing, for song is their pleasure since they were created for singing. Similarly, we ought not to ask why the human mind troubles to fathom the secrets of the heavens. The diversity of the phenomena of Nature is so great, and the treasures hidden in the heavens so rich, precisely in order that the human mind shall never be lacking in fresh nourishment.

We do not ask for what useful purpose the birds do sing, for song is their pleasure since they were created for singing. Similarly, we ought not to ask why the human mind troubles to fathom the secrets of the heavens... The diversity of the phenomena of Nature is so great and the treasures hidden in the heavens so rich, precisely in order that the human mind shall never be lacking for fresh nourishment.

Magnetism also was an influence felt at a distance, and in a stunning anticipation of the idea of universal gravitation, Kepler suggested that the underlying cause was akin to magnetism: My aim in this is to show that the celestial machine is to be likened not to a divine organism but rather to a clockwork …, insofar as nearly all the manifold movements are carried out by means of a single, quite simple magnetic force, as in the case of a clockwork [where] all motions [are caused] by a simple weight.

no simple mechanism could do the job as well or better. It might simply be that nobody has yet found the simpler alternative. The Ptolemaic system (with the Earth in the center, orbited by the Sun, the Moon, planets, and stars) represented the state of the art in astronomy for over a thousand years, and its predictive accuracy was improved over the centuries by progressively complicating the model: adding epicycles upon epicycles to the postulated celestial motions. Then the entire system was overthrown by the heliocentric theory of Copernicus, which was simpler and—though only after further elaboration by Kepler—more predictively accurate.63 Artificial intelligence methods are now used in more areas than it would make sense to review here, but mentioning a sampling of them will give an idea of the breadth of applications. Aside from the game AIs

The Somnium makes clear to us, although it did not to all of Kepler’s contemporaries, that “in a dream one must be allowed the liberty of imagining occasionally that which never existed in the world of sense perception.” Science fiction was a new idea at the time of the Thirty Years’ War, and Kepler’s book was used as evidence that his mother was a witch.

God lost me somewhere along the way … and didn’t come back to look for me.

I especially love analogies, my most faithful masters, acquainted with all the secrets of nature… One should make great use of them.

«hay que tener la mente abierta, pero no tanto que se te salgan las ideas».

Ubi materia, ibi geometria.

Sólo hay 10 tipos de personas en el mundo: las que entienden el sistema binario y las que no.

When the storm rages and the shipwreck of the state threatens, we can do nothing more worthy than to sink the anchor of our peaceful studies into the ground of eternity.

Kepler’s discovery would not have been possible without the doctrine of conics. Now contemporaries of Kepler—such penetrating minds as Descartes and Pascal—were abandoning the study of geometry ... because they said it was so UTTERLY USELESS. There was the future of the human race almost trembling in the balance; for had not the geometry of conic sections already been worked out in large measure, and had their opinion that only sciences apparently useful ought to be pursued, the nineteenth century would have had none of those characters which distinguish it from the ancien régime.

Matthew Henry said, "When God intends great mercy for His people, He sets them apraying." Indeed, when God wants anything accomplished in His Kingdom, He moves men to pray. God is always the initiator. All effectual prayer was moving in the heart of God before ever it began to move in the heart of man. What Kepler said as he unlocked the secrets of the heavens, could well be said by the man who prays in the Spirit: "O God, I am thinking Thy thoughts after Thee.

Dynamical beauty transcends specific objects and phenomena, and invites us to imagine the expanse of possibilities. For example, the sizes and shapes of actual planetary orbits are not simple. They are neither the (compounded) circles of Aristotle, Ptolemy, and Nicolaus Copernicus, nor even the more nearly accurate ellipses of Kepler, but rather curves that must be calculated numerically, as functions of time, evolving in complicated ways that depend on the positions and masses of the Sun and the other planets. There is great beauty and simplicity here, but it is only fully evident when we understand the deep design. The appearance of particular objects does not exhaust the beauty of the laws.

