Creation, Day Four: Dancing with the Stars

And God said, “Let there be lights in the expanse of the heavens to separate the day from the night.  And let them be for signs and for seasons, and for days and years, and let them be lights in the expanse of the heavens to give light upon the earth.”  And it was so.  And God made the two great lights—the greater light to light the day and the lesser light to rule the night and the stars.  And God set them in the expanse of the heavens to give light on the earth, to rule over the day and over the night, and to separate the light from the darkness.  And God saw that it was good.  And there was evening and there was morning, the fourth day.         Gen. 1:14-19

Hum the first two notes of “Over the Rainbow.”  (I’m not kidding: hum it!)

You’ve just hummed an octave, with eight musical steps between the low pitch and the high pitch (octave stemming from the Latin word for “eight”).  If you’ve ever taken piano lessons or sung in a choir, you know what a musical scale sounds like: do-re-mi-fa-so-la-ti-do.  From the first do to the next do is eight tones, and if you sang only those two notes with no others in between, it would sounds like the first two notes of “Over the Rainbow.”

Now try humming the first five tones of the scale: do-re-mi-fa-so.  Hum the first do again, then go directly to so, leaving out the notes in between.  One time, but hum do twice, followed by so twice.  Does it sounds like “Twinkle, Twinkle, Little Star”  (or “The Alphabet Song”)?

One more: think of the first three notes of “Taps,” the bugle call played at military funerals.  Or the first four notes of Wagner’s “Wedding March,” also known as “Here Comes the Bride.”   Or, if you’re from the same great state as I am, “The Eyes of Texas.”  With the first note as do, the second note is four steps up the scale: do-re-mi-fa.

We call the interval between the pitches in “Somewhere over the Rainbow” an eighth, or an octave, the opening interval in “Twinkle Twinkle” a fifth, and the opening interval in the “Wedding March” a fourth.  And none of this seems to have anything to do with Day Four of creation, when heavenly bodies appeared in the sky.  But roughly 2600 years ago, Pythagoras thought differently.

Pythagoras is such a shady figure he may not have existed at all.  But no one doubts the existence of the “Pythagorean School” of scholars and mystics who congregated on the island of Samos and pledged to eat no meat and have no sex.  For a small group of bachelor vegetarians with a possibly mythical leader, their influence on history was profound.

A major principle of Pythagorean thought is that reality is based on mathematical relationships.  His famous theory of triangles* is only part of it.  Even more fascinating, and apropos for our purpose, were his experiments with music.

Pythagoras discovered that a string tuned to any musical tone, when cut in half, will produce the same tone at a higher pitch.   Hum the first two notes of “Somewhere over the Rainbow” again.  These two notes have a precise mathematical relationship.  Pythagoras had discovered the octave; to get the same tone, eight steps higher, divide the string exactly in half.  Mathematically, the ratio is 2:1.  Scientifically, the half string vibrates exactly twice as fast as the full string, producing a note that is equal in tone but higher in pitch.

Continuing his experiments, Pythagoras cut an identical string 1/3 from the lower end.  The new pitch, combined with the original, now sounded like the first notes of “Twinkle, Twinkle, Little Star.”  (Could Pythagoras have been the mythical author of that ancient ditty?)   Not an echo, like the octave, but a pleasing transition with, again, a precise mathematical relationship: 3:2.  The short string vibrates two-thirds as fast as the long one.

What if he divided another identical string in half, and half again, so that the length of the string was one-fourth the length of the original?  Now the transition between the two notes sounded like “The Eyes of Texas” (or rather, “The Eyes of Samos”)—another pleasing interval with a mathematical relationship of 4:3.

As it happens, the Octave (Somewhere), the Perfect fifth (as in Twinkle, Twinkle), and the Perfect Fourth (Wedding March) are musical intervals common to all cultures everywhere.   Eastern music and primitive music have distinctive scales, tones, and rhythmic patterns that mystify Westerners , but all cultures make use of octaves, fourths, and fifths.

All melodies consist of stepping from one note to another, and the distance one note to the next is noted mathematically: not merely fourths and fifths, but thirds, seconds, sixths, sevenths, and descending, augmented, and diminished versions of all those.  Pythagoras would have said that music is mathematics, and mathematical relationships are a form of music, extending throughout the cosmos.  Each heavenly body, each star and planet, has its own pitch, hummed in harmony with all the rest.

Here the mystical side of Pythagoras overreached the scientific, but he was on to something.  A couple of thousand years later, Western science would come to the conclusion that the key to the universe, its language or code, was numbers—or, more precisely—numerical relationships:   intervals, measurements, calibrations.

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Let them be for signs and seasons, and for days and years.

