By Daniel Tammet from Thinking in Numbers
Outside it is cold, cold. Ten degrees below give or take. I step out with my coat zipped up to my chin and my feet encased in heavy rubber boots. The glittering street is empty; the wool-gray sky is low. Under my scarf and gloves and thermals I can feel my pulse begin to make a racket. I do not care. I wait.
A week before, the trees’ bare branches stood clean against blue sky. Now the sight of falling snowflakes makes me shiver; it fills the space in my head that is devoted to wonder. How beautiful they are, I think. When will they stop? In an hour? A day? A month?
The neighbors, who’ve lived in Ottawa far longer than I, tell me they have not seen this snowfall’s like in a generation. Shovels in hand, they dig paths from their garage doors out to the road. The older men affect expressions of both nonchalance and annoyance, but soon faint smiles form at the corners of their wind-chapped mouths.
Granted, it is exhausting to trudge to the shops. Every step seems to take an age. Hot under my onion layers of clothing, I carry a shirtful of perspiration back into the house. Wet socks unpeel like plasters from my feet; the warm air smarts my skin. Later, around a table, in the dusk of a candlelit supper, my friends and I exchange recollections of winters past. We talk sleds and toboggans and fierce snowball fights. I recall a childhood memory from London: the first time I heard the sound of falling snow.
“What did it sound like?” the evening’s host asks me.
“It sounded like someone slowly rubbing his hands together.”
Yes, my friends say, laughing. Yes, we can hear what you mean.
One man laughs louder than the others. I do not catch his name; he is not a regular guest. I gather he is some kind of scientist.
“Do you know why we see snow as white?” he asks. “It is all to do with how the sides of the snowflakes reflect light.” All the colors in the spectrum, he explains to us, scatter out from the snow in roughly equal proportions, which we perceive as whiteness.
Now our host’s wife has a question. “Could the colors never come out in a different proportion?”
“Sometimes, if the snow is very deep,” he answers. In which case, the light that comes back to us can appear tinged with blue. “And sometimes a snowflake’s structure will resemble that of a diamond,” he continues. Light entering these flakes becomes so mangled as to dispense a rainbow of multicolored sparkles.
“Is it true that no two snowflakes are alike?” This question comes from the host’s teenage daughter.
It is true. Every snowflake has a basic six-sided structure, he says, but its spiraling descent sculpts each in a unique way: The minutest variations in air temperature or moisture make all the difference.
Still, researchers classify snowflakes by size, shape, and symmetry. For example, some snowflakes are flat and have broad arms, resembling stars, so that meteorologists speak of stellar plates, while those with deep ridges are called sectored plates. Branchy flakes, like those in Christmas decorations, go by the term stellar dendrites—from the Greek word for tree.
Sometimes snowflakes fall as columns of ice, which are called needles. Some, like conjoined twins, show 12 sides instead of the usual six, while others resemble bullets. Other possible shapes include the cup, the sheath, and arrowhead twins.
We listen wordlessly to the scientist’s explanations. Our rapt attention flatters him. His white hands, as he speaks, draw the shape of every snowflake in the air.
That night, the snow reaches into my dreams. My warm bed offers no protection from my childhood memories of the cold. I dream of a distant winter in my parents’ garden: The powdery snow, freshly fallen, was like sugar to my younger brothers and sisters, who hastened outside with shrieks of delight. I hesitated to join them, preferring to watch from the safety of my bedroom window. But later, after they had all wound up their games and headed back in, I ventured out alone and started to pack the snow. Like the Inuit (who call it igluksaq—house-building material), I wanted to build myself a shelter. The crunching snow gradually encircled me, the walls rising higher until at last they covered me completely. My boyish face and hands smeared with snow, I crouched deep inside feeling sad and feeling safe.
In the morning, my friends call up to my room. “We are ready and waiting!” I am the English slowpoke, unaccustomed to this freezing climate, to the lethargy it imposes on the body.
London’s wet slush was quick to blacken, but here the snow is incandescent white. Canadians have no fear of winter. Stockpiling milk and bread is unheard-of. Traffic jams, canceled meetings, and energy blackouts are rare. The faces that greet me downstairs are smiling. They know that the roads will have been salted, that their letters and parcels will arrive on time, that the shops will be open.
In the schools of Ottawa, children extract snowflakes from white sheets of paper. They fold the crisp sheet to an oblong, and the oblong to a square, and the square to a right-angled triangle. With scissors, they snip the triangle on all sides; every pupil folds and snips the paper in his own way. When they unfold the paper, different snowflakes appear, as many as there are children. But every one has something in common: They are all symmetrical. Shorn of nature’s imperfections, the children’s flakes represent an ideal.
At the University of Wisconsin, mathematician David Griffeath has improved on the children’s game by modeling snowflakes on a computer. In 2008, Griffeath and his colleague Janko Gravner produced an algorithm that mimics the many physical principles that underlie how snowflakes form. The project proved slow and painstaking. It can take up to a day for the algorithm to perform the hundreds of thousands of calculations necessary for a single flake. Parameters were set and reset to make the simulations as lifelike as possible. But the end results were extraordinary. On the mathematicians’ computer screen shimmered a galaxy of three-dimensional snowflakes: elaborate, finely ridged stellar dendrites and 12-branched stars, needles, prisms of every known configuration, and others resembling butterfly wings, which no one had identified before.
My friends take me on a trek through the forest, where flakes fall intermittently and sunlight glistens on hillocks of snow. We tread slowly, rhythmically, across the shifting surfaces, which squirm and squeak under our boots.
Whenever snow falls, people look at things and suddenly see them. Lampposts and doorsteps and tree stumps and telephone lines take on a whole new aspect. We notice what they are and not simply what they represent. Their curves, angles, and repetitions command our attention. Visitors to the forest stop and stare at the geometry of branches, of fences, of trisecting paths. They shake their heads in silent admiration.
A voice somewhere says the river Hull has frozen over. I disguise my excitement as a question. “Shall we go?” I ask my friends. For where there is ice, there are inevitably skaters, and where there are skaters, there is laughter and lightheartedness and stalls selling hot pastries and spiced wine. We go.
The frozen river brims with action: Parkas pirouette, wet dogs give chase, and customers line up in queues. The air smells of cinnamon. Everywhere, the snow is on people’s lips: It serves as the icebreaker for every conversation. Nobody stands still as they are talking; they shift their weight from leg to leg, stamp their feet, wiggle their noses, and exaggerate their blinks.
The flakes fall heavier, whirling in the wind. Human noises evaporate; now nobody moves.
Snow comes to earth and forms snow lampposts, snow trees, snow cars, snowmen. Nothing is indifferent to its touch. New worlds appear and disappear, leaving their prints upon our imagination.
Daniel Tammet was diagnosed with autistic savant syndrome at the age of 24. He has subsequently written bestselling books about mathematics, neuroscience, and living with Asperger’s syndrome.