The German astronomer Johannes Kepler coined the term “camera obscura” in the early seventeenth century, but by then the phenomenon had been known for millennia; in fact, it is perhaps the oldest known optical illusion. Some form of camera obscura was most likely behind a popular illusion performed in ancient Greece and Rome, in which spectral images were cast upon the smoke of burning incense by performers using concave metal mirrors—hence the expression “smoke and mirrors.

It is remarkable, however, that at the very lowest point of Kant's depression, when he became perfectly incapable of conversing with any rational meaning on the ordinary affairs of life, he was still able to answer correctly and distinctly, in a degree that was perfectly astonishing, upon any question of philosophy or of science, especially of physical geography, [Footnote: Physical Geography, in opposition to Political.] chemistry, or natural history. He talked satisfactorily, in his very worst state, of the gases, and stated very accurately different propositions of Kepler’s, especially the law of the planetary motions. And I remember in particular, that upon the very last Monday of his life, when the extremity of his weakness moved a circle of his friends to tears, and he sat amongst us insensible to all we could say to him, cowering down, or rather I might say collapsing into a shapeless heap upon his chair, deaf, blind, torpid, motionless,—even then I whispered to the others that I would engage that Kant should take his part in conversation with propriety and animation. This they found it difficult to believe. Upon which I drew close to his ear, and put a question to him about the Moors of Barbary. To the surprise of everybody but myself, he immediately gave us a summary account of their habits and customs; and told us by the way, that in the word Algiers, the g ought to be pronounced hard (as in the English word gear).

In an age when alchemy was still a common approach to natural phenomena, Kepler filled the universe with invisible forces acting all around us, and helped usher in the Scientific Revolution. His fastidious documentation of every meandering path his brain blazed is one of the great records of a mind undergoing creative transformation. It is a truism to say that Kepler thought outside the box. But what he really did, whenever he was stuck, was to think entirely outside the domain.

Magnetism is, of course, not the same as gravity, but Kepler’s fundamental innovation here is nothing short of breathtaking: he proposed that quantitative physical laws that apply to the Earth are also the underpinnings of quantitative physical laws that govern the heavens. It was the first nonmystical explanation of motion in the heavens; it made the Earth a province of the Cosmos. “Astronomy,” he said, “is part of physics.” Kepler stood at a cusp in history; the last scientific astrologer was the first astrophysicist. Not given to quiet understatement, Kepler assessed his discoveries in these words: With this symphony of voices man can play through the eternity of time in less than an hour, and can taste in small measure the delight of God, the Supreme Artist … I yield freely to the sacred frenzy … the die is cast, and I am writing the book—to be read either now or by posterity, it matters not. It can wait a century for a reader, as God Himself has waited 6,000 years for a witness.

I compared what was really known about the stars with the account of creation as told in Genesis. I found that the writer of the inspired book had no knowledge of astronomy -- that he was as ignorant as a Choctaw chief -- as an Eskimo driver of dogs. Does any one imagine that the author of Genesis knew anything about the sun -- its size? that he was acquainted with Sirius, the North Star, with Capella, or that he knew anything of the clusters of stars so far away that their light, now visiting our eyes, has been traveling for two million years? If he had known these facts would he have said that Jehovah worked nearly six days to make this world, and only a part of the afternoon of the fourth day to make the sun and moon and all the stars? Yet millions of people insist that the writer of Genesis was inspired by the Creator of all worlds. Now, intelligent men, who are not frightened, whose brains have not been paralyzed by fear, know that the sacred story of creation was written by an ignorant savage. The story is inconsistent with all known facts, and every star shining in the heavens testifies that its author was an uninspired barbarian. I admit that this unknown writer was sincere, that he wrote what he believed to be true -- that he did the best he could. He did not claim to be inspired -- did not pretend that the story had been told to him by Jehovah. He simply stated the "facts" as he understood them. After I had learned a little about the stars I concluded that this writer, this "inspired" scribe, had been misled by myth and legend, and that he knew no more about creation than the average theologian of my day. In other words, that he knew absolutely nothing. And here, allow me to say that the ministers who are answering me are turning their guns in the wrong direction. These reverend gentlemen should attack the astronomers. They should malign and vilify Kepler, Copernicus, Newton, Herschel and Laplace. These men were the real destroyers of the sacred story. Then, after having disposed of them, they can wage a war against the stars, and against Jehovah himself for having furnished evidence against the truthfulness of his book.

