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The Secret of the Universe
Dual language edition (original Latin as originally printed verso facing authoritative English translation of same page recto).
Translated by A.M. Duncan.
Introduction and commentary by E.J. Aiton.
Preface by I. Bernard Cohen
Part of the Janus Series
Translated by A.M. Duncan.
Introduction and commentary by E.J. Aiton.
Preface by I. Bernard Cohen
Part of the Janus Series
267 pages, Paperback
Published January 1, 1979
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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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June 29, 2022
At the threshold between the medieval and early modern eras, when an entirely novel conception of the nature of scientific inquiry surfaces, stands Johannes Kepler’s bellwether text, Mysterium Cosmographicum, or the secret of the universe, translated into English by A.M. Duncan and published with introduction and commentary by E.J. Aiton in 1981. An extraordinary document affording invaluable insight into the great astronomer’s thought process! There is not much to say about the front matter and critical apparatus, sufficient to the purpose if not all that inspired. The main thing is that one gets a facsimile of the original Latin text and drawings, along with a facing English translation. Kepler originally wrote in 1596 but published a second edition in 1621, which rather than rewrite completely to reflect his later discoveries he outfits with lengthy corrections and retractions of his own at the end of each chapter, in uncommonly small print. All through his life he kept up a half-belief in this product of his youthful fantasy, however inconsistent it may have been to shoe-horn his later verified scientific work into its framework, for it was elation over this genial idea that motivated him to undertake his tireless labors in the first place.
But there is much more to seek in this work than an obsolete model of the solar system. First of all, under the influence of his teacher Michael Maestlin at the university of Tübingen, Kepler was from the start a convinced Copernican. In his own words:
For the [Ptolemaic] model does not fit. The conclusion from false premises is accidental, and the nature of the fallacy betrays itself as soon as it is applied to another related topic – unless you gratuitously allow the exponent of that argument to adopt an infinite number of other false propositions, and never in arguing forwards and backwards to reach consistency. That is not the case with someone who places the Sun at the center. For if you tell him to derive from the hypothesis, once it has been stated, any of the phenomena which are actually observed in the heavens, to argue backwards, to argue forwards, to infer from one motion to another, and to perform anything whatever that the true state of affairs permits, he will have no difficulty with any point, if it is authentic, and even from the most intricate twistings of the argument he will return with complete consistency to the same assumptions….The old hypotheses simply do not account at all for a number of outstanding features. For instance, they do not give the reasons for the number, extent and time of the retrogressions, and why they agree precisely, as they do, with the positions and mean motion of the Sun. On all these points, as a magnificent order is shown by Copernicus, the cause must necessarily be found in it. [pp. 75-77]
For Kepler astronomy is definitely not just a mathematical means of saving the phenomena! Neither is he a Bayesian! Copernicus’ reasoning persuades him by virtue of its logical coherence – the unified field theory of its day, whereas Ptolemy posits a completely unrelated epicyclic model for each planet, somewhat like the standard model of elementary particle physics before Glashow-Weinberg-Salam’s electroweak unification. Kepler notes that Copernicus is logically simpler even if the total number of circles comes to about the same [p. 80]. Observe how Kepler enters into many recondite details [p. 81] because he has actually followed Copernicus’ constructions which nobody today bothers to!
The succeeding theologically inflected chapters are revelatory of what to modern eyes appear to be Kepler’s own strange thought processes. He unveils his trinitarian analogy of the solar system (where the sun represents God the Father, interplanetary space God the Son and the circumference of fixed stars God the Holy Spirit) and tells us that quantity is the firstborn of the creation – spherical surfaces being the most divine hence a perfect quantity, while a straight line is earthly [p. 93]. The universe would be disordered if infinite [p. 97]. The Platonic regular solids (viz., tetrahedron, cube, octahedron, dodecahedron and icosahedron) approach the sphere in perfection [p. 101]. At this stage, the age-old premise that circular resp. spherical forms are preferred by nature due to their perfection is still paramount (Kepler’s contemporary Galileo thinks along similar lines as well).
