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Harmonies of the World
Book Five of Johannes Kepler's great masterpiece on planetary motion is presented with an introduction by the ultimate authority on this topic, noted physicist and bestselling author Stephen Hawking. Modifying Copernicus's sun-centered model of the universe, Kepler's 1619 work went on to establish laws of planetary motion, forming the basis for Newton's discoveries some 60 years later. As part of our On the Shoulders of Giants series, this translation of the original edition of Kepler's monumental essay includes an insightful biography and a highly accessible summary putting into context the significance of Harmony of the World .
92 pages, Paperback
First published January 1, 1619
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About the author
Johannes Kepler
252 books162 followersJohannes Kepler (German pronunciation: [ˈkɛplɐ]) was a German mathematician, astronomer and astrologer, and key figure in the 17th century scientific revolution. He is best known for his eponymous laws of planetary motion, codified by later astronomers, based on his works Astronomia nova, Harmonices Mundi, and Epitome of Copernican Astronomy. These works also provided one of the foundations for Isaac Newton's theory of universal gravitation.
During his career, Kepler was a mathematics teacher at a seminary school in Graz, Austria, where he became an associate of Prince Hans Ulrich von Eggenberg. Later he became an assistant to astronomer Tycho Brahe, the imperial mathematician to Emperor Rudolf II and his two successors Matthias and Ferdinand II. He was also a mathematics teacher in Linz, Austria, and an adviser to General Wallenstein. Additionally, he did fundamental work in the field of optics, invented an improved version of the refracting telescope (the Keplerian Telescope), and mentioned the telescopic discoveries of his contemporary Galileo Galilei.
Kepler lived in an era when there was no clear distinction between astronomy and astrology, but there was a strong division between astronomy (a branch of mathematics within the liberal arts) and physics (a branch of natural philosophy).
During his career, Kepler was a mathematics teacher at a seminary school in Graz, Austria, where he became an associate of Prince Hans Ulrich von Eggenberg. Later he became an assistant to astronomer Tycho Brahe, the imperial mathematician to Emperor Rudolf II and his two successors Matthias and Ferdinand II. He was also a mathematics teacher in Linz, Austria, and an adviser to General Wallenstein. Additionally, he did fundamental work in the field of optics, invented an improved version of the refracting telescope (the Keplerian Telescope), and mentioned the telescopic discoveries of his contemporary Galileo Galilei.
Kepler lived in an era when there was no clear distinction between astronomy and astrology, but there was a strong division between astronomy (a branch of mathematics within the liberal arts) and physics (a branch of natural philosophy).
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Displaying 1 - 16 of 16 reviews
March 2, 2021
The universe is an embodiment of symmetrical patterns and rhythmical movements, where the celestial bodies stroke against the sky to conduct a cosmic harmony of musical sounds.
Kepler proposes that the five regular solid figures are in a proportional distance relationship with the six, then known, planets and behave as a structure for our solar system.
Kepler also explores the audio space of our planetary system in which the Sun is the composer and the source of musical harmony amongst the planets. He finds that the ratio between the two extremes motions of an elliptical orbit (perihelion and aphelion) correlate to a different harmonic interval and that a pair of any two planets will always strive for a perfect consonance. Where the "movements of the heavens are nothing except a certain everlasting polyphony" orchestrated by the Creator.
While reading Harmonices Mundi you get the sense that, Kepler, vision of the universe is an idealistic one, and his approach to philosophy is more Platonic or Pythagorean, rather than Aristotelian, even though his laws of planetary motion were derived from observations by the senses, therefore, are based on empirical evidence i.e. which is more Aristotelian. At times it felt like I was reading about an esoteric science that is substantiated by mathematics expressions. Although, the numerous propositions discussed have not been confirmed or are incorrect, except for one, that is mentioned at the end of the book: the time it takes any one of our planet’s to revolve around the Sun, squared, is proportional to the planet’s average distance from the Sun, cubed. This came to be known as Kepler’s third law of planetary motion. The book is too dense in content and not as clear as I would like it to be, therefore, somewhat difficult to follow but that should be expected when indulging into the mystical realm of the cosmos.
