Epitome of Copernican Astronomy and Harmonies of the World (Great Minds) Info

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Reviews for Epitome of Copernican Astronomy and Harmonies of the World (Great Minds):

3

Sep 14, 2018

The Earth sings MI, FA, MI so that you may infer even from the syllables that in this our domicile MIsery and FAmine obtain.
Thomas Kuhn switched from studying physics to the history of science when, after teaching a course on outdated scientific models, he discovered that his notion of scientific progress was completely mistaken. As I plow through these old classics in my lackadaisical fashion, I am coming to the same conclusion. For I have discovered that the much-maligned Ptolemy produced a The Earth sings MI, FA, MI so that you may infer even from the syllables that in this our domicile MIsery and FAmine obtain.
Thomas Kuhn switched from studying physics to the history of science when, after teaching a course on outdated scientific models, he discovered that his notion of scientific progress was completely mistaken. As I plow through these old classics in my lackadaisical fashion, I am coming to the same conclusion. For I have discovered that the much-maligned Ptolemy produced a monument of observation and mathematical analysis, and that Copernicus’s revolutionary work relied heavily on this older model and was arguably less convincing. Now I discover that Johannes Kepler, one of the heroes of modern science, was also something of a crackpot.

The mythical image of the ideal scientist, patiently observing, cataloguing, calculating—a person solely concerned with the empirical facts—could not be further removed from Kepler. Few people in history had such a fecund and overactive imagination. Every new observation suggested a dozen theories to his feverish mind, not all of them testable. When Galileo published his Siderius Nuncius, for example, announcing the presence of moons orbiting Jupiter, Kepler immediately concluded that there must be life on Jupiter—and, why not, on all the other planets. Kepler even has a claim of being the first science-fiction writer, with his book Somnium, describing how the earth would appear to inhabitants of the moon (though Lucian of Samothrace, writing in the 2nd Century AD, seems to have priority with his fantastical novella, A True Story). This imaginative book, by the way, may have contributed to the accusations that Kepler’s mother was a witch.

In reading Kepler, I was constantly reminded of a remark by Bertrand Russell: “The first effect of emancipation from the Church was not to make men think rationally, but to open their minds to every sort of antique nonsense.” Similarly, the decline in Aristotle’s metaphysics did not prompt Kepler to reject metaphysical thinking altogether, but rather to speculate with wild abandon. But Kepler’s speculations differed from the ancients’ in two important respects: First, even when his theories are not testable, they are mathematical in nature. Gone are the verbal categories of Aristotle; and in comes the modern notion that nature is the manifestation of numerical harmonies. Second, whenever Kepler’s theories are testable, he tested them, and thoroughly. And he had ample data with which to test his speculations, since he was bequeathed the voluminous observations of his former mentor, Tycho Brahe.

At its worst, Kepler’s method resulted in meaningless numerical coincidences that explain nothing. As many a statistician has learned, if you crunch enough numbers and enough variables, you will eventually stumble upon a serendipitous correlation. This aptly describes Kepler’s use of the five Platonic solids to explain planetary orbits; by trying many combinations, Kepler found that he could create an arrangement of these regular solids, nested within one another, that mostly corresponded with the size of the planets’ orbits. But what does this explain? And how does this help calculation? The answer to both of these questions is negative; the solution merely appeals to Kepler’s sense of mathematical elegance, and reinforced his religious conviction that God must have arranged the world harmoniously.

Another famous example of this is Kepler’s notion of the “harmonies of the world.” By playing with the numbers of the perihelion, aphelion, orbital lengths, and so forth, Kepler assigns a melodic range to each of the planets. Mercury, having the most elongated orbit, has the biggest range; while Venus’s orbit, which most approximates a perfect circle, only produces a single note. Jupiter and Saturn are the basses, of course, while Mars is the tenor, Earth and Venus the altos, and Mercury the soprano. He then suggests (though vaguely) that there are beings on the sun, capable of sensing this heavenly music. (The composer Laurie Spiegel created a piece in which she recreates this music; it is not exactly Bach.) Once more, we naturally ask: What would all this speculation on music and harmonies explain? And once more, the answer is nothing.

