Johannes Kepler’s Harmony of the World

Readers of this blog may recall a post from some time ago about the William Marshall Bullitt Collection in the Archives and Special Collections (ASC) of the Ekstrom Library of the University of Louisville here in Kentucky.  I had the enjoyable task of studying the books in the collection and writing discussions of them for the ASC—discussions specifically intended for a diverse audience that might include scholars, students at varying levels, and interested members of the general public.  One of the books in the collection that will interest readers of this blog (and that they can go to see and study at the University of Louisville) is Johannes Kepler’s 1619 Harmonices Mundi or Harmony* of the World.  This post is an adaptation (with permission) of the discussion I wrote for the ASC.

Readers who peruse Harmony will discover it to be partly a work of science, partly a prayer, and partly an exhibition of unconstrained creativity.  To Kepler, the universe is the work of God, the ultimate in creativity, and Kepler has discovered something of God’s design.  Kepler cannot contain himself.  He does not care to.  Acknowledging a debt to the Harmonics of the second-century Egyptian astronomer Ptolemy, he writes,

Nothing holds me back.  I am free to give myself up to the sacred madness, I am free to taunt mortals with the frank confession that I am stealing the golden vessels of the Egyptians, in order to build of them a temple for my God, far from the territory of Egypt.  If you pardon me, I shall rejoice; if you are enraged, I shall bear up.  The die is cast, and I am writing the book—whether to be read by my contemporaries or by posterity matters not.  Let it await its reader for a hundred years, if God himself has been ready for His contemplator for six thousand years.

Kepler begins by noting that in an earlier work, his Cosmographic Mystery, he had shown that the solar system was constructed around, as he saw it, the five Platonic solids.  The geocentric system of Ptolemy had operated via a complicated epicyclical celestial machinery that occupied so much space that it filled the universe and demanded a certain spacing between the planets.  But the Copernican system did not require such machinery.  Thus there was no obvious reason for why the six known planets—Mercury, Venus, Earth, Mars, Jupiter and Saturn—were spaced the way they were (so that, for example, there was far less distance between the orbits of Mercury and Venus than between the orbits of Jupiter and Saturn).  Kepler thought he had found that reason: God, who Kepler says “has established nothing without geometrical beauty,” spaced the planets according to a certain nesting of the Platonic solids.

Kepler’s use of the ‘Platonic Solids’ (tetrahedron, cube, octahedron, dodecahedron, or icosahedron) to explain the spacing of the orbits of the planets in the heliocentric system.

Kepler’s use of the ‘Platonic Solids’ (tetrahedron, cube, octahedron, dodecahedron, and icosahedron) to explain the spacing of the orbits of the planets in the heliocentric system.

Video from the University of Notre Dame: Kepler's Mysterium Cosmographicum Realized in Fulldome

Video from the University of Notre Dame: ‘Kepler's Mysterium Cosmographicum Realized in Fulldome’—click here to watch the video.

You can even build your own model of Kepler's Cosmographic Mystery!

You can even build your own model of Kepler's Cosmographic Mystery!


In Harmony of the World, Kepler goes further in illustrating the mathematical elegance God built into the universe, and shows that the movements of the planets are actually musical.  Says Kepler,

the movements of the heavens are nothing except a certain everlasting polyphony (intelligible, not audible) with dissonant tunings... which marks out and distinguishes the immensity of time with those notes.

Notes and planets from Kepler's Harmony of the World. Click here for an English translation.

Notes and planets from Kepler's Harmony of the World. For an English translation, click here.

Thus readers will find within Harmony chapter titles such as “In What Things Having to do with the Planetary Movements Have the Harmonic Consonances been Expressed by the Creator, and in What Way?” and “In the Celestial Harmonies Which Planet Sings Soprano, Which Alto, Which Tenor, and Which Bass?”  Readers will also find Kepler closing chapters with sentences such as this:

Holy Father, keep us safe in the concord of our love for one another, that we may be one, just as Thou art one with Thy Son, Our Lord, and with the Holy Ghost, and just as through the sweetest bonds of harmonies Thou hast made all Thy works one; and that from the bringing of Thy people into concord the body of Thy Church may be rebuilt up in the Earth, as Thou didst erect the heavens themselves out of harmonies.

It is difficult to overstate the religious content of Harmony.  Yet this is a book that contains important scientific content as well.  Generally, Kepler is proclaiming in Harmony the mathematical nature of the universe.  Specifically, he states what are today referred to as his Three Laws of Planetary Motion, mathematical descriptions of the orbital motion of a planet that are a staple of introductory astronomy classes everywhere.  These are (1) that every planet moves about the sun in an elliptical orbit where the sun lies at a focus of that ellipse; (2) that the line between the sun and the planet sweeps out equal areas in equal times, so that the planet moves faster when closer to the sun, and slower when farther away; and (3) that the square of the period of planetary orbits is directly proportional to the cube of the planet’s average distance from the sun.  The first two he had published before, but the third he first published in Harmony.  The physicist Stephen Hawking attributes this third law with inspiring Isaac Newton to work out the physics of planetary motion in a heliocentric system.  Hawking writes, “Kepler discovered how planets orbited, and in so doing paved the way for Newton to discover why.”

But Kepler wrote before Newton, and one interesting aspect of Harmony is that while within it Kepler favors a heliocentric system, he makes allowances for a geocentric one.  He notes that “these harmonical speculations are possible even with the hypotheses of Tycho Brahe.”  Brahe was the leading astronomer of the time, whose work Kepler built upon, and Brahe had proposed a system in which the sun, moon, and stars circled the earth while the planets circled the sun—a system mathematically equivalent to that of Copernicus in many ways, and wholly compatible with astronomical observations of the time.  This is all because, as Kepler says, “in Brahe the Earth occupies at any time the same place that Copernicus gives it... at least in the system of the planetary world.”

The Tychonic geocentric (left) and Copernican heliocentric

The Tychonic geocentric (left) and Copernican heliocentric (right) theories.

Another interesting aspect of Harmony is that Kepler speculates at length about life on other planets, rooting his speculations, of course, in his belief in God.  Kepler asked,

shall we make a conjecture as to God's works and designs even for the other globes, from that variety which we discern in this globe of the Earth. For He Who created the species which should inhabit the waters, beneath which however there is no room for the air which living things draw in; Who sent birds supported on wings into the wilderness of the air; Who gave white bears and white wolves to the snowy regions of the North, and as food for the bears the whale, and for the wolves, birds' eggs; Who gave lions to the deserts of burning Libya and camels to the wide-spread plains of Syria, and to the lions an endurance of hunger, and to the camels an endurance of thirst: did He use up every art in the globe of the Earth so that He was unable, every goodness so that he did not wish, to adorn the other globes too with their fitting creatures, as either the long or short revolutions, or the nearness or removal of the sun, or the variety of eccentricities or the shine or darkness of the bodies, or the properties of the figures wherewith any region is supported persuaded?

Thus Harmony of the World is a marvelously multifaceted book.  Kepler ends this work of science, prayer, and creativity with, of course, a prayer: “To Him be praise, honour, and glory, world without end.  Amen.”

The closing lines of Kepler's Harmony of the World: a prayer.

The closing lines of Kepler's Harmony of the World: a prayer.


*Originally I had used the translation “Harmonies” in this post, but a knowledgeable reader, Owen Gingerich, pointed out to me that even though a standard translation of Kepler’s work has it “Harmonies,” the proper translation is “Harmony”. “Harmonices is not a Latin plural but a Greek singular,” notes Gingerich, “one of those little touches of erudition that Kepler adopts to amuse his classically trained colleagues.”


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