Figuring

by Maria Popova

How can we know this and still succumb to the illusion of separateness, of otherness? This veneer must have been what the confluence of accidents and atoms known as Dr. Martin Luther King, Jr., saw through when he spoke of our “inescapable network of mutuality,” what Walt Whitman punctured when he wrote that “every atom belonging to me as good belongs to you.”

We spend our lives trying to discern where we end and the rest of the world begins.

History is not what happened, but what survives the shipwrecks of judgment and chance.

How, in this blink of existence bookended by nothingness, do we attain completeness of being?

There is no static, solid self. Throughout life, our habits, beliefs, and ideas evolve beyond recognition. Our physical and social environments change. Almost all of our cells are replaced. Yet we remain, to ourselves, “who” “we” “are.”

How many revolutions does the cog of culture make before a new truth about reality catches into gear?

Newton would later refine Kepler’s three laws of motion with his formidable calculus and richer understanding of the underlying force as the foundation of Newtonian gravity. In a quarter millennium, the mathematician Katherine Johnson would draw on these laws in computing the trajectory that lands Apollo 11 on the Moon. They would guide the Voyager spacecraft, the first human-made object to sail into interstellar space.

those who stand to gain from the manipulation of truth often prey on those bereft of critical thinking.

Kepler was unconsoled by the decree—perhaps he knew that policy change and cultural change are hardly the same thing, existing on different time scales. He spent the remaining years of his life obsessively annotating The Dream with two hundred twenty-three footnotes—a volume of hypertext equal to the story itself—intended to dispel superstitious interpretations by delineating his exact scientific reasons for using the symbols and metaphors he did. In his ninety-sixth footnote, Kepler plainly stated “the hypothesis of the whole dream”: “an argument for the motion of the Earth, or rather a refutation of arguments constructed, on the basis of perception, against the motion of the Earth.” Fifty footnotes later, he reiterated the point by asserting that he envisioned the allegory as “a pleasant retort” to Ptolemaic parochialism.

The night after the funeral, a full moon passed through Earth’s shadow in a lunar eclipse governed by eternal forces deaf to human words—fundamental truths of nature, which Kepler had spoken in the native tongue of the universe: mathematics. Three hundred thirty-nine years later, his Dream would come true as the first human foot stepped onto the Moon, leaping humankind via a trajectory calculated by his laws.

The Copernican model was the first major idea to challenge our self-importance. The challenge has taken many guises in the centuries since, as new world orders have been introduced—from evolutionary theory to civil rights to marriage equality, which society has initially met with antagonism comparable to that shown by the denizens of Kepler’s hometown.

Edgeworth was one of a handful of women, alongside Joan of Arc, Sappho, and several saints, whom Auguste Comte included in his Calendar of Great Men—a landmark cultural biography of 559 world-changing minds, “worthiest of all ages & nations,” spanning from Euclid and Pythagoras to Kepler and Galileo to Beethoven and Milton. It was part of Comte’s proposal for a “positivist” solar calendar to replace the Gregorian, comprising thirteen months of twenty-eight days, each day named not for a religious saint but for a hero of secular culture—a scientist, poet, philosopher, painter, inventor, explorer.

Galileo had made known the existence of the satellites of Jupiter, the belts of Saturn, the inequalities of the moon’s surface, and had declared with fear and trembling, which time showed to be well-grounded, the motion of the earth.

Maria Mitchell had written in her diary: He who has never failed somewhere, that man can not be great. Failure is the true test of greatness.

We navigate the unknown frontiers of the social universe through a sextant of existing relationships—nearly every new person we meet is within only a few degrees of separation from someone we already know. But every once in a while, pure chance intercedes to remind us that whatever structures of control we may put into place, however much we may mistake the illusion of choice for the fact of choice, randomness is the reigning monarch of the universe.

John Herschel coined the word photography in 1839, the year Margaret Fuller launched her “Conversations,” in his correspondence with Henry Fox Talbot—a onetime aspiring artist turned amateur inventor and polymath.

“Best Witchcraft is Geometry,” Emily Dickinson would write.

Pythagoras, whose identity is as mysterious as Shakespeare’s, his persona as adrift in the lacuna between myth and truth, set into motion the golden age of mathematics with the development of numerical logic—the foundation of mathematical physics. His ideas went on to influence Plato, Copernicus, Descartes, Kepler, Newton, and Einstein. To Pythagoras, numbers were more than tools for counting and computing. He studied their properties and relational patterns, seeking to extract from them some larger revelation about the nature of reality, the way a poet uses words not merely to denote and describe the world but to evoke and wrest meaning via symbolic logic.

Alongside his mathematics, Pythagoras coined the word philosopher to describe himself as a “lover of wisdom” and invented a whole symbolic language of mysticism. His progressive views on social reform led him to flee the tyrannical rule of his native Samos. When he settled in the Greek colony of Croton, he founded a philosophical school whose sect of disciples, known as the Pythagoreans, originated a novel conception of the universe—they placed at its center a ball of fire more than a millennium before Copernicus proffered his heliocentric model. In fact, in his letter to the Pope, Copernicus cited the Pythagoreans as his inspiration for upending the Ptolemaic system. In another highly unusual model for their time, the Pythagoreans admitted women. One of them, Hypatia of Alexandria, became the world’s first known woman astronomer, predating Caroline Herschel by fourteen centuries. A millennium and a half before Kepler’s Harmonices Mundi, Pythagoras discovered the relationship between musical harmony and the mathematical harmony of numbers. In his day, the most widespread musical instrument was the tetracord—the Hellenic four-string lyre. Musicians had no standardized system of tuning their instruments and only an intuitive sense of how to produce harmonious melodies rather than discord, with no understanding of the underlying tonal patterns. According to the fourth-century Syrian scholar Iamblichus, who became Pythagoras’s foremost biographer, Pythagoras took it upon himse...

A century and a half later, I find a tattered paperback copy of Little Women in my grandmother’s library in Bulgaria, among the books that belonged to her father, Georgi. I never met my great-grandfather—he died six days before I was born—but I got to know him through my grandmother’s stories. An astronomer and mathematician born at the dawn of the twentieth century, into Bulgaria’s nascent monarchy after five hundred years under the Ottoman yoke, he lived through two world wars only to see his homeland, ravaged by centuries of oppression and decades of war, succumb to Communism in the 1940s. When the Iron Curtain dropped, the dictatorial government took great pains to silence any cultural signal from the other side.

In four billion years, our own star will follow its fate, collapsing into a white dwarf. We exist only by chance, after all. The Voyager will still be sailing into the interstellar shorelessness on the wings of the “heavenly breezes” Kepler had once imagined, carrying Beethoven on a golden disc crafted by a symphonic civilization that long ago made love and war and mathematics on a distant blue dot.

But until that day comes, nothing once created ever fully leaves us. Seeds are planted and come abloom generations, centuries, civilizations later, migrating across coteries and countries and continents. Meanwhile, people live and people die—in peace as war rages on, in poverty and disrepute as latent fame awaits, with much that never meets its more, in shipwrecked love. I will die. You will die. The atoms that huddled for a cosmic blink around the shadow of a self will return to the seas that made us. What will survive of us are shoreless seeds and stardust.