Johannes Kepler Quotes

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

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

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?

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

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?

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.

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}

Nature uses as little as possible of anything.

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.

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.

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

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.

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.

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!

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.

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.

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 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.

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.

…   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.

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.

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.

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

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.

The astronomer Johannes Kepler declared that “nature loves simplicity and unity.” So did Steve Jobs.

the treasures hidden in the heavens so rich, precisely in order that the human mind shall never be lacking in fresh nourishment. —JOHANNES KEPLER

The Influence of Archetypal Ideas on the Scientific Theories of Johannes Kepler.

Ships and sails proper for the heavely air should be fashioned." Johannes Kepler to Galileo 1609

Geometry existed before the Creation. It is co-eternal with the mind of God... Geometry provided God with a model for the creatin... Geometry is God Himself. Johannes Kepler

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?

Johannes Kepler published his book Harmonices Mundi in 1619. In it he proposed that it was the Creator who “decorated” the whole world, using mathematical and musical harmonic proportions. The spiritual and the physical are united.

Johannes Kepler, who was one of the first to apply mathematics to the motion of the planets, was an imperial adviser to Emperor Rudolf Il and perhaps escaped persecution by piously including religious elements in his scientific work.

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. —Johannes Kepler

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 was Johannes Kepler who first noticed the effect when he realized that, contrary to expectations, comet tails always point away from the sun. Kepler correctly surmised that pressure from sunlight creates these tails by blowing dust and ice crystals in comets away from the sun.

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.

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.

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.

Truthfully I may confess that as often as I contemplate the proper order, as one results from another and becomes diminished, it is as if I have read a heavenly passage not written in meaningful letters but with the essential things in this world which tells me: Put your reason herein to comprehend these things. JOHANNES KEPLER, IN HIS CALENDAR FOR 1604

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.

Ships and sails proper for the heavenly air should be fashioned. Then there will also be people, who do not shrink from the dreary vastness of space.

The harnessing to a rational pursuit of the immense psychic energies derived from an irrational obsession seems to be another secret of genius, at least of genius of a certain type.

There must be some definite cause why, whenever snow begins to fall, its initial formation invariably displays the shape of a six-cornered starlet. For if it happens by chance, why do they not fall just as well with five corners or with seven? . . . Who carved the nucleus, before it fell, into six horns of ice? —From “On the Six-Cornered Snowflake,” by Johannes Kepler, 1610

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.

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

Kita tidak mempertanyakan apa guna burung berkicau, sebab kicauan adalah kenikmatan mereka sejak mereka diciptakan untuk berkicau. Kita pun semestinya tidak mempertanyakan mengapa manusia bersusah payah menyingkap rahasia langit... Keanekaragaman fenomena alam sungguh luar biasa, harta karun yang tersembunyi di langit bergitu banyak dan tertata dengan sangat baik sehingga akal manusia tidak akan pernah kekurangan nutrisi segar”---Johannes Kepler__ Hal.45

Johannes Kepler, who was one of the first to apply mathematics to the motion of the planets, was an imperial adviser to Emperor Rudolf Il and perhaps escaped persecution by piously including religious elements in his scientific work. The former monk Giordano Bruno was not so lucky. In 1600, he was tried and sentenced to death for heresy. He was gagged, paraded naked in the streets of Rome, and finally burned at the stake. His chief crime? Declaring that life may exist on planets circling other stars.

As Galileo said in a letter to the German mathematician Johannes Kepler:   My dear Kepler, I wish that we might laugh at the remarkable stupidity of the common 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.

To our ancestors there was much in Nature to be afraid of—lightning, storms, earthquakes, volcanos, plagues, drought, long winters. Religions arose in part as attempts to propitiate and control, if not much to understand, the disorderly aspect of Nature. The scientific revolution permitted us to glimpse an underlying ordered Universe in which there was a literal harmony of the worlds (Johannes Kepler’s phrase). If we understand Nature, there is a prospect of controlling it or at least mitigating the harm it may bring. In this sense, science brought hope.

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.

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.

Some of the greatest mathematical minds of all ages, from Pythagoras and Euclid in ancient Greece, through the medieval Italian mathematician Leonardo of Pisa and the Renaissance astronomer Johannes Kepler, to present-day scientific figures such as Oxford physicist Roger Penrose, have spent endless hours over this simple ratio and its properties. But the fascination with the Golden Ratio is not confined just to mathematicians. Biologists, artists, musicians, historians, architects, psychologists, and even mystics have pondered and debated the basis of its ubiquity and appeal. In fact, it is probably fair to say that the Golden Ratio has inspired thinkers of all disciplines like no other number in the history of mathematics.

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.