Kepler proposes that the five regular solid figures are in a proportional distance relationship with the six, then known, planets and behave as a structure for our solar system.
Kepler also explores the audio space of our planetary system in which the Sun is the composer and the source of musical harmony amongst the planets. He finds that the ratio between the two extremes motions of an elliptical orbit (perihelion and aphelion) correlate to a different harmonic interval and that a pair of any two planets will always strive for a perfect consonance. Where the "movements of the heavens are nothing except a certain everlasting polyphony" orchestrated by the Creator.
While reading Harmonices Mundi you get the sense that, Kepler, vision of the universe is an idealistic one, and his approach to philosophy is more Platonic or Pythagorean, rather than Aristotelian, even though his laws of planetary motion were derived from observations by the senses, therefore, are based on empirical evidence i.e. which is more Aristotelian. At times it felt like I was reading about an esoteric science that is substantiated by mathematics expressions. Although, the numerous propositions discussed have not been confirmed or are incorrect, except for one, that is mentioned at the end of the book: the time it takes any one of our planet’s to revolve around the Sun, squared, is proportional to the planet’s average distance from the Sun, cubed. This came to be known as Kepler’s third law of planetary motion. The book is too dense in content and not as clear as I would like it to be, therefore, somewhat difficult to follow but that should be expected when indulging into the mystical realm of the cosmos.
March 16, 2015
I claim no comprehension of his mathematics, but everything else was very inspiring. Regardless of his mathematical errors- so I'm told- the idea that the distances between the planets could correspond to the intervals between notes on an instrument is so beautiful. Even with Kepler's application with the Platonic solids are really interesting. It is the opinion of many that a religiously-minded and 'rationally'- minded person are at complete opposite ends of each other, but to claim that reveals historical illiteracy and shallowness of thought: Copernicus, Galileo, Brache, Kepler and Newton all believed in God and it in no way stopped them from being the most important figures of the scientific revolutions- not even to mentions that the last two were also involved in Alchemical activities. Without even going into the Islamic Renaissance- which was inseparably significant to ours- God was their main motive for understanding the world, marveling at creation and reading the sacred signs hidden within the labyrinth of mathematical symbols which beckon us to understand our place in the universe and at the miraculous nature of our tools. Kepler was a dreamer like the rest of them and in doing so, left an irreplaceable mark on our understanding of the universe as well as on our wonder at life.
January 15, 2020
This is interesting in theory - uniting three of my major interests (music, geometry and astronomy) - but it felt like he was forcing the numbers to fit the pattern (they don't exactly) and the measurements he was using from are not accurate by today's standards. So, it's just an intellectual curiosity.
December 17, 2020
Kepler pushes a very interesting interpretation of the planetary system that would link it to both music and geometry. The theory is so beautiful, that I am not surprised he is so engrossed by it. At the same time, he makes a significant discovery - Kepler's third law. But considering how well hidden it is in the work that is otherwise a treatise of musical planets, I'm not surprised Galileo failed to take much not of it.
January 4, 2008
Kepler is a bad ass genius and the best thing about reading his writings is that he'll take you through his process of discovery and show you just what he was thinking. Did I finish this book? No. But I worked through alot of it. If you want to read something easier to swallow from Kepler try starting with his short paper on the snowflake.
November 4, 2008
Of course I could not get into all the astronomy explanations, that's why I read the book so fast, by skipping over, but I still think it's amazing how astronomy, mathematics, music, philosophy, religion and mythology harmonize, tie in, and make perfect sense in the same treatise.
October 28, 2020
Kepler, by labor, observations and meditation “…outfought the darkness of [his] mind… uniting [astronomical observations] in one concord, in such a fashion that [he] first believed [he] was dreaming.” This was his account of the discovery of his third law of planetary motion showing the mathematically elegant 3/2 power relationship between planetary periodic times and mean distances. But not only elegant, divine in Kepler’s conception. Kepler found God in his work. He bridged the God of the dark ages and the god of science: mathematics. He revived the intuition of Pythagoras, the hopefulness and geometric mysticism of Plato, and the comprehensiveness of Ptolemy through Euclid.
