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I will never listen to ocean waves or view a beautiful sunset in quite the same way again. That is perhaps the greatest gift one can gain by delving into calculus: It is a whole new way of looking at the world, accessible only through the realm of mathematics. I looked out over the ocean that evening and saw a picture-perfect ocean sunset, but there was so much more that I missed. Sean looked out onto the same scene and saw the rich complexity of nature expressed in mathematical symbols, the fundamental abstract order lying just beneath the surface.

EPILOGUE

The Mimetics of Math

I’m very good at integral and differential calculus,

I know the scientific names of beings animalculous;

In short, in matters vegetable, animal, and mineral,

I am the very model of the modern Major General.

—GILBERT AND SULLIVAN,

The Pirates of Penzance

A pretty peach-hued building with an octagonal turret facing the Pacific Ocean is nestled on the edge of the University of California campus in Santa Barbara. This is the Kavli Institute of Theoretical Physics, where the world’s best physicists gather to exchange ideas that will usher in the revolutionary breakthroughs of tomorrow. The setting is idyllic, right next to the beach, so the siren song of sun and surf inevitably vies for my attention. On this particular day, the science is winning. There is a “blackboard lunch talk” by Joe Burns, a friendly and engaging astrophysicist from Cornell University. He is among the many scientists involved with analyzing data collected by NASA’s Cassini spacecraft orbiting Saturn to learn more about this distant planet—especially its mysterious rings.

It has been my custom during technical talks at KITP to focus on the concepts and let my eyes glaze over whenever an equation appears; much of the math is far too advanced for a fledgling calculus student to follow anyway. At first, Burns’s talk—while less technical than some of the brain-melting lectures I’ve attended—looks to be no exception. Inevitably, Burns turns to the blackboard and starts scratching out equations. But this time, I recognize the notation. Burns is taking a derivative. In a flash, I realize this means he is calculating a varying rate of change: the minute changes in velocity of the millions of icy particles (ranging from the size of seashells to surfboards) that orbit Saturn and make up its rings.

That lecture was a “mimetic moment” for me—the point where the abstract symbols in my calculus books finally began to make some sense, because I could connect them with something recognizable in the real world. In ancient Greece, mimesis referred to the artistic representation of nature, although two philosophers differed dramatically in their interpretations of the term. In one corner, I give you Plato, of cave-allegory fame, who believed in a divine realm of Ideal Forms. All creation, including Nature, was imitation in his eyes, and artistic imitation was by definition twice-removed from the Ideal. Ergo, all art (created fictions) is inferior to the “real” world, which is in turn inferior to the realm of Ideal Forms.

In the other corner, we have Aristotle, who took some time off from speculating that we see by shooting rays of light out of our eyes that reflect off nearby objects, to write his famed treatise Poetics. Aristotle was more forgiving of mimetic make-believe, for he thought that human beings have an inherent need to create artistic fictions as a form of catharsis, although he valued tragedy over comedy, via a rather convoluted process of reasoning. (He was wrong about how human vision works, too.) Our modern aesthetic still owes something to Plato and Aristotle, both of whom distinguished between diegesis, the act of telling, such as indirect narration of action or lecturing to students about calculus, and mimesis, the act of showing a character’s internal thoughts and emotions via external actions. It’s a dictum of modern entertainment: Show, don’t tell.

Anyone who’s taken Philosophy 101 could tell you that much.