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Johannes Kepler

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 enrichment.

Johannes Kepler (December 27 1571November 15 1630) was a German Lutheran mathematician, astronomer and astrologer, and a key figure in the 17th century astronomical revolution. He is best known for his laws of planetary motion, which provided one of the foundations of Isaac Newton's law of universal gravitation.


Discover the force of the heavens O Men: once recognised it can be put to use.
I used to measure the Heavens, now I measure the shadows of Earth...
Truth is the daughter of time, and I feel no shame in being her midwife.
  • Vim coeli reserate viri: venit agnita ad usus:
    Ignotae videas commoda nulla rei.
    • Discover the force of the heavens O Men:
      Once recognised it can be put to use.
    • De fundamentis astrologiae certioribus [On the more Certain Fundamentals of Astrology or On Giving Astrology Sounder Foundations] (written 1601; published 1602) in Opera Omnia, Vol. 1, Heyder & Zimmer, 1858, p. 417 (title-page)
  • He who will please the crowd and for the sake of the most ephemeral renown will either proclaim those things which nature does not display or even will publish genuine miracles of nature without regard to deeper causes is a spiritually corrupt person… With the best of intentions I publicly speak to the crowd (which is eager for things new) on the subject of what is to come.
    • De fundamentis astrologiae certioribus (1601), foreword
  • Nature uses as little as possible of anything.
    • Viking Book of Aphorisms: A Personal Selection (1920) by W. H. Auden and Louis Kronenberger, p. 98; also in The Infinite Cosmos: Questions from the Frontiers of Cosmology (2006) by Joseph Silk
  • 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.
  • In Terra inest virtus, quae Lunam del.
    • There is a force in the earth which causes the moon to move.
      • Essay dedicated to the Archduke Ferdinand, as quoted in Kepler (1993) by Max Caspar, Sect. II, Ch. 9, p. 110
  • 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.
    • As quoted in The Golden Ratio : The Story of Phi, the World's Most Astonishing Number (2003) by Mario Livio, p. 62
  • I much prefer the sharpest criticism of a single intelligent man to the thoughtless approval of the masses.
    • As quoted in (K)new Words: Redefine Your Communication (2005) by Gloria Pierre, p. 147
  • I used to measure the heavens, now I measure the shadows of Earth.
    Although my mind was heaven-bound, the shadow of my body lies here.
    • Epitaph he composed for himself a few months before he died, as quoted in Calculusː Multivariable (2006) by Steven G. Krantz and Brian E. Blank. p. 126
    • Unsourced variant: I used to measure the Heavens, now I measure the shadows of Earth. The mind belonged to Heaven, the body's shadow lies here.
  • Temporis filia veritas; cui me obstetricari non pudet.
    • Truth is the daughter of time, and I feel no shame in being her midwife.
    • As quoted in The Ismailis in the Middle Ages : A History of Survival, A search for Salvation (2007) by Shafique N. Virani, p. 28

Mysterium Cosmographicum (1596)Edit

  • The earth is the sphere, the measure of all; round it describe a dodecahedron; the sphere including this will be Mars. Round Mars describe a tetrahedron; the sphere including this will be Jupiter. Describe a cube round Jupiter; the sphere including this will be Saturn. Now, inscribe in the earth an icosahedron, the sphere inscribed in it will be Venus: inscribe an octahedron in Venus: the circle inscribed in it will be Mercury.
    • Walter William Bryant, Kepler (1920), pp. 16–17
  • Either... the moving intelligences of the planets are weakest in those that are farthest from the sun, or... there is one moving intelligence in the sun, the common center, forcing them all round, but those most violently which are nearest, and that it languishes in some sort and grows weaker at the most distant, because of the remoteness and the attenuation of the virtue.
    • Walter William Bryant, Kepler (1920), p. 17

Astronomia nova (1609)Edit

Note full title: Astronomia Nova ΑΙΤΙΟΛΟΓΗΤΟΣ seu physica coelestis, tradita commentariis de motibus stellae Martis ex observationibus G.V. Tychonis Brahe (New Astronomy, Based upon Causes, or Celestial Physics, Treated by Means of Commentaries on the Motions of the Star Mars, from the Observations of Tycho Brahe, Gent) also known as "Commentaries on the Motions of Mars"