Kepler’s writing is full of this sort of thing—torturous explorations of ratios, data, figures, which strike the modern mind as ravings rather than reasoning. But the fact remains that Kepler was one of the great scientific geniuses of history. He was writing in a sort of interim period between the fall of Aristotelian science and the rise of Newtonian physics, a time when the mind of Europe was completely untethered to any recognizable paradigm, free to luxuriate in speculation. Most people in such circumstances would produce nothing but nonsense; but Kepler managed to invent astrophysics.

What gives Kepler a claim to this title was his conception of a scientific law (though he did not put it as such). Astronomers from Ptolemy to Copernicus used schemes to predict planetary movements; but there was no one underlying principle which could explain everything. Kepler’s relentless search for numerical coincidences led him to statements that unified observations of all the planets. These are now known as Kepler’s Laws.

The first of these was the seemingly simple but revolutionary insight that planets orbit in ellipses, with the sun at one of the foci. It is commonly said that previous astronomers preferred circles for petty metaphysical reasons, seeing them as perfect. But there were other reasons, too. Most obviously, the mathematics of shapes inscribed in circles was well-understood; this was the basis of trigonometry.

Yet the use of circles to track orbits that, in reality, are not circular, created some problems. Thus in the Ptolemaic system the astronomer used one circle (the eccentric) for the distance, and another, overlapping circle (the equant) for the speed. When these were combined with the epicycles (used to explain retrogression) the resultant orbits, though composed of perfect circles, were anything but circular. Kepler’s use of ellipses obviated the need for all these circles, reducing a complicated machinery into a single shape. It was this innovation that made the Copernican system so much more efficient than the Ptolemaic one. As Owen Gingerich, a Copernican scholar, has said: “What passes today as the ‘Copernican System’ is in detail the Keplerian system.”

Yet the use of ellipses, by itself, would not have been so useful were it not for Kepler’s Second Law: that planets sweep out equal areas in equal times of their orbits. For when a planet is closest to the sun (at perihelion) it is moving its fastest; and when it is furthest (at aphelion) it is slowest; and this creates a constant ratio (which is the result of the conserved angular momentum of each planet). Ironically, of the two, Ptolemy was closer than Copernicus to this insight, since Ptolemy’s much-maligned equant (the imaginary point around which a planet travels at a constant speed) is a close approximation of the Second Law. Even so, I think that Kepler moved far beyond all previous astronomy with these insights, jumping from observed and analyzed regularities to general principles.

Kepler’s Third Law seemed to have excited the astronomer the most, since he even includes the exact date at which he made the realization: “… on the 8th of March in this year One Thousand Six Hundred and Eighteen but unfelicitously submitted to calculation and rejected as false, finally, summoned back on the 15th of May, with a fresh assault undertaken, outfought the darkness of my mind.” This law states that, for every planet, the ratio of the orbital period squared to the orbital size cubed, is constant. (For the orbital size Kepler used half the major axis of the ellipse.)

While it is no doubt striking that this ratio is almost the same for every planet (this is because the planet’s mass is negligible compared with the sun’s), it is difficult to completely sympathize with Kepler’s excitement, since the resultant law is not useful for predicting orbits, and its significance was only explained much later by Newton as a derivable conclusion from his equations. Kepler, being the man he was, used this mathematical constant to fuel his metaphysical speculations.

However much, then, that Kepler’s theories may strike us nowadays as baseless, crackpot theorizing, he must be given a commanding place in the history of science. The reason I cannot rate this collection any higher is that Kepler is extremely tiresome to read. In his more lucid moments, his imaginative energy is charming. But much of the book consists of whole paragraphs of ratio after ratio, shape after shape, number after number, and so it is easy to get lost or bored. Since I have a decent grasp of music theory, I thought I might be able to get something out of his Harmonies of the World, but I found even that section mostly opaque, swirling in obscure and impenetrable reasoning.

