Spirals: Variations on a Theme

Although music like Beethoven's Fifth Symphony sounds complicated, it's built around simple themes, like the opening "tah-tah-tah-tum:"


(From "Symphony No. 5 (Beethoven)," Wikipedia, used w/o permission.)

I see the same sort of 'variations on a theme' in nature, partly because I know my culture's history. Comparing nature's regularities to musical harmony is hardly a new idea.

Pythagorean Lore: Saved by the Pirates

Pythagoras noticed the world's regularities and came up with "music of the spheres." He also saw odd numbers as masculine, even numbers as feminine; and founded an academy called Order of the Pythagoreans.

Ancient Greece flourished, then joined the Neo-Sumerian Empire in history's archives. Some Pythagorean didn't follow their order's habit of not writing stuff down: which allows us to know something about Pythagoras. I suspect that what they did was a little like the media pirating that goes on today, and that's another topic.

Music of the Spheres: Renaissance Style

(From Wikimedia Commons, used w/o permission.)
"Engraving from Renaissance Italy showing Apollo, the Muses, the planetary spheres and musical ratios."
(Wikipedia)

This pirated Pythagorean lore reached Europe about half a millennium back, along with the works of Aristotle and the habit of copying ancient Roman architecture. Many Europeans shared the Pythagorean enthusiasms for order, harmony, and mystic numbers. Some of what they came up with was: imaginative.

More than two dozen centuries after Pythagoras lived and died, we've learned that stars don't sit on a crystal sphere, and that planets don't float in the air. Pythagoras wasn't all wrong, though.

Kepler discovered that the size and period of a planet's orbit has a sort of harmony, although it's not an exact square-cube relationship. For example, Mercury's orbit doesn't work quite the way Kepler and Newton expected, and that's almost another topic.

Order and Beauty

Observing this creation's order and beauty can help us learn about God. (Catechism of the Catholic Church, 32)

Granted, some folks look at life's wonderful complexity and the awesome vastness beyond our galaxy: and apparently decide that because life is complex and the universe is big, God can't exist.

That notion is fairly new, but it's been fashionable for several generations now. I think it's silly, but I also think that God doesn't look like Charleton Heston's Moses. More topics. (May 2, 2012)

My faith doesn't depend on keeping up with science news, but it's not threatened by what we're learning about the universe. If anything, knowing how unimaginably vast and ancient this universe is helps me appreciate the infinite power and wisdom of God.

Science and technology, learning about this creation and developing new ways to use it, are part of being human. What we decide to do with our knowledge is where ethics come in. Still more topics. (Catechism, 2292-2295)

Origins, Discoveries, Wisdom

That quote is from Wisdom 7:15-18.

I don't expect science to answer questions about why we're here: but I'm about as sure as I can be that it's okay for us to use our brains in a systematic study of this wonder-filled creation:

"The question about the origins of the world and of man has been the object of many scientific studies which have splendidly enriched our knowledge of the age and dimensions of the cosmos, the development of life-forms and the appearance of man. These discoveries invite us to even greater admiration for the greatness of the Creator, prompting us to give him thanks for all his works and for the understanding and wisdom he gives to scholars and researchers. With Solomon they can say: 'It is he who gave me unerring knowledge of what exists, to know the structure of the world and the activity of the elements. . . for wisdom, the fashioner of all things, taught me.'¹²¹"
(Catechism, 283)

Variations on a Theme: Spirals

Getting back to 'variations on a theme:' I see patterns repeated at a dizzying range of scales throughout the universe.

For example, we see spherical shapes in some bacteria, bubbles, and stars. That's because the most efficient shape for enclosing an area is the sphere: at least when you're working with three spatial dimensions.

Is God inordinately fond of spheres? I don't think so. I see this as another example of order and structure in the universe: a reflection of the rational and orderly Creator.

Another often-repeated visual theme in this universe is the spiral. Despite what you've probably read, nautilus shells aren't quite exactly logarithmic spiral: but they're close. So are Fibonacci spirals, and that's yet another topic.

I'm not surprised that spirals we see in nature don't all follow a logarithmic spiral's precise geometric progression: any more than I'm surprised that Beethoven didn't keep repeating the same eight notes throughout his fifth symphony.

Finally, a few spirals:


(From Newsdesk, Newsroom of the Smithsonian, used w/o permission.)


(From Shutinc, via Wikimedia Commons, used w/o permission.)


(From Brandon Weeks (August 7, 2004), via Wikimedia Commons, used w/o permission.)


(From Astronomy Picture of the Day, FORS, ESO, NASA, used w/o permission.)

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