In what manner does the countenace of the sky at the moment of a man's birth determine his character? It acts on the person during his life in the manner of the loops which a peasant ties at random around the pumpkins in his field: they do not cause the pumpkin to grow, but they determine its shape. The same applies to the sky: it does not endow man with his habits, history, happiness, children, riches, or a wife, but it moulds his condition....

In this book, you will encounter various interesting geometries that have been thought to hold the keys to the universe. Galileo Galilei (1564-1642) suggested that "Nature's great book is written in mathematical symbols." Johannes Kepler (1571-1630) modeled the solar system with Platonic solids such as the dodecahedron. In the 1960s, physicist Eugene Wigner (1902-1995) was impressed with the "unreasonable effectiveness of mathematics in the natural sciences." Large Lie groups, like E8-which is discussed in the entry "The Quest for Lie Group E8 (2007)"- may someday help us create a unified theory of physics. in 2007, Swedish American cosmologist Max Tegmark published both scientific and popular articles on the mathematical universe hypothesis, which states that our physical reality is a mathematical structure-in other words, our universe in not just described by mathematics-it is mathematics.

Johannes Kepler, who was one of the first to apply mathematics to the motion of the planets, was an imperial adviser to Emperor Rudolf Il and perhaps escaped persecution by piously including religious elements in his scientific work. The former monk Giordano Bruno was not so lucky. In 1600, he was tried and sentenced to death for heresy. He was gagged, paraded naked in the streets of Rome, and finally burned at the stake. His chief crime? Declaring that life may exist on planets circling other stars. The great Galileo, the father of experimental science, almost met the same fate. But unlike Bruno, Galileo recanted his theories on pain of death. Nonetheless, he left a lasting legacy with his telescope, perhaps the most revolutionary and seditious invention in all of science. With a telescope, you could see with your own eyes that the moon was pockmarked with craters; that Venus had phases consistent with its orbiting the sun; that Jupiter had moons, all of which were heretical ideas. Sadly, he was placed under house arrest, isolated from visitors, and eventually went blind. (It was said because he once looked directly at the sun with his telescope.) Galileo died a broken man. But the very year that he died, a baby was born in England who would grow up to complete Galileo's and Kepler's unfinished theories, giving us a unified theory of the heavens.

Though all Christians start a wedding invitation by solemnly declaring their marriage is due to special Divine arrangement, I, as a philosopher, would like to talk in greater detail about this … —JOHANNES KEPLER If you prefer Mr. Martin to every other person; if you think him the most agreeable man you have ever been in company with, why should you hesitate? —JANE AUSTEN, EMMA

THE DANGEROUS VICE OF ASKING Which is worth more? Experience or doctrine? By dropping stones and pebbles, big balls and little balls, Galileo Galilei proved that velocity remains the same no matter the weight. Aristotle was wrong, and for nineteen centuries no one had noticed. Johannes Kepler, another curious fellow, discovered that plants do not rotate in circles when they follow the light over the course of a day. Wasn’t the circle supposed to be the perfect path of everything that revolves? Wasn’t the universe supposed to be the perfect work of God? “This world is not perfect, not nearly,” Kepler concluded. “Why should its paths be perfect?” His reasoning seemed suspicious to Lutherans and Catholics alike. Kepler’s mother had spent four years in prison accused of practicing witchcraft. They must have been up to something. But

75 JOHANNES KEPLER 1571-1630

Plato advanced into domains far vaster and more exotic than merely the pipe-smoke-garlanded realms of university philosophy departments. His ideas shaped countless cultural and intellectual trends: ideas of love, of magic and the occult, of art and imitation, of creativity through the divine frenzy of the “mad poet.” His theories on the structure of the cosmos influenced such pioneers of the Scientific Revolution as Johannes Kepler (who used the Platonic solids described in the Timaeus to determine the number of the planets and their distances from the Sun) and Galileo (who credited Plato with the theory of the common origin of the planets). His theories of the soul have been said to prefigure Sigmund Freud’s understanding of the psyche, while Friedrich Nietzsche argued in The Birth of Tragedy that Plato’s dialogues inspired the novel. Few things in heaven and earth were not dreamt of in Plato’s philosophy.

Most early scientists were compelled to study the natural world because of their Christian worldview. In Science and the Modern World, British mathematician and philosopher Alfred North Whitehead concludes that modern science developed primarily from “the medieval insistence on the rationality of God.” Modern science did not develop in a vacuum, but from forces largely propelled by Christianity. Not surprisingly, most early scientists were theists, including pioneers such as Francis Bacon (1561–1626), Johannes Kepler (1571– 1630), Blaise Pascal (1623–62), Robert Boyle (1627–91), Isaac Newton (1642–1727), and Louis Pasteur (1822–95). For many of them, belief in God was the prime motivation for their investigation of the natural world. Bacon believed the natural world was full of mysteries God intended for us to explore. Kepler described his motivation for science: “The chief aim of all investigations of the external world should be to discover the rational order and harmony which has been imposed on it by God, and which he revealed to us in the language of mathematics.