  • Every corporeal substance, so far forth as it is corporeal, has a natural fitness for resting in every place where it may be situated by itself beyond the sphere of influence of a body cognate with it.
    • As quoted in Kepler by Walter William Bryant (1920), p. 35
  • Gravity is a mutual affection between cognate bodies towards union or conjunction (similar in kind to the magnetic virtue), so that the earth attracts a stone much rather than the stone seeks the earth.
    • As quoted by Bryant, ibid., pp. 35–36
  • ...wheresoever the earth may be placed, or whithersoever it may be carried by its animal faculty, heavy bodies will always be carried towards it.
    • As quoted by Bryant, ibid., p. 36
  • If the earth were not round, heavy bodies would not tend from every side in a straight line towards the center of the earth, but to different points from different sides.
    • As quoted by Bryant, ibid.
  • If two stones were placed... near each other, and beyond the sphere of influence of a third cognate body, these stones, like two magnetic needles, would come together in the intermediate point, each approaching the other by a space proportional to the comparative mass of the other.
    • As quoted by Bryant, ibid.
  • If the moon and earth were not retained in their orbits by their animal force or some other equivalent, the earth would mount to the moon by a fifty-fourth part of their distance, and the moon fall towards the earth through the other fifty-three parts, and they would there meet, assuming, however, that the substance of both is of the same density.
    • As quoted by Bryant, ibid.
  • If the earth should cease to attract its waters to itself all the waters of the sea would be raised and would flow to the body of the moon.
    • As quoted by Bryant, ibid.
  • The sphere of the attractive virtue which is in the moon extends as far as the earth, and entices up the waters; but as the moon flies rapidly across the zenith, and the waters cannot follow so quickly, a flow of the ocean is occasioned in the torrid zone towards the westward.
    • As quoted by Bryant, ibid.
  • If the attractive virtue of the moon extends as far as the earth, it follows with greater reason that the attractive virtue of the earth extends as far as the moon and much farther; and, in short, nothing which consists of earthly substance anyhow constituted although thrown up to any height, can ever escape the powerful operation of this attractive virtue.
    • As quoted by Bryant, ibid.
  • Nothing which consists of corporeal matter is absolutely light, but that is comparatively lighter which is rarer, either by its own nature, or by accidental heat. And it is not to be thought that light bodies are escaping to the surface of the universe while they are carried upwards, or that they are not attracted by the earth. They are attracted, but in a less degree, and so are driven outwards by the heavy bodies; which being done, they stop, and are kept by the earth in their own place.
    • As quoted by Bryant, ibid.
  • But although the attractive virtue of the earth extends upwards, as has been said, so very far, yet if any stone should be at a distance great enough to become sensible compared with the earth’s diameter, it is true that on the motion of the earth such a stone would not follow altogether; its own force of resistance would be combined with the attractive force of the earth, and thus it would extricate itself in some degree from the motion of the earth.
    • As quoted by Bryant, ibid.
  • I was almost driven to madness in considering and calculating this matter. I could not find out why the planet would rather go on an elliptical orbit. Oh, ridiculous me! As the liberation in the diameter could not also be the way to the ellipse. So this notion brought me up short, that the ellipse exists because of the liberation. With reasoning derived from physical principles, agreeing with experience, there is no figure left for the orbit of the planet but a perfect ellipse.
    • Ch.58, as quoted in John Freely, Before Galileo: The Birth of Modern Science in Medieval Europe (2012)

Dissertatio cum Nuncio Sidereo (1610)Edit

Some will brave even that great void.
  • It is not improbable, I must point out, that there are inhabitants not only on the moon but on Jupiter too, or (as was delightfully remarked at a recent gathering of certain philosophers) that those areas are now being unveiled for the first time. But as soon as somebody demonstrates the art of flying, settlers from our species of man will not be lacking. Who would once have thought that the crossing of the wide ocean was calmer and safer than of the narrow Adriatic Sea, Baltic Sea, or English Channel? Given ships or sails adapted to the breezes of heaven, there will be those who will not shrink from even that vast expanse. Therefore, for the sake of those who, as it were, will presently be on hand to attempt this voyage, let us establish the astronomy, Galileo, you of Jupiter, and me of the moon.
    • Translated by Edward Rosen, Kepler's Conversation with Galileo's Sidereal Messenger (1965), p. 39
    • Unsourced variant translation: Provide ships or sails fit for the winds of heaven, and some will brave even that great void.

