are great fun to play with. Sometimes, you can reveal deep eternal truths
values all over. But, as any politician
can tell you, numbers are tricky - they can lead
you down false pathways
. And it can be hard to tell the difference
if the math
is technically correct.
Pythagoras, he of the great Theorem that we've all had burned in our brain, discovered the mathematical relationship between notes in the Western scale. This was great news to Pythagoras - he was working on a (grand unifying) theory that the entire universe was based on a number (representing a higher power, maybe, as in the movie Pi). So he accordingly went out in search of the different places where different notes and different harmonies could be found. Since the octaves he discovered were totally based on distance (the length of a stretched catgut string on a harp, say), anything with a good fixed dimension or two was fair game. The celestial spheres were a good match - ten planets, all perfectly circling the center of the universe, the Terra. Pythagoras devised notes based on the distance between the spheres. The moon was a whole tone up from the base C of the earth; Mercury and Venus were half steps up each. Saturn - three tones up from Terra. And the Music of the Spheres was born, heavenly bodies, circling in pure tones, creating music. It was all inherent in the math, the numbers, and maybe a fudge factor or two. Or three. But the notes were the thing.
This idea was incredibly popular. Many two-bit philosophical students took the idea and ran with it, making their own measurements, coming up with different but more aesthetically pleasing (to them) scales. Different numbers, different math, different notes, but still manipulating away, twisting the numbers until they screamed. The idea of ten planets and ten notes were intoxicating; one A. Kircher tied in the nine circling planets to the nine Muses of lore; one Albert Freiherr applied the ten primal numbers, the Sephiroth, to the scale, trying to add Cabalistic lore to the equation (and succeeding enough to that Madame Blatavsky picked up the idea in Isis Unveiled).
One such man was inspired by the idea of a celestial harmony, but disagreed with the idea of the Earth at the center of the universe on both scientific and aesthetic grounds - and so Copernicus created his view of a Sun-centered universe, and a new harmony. Honestly, in Copernicus's case, it seems that the new ordering of the planets was the thing; the new scale was secondary, unlike the next guy, Kepler...
... who took this one step further. He also played with the numbers to reveal deep truths - he believed in a self-created version of astrology, so it went beyond the music for him. The problem is when the facts started staring him in the face - these damn planets weren't traveling in circles. So much for those wonderful theories about Euclidian solids inside each orbit. So Kepler banged out the Laws of Planetary Motion as an aside, and got back to work on harmony and astrology. After a few (or more) misstarts, he eventually tried the measurement of ratios between the angular velocities of the planets at the extremes of the oval pathways. Bingo! It worked out - the ratios matched up with the standard chords! And so he created times that the planets were in alignment, when the celestial music was harmonious, and (I think) put his trust in Lady Luck on those instances.
Now, Foucault's-Pendulum-style-Cabalists notwithstanding, there is no known harmony; but there were myriad ways to twist the numbers to come up with these notes and chords. The instant you see some equation work out to a major third, bulldada! You've got harmony, heavenly music! Obviously, it was the way your own personal Creator intended, part of the overall master plan. And, to these now famous scientists, it was all part of the end goal - eternal truths. Pythagoras sought music everywhere, and therefore saw music everywhere; Kepler needed grist for his astrological predictions, and hunted long and hard to find these major and minor chords in the sky. And both did find important truths in the process, ones that live on today. But who could tell at the time what was the real deal and what wouldn't? It was all so terribly exciting. The math, no matter how tortured, always worked... and it usually wasn't so twisted anyways. Those ratios were there, just waiting to be discovered... so you can't blame these great scientists for appearing to be baselessly and illogically mystical today.
And who's to say they weren't right?
This node is dedicated to John Hagelin, the nuclear physicist and transendental meditation disciple, the (other) Reform Party's U.S. presidential candidate in the year 2000. If he was able to snag a (semi)major nomination, then maybe this yogic flying stuff does have something to it...