And again, as in the Mysterium, he cites his discovery, as if it is a light or revelation, out of darkness and dreams. There certainly seemed much about intuition involved, which led to apparitions of science that never really existed, but also to the most accurate truth. The astrology in this book seems a necessity. The coincidences in astrology may have seemed similar to mathematical or geometric coincidences in physics. In Kepler’s day, both were kind of muddy and inexact. Kepler, however, mathematizes coincidence and discovers in what places God is a mathematician. In a world juxtaposed by witch trials, which were basically suspicion followed by coincidence, Kepler redirects to a better way to understand the world. He tirelessly seeks all harmony. “Holy father, keep us safe in concord of our love for one another, that we may be one… just as through the sweetest bonds of harmony Thou hast made all thy works one.”
And again, as in the Mysterium, he cites his discovery, as if it is a light or revelation, out of darkness and dreams. There certainly seemed much about intuition involved, which led to apparitions of science that never really existed, but also to the most accurate truth. The astrology in this book seems a necessity. The coincidences in astrology may have seemed similar to mathematical or geometric coincidences in physics. In Kepler’s day, both were kind of muddy and inexact. Kepler, however, mathematizes coincidence and discovers in what places God is a mathematician. In a world juxtaposed by witch trials, which were basically suspicion followed by coincidence, Kepler redirects to a better way to understand the world. He tirelessly seeks all harmony. “Holy father, keep us safe in concord of our love for one another, that we may be one… just as through the sweetest bonds of harmony Thou hast made all thy works one.”
March 28, 2019
Have to say, I'm a little disappointed! After getting through the neo-platonist rehashings of the first books, I was very excited to see at last the geometrical proofs of celestial harmony! When Kepler finally comes to treat on this topic though, it turns out that discord tends to be the rule. In fact, among the scores of magnitudes which Kepler considers only a handful are in fact harmonic. Actually, exactly one relation is perfectly harmonic, and that is the relation between the diverging movements of Saturn and Jupiter, which forms an octave. Still, despite this disappointment, this is fascinating insight into one of astronomy's most important historical minds. And though the neo-platonic philosophy should probably be jettisoned (or at least revised), modern scientists and scholars can take Kepler's obsessive consideration of the experimental data as a worthy example.
October 9, 2018
One of the best ever. Must read
July 11, 2024
It's thought-provoking and captivating. Besides everything Keppler represents, this romance makes you fall for the resilient man Johannes.
September 18, 2025
A book of historical value.
June 10, 2022
I really, I mean REALLY wanted to love this book. The promising convergence of sacred geometry, musical harmony of the spheres and intelligently directed cosmic balance was enough to make me dive in. Quickly the realization struck that I was in way over my head. Only two things were apparent, Kepler is a genius and I am far from. If I was half the nerd I imagined myself to be, I would have scribbles covering the walls, trying to connect the dots of everything he was trying to expound upon. Instead I became a shaking, huddled mess praying for the diatribe to quickly resolve. With that behind me, I now pray for someone to write a book explaining it all in terms that a neophyte like myself can digest. YouTube, my normal go-to for simple explanations of complicated subject matter, proved of no use. All that for what was proven incorrect theory centuries ago.
March 7, 2017
wonderfull!
January 13, 2015
[A] very excellent order of sounds or pitches in a musical system or scale has been set up by men, since you see that they are doing nothing else in this business except to play the apes of God the Creator and to act out, as it were, a certain drama of the ordination of the celestial movements.
Really a four star book, but I had to subtract a star for an inexcusable lack of explanatory notes. The few that were provided were helpful, but, really, with the spate of obscure terms and confusing concepts in this book, couldn't the editors do better? I have a Bachelor's degree in music, and I still had to look up the obscure terms diesis, lemma, and comma; all of which have to do with just tuning, the system used in Kepler's time but which has now been discarded in favor of even tempered tuning. I could follow the spate of ratios pretty well, but I can't imagine that even a reader reasonably well versed in music could get very far without becoming hopelessly lost. Since this volume contains only book five of Harmonies of the World, Kepler keeps referring back to the previous four volumes of this work. Would it have been too much for the editors to explain these references more fully, to clue in those of us who missed the first four books? I found myself having to take Kepler's word for it that the ratios provided matched his real world observations, but even here I kept getting confused as to whether he was talking about ratios in distance or velocity or both.