Harmonices Mundi (1618)Edit

Translated asThe Harmonies of Worlds or The Harmony of the World
Geometry is one and eternal shining in the mind of God.
  • Geometry is one and eternal shining in the mind of God. That share in it accorded to humans is one of the reasons that humanity is the image of God.
    • Book III, Ch. 1 as quoted in "Astrology in Kepler's Cosmology" by Judith V. Field, in Astrology, Science, and Society: Historical Essays (1987) edited by P. Curry, p. 154
    • Geometry, coeternal with God and shining in the divine Mind, gave God the pattern... by which he laid out the world so that it might be best and most beautiful and finally most like the Creator.
      • As quoted in Kepler's Geometrical Cosmology (1988), p. 123
    • Geometry is one and eternal shining in the mind of God. That share in it accorded to men is one of the reasons that Man is the image of God.
      • Unsourced variant
  • Since geometry is co-eternal with the divine mind before the birth of things, God himself served as his own model in creating the world (for what is there in God which is not God?), and he with his own image reached down to humanity.
    • Book IV, Ch. 1, as quoted in "Kepler's Astrology"in Kepler, Four Hundred Years (1975) edited by Arthur and Peter Beer.
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.
  • 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.
    • Book V, Introduction
    • Variant translation: It may well wait a century for a reader, as God has waited six thousand years for an observer.
      • As quoted in The Martyrs of Science; or, the Lives of Galileo, Tycho Brahe, and Kepler (1841) by David Brewster, p. 197. This has sometimes been misquoted as "It may be well to wait a century for a reader, as God has waited six thousand years for an observer."
    • Variant translation: I feel carried away and possessed by an unutterable rapture over the divine spectacle of heavenly harmony... I write a book for the present time, or for posterity. It is all the same to me. It may wait a hundred years for its readers, as God has also waited six thousand years for an onlooker.
      • As quoted in Calculus. Multivariable (2006) by Steven G. Krantz and Brian E. Blank. p. 126
    • Variant translation: I am stealing the golden vessels of the Egyptians to build a tabernacle to my God from them, far far away from the boundaries of Egypt. If you forgive me, I shall rejoice.; if you are enraged with me, I shall bear it. See, I cast the die, and I write the book. Whether it is to be read by the people of the present or of the future makes no difference: let it await its reader for a hundred years, if God himself has stood ready for six thousand years for one to study him.
      • Unsourced translation
  • If you want the exact moment in time, it was conceived mentally on 8th March in this year one thousand six hundred and eighteen, but submitted to calculation in an unlucky way, and therefore rejected as false, and finally returning on the 15th of May and adopting a new line of attack, stormed the darkness of my mind. So strong was the support from the combination of my labour of seventeen years on the observations of Brahe and the present study, which conspired together, that at first I believed I was dreaming, and assuming my conclusion among my basic premises. But it is absolutely certain and exact that "the proportion between the periodic times of any two planets is precisely the sesquialterate proportion of their mean distances..."
    • Book V, Ch. 3 dates that his Third Law of Planetary Motion occurred to him, translation by E. J. Aiton, A. M. Duncan, and J. V. Field, The Harmony of the World (1997), Vol. 209, p. 411
    • Variant translation: A fresh assault overcame the darkness of my reason...
      • As quoted in Calculus. Multivariable (2006) by Steven G. Krantz and Brian E. Blank. p. 126
  • The Earth sings Mi-Fa-Mi, so we can gather ever from this that Misery and Famine reign in our habitat.
    • Book V, Ch. 6 as quoted in Arthur Koestler, The Sleepwalkers (1959)
  • The heavenly bodies are nothing but a continuous song for several voices (perceived by the intellect, not by the ear); a music which... sets landmarks in the immeasurable flow of time. It is therefore, no longer surprising that man, in imitation of his creator, has at last discovered the art of figured song, which was unknown to the ancients. Man wanted to reproduce the continuity of cosmic time... to obtain a sample test of the delight of the Divine Creator in His works, and to partake of his joy by making music in the imitation of God.
    • Book V, Ch. 7 as quoted in Arthur Koestler, The Sleepwalkers (1959)
  • 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 wisdom of the Lord is infinite as are also His glory and His power. Ye heavens, sing His praises., sun, moon, and planets, glorify Him in your ineffable language! Praise Him, celestial harmonies, and all ye who can comprehend them! And thou, my soul, praise thy Creator! It is by Him and in Him that all exist.
    • Reported in Methodist Review (1873), vol. 55, pp. 187–88.
  • 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?(War of the Worlds by HG Wells)

