The Ecphorizer

Pythagoras Was Right!
Gareth Penn

Issue #08 (April 1982)

I became a free-lance writer because I wanted to structure my own time. It often happens that I wind up with more time than structure and have to find something to do with it. The other day I had a couple of idle hours to pass and, for want of anything better to do, I restructured the universe. No fooling. I think I did. What started it was a remark from a friend of mine about Bode's Law, which I had forgotten about. But first, let me fill in the background. Cast your mind back, if you will, 2500 years.

Pythagoras and his followers believed that planets, including the earth, all revolve about a central point. Pythagoras was also a pioneer in music; he discovered the diatonic scale. By experimenting with vibrating strings, he found that there was absolute agreement in tone between strings whose lengths were proportional to one another by powers of two: 1/2, 2, 4, etc. Each octave is double the octave below, half the one above, in frequency. The Pythagoreans synthesized astronomy and music by [quoteright]proposing what they called The Music Of The Spheres. They said the planets were spaced from the center by whole-number multiples of some base distance. Each planet had a particular note in the diatonic scale, which it expressed by moving. Fast-moving planets had a high note, slower planets a lower note. The resulting harmony permeated the universe. We couldn't hear it, or weren't aware of it, they said, because we had never heard anything else. In the following 2500 years, this theory has turned out to be the most consistent theme in astronomy.

The geocentric universe that Copernicus demolished was a later development. Ptolemy devised his complicated scheme of cycles and epicycles to explain planetary motion around the earth in the 2nd century A.D. While Copernicus based his refutation of Ptolemy on solid scientific observation, he himself wrote that the germ of the idea of a heliocentric system had been put into his mind by his reading of Pythagoras.

The great discoveries of Copernicus, Galileo, and Huygens were then given a solid mathematical foundation in the early 17th century by Kepler, who devised the classic scheme of celestial mechanics, and it was that scheme that led to Newton's laws of physics. According to folklore, Newton was inspired by an apple falling on his head. In fact, what fell on his head was Kepler.

At all events, Kepler then did something that seems regressive to the modern mind. He set out to prove the existence of The Music Of The Spheres. In an ingenious tour de force, De harmonica mundi (1619), he demonstrated relationships between the orbital velocities of the planets corresponding to musical intervals. At that point, he switched from mathematical to musical notation. Pythagoras was hard to shake.

Later, astronomy adopted the Astronomical Unit as a means of measuring, well, astronomical distances. The A.U. is the mean distance between the earth and the sun. In 1776, Bode published an amazing computation that seemed to prove the validity of the Pythagorean concept another way. A series of intervals of 3 multiplied by powers of 2 (0-3-6-12-24-48-96, etc.), when added to 4, then divided by 10, expressed the mean distance from the sun of all the then-known planets, measured in A.U.

There was a gap at 2.8 A.U. (24 plus 4 over 10), and there was room for infinite expansion beyond Saturn. Five years later, Herschel discovered Uranus, whose mean distance was quite close to the 19.6 A.U. predicted by Bode. And in 1801, Piazzi discovered the first of the asteroids, Ceres, right on the money at 2.8 A.U.

Bode was riding high until 1846, when Leverrier discovered a new planet, Neptune. It was nearly 9 A.U. closer to the sun than it should have been, a la Bode. The Law had been astonishingly accurate but now failed utterly. It was relegated to that scientific twilight world where old truths rub elbows with fallacy. But the fascination is still there: it's more than a curiosity, yet there's something wrong with it.

One thing wrong with it is the initial series of numbers. 0-3-6-12 is not a true progression. It should begin either with 1.5 or else read 0-3-6-9-12, etc. The second thing wrong with it is the A.U. Using the A.U. as a yardstick is like using the Stone-Rod-Fortnight System when you have Metric. The only justification for using the earth as the other end of the yardstick is planetary chauvinism.

If I were an impartial outsider (let's say from Aldebaran), I would use the mean distance between the sun and Jupiter as my basic measure. Jupiter is the second-largest object in the system and almost large enough to be a star in its own right. And so I invented the Jovian Unit (J.U.) and used it to re-survery the solar system. That's when I found something that I think you will find intriguing.

The first three planets, Mercury, Venus, and Earth, express two intervals that are almost exactly identical to one another: 0.0577 J.U. The overwhelming majority of the asteroids are grouped in three large clumps. Again, these clumps are separated by intervals almost exactly identical to one another: 0.067 J.U. each. Beyond Jupiter, Saturn, Uranus, and Neptune are found at 1.8, 3.7, and 5.8 J.U., respectively. The intervals here are far from perfect, but they don't deviate from the model any more than anything but Neptune does from Bode's Law. What about the loose ends?

If you treat these triads as units, it seems logical to measure from the center member of each. The mean distance of Venus is just about exactly 1/8 J.U. from the sun. Asteroid Clump #2 is very close to 1/2 J.U. (That was when I first became aware of hearing The Music.) If Pythagoras were right, there would have to be something at or close to 1/4 J.U. And there is: Mars. There are four diatonic octaves between the sun and Jupiter.

I'm the next best thing to illiterate when it comes to celestial mechanics. Somebody who knows anything about it may tear down what follows as a house of cards contrived by a dilettante with a Radio Shack pocket calculator and nothing better to do with his time. But here it is anyway.

I read that gravity is theoretically supposed to be a wave-phenomenon. If gravity-waves behave like other waves (e.g, sound) might not there be a beat-frequency relationship between the two most prodigious sources of gravity-waves in these parts - the sun and Jupiter? The planets beyond Jupiter would be subject to the influence of gravity-waves, but they would express themselves in different dimensions. The intervals expressed by the third triad are just about one J.U. times 21. If wave-mechanics had anything to do with the formation of the planets, it might explain why the inner planets are all tiny and the outer ones huge.

Pluto is the fly in the ointment. It's a renegade in a lot of respects. But it does conform to one pattern expressed by the other planets: Triad-Singleton, Triad-Singleton, Triad-Singleton. At worst, my scheme includes Neptune, which beats Bode by a whole planet, and a big one at that.

I think I'll wait for feedback before I book my seat on SAS. If you have positive comments, please copy the Swedish Academy. God knows I can use the money. But easy come, easy go. It took me only a couple of hours, and I had fun doing it. Now if you'll excuse me, I have to get back to work. 

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