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abecedariusNov 2023

Man, Kepler would've loved this. One of his books was titled https://en.wikipedia.org/wiki/Harmonices_Mundi

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cimusJul 2023

Inspired by the book Harmonices Mundi by Johannes Kepler.

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dav_OzMay 2023

Distance: a straight line (i.e. shortest line in Euclidean geometry) between two points - is a one dimensional object/projection. On Earth crust where we evolved as 1 m long objects immersed in 1 atm of mostly nitrogen at around 290 K and at a constant pull at 1 g on a spinning ball at 11.5 µHz ... you get the idea ... a very straightforward concept.

Applying it to dust and gas particles (massive enough for gravity to shape it into a spinning sphere) in a vacuum falling towards (on a stable enough orbit) a gas ball with 99.8% of the total mass in the system, itself in hydrostatic equilibrium with its own gravity pull through nuclear fusion of hydrogen into helium ... Well, we are not used to that kind of motion i.e. geometry on astronomical scales. But once you see what dictates the (near) stable motions of all those tiny particles the solution is simple: in the solar system the sun is nearest to all objects in the system, on average. Whatever is nearest to the Sun is the closest on average to all other elliptical moving objects. From Neptune's perspective Mercury is barely moving and oscillating so fast as to standing still. So, in the case of planets the underlying geometry is moving along (stable) elliptical (i.e. closed path) orbits (approx. Newtonian mechanics), applying our "straight" lines for "distance" is amiss here and can lead to confusion. I personally like to see it more - inspired through e.g. Kepler's imagination[0] - as a geometrical-dynamic system (Kepler orbits) more akin to music.

[0]https://en.m.wikipedia.org/wiki/Harmonices_Mundi

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nickbaumanDec 2015

I don't know it by name but this quote reveals it pretty soundly: "We shall approach astronomy as we do geometry, by way of problems, and ignore what is in the sky." (Plato's Republic) This kind of thinking is likely the same sort of thinking that got Kepler off the track trying to force the Pythagorean solids into planetary orbits in his Harmonices Mundi.

(maybe call it "Pseudoscientism" a belief that merely scientific-looking commonalities are in fact universalities)

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antogniniOct 2015

It's interesting to note that even though Kepler is exclusively remembered today for his three laws, Kepler himself considered them a somewhat minor result. Most of the book in which he describes his third law, Harmonices Mundi, is concerned with astrology, music theory, and (for lack of a better word) mysticism.

An excerpt from the Wikipedia article gives a flavor:

'''

While medieval philosophers spoke metaphorically of the "music of the spheres", Kepler discovered physical harmonies in planetary motion. He found that the difference between the maximum and minimum angular speeds of a planet in its orbit approximates a harmonic proportion. For instance, the maximum angular speed of the Earth as measured from the Sun varies by a semitone (a ratio of 16:15), from mi to fa, between aphelion and perihelion. Venus only varies by a tiny 25:24 interval (called a diesis in musical terms).[6] Kepler explains the reason for the Earth's small harmonic range:

"The Earth sings Mi, Fa, Mi: you may infer even from the syllables that in this our home misery and famine hold sway."[9]

The celestial choir Kepler formed was made up of a tenor (Mars), two bass (Saturn and Jupiter), a soprano (Mercury), and two altos (Venus and Earth). Mercury, with its large elliptical orbit, was determined to be able to produce the greatest number of notes, while Venus was found to be capable of only a single note because its orbit is nearly a circle.[6]

At very rare intervals all of the planets would sing together in "perfect concord": Kepler proposed that this may have happened only once in history, perhaps at the time of creation.[10] Kepler reminds us that harmonic order is only mimicked by man, but has origin in the alignment of the heavenly bodies:

"Accordingly you won’t wonder any more that 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." (Harmonice Mundi, Book V).[6]

'''

We had a very interesting colloquium in my astronomy department a few years back by someone from the music department who had studied Kepler's musical theories in great detail. Evidently his musical theories have inspired a few modern composers. Here are two such compositions:

https://www.youtube.com/watch?v=neJ9qViszVs

https://www.youtube.com/watch?v=wLkmMEEiNBk

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