The 32 films in Labocine's August selection THE POETRY OF MATH include both poetic and prosaic mathematical moments, and to carry the literary analogy further, fictionalized moments as well. All these are welcome. People like me who write about science know that showing non-mathematicians and non-scientists what math is all about, from its abstractions to its applications, is a big challenge. Displaying the richness of math in visual and cinematic terms can help people understand the prose, math applied to the sciences and to society; and the poetry, math as an innate human capacity and an adventure of the human spirit that has much in common with art. In this article I’ll talk about the poetry and how to convey it. I’ll move on to the prose in a second article.
In 1623, the great Renaissance figure Galileo Galilei, a founder of modern science, wrote that the book of nature is “written in the language of mathematics.” Math is a product of the human mind, but it has been inspired by nature and we in turn use it to analyze nature. Some think that seeing nature through a mathematical lens diminishes the appreciation of its beauty and wonder; but I think these insights only enhance the appreciation, part of the poetry of math.
That view is shared in the documentary Matter Patterns (2014, Olga Yakimenko). Combining a narrator’s comments with images of nature, the film illustrates the abstract idea of self-similarity, where the repeated application of simple rules produces much of the world’s enormous complexity. As the film’s images illustrate, self-similarity determines how trees branch and rivers flow, how color is distributed on butterfly wings and zebras, how biological cells change and combine. At the end of a stunning visual tour, the narrator restates the film’s premise that it’s “nonsense” to conclude that seeing nature mathematically “can somehow make beauty evaporate.” Instead, we can “develop understanding where there was once only seeing” – a strong argument for the power of mathematics to broaden our perception of the world and its beauty
Matter Patterns (2014, Olga Yakimenko)
Math can also carry us into worlds we have never seen. The documentary The Mathematics Engraver (2016, Quentin Lazzarotto) displays this magical ability through the work of an unusual artist. Patrice Jeener lives in the medieval village La Motte-Chalancon in south-eastern France, where for decades he has taken images from mathematics as the inspiration for his art.
The Mathematics Engraver (2016, Quentin Lazzarotto)
Any mathematical equation can be turned into an image by graphing it. Simple equations yield simple flat shapes such as circles. Intricate equations produce other-worldly three-dimensional shapes that curve, undulate, coil, and twist in ways rarely seen in actual natural or artificial objects. Some of these abstract mathematical objects represent shapes from imaginary worlds with four or more spatial dimensions, projected onto our 3D world. Jeener generates these fantastical shapes from equations and makes etchings of those he finds “pleasing.” He copies the image onto a copper sheet and gouges out its curves by small, meticulous bites of a sharp chisel. Then mounting the inked plate in a hand press, he prints replicas on paper until he is satisfied with the quality of the reproduction as the final print.
These visions of abstract math, shown in loving detail throughout the film, evoke varied reactions from mathematicians. One says that the prints are like special glasses “for seeing things that we couldn’t even imagine being able to construct or touch.” Another notes that the shapes Jeener finds artistically elegant are also mathematically elegant, in that they represent the most compact, efficient solutions to certain problems. Jeener shares another trait with mathematicians, who “enjoy getting away from reality” as one of them says. Jeener too escapes reality in his work. “I’d like to have lived in a space I’d thought up myself,” he says, as he imagines himself walking there. Mathematicians enter that world too, but it is Jeener who brings back pictures of his travels.
How and why does anyone enter that abstract world sufficiently to appreciate the poetry of math or create new poetry as a mathematician? Why do some people naturally take to math with pleasure and even pursue it professionally, whereas many others fear it? Logically Policed (2014, Damiano Petrucci) offers clues to answers and to the origins of mathematical abstraction.
Logically Policed (2014, Damiano Petrucci)
Interviewing mathematicians and math communicators, the film elicits their childhood experiences with numbers that inspired them, such as mentally making change in a family shop within the complicated English system of pounds, shillings and pence; or being challenged to use speed and distance to find arrival times for trips in the family car. Sara Santos, founder of MathsBusking which provides entertaining mathematical street experiences, explains how such encounters lead to higher levels. The first person to look at two stones, two sheep, and two grapes, she says, and realize that these disparate objects share “twoness,” was making a leap into mathematical abstraction. Because math is not a collection of equations but a mental activity, she adds, evolution has since then carried us to our present levels of math and its abstractions.
The power of abstraction to encompass a multitude of things gives pure math its real-world influence in telecommunications, laser technology, smartphones and more, as the interviewees point out. But learning these abstractions requires good math teaching, which is in short supply, and persistence from the student. To become a creative mathematician, it also requires what one interviewee calls “a thorn in the side,” the unbearable mental itch that makes a person relentlessly seek the answer to a math problem. We never know for sure that the answer, once found, will spark important new mathematical thought or lead to a significant real world result. But the interviewees present examples where exercises in pure math, such as proposing numbers involving the square root of -1, have had profound real outcomes.
That is where the poetry turns into prose, as I’ll discuss in Part 2.
About the author
Sidney Perkowitz writes frequently about science in film and other topics in popular science. His most recent books are Frankenstein: How a Monster Became an Icon; Physics: A Very Short Introduction; and Real Scientists Don’t Wear Ties: When Science Meets Culture. http://sidneyperkowitz.net, @physp