Let it snow, let it snow, let it snow!
“Just then, by happy occurrence, some of the vapour in the air was gathered into snow by the force of the cold, and a few scattered flakes fell on my coat, all six-cornered, with tufted radii. By Hercules! Here was something smaller than a drop, yet endowed with a shape.” from Strena seu de nive sexangula (The six-cornered snowflake) (1611) by Johannes Kepler (1571-1630)
“But today the Royal Astronomer’s late, hunched there, his mind aswirl with more, than whimwhams of an emperor – all bemused by signatures of something from above: the daedal snowflake crystaling in six.” from The Six-Cornered Snowflake, A Poem by John Frederick Nims (1913-1999)
The first snowfall marks a complete change in the world. The fresh, white blanket transforms all – a decided upgrade from the dreariness of bare branches and faded flora. Everything feels renewed – crisp and clean – with a sharpness of light even in the short, dull days of early winter.
The dogs welcome the first snowfall with overwhelming exuberance.
Snouts plough through the new-laid cover, followed by snorts and spins, rolls and bows. Snow flies with explosive gallop runs, quick turns, and deliberate sliding stops. Playful, inviting barks require little interpretation – “Chase me! Chase me!”
The dogs’ behaviour lifts the spirits, and makes the world feel a wholly better place.
It’s hard to know precisely what it is about this first snowfall that resonates so deeply with the dogs. Perhaps it is the marked change after the tedium of late autumn. Perhaps it is the fact that it indicates the passage of time – the exit from one season and the start of another – a time when new behaviours are warranted with the new conditions. Perhaps this is something deeply ingrained in their biology – the necessity to default to playful behaviour when conditions are about to be the most adverse, and resources their most limiting – a time when bonding, camaraderie, and teamwork are most valuable. Perhaps it is the brightening of the world at a time when it is at its darkest – a quality of light that stimulates a brain dulled by both short days and a sun that sits low in the sky.
Perhaps it is these things, combined with an infectiousness of spirit with their human companions. It seems certain that the feelings of elation and playfulness induced by the first snowfall are shared amongst humans and non-human animals alike.
At first snowfall, humans, adults and children together, seem energised. Seriousness gives way to frivolity as toboggans are ridden, skis strapped on, skates laced up, snowmen take shape, and snowballs flung. The trudge of autumn is displaced with a merry bound into winter.
But the first snowfall has another effect on humans.
Faces turn skyward for fluttering flakes to alight. Eyelashes and eyebrows are lightly dusted as the snow swirls from above. Tongues are outstretched to catch the fleeting frozen droplets as they make their descent.
Our enchantment is well founded, as snowflakes are a thing of wonder.
Just over 400 years ago, a 40-year-old astronomer turned his mind to the wonder of snowflakes.
The astronomer was no less than Johannes Kepler, who at that time was the imperial astronomer to the Holy Roman Emperor, Rudolph II. The emperor had been remiss in paying Kepler, who was therefore on the lookout for inexpensive ways to gift his friends during the holiday season. Good fortune in this regard literally fell his way while crossing a bridge in Prague – when a snowflake tumbled onto his coat. Kepler was bemused by this snowflake, and used his musings on it to construct a scholarly gift like no other – a delightful treatise entitled “Strena seu de nive sexangula”. The title, like the rest of the tiny book, was written in Latin, and translates as “The six-cornered snowflake”. Kepler viewed the snowflake and his ponderings as the ideal gift, as the snowflake came from the heavens, like a fallen star.
Kepler was captivated by the shape of the snowflake. Like other individual snowflakes, it had six sides. Why six? Why not five or seven? What were the natural laws governing this shape?
To derive an answer, Kepler let his thoughts swing widely.
Kepler knew that snowflakes emerged from water vapour. What was it about water vapour that would allow it to aggregate into a six-sided shape? How might the constituents of a vapour condense so as to make a shape?
Kepler observed that there were only certain shapes in nature that could aggregate optimally with no spaces between them to give rise to a large structure. Consider the honeycomb, for example. Like triangles, and squares, the hexagons of the beehive could be stacked together so as to leave no spaces between them. Is this how the snowflake arose?
The honeycomb held special appeal to Kepler. The hexagonal cells of the honeycomb might have something to say about the six-sided nature of the snowflake. In considering the honeycomb further, Kepler observed that the hexagon was not the only shape at play to give rise to a beehive. Strikingly, at the end of each hexagonal cell of the honeycomb, the walls were pared back to that each cell end connected with four other hexagonal cells. This was achieved through the creation of a rhombus shape at the end of each cell.
Kepler took inspiration from the rhombus.
