Margaret Wertheim is a science writer and artist who founded the Institute For Figuring, an organization through which she creates projects at the intersection of mathematics, science and art. She is the author of “Pythagoras Trousers,” a cultural history of physics and women.

In 1609 Johannes Kepler wrote a curious tale about a trip to the moon, hailed now as one of the first works of science fiction. Titled “Somnium,” or “The Dream,” the tale has its young astronomer protagonist encountering a race of lizard beings on the moon who have developed technology tailored to the conditions of their lunar environment, a radical attempt on Kepler’s part to envision what science might produce on an alien “world.” Looking up at the Earth, these moon creatures believe that our orb is revolving around them, much as many of Kepler’s contemporaries believed that the sun was revolving around the Earth. Through the lens of fiction, Kepler took the bold step of trying to convey to late-Renaissance readers the scientific claim that how we see the universe is a matter of perspective. What we see is dependent on where we see from.

Maria Popova, creator of the much-admired Brain Pickings blog, begins her new book, “Figuring,” with a chapter about Kepler, and the resonances she sees rippling out from his surreal personal and professional life to a litany of figures in astronomy and the arts ever since.

With nearly 900,000 Twitter followers, Popova is a member of a rare pantheon of “influencers” for the brainiac crowd. Miraculously, she makes a living writing a blog about science, literature, philosophy, feminism and whatever else takes her voracious and generous fancy. Full disclosure: I’ve been a Brain Pickings supporter for years.

When I read that the subject of her first long-format book was “figuring,” my interest was piqued. Not only because I’m a fan of her site but because figuring — a multifaceted, multidisiplinary term that spans the domains of science, mathematics, the arts and human cognition — has been at the core of my own work for decades. In 2003, I started an organization called the Institute for Figuring, whose mission is to engage audiences with the aesthetic and poetic dimensions of science and mathematics. One inspiration for this practice has been Kepler, among the foremost figurers in science.

For Popova, Kepler becomes a kind of ur-figure, a man whose multiplexed life, entwining science, aesthetics and theology, she uses to set the stage for a cast of later historical characters who also crossed discplines and boundaries in pursuit of truth, beauty and a life well-lived.

In a book titled “Figuring,” it would be hard to find a more fitting muse. Kepler wrote a treatise on the shapes of snowflakes and made a mathematical conjecture about the optimal way to stack spheres, which was finally proved in 1998. Most famously, he figured out the laws of planetary motion. These cosmic rules, which include the fact that planets travel in ellipses rather than circles around the sun, overthrew 2,000 years of astronomical dogma and paved the way for Newton’s law of gravity and his subsequent cosmic synthesis.

Though Kepler isn’t nearly as famous as Newton or Copernicus, he is their equal — and arguably a more important figure than Copernicus. It was Kepler who understood first that mathematical figures hidden in the dance of the planets implied that these bodies are driven by real physical forces, thereby making him the first true astrophysicist.

Kepler is beloved by historians for the powerful mixing in his life of mathematical rigor and aesthetical play. He did nothing by halves, including defending his mother from accusations of witchcraft, a charge that he believed was precipitated by his “Dream” book. At the end of a long and painful process his mother was saved, but her treatment in prison weakened and finally killed her. Popova movingly reports that this led Kepler to another leap of perspectival insight: that, being female, his mother had not had the benefit of an education and was thus at the mercy of “learned” men. As Popova writes, “The difference between the fates of the sexes, Kepler suggests, is not in the heavens but in the earthly construction of gender.”

Popova’s book, which from here focuses mainly on female stories, is about the lives of some remarkable women — all undaunted thinkers — who overcame immense obstacles and “the earthly construction of gender” in their time to make astronomical discoveries, to write poetry, paint pictures and found the environmental movement.

Chief among them are Kepler’s intellectual descendents, astronomers Maria Mitchell and Caroline Herschel, mathematician Mary Somerville, marine biologist/environmentalist Rachel Carson, writer/critic Margaret Fuller, artist Harriet Hosmer, and poet Emily Dickinson — women who all embody the landmark assertion of 17th-century philosopher Francois Poullain de la Barre that “the mind has no sex.”

Popova’s “Figuring” is an intricate tapestry in which the lives of these women, and dozens of other scientific and literary figures, are woven together through threads of connection across four centuries, linking one to another in unexpected chains through mutual friends, serendipity, meetings, letters and even lovers. It is as if in her vast reading of source materials, especially original correspondence, she has fitted her brain with a set of filters to sift out references that might link any of her figures to any other. One is reminded of the 18th-century polymath Athanasius Kircher’s declaration: “The world is bound by secret knots.”

Most overtly, the “figures” of Popova’s narrative are the human beings whose stories she uses to illuminate her thesis that, as per Kepler’s journey of triumph and terror, life is lived for us all “between chance and choice.”

But the word “figure” has other connotations, too, and one suspects that Popova may have been drawn to these further dimensions of its meaning from a quote in Maria Mitchell’s diary. While on her first trip to Europe in 1857, Mitchell, by then a famous astronomer and the only female member of the American Astronomical Society, met with many of her scientific, literary and artistic heroes. Between them all, she wrote, “figures are a common language.”

The languages that nonhuman figures speak are varied in the extreme. In mathematics, figures are numbers and geometric forms. Figures are also diagrams in scientific texts. In the Middle Ages, what became perspectival imagery was originally called “geometric figuring.” Humans have figures that painters draw and sculptors render in marble. In literature, there are figures of speech and figures of fun. Drama has its tragic figures and comic figures. Dancers at cotillion balls spin figures across the floor, while the floor itself may be figured with parquet patterns, that mathematicians study as “tessellations.” As cognitive beings we are constantly engaged in figuring things out, and it is a pleasure to observe the mental subtleties of Popova’s formidably gifted characters as each of them figures the world anew.

In “Figuring,” we are thrust into a waltz of exquisitely honed minds — most of them belonging to women, many of them sexually queer — all insisting on living to their fullest. “Mingle the starlight with your lives,” Mitchell exhorted her students at Vassar. Kepler, the patron saint of cosmic figuring, would have agreed.


By Maria Popova

Pantheon. 578 PP. $30