Joannis Kepleri Astronomi Opera Omnia, ed. Christian Frisch (1858)Edit

Translation from Edwin Arthur Burtt The Metaphysical Foundations of Modern Physical Science (1925) unless otherwise noted
  • Without proper experiments I conclude nothing.
    • Vol. V. p. 224, Vol. I, p. 143
  • Of a number of variant hypotheses about the same facts, that one is true which shows why facts, which in the other hypotheses remain unrelated, are as they are, i.e., which demonstrates their orderly and rational mathematical connexion.
    • Vol. I, p. 238
  • Indeed I reply in a single word to the sentiments of the saints on these questions about nature; in theology, to be sure, the force of authorities is to be weighed, in philosophy, however, that of causes. Therefore, a saint is Lactantius, who denied the rotundity of the earth; a saint is Augustine, who, admitting the rotundity, yet denied the antipodes; worthy of sainthood is the dutiful performance of moderns who, admitting the meagreness of the earth, yet deny its motion. But truth is more saintly for me, who demonstrate by philosophy, without violating my due respect for the doctors of the church, that the earth is both round and inhabited at the antipodes, and of the most despicable size, and finally is moved among the stars.
    • Vol. III, p. 156
  • I certainly know that I owe it [the Copernican theory] this duty, that as I have attested it as true in my deepest soul, and as I contemplate its beauty with incredible and ravishing delight, I should also publicly defend it to my readers with all the force at my command.
    • Vol. VI, p. 116, Vol. VIII, p. 266ff.
  • Wherever there are qualities there are likewise quantities, but not always vice versa.
    • Vol. VIII, p. 47ff.
  • There are, in fact, as I began to say above, not a few principles which are the special property of mathematics, such principles as are discovered by the common light of nature, require no demonstration, and which concern quantities primarily; then they are applied to other things, so far as the latter have something in common with quantities. Now there are more of these principles in mathematics than in the other theoretical sciences because of that very characteristic of the human understanding which seems to be such from the law of creation, that nothing can be known completely except quantities or by quantities. And so it happens that the conclusions of mathematics are most certain and indubitable.
    • Vol. VIII, p. 148
  • [Quantity is the fundamental feature of things,] the 'primarium accidens substantiae,' ...prior to the other categories.
    • Vol. VIII, p. 150
  • God gives every animal the means of saving its life—why object if he gives astrology to the astronomer?
    • Vol. VIII, p. 705