I believe Divine Providence arranged matters in such a way that what I could not obtain with all my efforts was given to me through chance; I believe all the more that this is so as I have always prayed to God that he should make my plan succeed, if what Copernicus had said was the truth.

After a duration of a thousand years, the power of astrology broke down when, with Copernicus, Kepler, and Galileo, the progress of astronomy overthrew the false hypothesis upon which the entire structure rested, namely the geocentric system of the universe. The fact that the earth revolves in space intervened to upset the complicated play of planetary influences, and the silent stars, related to the unfathomable depths of the sky, no longer made their prophetic voices audible to mankind. Celestial mechanics and spectrum analysis finally robbed them of their mysterious prestige.

You say 'love' too easily, Kepler." "No, not rally - please don't call me that. The idea that love has to be a blazing romantic thing of monogamous stability is innately ludicrous. You loved your parents, perhaps, because they were the warmth you could flee to. You loved your first childhood crush with a passion that made your lips tingle, your flesh grow light in their presence. You loved your wife with the steadiness of an ocean against the shore; your lover with the blaze of a shooting star, your best friend with the confidence of a mountain. Love is a many-splendorous thing, as the old song says....

Having witnessed in his own life much agony and the horrors of war, Kepler concluded that Earth really created two notes, mi for misery ("miseria" in Latin) and fa for famine ("fames" in Latin). In Kepler's words: "the Earth sings MI FA MI, so that even from the syllable you may guess that in this home of ours Misery and Famine hold sway.

Foreshadowings of the principles and even of the language of [the infinitesimal] calculus can be found in the writings of Napier, Kepler, Cavalieri, Fermat, Wallis, and Barrow. It was Newton's good luck to come at a time when everything was ripe for the discovery, and his ability enabled him to construct almost at once a complete calculus.

...I maintain that cosmic religiousness is the strongest and most noble driving force of scientific research. Only the man who can conceive the gigantic effort and above all the devotion, without which original scientific thought cannot succeed, can measure the strength of the feeling from which alone such work...can grow. What a deep belief in the intelligence of Creation and what longing for understanding, even if only of a meagre reflection in the revealed intelligence of this world, must have flourished in Kepler and Newton, enabling them as lonely men to unravel over years of work the mechanism of celestial mechanics....Only the man who devotes his life to such goals has a living conception of what inspired these men and gave them strength to remain steadfast in their aims in spite of countless failures. It is cosmic religiousness that bestows such strength. A contemporary has said, not unrightly, that the serious research scholar in our generally materialistic age is the only deeply religious human being.

If my false figures came near to the facts, this happened merely by chance....These comments are not worth printing. Yet it gives me pleasure to remember how many detours I had to make, along how many walls I had to grope in the darkness of my ignorance until I found the door which lets in the light of truth....In such manner did I dream of the truth.

Thus Kepler's three laws are: I. Each planet moves around the sun in an ellipse, with the sun at one focus. II. The radius vector from the sun to the planet sweeps out equal areas in equal intervals of time. III. The squares of the periods of any two planets are proportional to the cubes of the semimajor axes of their respective orbits : T - a'3/2

Wer aber soll hausen in jenen Welten, wenn sie bewohnt sein sollten? ... Sind wir oder sie die Herren des Alls? ... Und ist dies alles dem Menschen gemacht?

O God, I'm merely thinking you're thoughts after you.