Another pioneer of the scientific revolution, Johannes Kepler, was the first to couch an earnest scientific argument – a representation of the Copernican theory of the solar system – as a visionary fantasy. His Somnium (A Dream, 1634) also includes an ingenious attempt to imagine how life on the moon might have adapted to the long cycle of day and night.

In addition, it is part of our God-given vocation to find as much of that order as we can and to praise God for the wonders of creation. Johann Kepler (1571-1630), one of the pioneering giants of classical science, and Francis Bacon (1561-1626) were the most influential proponents of the importance and value of science; both stressed this religious motive for doing science. It is our divinely given vocation to render praise to God by achieving a sounder understanding of God's handiwork. They passionately believed and advocated this view.

But more important, for what useful purpose do birds sing? Johannes Kepler responded to the last question in his book Mysterium Cosmographicum (The Cosmic Mystery) more than 400 years ago. “We do not ask for what useful purpose the birds do sing, for song is their pleasure,” he wrote. “Similarly we ought not ask why the human mind troubles to fathom the secrets of the heavens.

Nu ne întrebăm în ce scop util cântă păsările, cântecul este bucuria lor de când au fost zămislite pentru cântat. La fel, n-ar trebui să ne întrebăm de ce spiritul omului se străduieşte să pătrundă secretele cerurilor. Diversitatea fenomenelor naturii e atât de mare, iar comorile ascunse în ceruri atât de bogate, tocmai pentru ca spiritul omului să nu fie nicicând lipsit de hrană proaspătă.

Whenever an error pops up, the usual response is “Jeez, another screwup, what went wrong this time?” The creative thinker, on the other hand, will realize the potential value of errors, and perhaps say something like, “Would you look at that! Where can it lead our thinking?” And then he or she will go on to use the error as a stepping stone to a new idea. Indeed, the whole history of discovery is filled with people who used erroneous assumptions and failed ideas as stepping stones to new ideas. Columbus thought he was finding a shorter route to India. Johannes Kepler stumbled on to the idea of interplanetary gravity because of assumptions which were right for the wrong reasons. Thomas Edison knew 1,800 ways not to build a light bulb. Freud had several big failures before he developed psychoanalysis. One of Madame Curie’s failures was radium.

Johannes Kepler, the discoverer of the laws of planetary motion, was born in 1571, in the town of Weil der Stadt, Germany.

Galileo also wanted to avoid the error of his colleague Johannes Kepler (1571–1630). For all his brilliant work, Kepler had insisted on making the five Platonic solids the basis for his model of the solar system, rendering it useless for further empirical research. It was a bizarre example of carrying the faith in the perfection of mathematics too far.35 By contrast, Galileo understood that even a divinely ordered cosmos could not be perfect. There were craters on the moon and spots on the sun. Kepler himself had shown that the planetary orbits were not perfect circles as Aristotle and even Copernicus had assumed, but ellipses.

When Kepler suggested that the tides are due to attractive forces emanating from the moon, Galileo shrugged the idea off as 'occult fantasy' because it involved action-at-a-distance and thus contradicted the laws of nature.

many of history’s greatest mathematicians and scientists have come down with cases of Pythagorean fever. The astronomer Johannes Kepler had it bad. So did the physicist Paul Dirac. As we’ll see, it drove them to seek, and to dream, and to long for the harmonies of the universe.

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.

indeed, Johannes Kepler fell into a state of self-described “sacred frenzy” when he found his laws of planetary motion—because those patterns seemed to be signs of God’s handiwork.

[Albert of Wallenstein] loved war. He was very tall and skeletally thin, usually dressed in sinister black, with a single streak of red. "[He is] unmerciful," wrote the astronomer Johannes Kepler, describing Wallenstein, "devoted only to himself and his desires...covetous, deceitful...usually silent, often violent.

Before the Enlightenment, early scientists in the West wrote in their notes that they prayed. Johannes Kepler, the Danish astronomer who discovered the laws of interplanetary motion, wrote that he was “thinking God’s thoughts after him.”[7] Newton and others regularly gave glory to God in their writings. Ironically, modern science is possible because Christianity taught that God created a world separate from himself. If the world is separate, we can investigate it.