Might it be possible to create a three dimensional object with no spaces by using rhombi to construct the object? That is, could rhombi fill three-dimensional space in the same way that squares, triangles and hexagons could be stacked to fill two-dimensional space? The short answer is yes, they can.
Using rhombi called rhombic dodecahedrons, Kepler could create three-dimensional solids similar in appearance to other shapes observed in nature, like the honeycomb. Kepler specifically considered the arrangement of pomegranate seeds. Seeds from the pomegranate could be packed closely together with no spaces between them, effectively following the structure that Kepler observed with the packing of rhombic dodecahedrons. Indeed, even spheres could be packed together tightly in this manner if they were at right angles to each other in the arrangement. That is, even spheres could fill three dimensional space, provided they were configured in a manner that was akin to the rhombic dodecahedrons.
Kepler proposed that snowflakes, and indeed other crystals, might arise in a similar manner, simply by packing smaller components together in such an optimised manner. While he had no idea of the precise features of water vapour that would enable this, or the precise nature of the forces that might bring the smaller components together, he imagined that processes like the packing of rhombic dodecahedrons might come into play. He speculated that the removal of heat from water vapour was crucial in making the process occur for snowflakes. What’s more, he proposed that the optimised packing of smaller components to create larger solids may be a common occurrence in nature.
We now know that Kepler was right on all counts. Kepler’s hypothesis on optimised space-filling by spheres, known as the Kepler conjecture, has been proven and has been a useful means to account for the generation of three-dimensional solids from spherical constituents. Kepler’s conjecture not only explains the formation of snowflakes but almost all crystals known.
We now know that snow is made of water, H2O, comprising two atoms of hydrogen and one atom of oxygen. Water molecules organise into a hexagonal lattice. As predicted by Kepler, this hexagonal substructure is what determines the overall six-sided shape of the snowflake. When water is chilled to the freezing point, 0C, snowflakes form from the lattice when initiated by a “seed” – like a small piece of dust.
In even a small snowflake, there are approximately 1018 water molecules. As they assemble into the interconnected hexagonal lattice, they create the six-sided shape observed by Kepler, but the specific elaboration of this shape differs from one snowflake to another. That is, while the same fundamental mechanism underpins the formation of each and every snowflake, each and every one varies slightly from the other in terms of its elaborated structure. This elaborated structure, or snowflake morphology, varies from small six-sided columns, to large, branching, flat structures, like those depicted in seasonal decorations. As more that 1018 water molecular contribute to the snowflake’s morphology, incredible variation is possible. Indeed, for all intents and purposes, it is true that no two snowflakes are likely to be identical.
The variation in snowflake morphology is a product of the number of molecules of water that participate in making the crystal, and the way they assemble in the lattice. This variation is a product of two major environmental factors – temperature and humidity. That is, depending on how cold it is, and how much moisture there is in the air, one gets different kinds of snowflakes. In keeping with this, there is an optimal humidity and temperature to generate those large, iconic snowflakes so many of us enjoy.
Like so much in the natural world, a snowflake is the product of a fundamental set of rules, governed by physics and chemistry. But each snowflake is also honed by a number of contingencies, including the dust particle that seeds the snowflake, and the temperature and humidity that determine its size and outgrowth. Physical laws sit at the foundation of a snowflake’s existence, but its environment determines its individual morphology. Similarly, genes function according to a particular set of physical and chemical rules, and lifetime events and environmental factors shape the individuality of a living organism.
Snowflakes are a lovely reminder of the parallels between the animate and the inanimate in our universe – the wonderful diversity that arises from the interplay between fundamental processes and a changing environment. When next you look at a snowflake, reflect on its individuality and your own individuality – dissimilar you may seem, but alike you are also.
The dogs of course, are unaware of any of these amazing aspects of the snowflakes amongst which they play. For them, the first snowfall is a beautiful, spotless canvas on which to paint delight. Their fresh laid tracks on the new-fallen snow are etchings of the purest of animal joy.
And this is the best thing about the first snowfall.
The first snowfall holds so much potential – it creates a new playground, and a place to reflect on the remarkable intricacies of nature. It can generate the greatest feelings of excitement, and the greatest of serenity. It can connect you with the here and now, and with the timeless mechanisms that shape the universe in which we live. It can be appreciated for its fleeting beauty, or for its ability to instil longstanding memories. It puts the wonder in the winter wonderland. Let it snow!
Images: All photographs by Malcolm M. Campbell.
Kepler J (1611) Strena seu de nive sexangula.
Libbrecht KG (2005) The physics of snow crystals. Reports on progress in physics 68: 855-895