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The Music of the Spheres
Geometry as Heaven's Hymnody
Alan G. Padgett

The psalmist sings forth with unashamed faith, "The heavens declare the glory of God." For almost two thousand years, the best minds of Europe, the Near East, and North Africa agreed, at least to some extent. For the world of classical, medieval, and Renaissance thought, the stars and planets make beautiful music in the course of their journey about the earth. This is the source of the romantic notion of the "music of the spheres."

In his wonderful series of popular lectures given at Oxford, The Discarded Image, C. S. Lewis introduces us to the worldview of ancient, medieval, and Renaissance culture. Instead of the usual brush-off, Lewis gives the great minds of the so-called "dark ages" a place to shine. These lectures create genuine appreciation for medieval culture and literature in the reader. Lewis includes a wonderful section on this idea that the planets and stars orbit the earth in pure crystalline spheres (for, of course, the earth is the center of creation). For Pythagoras (sixth century BC) and his school, this also meant that the spheres were spaced in such a way that their motion and vibration created a beautiful harmony of sound, which echoed throughout the heavens.

It is to Pythagoras and his school of mystical mathematicians that we owe the term harmony (harmonia), a Greek word meaning that the parts of a thing fit together in symmetry and beauty. The Pythagoreans were nuts about numbers, finding in them the mystical key to all reality. They discovered the relationship between length, ratio, and musical tones that forms the basis of all music theory today. For example, what we call an octave is expressed as the ratio of 1:2 in the length of a string or a simple wind instrument. This was one of the more exciting discoveries of the Pythagoreans. Because they thought that numbers and geometrical shapes were the eternal structure behind all reality (an idea also attractive to Plato), the astronomy of the Pythagoreans reflected their basic worldview. The planets (they knew of six) would have to be spaced at perfect distances, and the crystalline spheres upon which the planets and stars rotated in serene, eternal motion would be of proportionate sizes in order to create a musical harmony of the heavens. All of this was translated and taken up by Plato, Aristotle, and classical astronomy and incorporated into the Christian worldview of the Middle Ages. Of course, this image of the universe has been discarded, overturned by the development of modern physics and astronomy.

But has this hauntingly beautiful notion of a harmony of the spheres been completely falsified? Is there nothing we can accept from this world picture for our own time? Is this vision embedded only in the poetic imagination, being banished forever from science? In all sobriety, I will argue No: the harmony of the heavens can still be accepted. Indeed this harmony is essential to modern scientific cosmology, but of course in a very new and different way.

On this topic the most important figure to stand between the discarded image and our own time is the Lutheran astronomer and mathematician, Johannes Kepler. Kepler is one of the greatest figures in the history of astronomy, putting forth a new mathematical theory of the universe in defense of Copernicus and Galileo. Kepler first studied theology at Tubingen (M.A., 1591), but soon moved into mathematics, and eventually became the imperial mathematician of the Holy Roman Empire. Even though he was a solid evangelical believer and a brilliant scientist, Kepler was also deeply influenced by the Pythagorean-Platonic tradition, and spent much of his energy seeking to transform the older perspective on the heavens into terms and models fitting the new scientific discoveries of his day. Kepler was convinced that God is a mathematician, and the universe was founded upon solid geometrical principles. In his Harmonice Mundi (harmonics of the world-system), Kepler blended his Pythagorean presuppositions, his biblical faith in God as creator, and the latest results of astronomy into a new world picture. The planets are material bodies, just like earth, rather than a special quintessence. Their orbits about the Sun are elliptical, not perfect circles as the Greeks assumed.

Not everything Kepler argued for is correct, but he discovered several laws that still apply to our understanding of the geometry of the solar system. The principles Kepler first propounded fit the data of observation better than any other astronomical model available at that time. What was lost in this new astronomy, however, was the music of the spheres, viz., any basis for believing that there was actual sound made by the heavens. What Kepler put in its place was a harmony of geometrical proportion (which was the basis, remember, of Pythagorean musical theory). His Harmonice Mundi replaced musical harmony with the beauty of geometry. This basic position we can still affirm.

God the Creator is indeed a mathematician, and the heavens still move to the musical harmony of geometry. Two elements of modern astronomy and geometry make this point in a particularly powerful way: radio telescopy and fractal geometry. The invention of the radio telescope suggests that the stars are indeed still singing: but with a song only a radio can hear! The stars, galaxies, novae, and quasars all vibrate with living energy, which makes the radio telescope possible. Kepler and Pythagoras would, I think, be pleased.

Equally interesting is the development in only the last thirty years of a new branch of geometry: fractal geometry, founded by B. B. Mandelbrot. Fractals are distinct from the pure shapes of Pythagoras (square, circle, sphere, etc.) in being capable of describing many irregular-shaped objects, the kind we find in nature all around us. Fractal geometry is based upon self-similar patterns that repeat again and again, at smaller and smaller levels, creating patters of astonishing beauty. The world turns out to be fractal in many ways: clouds, snowflakes, shorelines, mountains. It even turns out that giant galactic clusters, the super-huge objects of modern astronomy, have a fractal shape and dimension. Kepler was right all along. God loves geometry, and there really is a true harmonice mundi in the amazing forces which adorn our beautiful cosmos.

In a few months, as we prepare for Christmas, we will no doubt sing once again the old hymn, "Silent Night." The night is indeed silent—not because the stars are not singing, but only because our ears cannot hear their eternal hymn. But we can tune in by radio. The universe does indeed dance to the harmonics of a universal geometry, just as Kepler labored to prove. It governs the movements of the planets, the steady spiral dance of the stars, and the fractal patterns of galaxy clusters. The stars and planets still move in a silent hymn to the majesty of their Creator, one whose deep structure lies in the beauty of geometry. Silent night, holy night indeed.

 

Alan Padgett teaches systematic theology at Luther Seminary in Minnesota. A lover of music more than a musician, his current research and writing focus on science and theology.

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