You want numbers?  Here are some numbers:

• Two of the great forces in the universe, gravity and electromagnetism, have to be balanced in a precise ratio, namely 1 over 10⁴⁰, or one part in ten thousand trillion trillion trillion.  If the ratio is off, physical life is impossible.
• Space energy density, or the self-stretching property of the universe, can’t vary more than one part in 10¹²⁰ and still produce stars and planets.
• Our home galaxy, the Milky Way, measures approximately100,000 light years from one arm to the other.  Our sun is located far from the center, but if it were any closer radiation would have destroyed it.
• The distance from earth to the moon varies a bit depending on where the moon is in its orbit.  The average is 238,857 miles—much closer, and the moon would have crashed into the earth.  Any farther, and the moon’s gravitational effect would have no influence.  As it is, that cratered chunk of rock stabilizes the earth at an axial tilt of approximately 23.5 degrees (it varies slightly with the moon’s orbit).  Without the pull of the moon, earth would wobble from burning hot to freezing cold, a variation of 200 degrees.  Because the moon is where it is, we have signs and seasons, days and years.

Signs and seasons, days and years.  Light exists—we know it does, even if we haven’t exactly figured out what it is.  Time exists, too—we know that because there was “a beginning.”  But what was the form of time?   Were days always marked by twenty-four hours, or was there a time when time itself roamed outside the discipline of measurement, stretching thin and bunching up?  Is there a master clock?  When was it set, and who set it?

Day Four marks several new developments.  First, the heavenly bodies appear: a kingly sun, a queenly moon, and attendant stars beyond number.  The language of Genesis gives a nod to mythological notions of the sun “ruling” the day, like Apollo’s flaming chariot, and the moon presiding over night like the huntress Diana, stalking her prey.

Secondly, Day Four sets up a parallel structure.  On days one, two, and three, we have regions, or territories: the heavens (and earth), air and seas, dry land.  Day Four begins the process of populating those regions.  “The heavens” are the realm of heavenly bodies, whose mysterious influence and regular movement would occupy thinkers and observers for millennia.

But another significance of Day Four is often overlooked: in it, God establishes the principle of measurement.  Not only for time (“days and seasons and years”) but also, I think it’s safe to infer, for space.  I remember past events based partly on where we were at the time: the where indicates the when.  I interpret what happens to me partly by locating myself in space.  Spatial relationships, ratios, and measurement are essential to figuring out where we are, where we’re going, and how to get there, both practically and scientifically.  And numbers are the key.

Pythagoras may have been the first to link numbers with music and space.  But two thousand years later, in the pursuit of science, Johannes Kepler made an amazing discovery that hearkened back to the Island of Samos.

While drawing a geometric figure of a circle within an equilateral triangle, circumscribed by another perfect circle, it struck him that the ratio of the two circles equaled the orbits of Jupiter and Saturn.  What if all the planetary orbits displayed a similar geometric relationship?  The hypothesis didn’t work out quite as well as he hoped, but speculation along this line led to Kepler’s three laws of planetary motion and the discovery that a) orbits are elliptical, not circular; b) a planet’s speed varies between aphelion (when it’s closest to the sun) and perihelion (its farthest distance from the sun); and c) the duration of any planet’s orbit depends on that planet’s distance from the sun.

We learn this in science class and file it with our other sets of “three laws” to remember for the test.  But Kepler’s laws not only provided the necessary foundation for Newton’s principles of universal gravity, they also reached back to the Pythagorean notion of universal harmony.  Pythagoras envisioned the planets ascending from earth at regular intervals, as though on the rungs of a ladder.  Each “rung” corresponded to a musical interval—the same intervals he had discovered on his cut-up lyre strings.  The cosmos, Pythagoras believed, danced to music.  Music was good for the soul and the body, and no wonder; it’s part of the stuff we’re made from.

In formulating his second law (that planets moved faster at perihelion and slower at aphelion), Kepler calculated their velocities at these two extremes and wrote down the ratio.  Saturn, for example, moves at a rate of 106 degrees per solar day at aphelion and 135 degrees at perihelion, thus a ratio of 106:135.  After he factored these numbers and cancelled the common factors the ratio differs by only two seconds from 4:5, or the interval of a major third.  It wasn’t just a coincidence: the ratio of velocities of all the known planets closely corresponded to musical intervals.

But that’s not all.  When he compared the velocity ratios for combined pairs of planets, (such as Jupiter’s perihelion and Mars’ aphelion) he found the intervals of a complete scale.  Jupiter and Mars sing a minor third, Earth and Venus a minor sixth.  His discovery of elliptical orbits was a disappointment to him at first—it seemed to spoil the beauty of perfect concentric circles.  But as the planets rolled along their elliptical paths, shifting speed and velocity, they described recognizable patterns, even harmonic chords.  “Henceforth,” he wrote, “it is no longer a harmony made for the benefit of our planet, but the song which the cosmos sings to its Lord and center, the Solar Logos.”

Modern science, while it doesn’t come to the same metaphysical conclusion as Kepler, finds his measurements to be “frighteningly good,” as the famed astronomer Fred Hoyle observed.

This is my father’s world, and to my listening ears

all nature sings, and round me rings the music of the spheres.

Mathematics and science were created on this day.  And so was music, “While the morning stars sang together, and all the sons of God shouted for joy.”**

Creation, Day Five – Being and Soaring

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*Pythagorean theorem: a fundamental relation in Euclidean geometry among the three sides of a right triangle. It states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

**Job 38:7