In the first place, a new synthesis never results from a mere adding together of two fully developed branches in biological or mental evolution. Each new departure, each reintegration of what has become separated, involves the breaking down of the rigid, ossified patterns of behaviour and thought. Copernicus failed to do so; he tried to mate the heliocentric tradition with orthodox Aristotelian doctrine, and failed. Newton succeeded because orthodox astronomy had already been broken up by Kepler and orthodox physics by Galileo; reading a new pattern into the shambles, he united them in a new conceptual frame. Similarly, chemistry and physics could only become united after physics had renounced the dogma of the indivisibility and impermeability of the atom, thus destroying its own classic concept of matter, and chemistry had renounced its doctrine of ultimate immutable elements. A new evolutionary departure is only possible after a certain amount of de-differentiation, a cracking and thawing of the frozen structures resulting from isolated, over-specialized development.

The importance of experimental proof, on the other hand, does not mean that without new experimental data we cannot make advances. It is often said that science takes steps forward only when there is new experimental data. If this were true, we would have little hope of finding the theory of quantum gravity before measuring something new, but this is patently not the case. Which new data were available to Copernicus? None. He had the same data as Ptolemy. Which new data did Newton have? Almost none. His real ingredients were Kepler's laws and Galileo's results. What new data did Einstein have to discover general relativity? None. His ingredients were special relativity and Newton's theory. It simply isn't true that physics only advances when it is afforded new data.

Contemporaries only know the authority figures and the loudmouths. And the people born into power. But it takes perspective to know who's carrying the load. Nobody here has a clue who Johannes Kepler is. All they know about Galileo is that he's a teacher who got in trouble with the Inquisition. I doubt anyone's heard of Francis Bacon. Even in Britain, nobody really knows him. He's just a guy with a funny name.

PREFACE Cosmology is the study of the universe as a whole, including its birth and perhaps its ultimate fate. Not surprisingly, it has undergone many transformations in its slow, painful evolution, an evolution often overshadowed by religious dogma and superstition. The first revolution in cosmology was ushered in by the introduction of the telescope in the 1600s. With the aid of the telescope, Galileo Galilei, building on the work of the great astronomers Nicolaus Copernicus and Johannes Kepler, was able to open up the splendor of the heavens for the first time to serious scientific investigation. The advancement of this first stage of cosmology culminated in the work of Isaac Newton, who finally laid down the fundamental laws governing the motion of the celestial bodies. Instead of magic and mysticism, the laws of heavenly bodies were now seen to be subject to forces that were computable and reproducible. A second revolution in cosmology was initiated by the introduction of the great telescopes of the twentieth century, such as the one at Mount Wilson with its huge 100-inch reflecting mirror. In the 1920s, astronomer Edwin Hubble used this giant telescope to overturn centuries of dogma, which stated that the universe was static and eternal, by demonstrating that the galaxies in the heavens are moving away

On the other hand, if string theorists are wrong, they can't be just a little wrong. If the new dimensions and symmetries do not exist, then we will count string theorists among science's greatest failures, like those who continued to work on Ptolemaic epicycles while Kepler and Galileo forged ahead. Theirs will be a cautionary tale of how not to do science, how not to let theoretical conjecture get so far beyond the limits of what can rationally be argued that one starts engaging in fantasy.

Forget your magic mirror," she decided to say. "If I lived here, I would spend my whole life in here, reading." "They're just... books...." He carefully lit the candelabra at the front and placed Lumière on the floor, dismissing him. "Just books? That's like saying Alexandria is just a library." She ran over to the closest shelf and tilted her head, reading the titles. "You don't understand. I don't understand how you don't understand. Look- here's an ancient text in Greek about astronomy... and next to it is everything Galileo Galilei ever wrote!! This whole section is about the stars and planets and the entire universe!" The Beast stood, looking slightly embarrassed, scratching the back of his neck with his hand. Belle grabbed a book and ran over to him, shoving it in his face. "Up until this man, Copernicus, everyone thought the entire universe rotated around the earth- that we were the center of it all." She flipped open to a page that had an engraving of planets and their paths, little callouts to their names and the length of their orbits. "Thanks to men like him and Tycho Brahe and Kepler, we now know nothing revolves around the earth- except the moon.