The great irony, then, is that Kepler’s writings can strike the modern-day reader as far less “scientific” than Ptolemy's; but perhaps we should expect such ironies from a man who helped to inaugurate modern science, but who made his living casting horoscopes. ...more
3

Apr 16, 2013

When I ran the randomizer on my list of like a million books, I just knew the first one would be some technical doozy. And the Debbie Downer inside of me was not wrong. Oh well; plenty of enthusiasm for my new project of reading through a big chunk of the worlds best and most influential books, so I can do this! Remember, one of my rules was that I would make it through every book word-by-word except for technical tomes.

Right away, I learned something that I put to use. If I am going to read When I ran the randomizer on my list of like a million books, I just knew the first one would be some technical doozy. And the Debbie Downer inside of me was not wrong. Oh well; plenty of enthusiasm for my new project of reading through a big chunk of the world’s best and most influential books, so I can do this! Remember, one of my rules was that I would make it through every book word-by-word except for technical tomes.

Right away, I learned something that I put to use. If I am going to read these kinds of books, I need to get annotated versions with explanations in close-to-laymans’ terms. Not only are Harmonies of the World‘s topics completely in fields that I don’t understand at this level (astronomy, math, and music theory), but the language usage is archaic and the history of the situation is lost on me. Therefore, I immediately ordered a preview copy of one of my next books–a Newton title–in its soon-to-be-released commentary version. Lesson learned.

Now, for the book itself.

I think we need to start with some history. Johannes Kepler was a key figure in the 17th century scientific revolution which included Isaac Newton’s theory of gravity, Galilieo’s world, Copernicus’ universe, and eventual shifts in the world of math, physics, astronomy, biology, medicine, and chemistry, which transformed our culture and views of nature. Kepler was officially a teacher and a mathematician to royalty, as well as an assistant to astronomer Tycho Brahe. He improved the telescope, married physics with astronomy (as opposed to astrology), and believed that “God had created the world according to an intelligible plan that is accessible through the natural light of reason” (“Johannes Kepler”, http://en.wikipedia.org/wiki/Johannes...).

Kepler’s first published work, Mysterium Cosmographicum, began his work as the updater of Copernican theory. After studying under Brahe and writing other works, he shifted his concentration to harmonies, or “music of the spheres,” which was an idea explored earlier by Pythagoras, Ptolemy, and many others. Music of the spheres is defined as “an ancient philosophical concept that regards proportions in the movements of celestial bodies—the Sun, Moon, and planets—as a form of musica (the Medieval Latin name for music). This ‘music’ is not usually thought to be literally audible, but a harmonic and/or mathematical and/or religious concept” (“Musica Universalis, http://en.wikipedia.org/wiki/Musica_u...).

Kepler himself considered Harmonies of the World (aka. Harmony of the World or Harmonices Mundi) to be his greatest work. He certainly seems excited in his writing. The basic premiss is that there are harmonies, or congruence, in all of God’s creation, which Kepler limits in his proving to three-dimensional geometry (later known as Kepler’s solids), relationships of magnitude, music, and the Solar System. He builds his arguments on the Platonic Solids, irrational numbers (think pi), and harmonic intervals (like the ratio of a C to its octave and a fifth). Are there harmonic ratios in the distance between planets? Conclusion: no. How about their velocities? Well, yes, it does appear so, both individually and converging and diverging. And since movement best approximates music, this makes perfect sense to Kepler.

