Forces of Nature. Andrew Cohen

The Universe in a snowflake

      I love the photograph of Wilson ‘Snowflake’ Bentley (see plate section here); a tilt of the head, content, protected from the cold by curiosity, absorbed in Nature’s detail which he holds carefully in both hands, oblivious to the snow falling on his hat. No gloves. As a 15-year-old farm boy from Jericho, Vermont, Bentley spent the snow days from November to April with a battered microscope sketching snowflakes before they melted away. Frustrated by their transience, too short-lived to capture in detail, he began experimenting with a camera and, on 15 January 1885, he took the first ever photograph of a snowflake. Over the next 45 years he collected over 5000 images and dedicated his life to carefully observing and documenting the raindrops, snowfalls and mists that swept across his farm.

      These delicate snapshots of a world available to everyone but rarely seen captured the public imagination. How could they not? They are magical, even today in an age familiar with photography. I challenge anyone to look at these structures, endless and most beautiful – to paraphrase Darwin – and not be curious. How do they form? What natural mechanism could mimic the work of a crazed, impatient sculptor obsessed with similarity and yet incapable of chiselling the same thing twice?

      These are questions that can be asked about any naturally occurring structure, and which Darwin famously answered for living things in On the Origin of Species. In May 1898 Bentley co-wrote an article for Appletons’ Popular Science with George Henry Perkins, Professor of Natural History at the University of Vermont, in which he argued that the evidence he’d collated frame by frame revealed that no two snowflakes are ever alike. ‘Every crystal was a masterpiece of design and no one design was ever repeated’, he wrote. Their uniqueness is part of their fascination and romance, yet there is undoubtedly something similar about them; they share a ‘six-ness’. Which is more interesting? Perhaps it depends on the character of the observer.

      Johannes Kepler is best known for his laws of planetary motion. He pored over the high-precision astronomical observations of the Danish astronomer Tycho Brahe, just as Snowflake Bentley pored over his photographs, and he noticed patterns in the data. These patterns led him to propose that planets move in elliptical orbits around the Sun, sweeping out equal areas in equal times and with orbital periods related to their average distances from the Sun. Kepler’s empirical laws laid the foundations upon which Isaac Newton constructed his Law of Universal Gravitation, published in 1687; arguably (I would say unarguably, but one has to keep argumentative historians happy) the first modern scientific work.

      In December 1610, shortly after the publication of two of his three laws in Astronomia Nova, Kepler was walking across the Charles Bridge in Prague through the Christmas dark when a snowflake landed on his coat. The evident structure of the elegant, white near-nothing interested him, and he wrote a small book entitled On the Six-Cornered Snowflake. It is a piece of scientific writing that transcends time and provides an illuminating and entertaining insight into a great mind at play. The title page of the book is addressed ‘To the honorable Counselor at the Court of his Imperial Majesty, Lord Matthaus Wacker von Wackenfels, a Decorated Knight and Patron of Writers and Philosophers, my Lord and Benefactor’. Modern language lacks a certain flourish; I wish I had something equally magnificent with which to begin this book.

      As a modern research proposal, Kepler’s Six-Cornered Snowflake would fall at the first hurdle because it begins: ‘I am well aware how fond you are of Nothing, not so much on account of its inexpensive price as for the charming and subtle jeu d’esprit of playful Passereau.¹ Thus, I can easily tell that a gift will be the more pleasing and welcome to you the closer it comes to nothing.’ Now there’s a statement of projected economic impact; the closer my research comes to nothing, the more valuable it is. Stick that on your spreadsheet… Kepler doesn’t succeed in explaining the structure of snowflakes – how could he? A full explanation requires atomic theory and a good fraction of the machinery of modern physics; we will get to that later on. What he does achieve is to make vivid the joy of science; the idea that the playful investigation of Nature has immense value, irrespective of the outcome. His book explodes with excited curiosity, fizzing with speculations on snowflakes and their similarities to other regular shapes in the natural world; five-petalled flowers, pomegranate seeds and honeycombs. He covers so much ground, bouncing thrillingly from subject to subject, that eventually, with magnificent perspicacity, he has to rein himself in: ‘But I am getting carried away foolishly, and in attempting to give a gift of almost Nothing, I almost make Nothing of it all. For from this almost Nothing, I have very nearly recreated the entire Universe, which contains everything!’

      Kepler does have a clear question, however, which surely occurs to anyone who studies Snowflake Bentley’s exquisite photographs: how do structures as ordered and regular as snowflakes form from apparently form-less origins? ‘Since it always happens, when it begins to snow, that the first particles of snow adopt the shape of small, six-cornered stars, there must be a particular cause; for if it happened by chance, why would they always fall with six corners and not with five, or seven, as long as they are still scattered and distinct, and before they are driven into a confused mass?’

      Kepler knew that snow forms from water vapour, which has no discernable structure. So how does the snowflake acquire structure? What is the ‘six-ness’ telling us about the building blocks of snowflakes and the forces that sculpt them? This is a modern way of looking at the world, one that any physicist would recognise. Kepler’s insight, and his delighted frustration at not possessing the knowledge to approach an answer, echoes loudly down the centuries. ‘I have knocked on the doors of chemistry,’ he writes, ‘and seeing how much remains to be said on this subject before we know the cause, I would rather hear what you think, my most ingenious man, than wear myself out with further discussion. Nothing follows. The End.’

      Science is delighted frustration. It is about asking questions, to which the answers may be unavailable – now, or perhaps ever. It is about noticing regularities, asserting that these regularities must have natural explanations and searching for those explanations. The aim of this chapter, inspired by Kepler and Snowflake Bentley, is to seek explanations for the complex shapes in Nature; from beehives to icebergs; planets to free-diving grandmothers (honestly!). This will lead us to think about how such diversity and complexity can emerge from laws of Nature that are few in number and simple in form. At the end of the chapter, we will explain the structure of snowflakes.

Why do bees build hexagons?

      Bees have a got a tricky problem to solve. How do you store honey, the food that will sustain your colony, through the long winter months? We know that bees build honeycombs for this purpose. Kepler was interested in the structure of honeycombs precisely because they are built, as he writes, by ‘an agent’. Since he was seeking the ‘agency’ that sculpts snowflakes,