Buckminster Fuller/Pythagoras/Tony Conrad—beautiful, beautiful bubbles

"Looking back at the wake of my ship one day in 1917, I became interested in its beautiful white path. I said to myself, 'That path is white because of the different refractions of light by the bubbles of water—H₂0 (not H_π0). The bubbles are beautiful little spheres. I wonder how many bubbles I am looking at stretching miles astern?'

"I began to make calculations of how many bubbles there were per cubic foot of water. I began to find that in calculating the ship's white wake I was dealing in quintillions to the fourth power times quintillions to the fourth power or some such fantastically absurd number of bubbles. And nature was making those bubbles in sublimely swift ease!

"Any time one looks carefully at a bubble, one is impressed with the beauty of its structure, its beautiful sphereicity glinting with the colors of the spectrum. It is ephemeral—elegantly conceived, beautifully manufactured and easily broken.

"Inasmuch as the kind of mathematics I had learned of in school required the use of the XYZ coordinate system and the necessity of placing π in calculating the spheres, I wondered, 'to how many decimal places does nature carry out π before she decides that the computation can't be concluded?' Next I wondered, 'to how many arbitrary decimal places does nature carry out the transcendental irrational before she decides to say it's a bad job and call it off?' If nature uses π she has to do what we call fudging of her design which means improvising, compromising. I thought sympathetically of nature's having to make all those myriad frustrated decisions each time she made a bubble. I didn't see how she managed to formulate the wake of every ship while managing the rest of the universe if she had to make all those decisions. So I said to myself, 'I don't think nature uses π. I think she has some other mathematical way of coordinating her undertakings.'"

—Buckminster Fuller, Your Private Sky, p.457

While I am generally wary of overly rational explanations of the universe (they remind me too much of a Kepler-esque Music of the Spheres and often fail to take into account the limitations of our human perceptive capabilities, which govern everything we do), R. Buckminster Fuller's unique perceptive abilities and refusal to accept age-old mathematic theorums at face value resulted in his lifelong quest to create positive change in the world.

Most natural phenomena are so enormously complex they require abstractions like π for us to even begin to be able to understand them. Fuller's ruminating about bubbles, however, and his serious apprehension at the unnatural notion of π, raises serious questions about the levels of abstraction we can be comfortable with and also calls attention to other instances of irrationalty in our culture (such as the logarithmically equivalent 12-note scale used in Western music).

For Fuller, surrendering to irrationality so early in history (π was familiar to the Ancient Egyptians and Hebrews and was studied in depth by Archimedes and Ptolemy) resulted in the widespread use of inefficient building materials in Western culture. By studying the geometric structures of atoms and molecules, he was able to extrapolate highly-efficient architectural designs such as the geodesic dome (used to build the Climatron in St. Louis' Missouri Botanical Gardens [above]) and find new ways to project flat depictions of the globe to reinvent our understanding of the layout of our planet.

Filmmaker/violinist/composer/mathematician Tony Conrad's project Slapping Pythagoras similarly calls into question many of the preconceived notions that exist about the rational ordering of the musical pitch universe (which can be traced back to the Greek philosopher Pythagoras [above]). However, Conrad, who seems to be largely railing against the pseudo-mystical hyper-rationalism of his onetime collaborator LaMonte Young, falls more in favor of irrationality than I believe Bucky would be comfortable with (by demonstrating how rational orderings, when taken far enough, result in a high degree of irrationality--in the same way that the rational patterns of water molecules create spheres which require an abstraction like π to measure), though both are concerned about the societal ramifications that accompany accepting ancient scientific dogmas as fact.

For Conrad, blind acceptance of Pythagoras' theories and mythologies results in an undemocratic, top-down worldview that stifles creativity and causes oppression. For Fuller, failing to recognize rational orderings in the universe has caused mankind to live wastefully and incongruously with nature, which ultimately threatens our survival on this "spaceship" called Earth.