Like Edwards, many of the best Renaissance thinkers were blessed with a jack-of-all-trades erudition. When he wasn’t revolutionizing astronomy, Copernicus practiced medicine and law. Johannes Kepler based his theory of planetary motion on the ebb and flow of musical harmony. Better known in his day as a lawyer, statesman, writer, and courtier, Francis Bacon helped to pioneer the scientific method. A theologian named Robert Boyle laid the foundations of modern chemistry. Leonardo da Vinci, the poster boy for polymaths, was a gifted painter, sculptor, musician, anatomist, and writer, as well as a startlingly prolific inventor.

The Catholic Church allowed the publication of his work, but Calvin and Luther (who called Copernicus an ass) condemned it on scriptural grounds. Some of the technical difficulties with Copernicus’s theory were dealt with by the German astronomer Johannes Kepler, who thus made the heliocentric theory more plausible. Kepler, however, was persecuted by the Protestants in Tubingen and had to flee to the Jesuits for protection in 1596.

Ships and sails proper for the heavenly air should be fashioned. Then there will also be people, who do not shrink from the dreary vastness of space.” — Johannes Kepler, letter to Galileo Galilei, 1609

Several major and significant discoveries in science occurred in the 19th and 20th century through the works of scientists who believed in God. Even in just the last 500 years of modern scientific enterprise, a great many scientists were religious including names like Isaac Newton, Nicholas Copernicus, Johannes Kepler, Robert Boyle, William Thomson Kelvin, Michael Faraday, James Clerk Maxwell, Louis Pasteur and Nobel Laureate scientists like: 1.Max Planck 2.Guglielmo Marconi 3.Robert A. Milikan 4.Erwin Schrodinger 5.Arthur Compton 6.Isidor Isaac Rabi 7.Max Born 8.Dererk Barton 9.Nevill F. Mott 10.Charles H. Townes 11.Christian B. Anfinsen 12.John Eccles 13.Ernst B. Chain 14.Antony Hewish 15.Daniel Nathans 16.Abdus Salam 17.Joseph Murray 18.Joseph H. Taylor 19.William D. Phillips 20.Walter Kohn 21.Ahmed Zewail 22.Aziz Sancar 23.Gerhard Etrl Thus, it is important for the torchbearers of science to know their scope and highlight what they can offer to society in terms of curing diseases, improving food production and easing transport and communication systems, for instance. To mock faith and faithful, the scientists who do not believe in God do not just hurt the faithful people who are non-scientists, but a great many of their own colleagues who are scientists, but not atheists.

As the writer Arthur Koestler astutely observed, “Johannes Kepler became enamored 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 immediate catalyst for the emergence of the Enlightenment in the eighteenth century was the scientific revolution of the sixteenth and seventeenth centuries, which included three momentous discoveries in astronomy: Johannes Kepler delineated the rules that govern the movement of the planets, Galileo Galilei placed the sun at the center of the universe, and Isaac Newton discovered the force of gravity, invented calculus (Gottfried Wilhelm Leibniz independently discovered it at the same time), and used it to describe the three laws of motion. In so doing, Newton joined physics and astronomy and illustrated that even the deepest truths in the universe could be revealed by the methods of science. These contributions were celebrated in 1660 with the formation of the first scientific society in the world: the Royal Society of London for Improving Natural Knowledge, which elected Isaac Newton as its president in 1703. The founders of the Royal Society thought of God as a mathematician who had designed the universe to function according to logical and mathematical principles. The role of the scientist—the natural philosopher—was to employ the scientific method to discover the physical principles underlying the universe and thereby decipher the codebook that God had used in creating the cosmos. Success in the realm of science led eighteenth-century thinkers to assume that other aspects of human action, including political behavior, creativity, and art, could be improved by the application of reason, leading ultimately to an improved society and better conditions for all humankind. This confidence in reason and science affected all aspects of political and social life in Europe and soon spread to the North American colonies. There, the Enlightenment ideas that society can be improved through reason and that rational people have a natural right to the pursuit of happiness are thought to have contributed to the Jeffersonian democracy that we enjoy today in the United States.

Advertencia para idiotas. Pero a todo aquel que sea demasiado estúpido para comprender la ciencia astronómica, o demasiado pusilánime para creer a Copérnico sin que afecte a su fe, le aconsejaría que, una vez renunciado a los estudios astronómicos, y tras haber condenado todos aquellos estudios filosóficos que le plazca, se preocupe de sus asuntos y se vaya a su casa a escarbar su terruño

But as the seventeenth century wore on, precision observations greatly improved due to the invention of the telescope and an increasingly mature application of mathematics to describe the data, and led a host of astronomers and mathematicians – including Johannes Kepler, Galileo and ultimately Isaac Newton – towards an understanding of the workings of the solar system. This theory is good enough even today to send space probes to the outer planets with absolute precision.