After Kepler sent Harmonies to the printer, his work came to another conclusion: “Kepler discovered that the ratio of the square of a planet’s period to the cube of its semi-major axis is constant for all orbits. Today, we know this relationship as Kepler’s Third Law. Many consider it to be one of the most elegant results in all of astronomy” (“Kepler’s Harmonices Mundi“, http://www.keplersdiscovery.com/Harmo...). Also, “when conjoined with Christian Huygens’ newly discovered law of centrifugal force it enabled [later, in the 1660s] Isaac Newton, Edmund Halley, and perhaps Christopher Wren and Robert Hooke to demonstrate independently that the presumed gravitational attraction between the Sun and its planets decreased with the square of the distance between them. This refuted the traditional assumption of scholastic physics that the power of gravitational attraction remained constant with distance whenever it applied between two bodies” (“Johannes Kepler”, http://en.wikipedia.org/wiki/Johannes...).

Kepler was not overly well received in the immediate. His theories were largely ignored by those in prominence in science. After some well-documented, third-party tests however, some scientists began pulling for a Keplerian model of astronomy. By 1630-1650, his was the most used textbook in astronomy, which set Kepler up to be the building block for Newtonian theory and its culmination in Principia Mathematica (which, by sheer coincidence, I will be reading this summer).

Besides all the boring numbers, the constant use of the run-on sentence, and the obvious issues with advances of science (like, he thinks there are only six planets and the universe orbits around the sun), it was interesting to witness his pure enthusiasm and conviction.

I would not recommend this book for reading, unless you are or are studying to be an astronomer, physicist, geometrician, science historian, or musical theorist. And if you really want to read it, accompany it with some sort of commentary or history. It consists largely of equations and “almost”s, stretching and fudging. (For example, Kepler says that because the earth sings “MI FA MI,” it is clear it is a place of MIsery and FAmine.) I think, with a much cleaner translation, it would be at least readable by the layman, but would still abound in equations. I think the following quotes will be enough for you:

“I commence a most sacred discourse, a most true hymn to God the Founder…. first to learn myself, and afterwards to teach others too, how great He is in wisdom, how great in power, and of what sort in goodness…. He can do by His unconquerable power all that He has decreed” (p169).

“…I brought it to light and found it to be truer than I had ever hoped, and I discovered among the celestial movements the full nature of harmony…” (p169).

“The very nature of things, in order to reveal herself to mankind, was at work in the different interpreters of different ages, and was the finger of God…” (p170).

“For the Creator, Who is the very source of geometry and, as Plato wrote, ‘practices eternal geometry,’ does not stray from His own archetype” (p177).

“…God has established nothing without geometrical beauty…” (p185).

“…they are doing nothing else in the 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” (p198).

“Accordingly the movements of the heavens are nothing except a certain everlasting polyphony (intelligible, not audible) with dissonant tunings” (p208).

REVIEW FROM MY BLOG, THE STARVING ARTIST. ...more
2

Oct 04, 2017

This is a collection of samples of two of Kepler's most important works: (1) The Epitome of Copernican Astronomy (only books 4 and 5) in which Kepler describes the heliocentric theory of Copernicus in an accessible way for laypeople and (2) Harmonies of the World (only book 5).

It is, surprisingly, well written and accessible, even for contemporary readers. Copernicus' theory was originally published in 1543 in his book De Revolutionibus. It didn't really cause a stir and went largely unnoticed This is a collection of samples of two of Kepler's most important works: (1) The Epitome of Copernican Astronomy (only books 4 and 5) in which Kepler describes the heliocentric theory of Copernicus in an accessible way for laypeople and (2) Harmonies of the World (only book 5).

It is, surprisingly, well written and accessible, even for contemporary readers. Copernicus' theory was originally published in 1543 in his book De Revolutionibus. It didn't really cause a stir and went largely unnoticed for decades - eventually, in the 17th century the Inquistion would put this book on the Index of Forbidden Books.

In The Epitome, Kepler gives an easy-to-understand description of the above mentioned Copernican theory: the earth revolves around the sun, just like the other planets; the sun is at the centre of the cosmos. This is mathematically a much simpler system than the Ptolemaic/Aristotelean system of epicycles, equants, deferents, etc.