Quotes about KeplerEdit

  • When Gilbert of Colchester, in his “New Philosophy,” founded on his researches in magnetism, was dealing with tides, he did not suggest that the moon attracted the water, but that “subterranean spirits and humors, rising in sympathy with the moon, cause the sea also to rise and flow to the shores and up rivers”. It appears that an idea, presented in some such way as this, was more readily received than a plain statement. This so-called philosophical method was, in fact, very generally applied, and Kepler, who shared Galileo’s admiration for Gilbert’s work, adopted it in his own attempt to extend the idea of magnetic attraction to the planets.
    • Note reference: William Gilbert's New Philosophy about our Sublunary World or De Mundo Nostro Sublunari Philosophia Nova (1651)
    • Walter William Bryant, Kepler The Macmillan Company (1920), p. 35
  • The Neo-Platonic background, which furnished the metaphysical justification for much of this mathematical development (at least as regards its bearing on astronomy) awoke Kepler's full conviction and sympathy. Especially did the aesthetic satisfactions gained by this conception of the universe as a simple, mathematical harmony, appeal vigorously to his artistic nature.
    • Edwin Arthur Burtt, The Metaphysical Foundations of Modern Physical Science (1925)
  • Founder of exact modern science though he was, Kepler combined with his exact methods and indeed found his motivation for them in certain long discredited superstitions, including what it is not unfair to describe as sunworship.
    • Edwin Arthur Burtt, The Metaphysical Foundations of Modern Physical Science (1925)
  • The effective inventor of the telescope and compound microscope was Galileo... Galileo's account of the path of the rays through the concave eye-piece and convex objective which he used was not satisfactory and was considerably improved by Kepler, who suggested the use of two convex lenses which became the basis of later instruments. Kepler had already written an important optical treatise in the form of a commentary on Witelo's Perspectiva... His improvements to the telescope may be regarded as what he had learned from the thirteenth-century writer.
    • A.C. Crombie, Robert Grosssteste and the Origins of Experimental Science (1953)
  • With the discovery of the law of inertia and the subsequent downfall of the Aristotelian theory of motion on which Kepler had based his work, his physical theories soon became outmoded and were then rendered obsolete by Newton's work. Yet Kepler's laws of planetary motion remained, so that Edmond Halley could write in his review of Newton's Principia that the first eleven propositions were found to agree with the phenomena of celestial motions, as discovered by the great sagacity and diligence of Kepler.
    • A.M. Duncan, J.V. Field, The Harmony of the World (1997), Preface, Vol.209
  • Although the concept of heavenly harmony was a theme mentioned in the literature of the time... Kepler's world harmony had little influence on his contemporaries. ...With the rise of the experimental science advocated by Francis Bacon and greatly facilitated by the invention and development of scientific instruments, the general trend of the seventeenth century was towards a mechanical natural philosophy in which metaphysical speculation would play little part. Another factor... may possibly be recognized in the nature of developments that had taken place in mathematics during the sixteenth century, for the advances in algebra and the introduction of symbolism favored a nominalist view of mathematics in contrast to the realist Platonic view of geometry that Kepler adopted as a foundation for his theory of a world harmony.
    • A.M. Duncan, J.V. Field, ibid.
  • When he discovered the polyhedral hypothesis soon after being sent to teach mathematics in Graz, he changed his mind [about becoming a Lutheran minister] , indicating... that he now saw his work in astronomy as an exercise of a priestly vocation. ...he claimed that, in the Harmonice mundi, he offered to the world nothing less than the plan of creation, which God himself had waited six thousand years for someone to comprehend.
    • A.M. Duncan, J.V. Field, ibid.
  • Dumbleton was one of the first to express functional relationships in graphical form. ...Dumbleton also gave a proof of the Merton mean-speed rule... stating that "the latitude of a uniformly difform movement corresponds to the degree of the midpoint." He used the method in the Suma [Suma logicæ et philosophiæ naturalis] to study the problem of the variation in the strength of light as a function of the distance from its source. ...He realized that that the decrease in intensity of illumination was not linearly proportional to the distance... But he did not succeed in finding the exact quantitative relationship, which is that the intensity of illumination due to a luminous source is inversely proportional to the square of the distance, a law discovered by Johannes Kepler in 1604.
    • John Freely, Before Galileo: The Birth of Modern Science in Medieval Europe (2012)
  • 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).
    • Galileo Galilei, Letter to Kepler (1596), as quoted in The Story of Civilization : The Age of Reason Begins, 1558-1648 (1935) by Will Durant, p. 603
  • I thank you because you are the first one, and practically the only one, to have complete faith in my assertions.