Kepler then describes how he fits the known proportions of spheres to his inscribed solids. What is characteristic of him, however, is that he does not rest content with a reasonably good model but goes on to read features into his arrangement we’d regard as accidental, almost like interpretation of a horoscope! Cranks and string theorists do the same thing: what makes the difference in Kepler? As we shall see below, he never wavers in his confidence that his model describes the real world and therefore should eventually connect with it, for all the extravagances he is willing to entertain along the way. From the perspective of the modern data scientist, Kepler could certainly use something like Akaike’s information criterion! It is obviously problematic to contrive another hypothesis to explain each datum. But Kepler may be excused for he is engaged in inventing the very scientific method. So we should not be surprised if, in the process, he has to sort his way through a plethora of trial balloons which to us don’t look very scientific. He will even apply aesthetic criteria to rank proposed relationships [p. 113]. What is more, he derives astrological properties of the planets [pp. 115-119]! What a method if it can do this! Note: he defends this acknowledged ‘game’ as being allegorical of real physical properties [p. 199].
Nevertheless, in all this profusion of ideas, Kepler’s core scientific bent shines through – unlike what is the case with another of his contemporaries, John Dee, who is likewise prone to speculate along the lines indicated by a mix of astrology and mystical theology but who, in contrast, fails to regulate his flights of fancy by sober examination of the observations. Naturally enough, once Kepler himself has arrived at his wonderful model of the solar system and shown its near agreement with Copernicus’ astronomical data, he wants to see how much he can figure out about the world by means of it. Regarding the origin of the zodiac: Kepler reviews arguments to show how the mutual orientations of the inscribed regular solids are not arbitrary [p. 123]. He is willing to entertain a twelvefold division of the zodiac hypothetically and seek to evaluate it according to numerological and musical criteria [p. 131].
Even though a modern person might be uncomfortable with some of Kepler’s criteria, he must approve the explanatory intent that guides the whole endeavor – one can always refine the criteria later, tighten them up to make them more rational. On a philosophical note, in a footnote he defends the mathematicals against Aristotle [p. 125]. Yet there are a few checks on enthusiasm. Kepler recognizes a distinction between accidental and archetypal conjunctions [p. 139], proffers an informal treatment of error bars [p. 177ff] and tries to reconcile the discrepancy between his solids and the motions [pp. 209-213]. Here, he is looking for ad hoc reasons, not to found a new paradigm on a sweeping theory – what most scientists do during a normal phase, seeking to resolve outstanding anomalies in the current paradigm by tinkering with it. In anticipation of Newton and his law of universal gravitation, Kepler posits the sun as the source of motive power propelling the planets along their paths [p. 199], which would agree after all with his theologically inspired philosophy:
Lastly the natural light of reason declares that it is a more worthy and archetypal emanation of the works of God, if all the motions flow from one source, than if most indeed flow from that one source but those of the source itself from another, more ignoble source [pp. 207-209, critical of Tycho Brahe].
Kepler resembles nothing so much as a man in a mental institution waking up from a schizophrenic delirium, still captivated by it but gradually freeing himself from delusion by regrounding himself in experienced reality. Thus, a struggle plays out in his mind between apparent and real harmonies, for Kepler takes the doctrine of proportions very literally. Compare with the Pythagorean construction of the musical scale; from an initial breakthrough discovery that the consonant intervals correspond to small-integer ratios of pitch, one can proceed to build up a scale on a piecemeal basis, exploiting accidental numerical coincidences (the reader may experiment by trying to divide the octave into twelve logarithmically equally spaced intervals and looking for a close fit to the consonant intervals; for instance, the fifth, or a ratio of 3/2 just happens to lie very near to 2^(7/12)). Kepler plainly wants to hit upon something similar with respect to the orbits of the planets. In so doing, he shows himself yet to be schooled by experience. We who enjoy a panoramic view of centuries of success of modern empirical science, on the other hand, feel entitled to demand more than Kepler – we do not satisfy ourselves with contingent, surface-level patterns that are for the most part spurious but appreciate how the regularities follow from Newton’s laws. A good illustration would be the Titius-Bode law, which predicts the spacing between the orbits of the planets and was originally proposed in 1772 on purely numerological grounds. Yet nowadays we understand that the architecture of the solar system is determined by its early history, when the major planets migrated until running up against mean motion resonances, the upshot of which is that one might expect something like a Titius-Bode law to hold in many solar systems. Hence, what started out as a coincidence might be a generic feature.