Nevertheless, it was neat to see Kepler demonstrate his main contention, which I extracted from p 34 at the beginning of this review. (Even though his argument seems forced to modern ears.) I'm sure that Kepler would be quite disappointed to find that not only have we discarded the "excellent order of sounds or pitches" in use in his time in favor of even temperament, but we have since discovered Uranus and Neptune, which really screws up his system.
Really a four star book, but I had to subtract a star for an inexcusable lack of explanatory notes. The few that were provided were helpful, but, really, with the spate of obscure terms and confusing concepts in this book, couldn't the editors do better? I have a Bachelor's degree in music, and I still had to look up the obscure terms diesis, lemma, and comma; all of which have to do with just tuning, the system used in Kepler's time but which has now been discarded in favor of even tempered tuning. I could follow the spate of ratios pretty well, but I can't imagine that even a reader reasonably well versed in music could get very far without becoming hopelessly lost. Since this volume contains only book five of Harmonies of the World, Kepler keeps referring back to the previous four volumes of this work. Would it have been too much for the editors to explain these references more fully, to clue in those of us who missed the first four books? I found myself having to take Kepler's word for it that the ratios provided matched his real world observations, but even here I kept getting confused as to whether he was talking about ratios in distance or velocity or both.
Nevertheless, it was neat to see Kepler demonstrate his main contention, which I extracted from p 34 at the beginning of this review. (Even though his argument seems forced to modern ears.) I'm sure that Kepler would be quite disappointed to find that not only have we discarded the "excellent order of sounds or pitches" in use in his time in favor of even temperament, but we have since discovered Uranus and Neptune, which really screws up his system.
February 5, 2017
I started reading this for how intelligent it made me feel...I'm continuing onward for the beautiful impenetrable prose...let's hope I make it through. Seems unlikely. Even if I make it through, all the lovely math, the proofs and theorems will be lost on me. I don't "do" math, much as I wish I did or could.
But even though the specifics of this book are truly lost on me, I am just so dazzled by the mind that moves so abley from solids to ratios to musical intervals, and from concepts of sexuality and marriage to harmonics to movements between rational and irrational. He stretches my mind by pushing against the hard lines I have in place between concepts. The modern mind does not consider divine planning when we consider the notes in the scale or the relationship between angles in a solid. We see the angles; we hear the intervals; we find somethings aesthetically pleasing or off-putting; but we don't ascribe the experience to the grand hand of God. But in 1627, I suppose they did. At least Kepler did. It's fantastic getting to see the world, if only for a moment and quite intuitively, through the mind of one of it's great thinkers.
But even though the specifics of this book are truly lost on me, I am just so dazzled by the mind that moves so abley from solids to ratios to musical intervals, and from concepts of sexuality and marriage to harmonics to movements between rational and irrational. He stretches my mind by pushing against the hard lines I have in place between concepts. The modern mind does not consider divine planning when we consider the notes in the scale or the relationship between angles in a solid. We see the angles; we hear the intervals; we find somethings aesthetically pleasing or off-putting; but we don't ascribe the experience to the grand hand of God. But in 1627, I suppose they did. At least Kepler did. It's fantastic getting to see the world, if only for a moment and quite intuitively, through the mind of one of it's great thinkers.
September 18, 2016
We are in 1618, Kepler is searching for patterns among ratios observed within our solar system. Look at the sky, we can see just six planets with today's technology. The warm-up includes the five platonic solids but the show starts when he jumps at Copernicus shoulder. The sun is the reference for planetary movements, which are the source of several ratios compiled for comparison. He even came up with an igneous way of plotting planets in the musical scale. The whole thing is knitted with a bit of superstition because it is early 17th century.
Displaying 1 - 16 of 16 reviews