    • Galileo Galilei, Letter to Kepler (1610) in gratitude for Kepler's Dissertio cum Nuncio sidereal (Answer to the Sidereal Messenger) after Galileo sent Kepler a copy of the Sidereal Messenger, as quoted in John Freely, Before Galileo: The Birth of Modern Science in Medieval Europe (2012)
  • To say... that the motion of the Earth meeting with the motion of the Lunar Orb, the concurrence of them occasioneth the Ebbing and Flowing [of the seas], is an absolute vanity, not onely be­cause it is not exprest, nor seen how it should so happen, but the falsity is obvious, for that the Revolution of the Earth is not con­trary to the motion of the Moon, but is towards the same way. So that all that hath been hitherto said, and imagined by others, is, in my judgment, altogether invalid. But amongst all the famous men that have philosophated upon this admirable effect of Nature, I more wonder at Kepler than any of the rest, who being of a free and piercing wit, and having the motion ascri­bed to the Earth, before him, hath for all that given his ear and assent to the Moons predominancy over the Water, and to oc­cult properties, and such like trifles.
  • J. Kepler was the first (that I know of) that discover'd the true cause of the Tide, and he explains it largely in his Introduction to the Physics of the Heavens, given in his Commentaries to the Motion of the Planet Mars, where after he has shewn the Gravity or Gravitation of all Bodies towards another, he thus writes: "The Orb of the attracting Power, which is in the Moon is extended as far as the Earth, and draws the Waters under the Torrid Zone, acting upon places where it is vertical, insensibly on included Seas, but sensibly on the Ocean, whose Beds are large, and the Waters have the liberty of reciprocation, that is, of rising and falling"; and in the 70th Page of his Lunar Astronomy,—"But the cause of the Tides of the Sea appear to be the Bodies of the Sun and Moon drawing the Waters of the Sea."
    • David Gregory, The Elements of Astronomy, Physical and Geometrical J. Nicholson (1715) Vol.2, p. 668
  • Afterwards that incomparable Philosopher Sir Isaac Newton, improv'd the hint, and wrote so amply upon this Subject as to make the Theory of the Tides his own, by shewing that the Waters of the Sea rise under the Moon and the Place opposite to it: For Kepler believ'd "that the Impetus occasion'd by the presence of the Moon, by the absence of the Moon, occasions another Impetus; till the Moon returning, stops and moderates the Force of that Impetus, and carries it round with its motion." Therefore this Spheroidical Figure which stands out above the Sphere (like two Mountains, the one under the Moon and the other in the place opposite to it) together with the Moon (which it follows) is carried by the Diurnal Motion, (or rather, according to the truth of the matter, as the Earth turns towards the East it leaves those Eminencies of Water, which being carried by their own motion slowly towards the East, are as it were unmov'd) in its journey makes the Water swell twice and sink twice in the space of 25 Hours, in which time the Moon being gone from the Meridian of any Place, returns to it again.
    • David Gregory, ibid., pp. 668–9
  • One wonders how many modern scientists faced by a similar situation in their work would fail to be impressed by such remarkable numerical coincidences.
    • Fred Hoyle on Kepler's attention to the apparent harmonics by which he deduced his planetary laws, as quoted in "Kepler's Astrology and Mysticism" by Arthur Beer in Vistas in Astronomy vol. 18 (1975).
  • The Pythagorean dream of musical harmony governing the motion of the stars never lost its mysterious impact, its power to call forth responses from the depth of the unconscious mind. ...But, one might ask, was the "Harmony of the Spheres" a poetic conceit or a scientific concept. A working hypothesis or a dream dreamt through a mystic's ear? ...Even Aristotle laughed "harmony, heavenly harmony" out of the courts of earnest, exact science. Yet... Johannes Kepler became enamoured with the Pythagorean dream, and on this foundation of fantasy, by methods of reasoning equally unsound, built the solid edifice of modern astronomy. It is one of the most astonishing episodes in the history of thought, and an antidote to the pious belief that the Progress of Science is governed by logic.
    • Arthur Koestler, The Sleepwalkers: A History of Man's Changing Vision of the Universe (1959, 1963)
  • The Harmony of the World is the continuation of the Cosmic Mystery, and the climax of his lifelong obsession. What Kepler attempted here is, simply, to bare the ultimate secret of the universe in an all-embracing synthesis of geometry, music, astrology, astronomy and epistemology. It was the first attempt of this kind since Plato, and it is the last to our day. After Kepler, fragmentation of experience sets in again, science is divorced from religion, religion from art, substance from form, matter from wind.
  • But to return to Kepler, his great sagacity, and continual meditation on the planetary motions, suggested to him some views of the true principles from which these motions flow. In his preface to the commentaries concerning the planet Mars, he speaks of gravity as of a power that was mutual betwixt bodies, and tells us that the earth and moon tend towards each other, and would meet in a point so many times nearer to the earth than to the moon, as the earth is greater than the moon, if their motions did not hinder it. He adds that the tides arise from the gravity of the waters towards the moon. But not having just enough notions of the laws of motion, he does not seem to have been able to make the best use of these thoughts; nor does he appear to have adhered to them steadily, since in his epitome of astronomy, published eleven years after, he proposes a physical account of the planetary motions, derived from different principles.