The point is that one never knows, a priori, which specious regularities are merely contingent and which reflect the operation of physical law. This consideration prompts the question, what criterion ought to determine the extent to which one may entertain a model hypothetically in order to investigate its consequences which if upheld by experience would tend to confirm it? Clearly one goes wrong if he loses sight of the fact that the deductions remain hypothetical in character only until they can be fitted into a connected theory of the phenomenon, grounded in physical principles and having empirical support. The young Kepler is groping towards a seasoned judgment of this kind, which is why the Mysterium Cosmographicum elicits our fascination. Somehow, Kepler negotiated his way through all his missteps to become the founder of modern astronomy.
To close, let us compare Kepler with today’s string theorists. Edward Witten is wont, in his lectures (such as at a colloquium this reviewer attended at MIT) to put the invention of the general theory of relativity, electroweak unification and supersymmetry on the same footing and even speculates that on other planets with intelligent life there might be a differing order of discovery among the three. Witten is evidently as beguiled by string theory as the young Kepler is by his nested Platonic solid model of the solar system, but Kepler himself manages to get past this preoccupation and to frame his three laws of planetary motion because he holds fast to a stringent empirical orientation that seems to be missing in Witten and other string theorists. That historians of science could be led to such extraordinary conceits as Richard Dawid’s post-empirical confirmation is a serious warning flag. As Kepler himself found out, internal evidence such as the supposed beauty of a theory may motivate, for a time, continued work on it but taken by itself is certainly quite unreliable as a criterion of its truth in nature; otherwise we should have to humor every crank!
But there is much more to seek in this work than an obsolete model of the solar system. First of all, under the influence of his teacher Michael Maestlin at the university of Tübingen, Kepler was from the start a convinced Copernican. In his own words:
For the [Ptolemaic] model does not fit. The conclusion from false premises is accidental, and the nature of the fallacy betrays itself as soon as it is applied to another related topic – unless you gratuitously allow the exponent of that argument to adopt an infinite number of other false propositions, and never in arguing forwards and backwards to reach consistency. That is not the case with someone who places the Sun at the center. For if you tell him to derive from the hypothesis, once it has been stated, any of the phenomena which are actually observed in the heavens, to argue backwards, to argue forwards, to infer from one motion to another, and to perform anything whatever that the true state of affairs permits, he will have no difficulty with any point, if it is authentic, and even from the most intricate twistings of the argument he will return with complete consistency to the same assumptions….The old hypotheses simply do not account at all for a number of outstanding features. For instance, they do not give the reasons for the number, extent and time of the retrogressions, and why they agree precisely, as they do, with the positions and mean motion of the Sun. On all these points, as a magnificent order is shown by Copernicus, the cause must necessarily be found in it. [pp. 75-77]
For Kepler astronomy is definitely not just a mathematical means of saving the phenomena! Neither is he a Bayesian! Copernicus’ reasoning persuades him by virtue of its logical coherence – the unified field theory of its day, whereas Ptolemy posits a completely unrelated epicyclic model for each planet, somewhat like the standard model of elementary particle physics before Glashow-Weinberg-Salam’s electroweak unification. Kepler notes that Copernicus is logically simpler even if the total number of circles comes to about the same [p. 80]. Observe how Kepler enters into many recondite details [p. 81] because he has actually followed Copernicus’ constructions which nobody today bothers to!
The succeeding theologically inflected chapters are revelatory of what to modern eyes appear to be Kepler’s own strange thought processes. He unveils his trinitarian analogy of the solar system (where the sun represents God the Father, interplanetary space God the Son and the circumference of fixed stars God the Holy Spirit) and tells us that quantity is the firstborn of the creation – spherical surfaces being the most divine hence a perfect quantity, while a straight line is earthly [p. 93]. The universe would be disordered if infinite [p. 97]. The Platonic regular solids (viz., tetrahedron, cube, octahedron, dodecahedron and icosahedron) approach the sphere in perfection [p. 101]. At this stage, the age-old premise that circular resp. spherical forms are preferred by nature due to their perfection is still paramount (Kepler’s contemporary Galileo thinks along similar lines as well).
Kepler then describes how he fits the known proportions of spheres to his inscribed solids. What is characteristic of him, however, is that he does not rest content with a reasonably good model but goes on to read features into his arrangement we’d regard as accidental, almost like interpretation of a horoscope! Cranks and string theorists do the same thing: what makes the difference in Kepler? As we shall see below, he never wavers in his confidence that his model describes the real world and therefore should eventually connect with it, for all the extravagances he is willing to entertain along the way. From the perspective of the modern data scientist, Kepler could certainly use something like Akaike’s information criterion! It is obviously problematic to contrive another hypothesis to explain each datum. But Kepler may be excused for he is engaged in inventing the very scientific method. So we should not be surprised if, in the process, he has to sort his way through a plethora of trial balloons which to us don’t look very scientific. He will even apply aesthetic criteria to rank proposed relationships [p. 113]. What is more, he derives astrological properties of the planets [pp. 115-119]! What a method if it can do this! Note: he defends this acknowledged ‘game’ as being allegorical of real physical properties [p. 199].