In The Harmonies, Kepler basically outlines the theory for which he is known nowadays: his three laws:

1. All planetary orbits are ellipses (instead of 'perfect' circles à la Aristotle).
2. During a given time interval, a line drawn from the planet to sun sweeps out an equal area anywhere along its path.
3. The square of the period of revolution of a planet is proportional to the third power of the mean radius of the planetary orbit.

It is said that Kepler found his first law when he tried over and over again (and failing each time) to fit the orbit of Mars in a circular movement. Kepler's use of 'Harmonies' relate to his third law, specifically in the harmony he saw in being able to relate the orbits of all the planets with one simple equation - this is what physicists call 'beautiful'. In the Harmonies he even relates this mathematical beauty to the tones of musical instruments. In the last part of the book, he speculates about the power of the sun that lets these planets orbit according to the formula.

Even though most (some) parts are fuly readably, you do need to have some background knowledge in geometry though. I'm not an expert, so I didn't get the whole book, but I only read it as additional source to a broader (self)study in physics. (The low score is mainly because of the incompleteness of the works).
...more
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Mar 05, 2011

Keplers work is another step away from the view that the universe and earth were governed by distinct physical rules. Though the variance from Aristotles Metaphysics and On the Heavens is noted by Kepler himself, there remains a key similarity. Both see in the sky a theological structure. Keplers overt religiosity is seen in everything including mans opportunity to study the heavens. Let the eighteenth argument come from the end of movement, by which it is proved that movement belongs to the Kepler’s work is another step away from the view that the universe and earth were governed by distinct physical rules. Though the variance from Aristotle’s Metaphysics and On the Heavens is noted by Kepler himself, there remains a key similarity. Both see in the sky a theological structure. Kepler’s overt religiosity is seen in everything including man’s opportunity to study the heavens. Let the eighteenth argument come from the end of movement, by which it is proved that movement belongs to the Earth as the home of the speculative creature. For it was not fitting that man, who was going to be the dweller in this world and its contemplator, should reside in one place of it as in a closed cubicle: in that way he would never have arrived at the measurement and contemplation of the so distant stars…”pg. 75-76 The quest to discover the design yields fascinating comparisons of harmonic theory and planetary orbits as well as stacked geometric shaped orbits (in Matryohka doll fashion). Kepler believed “God has established nothing without geometrical beauty…"pg. 185 and geometry predominates this work just as with the ancient Greeks.

Only books IV and V of Epitome of Copernican Astronomy are available in English. Most of it I didn’t understand anyway. But even those of us without mathematical talent can snatch moments of brilliance from Kepler. He seems slightly more accessible than Copernicus and Ptolemy. Slightly. ...more
3

Jan 22, 2013

(I did not read Kepler's work on musical harmony. This is my attempt at a review on his Epitome of Copernican Astronomy.)

Epitome of Copernican Astronomy is a challenging read for us not-so-technical types, but the "Q & A" format was an interesting approach. What one will not find is a formal layout of the laws of planetary motion. There are enough references to them in the book to see the laws at work, but the raw data and formal presentation is in his Commentary on Mars, a work to which the (I did not read Kepler's work on musical harmony. This is my attempt at a review on his Epitome of Copernican Astronomy.)

Epitome of Copernican Astronomy is a challenging read for us not-so-technical types, but the "Q & A" format was an interesting approach. What one will not find is a formal layout of the laws of planetary motion. There are enough references to them in the book to see the laws at work, but the raw data and formal presentation is in his Commentary on Mars, a work to which the reader is naturally referred several times. Do some background reading on the laws and the book is helpful. I would have liked to see the end of book 5 earlier in the work. It clarifies a lot of terminology which is in use throughout the earlier parts. The placement of that particular part is curious, but I suppose there are reasons for it. The blend of theological reasoning and application of his knowledge of musical harmony to astronomy might make scientific types scoff a little, but it's hard to argue with results, such as his accuracies regarding eccentric orbits and the 25-day axial rotation of the sun. Definitely worth a look. ...more

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