  • He [Kepler] supposes, in that treatise [epitome of astronomy], that the motion of the sun on his axis is preserved by some inherent vital principle; that a certain virtue, or immaterial image of the sun, is diffused with his rays into the ambient spaces, and, revolving with the body of the sun on his axis, takes hold of the planets and carries them along with it in the same direction; as a load-stone turned round in the neighborhood of a magnetic needle makes it turn round at the same time. The planet, according to him, by its inertia endeavors to continue in its place, and the action of the sun's image and this inertia are in a perpetual struggle. He adds, that this action of the sun, like to his light, decreases as the distance increases; and therefore moves the same planet with greater celerity when nearer the sun, than at a greater distance. To account for the planet's approaching towards the sun as it descends from the aphelium to the perihelium, and receding from the sun while it ascends to the aphelium again, he supposes that the sun attracts one part of each planet, and repels the opposite part; and that the part which is attracted is turned towards the sun in the descent, and that the other part is towards the sun in the ascent. By suppositions of this kind he endeavored to account for all the other varieties of the celestial motions.
    • Colin Maclaurin, ibid., p. 55
  • As living bodies have hair, so does the earth have grass and trees, the cicadas being its dandruff; as living creatures secrete urine in a bladder, so do the mountains make springs; sulphur and volcanic products correspond to excrement, metals and rainwater to blood and sweat; the sea water is the earth's nourishment … At the same time the anima terrae [soul of the earth] is also a formative power (facultas formatrix) in the earth's interior and expresses, for example, the five regular bodies in precious stones and fossils ..... It is important that in Kepler's view the anima terrae is responsible for the weather and also for meteoric phenomena. Too much rain, for instance, is an illness of the earth.
    • Wolfgang Pauli in "The Influence of Archetypal Ideas on the Scientific Theories of Kepler" in The Interpretation of Nature and the Psyche (1955) by Carl Jung and Wolfgang Pauli, as translated by Priscilla Silz
  • Kepler was a brilliant thinker and a lucid writer, but he was a disaster as a classroom teacher. He mumbled. He digressed. He was at times utterly incomprehensible. He drew only a handful of students his first year at Graz; the next year there were none. He was distracted by an incessant interior clamour of associations and speculations vying for his attention. And one pleasant summer afternoon, deep in the interstices of one of his interminable lectures, he was visited by a revelation that was to alter radically the future of astronomy. Perhaps he stopped in mid-sentence. His inattentive students, longing for the end of the day, took little notice, I suspect, of the historic moment.
  • A law explains a set of observations; a theory explains a set of laws. The quintessential illustration of this jump in level is the way in which Newton’s theory of mechanics explained Kepler’s law of planetary motion. Basically, a law applies to observed phenomena in one domain (e.g., planetary bodies and their movements), while a theory is intended to unify phenomena in many domains. Thus, Newton’s theory of mechanics explained not only Kepler’s laws, but also Galileo’s findings about the motion of balls rolling down an inclined plane, as well as the pattern of oceanic tides. Unlike laws, theories often postulate unobservable objects as part of their explanatory mechanism. So, for instance, Freud’s theory of mind relies upon the unobservable ego, superego, and id, and in modern physics we have theories of elementary particles that postulate various types of quarks, all of which have yet to be observed.
    • John L. Casti in "Correlations, Causes, and Chance," Searching for Certainty: How Scientists Predict the Future (1990).


  • The laws of nature are but the mathematical thoughts of God.
    • Attributed to Kepler in some sources (though more recent sources often attribute it to Euclid), such as Mathematically Speaking: A Dictionary of Quotations edited by Carl C. Gaither and Alma E. Cavazos-Gaither (1998), p. 214. The earliest publication located that attributes the quote to Kepler is the piece "The Mathematics of Elementary Chemistry" by Principal J. McIntosh of Fowler Union High School in California, which appeared in School Science and Mathematics, Volume VII (1907), p. 383. Neither this nor any other source located gives a source in Kepler's writings, however, and in an earlier source, the 1888 Notes and Queries, Vol V., it is attributed on p. 165 to Plato. It could possibly be a paraphrase of either or both of the following to comments in Harmonices Mundi: "Geometry is one and eternal shining in the mind of God" and "Since geometry is co-eternal with the divine mind before the birth of things, God himself served as his own model in creating the world".

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