Nevertheless, in all this profusion of ideas, Kepler’s core scientific bent shines through – unlike what is the case with another of his contemporaries, John Dee, who is likewise prone to speculate along the lines indicated by a mix of astrology and mystical theology but who, in contrast, fails to regulate his flights of fancy by sober examination of the observations. Naturally enough, once Kepler himself has arrived at his wonderful model of the solar system and shown its near agreement with Copernicus’ astronomical data, he wants to see how much he can figure out about the world by means of it. Regarding the origin of the zodiac: Kepler reviews arguments to show how the mutual orientations of the inscribed regular solids are not arbitrary [p. 123]. He is willing to entertain a twelvefold division of the zodiac hypothetically and seek to evaluate it according to numerological and musical criteria [p. 131].
Even though a modern person might be uncomfortable with some of Kepler’s criteria, he must approve the explanatory intent that guides the whole endeavor – one can always refine the criteria later, tighten them up to make them more rational. On a philosophical note, in a footnote he defends the mathematicals against Aristotle [p. 125]. Yet there are a few checks on enthusiasm. Kepler recognizes a distinction between accidental and archetypal conjunctions [p. 139], proffers an informal treatment of error bars [p. 177ff] and tries to reconcile the discrepancy between his solids and the motions [pp. 209-213]. Here, he is looking for ad hoc reasons, not to found a new paradigm on a sweeping theory – what most scientists do during a normal phase, seeking to resolve outstanding anomalies in the current paradigm by tinkering with it. In anticipation of Newton and his law of universal gravitation, Kepler posits the sun as the source of motive power propelling the planets along their paths [p. 199], which would agree after all with his theologically inspired philosophy:
Lastly the natural light of reason declares that it is a more worthy and archetypal emanation of the works of God, if all the motions flow from one source, than if most indeed flow from that one source but those of the source itself from another, more ignoble source [pp. 207-209, critical of Tycho Brahe].
Kepler resembles nothing so much as a man in a mental institution waking up from a schizophrenic delirium, still captivated by it but gradually freeing himself from delusion by regrounding himself in experienced reality. Thus, a struggle plays out in his mind between apparent and real harmonies, for Kepler takes the doctrine of proportions very literally. Compare with the Pythagorean construction of the musical scale; from an initial breakthrough discovery that the consonant intervals correspond to small-integer ratios of pitch, one can proceed to build up a scale on a piecemeal basis, exploiting accidental numerical coincidences (the reader may experiment by trying to divide the octave into twelve logarithmically equally spaced intervals and looking for a close fit to the consonant intervals; for instance, the fifth, or a ratio of 3/2 just happens to lie very near to 2^(7/12)). Kepler plainly wants to hit upon something similar with respect to the orbits of the planets. In so doing, he shows himself yet to be schooled by experience. We who enjoy a panoramic view of centuries of success of modern empirical science, on the other hand, feel entitled to demand more than Kepler – we do not satisfy ourselves with contingent, surface-level patterns that are for the most part spurious but appreciate how the regularities follow from Newton’s laws. A good illustration would be the Titius-Bode law, which predicts the spacing between the orbits of the planets and was originally proposed in 1772 on purely numerological grounds. Yet nowadays we understand that the architecture of the solar system is determined by its early history, when the major planets migrated until running up against mean motion resonances, the upshot of which is that one might expect something like a Titius-Bode law to hold in many solar systems. Hence, what started out as a coincidence might be a generic feature.
The point is that one never knows, a priori, which specious regularities are merely contingent and which reflect the operation of physical law. This consideration prompts the question, what criterion ought to determine the extent to which one may entertain a model hypothetically in order to investigate its consequences which if upheld by experience would tend to confirm it? Clearly one goes wrong if he loses sight of the fact that the deductions remain hypothetical in character only until they can be fitted into a connected theory of the phenomenon, grounded in physical principles and having empirical support. The young Kepler is groping towards a seasoned judgment of this kind, which is why the Mysterium Cosmographicum elicits our fascination. Somehow, Kepler negotiated his way through all his missteps to become the founder of modern astronomy.
