05 AUGUST, 2013
By: Maria Popova
“Like works of literature, mathematical ideas help expand our circle of empathy, liberating us from the tyranny of a single, parochial point of view.”
Daniel Tammet was born with an unusual mind — he was diagnosed with high-functioning autistic savant syndrome, which meant his brain’s uniquely wired circuits made possible such extraordinary feats of computation and memory as learning Icelandic in a single week and reciting the number pi up to the 22,514th digit. He is also among the tiny fraction of people diagnosed with synesthesia — that curious crossing of the senses that causes one to “hear” colors, “smell” sounds, or perceive words and numbers in different hues, shapes, and textures. Synesthesia is incredibly rare — Vladimir Nabokov was among its few famous sufferers — which makes it overwhelmingly hard for the majority of us to imagine precisely what it’s like to experience the world through this sensory lens. Luckily, Tammet offers a fascinating first-hand account in Thinking In Numbers: On Life, Love, Meaning, and Math (public library) — a magnificent collection of 25 essays on “the math of life,” celebrating the magic of possibility in all its dimensions. In the process, he also invites us to appreciate the poetics of numbers, particularly of ordered sets — in other words, the very lists that dominate everything from our productivity tools to our creative inventories to the cheapened headlines flooding the internet.
Reflecting on his second book, Embracing the Wide Sky: A Tour Across the Horizons of the Mind, and the overwhelming response from fascinated readers seeking to know what it’s really like to experience words and numbers as colors and textures — to experience the beauty that a poem and a prime number exert on a synesthete in equal measure — Tammet offers an absorbing simulation of the synesthetic mind:
Close your eyes and imagine a space without limits, or the infinitesimal events that can stir up a country’s revolution. Imagine how the perfect game of chess might start and end: a win for white, or black, or a draw? Imagine numbers so vast that they exceed every atom in the universe, counting with eleven or twelve fingers instead of ten, reading a single book in an infinite number of ways.
Such imagination belongs to everyone. It even possesses its own science: mathematics. Ricardo Nemirovsky and Francesca Ferrara, who specialize in the study of mathematical cognition, write that “like literary fiction, mathematical imagination entertains pure possibilities.” This is the distillation of what I take to be interesting and important about the way in which mathematics informs our imaginative life. Often we are barely aware of it, but the play between numerical concepts saturates the way we experience the world.
Sketches from synesthetic artist and musician Michal Levy's animated visualization of John Coltrane's 'Giant Steps.' Click for details.
Tammet, above all, is enchanted by the mesmerism of the unknown, which lies at the heart of science and the heart of poetry:
The fact that we have never read an endless book, or counted to infinity (and beyond!) or made contact with an extraterrestrial civilization (all subjects of essays in the book) should not prevent us from wondering: what if? … Literature adds a further dimension to the exploration of those pure possibilities. As Nemirovsky and Ferrara suggest, there are numerous similarities in the patterns of thinking and creating shared by writers and mathematicians (two vocations often considered incomparable.)
In fact, this very link between mathematics and fiction, between numbers and storytelling, underpins much of Tammet’s exploration. Growing up as one of nine siblings, he recounts how the oppressive nature of existing as a small number in a large set spurred a profound appreciation of numbers as sensemaking mechanisms for life:
Effaced as individuals, my brothers, sisters, and I existed only in number. The quality of our quantity became something we could not escape. It preceded us everywhere: even in French, whose adjectives almost always follow the noun (but not when it comes to une grande famille). … From my family I learned that numbers belong to life. The majority of my math acumen came not from books but from regular observations and day-to-day interactions. Numerical patterns, I realized, were the matter of our world.
This awareness was the beginning of Tammet’s synesthetic sensibility:
Like colors, the commonest numbers give character, form, and dimension to our world. Of the most frequent — zero and one — we might say that they are like black and white, with the other primary colors — red, blue, and yellow — akin to two, three, and four. Nine, then, might be a sort of cobalt or indigo: in a painting it would contribute shading, rather than shape. We expect to come across samples of nine as we might samples of a color like indigo—only occasionally, and in small and subtle ways. Thus a family of nine children surprises as much as a man or woman with cobalt-colored hair.
Daniel Tammet. Portrait by Jerome Tabet.
Sampling from Jorge Luis Borges’s humorous fictional taxonomy of animals, inspired by the work of nineteenth-century German mathematician Georg Cantor, Tammet points to the deeper insight beneath our efforts to itemize and organize the universe — something Umberto Eco knew when he proclaimed that “the list is the origin of culture” and Susan Sontag intuited when she reflected on why lists appeal to us. Tammet writes:
Borges here also makes several thought-provoking points. First, though a set as familiar to our understanding as that of “animals” implies containment and comprehension, the sheer number of its possible subsets actually swells toward infinity. With their handful of generic labels (“mammal,” “reptile,” “amphibious,” etc.), standard taxonomies conceal this fact. To say, for example, that a flea is tiny, parasitic, and a champion jumper is only to begin to scratch the surface of all its various aspects.
Second, defining a set owes more to art than it does to science. Faced with the problem of a near endless number of potential categories, we are inclined to choose from a few — those most tried and tested within our particular culture. Western descriptions of the set of all elephants privilege subsets like “those that are very large,” and “those possessing tusks,” and even “those possessing an excellent memory,” while excluding other equally legitimate possibilities such as Borges’s “those that at a distance resemble flies,” or the Hindu “those that are considered lucky.”
Reading Borges invites me to consider the wealth of possible subsets into which my family “set” could be classified, far beyond those that simply point to multiplicity.
Tammet circles back to the shared gifts of literature and mathematics, which both help cultivate our capacity for compassion:
Like works of literature, mathematical ideas help expand our circle of empathy, liberating us from the tyranny of a single, parochial point of view. Numbers, properly considered, make us better people.
The rest of the essays in Thinking In Numbers, ranging from fascinating biographical anecdotes to speculative fiction imagining young Shakespeare’s first arithmetic lessons in zero, are equal parts mind-bending and soul-stirring, and altogether delightful in innumerable ways. Complement it with Paul Lockhart’s multisensory exploration of the whimsy of math, then revisit the extraordinary feats of other autistic savants, from Gregory Blackstock’s astonishing visual taxonomies to Gilles Trehin’s remarkable imaginary city.
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