snowflakes and pomegranates
A young Johannes Kepler stands on the Charles Bridge in Prague, his breath clouding as snowflakes slalom their way down from heavens governed by the mathematics that he, decades later, would so famously unfurl.
To the horror of both the Church and the heretic Aristotelians, Kepler’s three eponymous laws would state that not only did the planets of our solar system orbit in ellipses rather than perfect circles, they didn’t even care to centre themselves around the sun itself (let alone the Earth). Instead, the annual ebb and flow of the seasons, the length of our night, our day, our king tides and our harvest moons were all governed by the distance between two barely symmetrical and blasphemously insignificant foci.
But, for now, the Earth still turns in perfect circles. It is 1611, and Kepler was working as the imperial astronomer for Emperor Rudolph II, who had neglected to pay his salary and so despite his illustrious title, Kepler was facing the predicament of postgraduates from time immemorial - he was broke.
As a snowflake alighted on his sleeve, Kepler paused, considering the unequivocal six-fold symmetry. The delicate, ephemeral balance between absolute, almost divine geometrical precision, and complete randomness. A fleeting solid form, bridging the vaporous cumuli of winter with the thawing rivers of spring.
Returning home, Kepler began working on an essay, a meditation on the snowflake, as a suitably parsimonious gift for a friend.
Writing in Latin, as was customary at the time, the word for snowflake is nix. A star fallen from the heavens, appropriate for Christmas time, and a subtle play on words for the polylingual Kepler, whose native Low Germanic language uses the word nix to mean nothing. After all, he muses in the essay’s dedication, what do astronomers and mathematicians “who have nothing and receive nothing have to give, but nothing?”
Rather than remaining preoccupied with this disconsolately poetic thought, the snowflake had precipitated more pressing questions for Kepler to explore.
“There must be some definite cause why, whenever snow begins to fall, its initial formations invariably display the shape of a six-cornered starlet”. Kepler was well aware that metallic salts and minerals form cubic, rhombic or even icosahedral crystals in predictable, but inexplicable ways.
There are only three shapes that can tesselate cover a two dimensional plane, the square, triangle, and, most commonly found in nature, the hexagon. Kepler notes that honeycombs each share six walls with their neighbour, maximising the space within the cell whilst minimising the material needed to build the walls. Offset at the rear, each comb joins four others, forming the same three dimensional shape as pomegranate seeds, basalt columns or leucosomes - the tiny crystals in the skin cells of iridescent fish. In fact, any vaguely spherical objects, when pressed together, will form these rhomboid hexagons, a theory still known as Kepler’s Conjecture.
Snowflakes, however, don’t need to pack together; they’re not concerned with efficiency, and they never form in three dimensions. Seeking sacred geometries throughout the cosmos would soon become Kepler’s life’s work, but the mysterious force behind those six corners was something he never managed to unfurl. But he was right to recognise the quiet symmetry of the snowflake as something more than merely nothing. Even today, despite our best efforts to understand the innate intermolecular forces that guide the arrangement of these ephemeral, aqueous crystals, we can’t say for sure that they aren’t indeed an echo of something more divine.
Kepler, Johannes. 1966. The Six-Cornered Snowflake. Edited and translated from the Latin by Colin Hardie, with essays by L. L. Whyte and B. F. J. Mason. Oxford, U.K.: Oxford University Press.