To close, let us compare Kepler with today’s string theorists. Edward Witten is wont, in his lectures (such as at a colloquium this reviewer attended at MIT) to put the invention of the general theory of relativity, electroweak unification and supersymmetry on the same footing and even speculates that on other planets with intelligent life there might be a differing order of discovery among the three. Witten is evidently as beguiled by string theory as the young Kepler is by his nested Platonic solid model of the solar system, but Kepler himself manages to get past this preoccupation and to frame his three laws of planetary motion because he holds fast to a stringent empirical orientation that seems to be missing in Witten and other string theorists. That historians of science could be led to such extraordinary conceits as Richard Dawid’s post-empirical confirmation is a serious warning flag. As Kepler himself found out, internal evidence such as the supposed beauty of a theory may motivate, for a time, continued work on it but taken by itself is certainly quite unreliable as a criterion of its truth in nature; otherwise we should have to humor every crank!
October 16, 2020
The first publication of a 16th century Christian pastor-in-training turned mathematician mystic philosopher astrologer astronomer who believed he had been granted divine knowledge of the Secret of the Universe—and he was! This work shows his foundational paradigms and modus operandi that would continue to bring such knowledge to fruition throughout his life. Considering Kepler’s own notes in his second edition 24 years after the original, and the modern commentary in this book, Kepler was the absent-minded professor type. His focus was the driver of details rather than the details themselves, which he often got wrong. He sought elegant mathematics revealing the beauty and unity of nature.
Kepler states “Copernicus’s purpose was not to deal with cosmography, but with astronomy.” Kepler envisioned a “graphic of the cosmos” which had previously been a mystery (hence “Mysterium Cosmographicum”). By his own account, he had a revelation of a “polyhedral hypothesis” to explain the cosmography of the universe, specifically proposing that each of the 5 Platonic solids fit precisely between the orbits of the planets as conceived as inscribed and circumscribed spheres of the polyhedra. But it isn’t the correctness of this ill-fated hypothesis that makes this book interesting. In fact, if this were all he was known for it seems he may be a mere footnote. What makes him and this book interesting is the way he approaches the search for truth. He seems to imagine a vague, but complete puzzle and looks for the pieces that go together to show it. He recalls his meandering, and “feeling along walls through the darkness of ignorance.”
The centrality he puts on God provides clarity for him. He believes “Nothing has been established by God at random.” This order in the book of Nature seems to above even the mere words of God. “…Everyone with strong religious scruples will take the greatest care not to twist the tongue of God so that it refutes the finger of God in Nature.” He believed that God has created Nature to provide for humans. The reason why there are “…treasuries so well concealed in the fabric of the heavens is so that fresh nourishment should never be lacking for the human mind…” For Kepler this was certainly true. This fruitful mindset led him to increasingly accurate discoveries of the inextricable link of mathematics and nature, both of which to him were divine and beautiful.
Kepler states “Copernicus’s purpose was not to deal with cosmography, but with astronomy.” Kepler envisioned a “graphic of the cosmos” which had previously been a mystery (hence “Mysterium Cosmographicum”). By his own account, he had a revelation of a “polyhedral hypothesis” to explain the cosmography of the universe, specifically proposing that each of the 5 Platonic solids fit precisely between the orbits of the planets as conceived as inscribed and circumscribed spheres of the polyhedra. But it isn’t the correctness of this ill-fated hypothesis that makes this book interesting. In fact, if this were all he was known for it seems he may be a mere footnote. What makes him and this book interesting is the way he approaches the search for truth. He seems to imagine a vague, but complete puzzle and looks for the pieces that go together to show it. He recalls his meandering, and “feeling along walls through the darkness of ignorance.”
The centrality he puts on God provides clarity for him. He believes “Nothing has been established by God at random.” This order in the book of Nature seems to above even the mere words of God. “…Everyone with strong religious scruples will take the greatest care not to twist the tongue of God so that it refutes the finger of God in Nature.” He believed that God has created Nature to provide for humans. The reason why there are “…treasuries so well concealed in the fabric of the heavens is so that fresh nourishment should never be lacking for the human mind…” For Kepler this was certainly true. This fruitful mindset led him to increasingly accurate discoveries of the inextricable link of mathematics and nature, both of which to him were divine and beautiful.
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