It is not difficult to imagine the Catholic Church adopting, after a Tychonic transition, the Copernican cosmology some 200 years earlier than she eventually did. The Galileo affair was an isolated episode in the history of relations between science and theology. But its dramatic circumstances, magnified out of all proportion, created a popular belief that science stood for freedom, the Church for oppression of thought. Some historians wish to make us believe that the decline of science in Italy was due to the "terror" caused by the trial of Galileo. But the next generation saw the rise of Toricelli, Cavallieri, Borelli, whose contributions to science were more substantial than those of any generation before or during Galileo's lifetime. The contemporary divorce between faith and reason is not the result of a contest for power or intellectual monopoly, but of a progressive estrangement. This becomes evident if we shift our attention from Italy to the Protestant countries of Europe, and to France. Kepler, Descartes, Barrow, Leibniz, Gilbert, Boyle and Newton himself, the generation of pioneers contemporary with and succeeding Galileo, were all deeply and genuinely religious thinkers. The pioneers of the new cosmology, from Kepler to Newton and beyond, based their search into nature on the mystic conviction that there must exist laws behind the confusing phenomena; that the world was a completely rational, ordered, harmonic creation.

When she looks up again, she sees something incomprehensible. An animal has come out of the forest on two legs. It's walking on the logging road, bent and stumbling. A tiny figure covered in dirt, blood and clay. Pia holds her breath. It isn't an animal after all. It's almost as if a part of the forest has freed itself and come alive. As if it's a little girl made from twigs.

Music of the Grid: A Poem in Two Equations _________________________ The masses of particles sound the frequencies with which space vibrates, when played. This Music of the Grid betters the old mystic mainstay, "Music of the Spheres," both in fantasy and in realism. LET US COMBINE Einstein's second law m=E/C^2 (1) with another fundamental equation, the Planck-Einstein-Schrodinger formula E = hv The Planck-Einstein-Schrodinger formula relates the energy E of a quantum-mechanical state to the frequency v at which its wave function vibrates. Here h is Planck's constant. Planck introduced it in his revolutionary hypothesis (1899) that launched quantum theory: that atoms emit or absorb light of frequency v only in packets of energy E = hv. Einstein went a big step further with his photon hypothesis (1905): that light of frequency v is always organized into packets with energy E = hv. Finally Schrodinger made it the basis of his basic equation for wave functions-the Schrodinger equation (1926). This gave birth to the modern, universal interpretation: the wave function of any state with energy E vibrates at a frequency v given by v = E/h. By combining Einstein with Schrodinger we arrive at a marvelous bit of poetry: (*) v = mc^2/h (*) The ancients had a concept called "Music of the Spheres" that inspired many scientists (notably Johannes Kepler) and even more mystics. Because periodic motion (vibration) of musical instruments causes their sustained tones, the idea goes, the periodic motions of the planets, as they fulfill their orbits, must be accompanied by a sort of music. Though picturesque and soundscape-esque, this inspiring anticipation of multimedia never became a very precise or fruitful scientific idea. It was never more than a vague metaphor, so it remains shrouded in equation marks: "Music of the Spheres." Our equation (*) is a more fantastic yet more realistic embodiment of the same inspiration. Rather than plucking a string, blowing through a reed, banging on a drumhead, or clanging a gong, we play the instrument that is empty space by plunking down different combinations of quarks, gluons, electrons, photons,... (that is, the Bits that represent these Its) and let them settle until they reach equilibrium with the spontaneous activity of Grid. Neither planets nor any material constructions compromise the pure ideality of our instrument. It settles into one of its possible vibratory motions, with different frequencies v, depending on how we do the plunking, and with what. These vibrations represent particles of different mass m, according to (*). The masses of particles sound the Music of the Grid.