Update 01/01: Do you love Xmas (or Newtonmas as scientists like to call it) as much as I do? Do you love science and symmetry? Are you a nerd? If you answered a resounding YES! to all three questions, then this post is for you!
Symmetry is all around us, begging for our admiration and contemplation. Symmetry also inspires; it stirs our imagination, and awakens our creativity. (I’ll come back to that in just a second!) Just think of Escher's masterpieces or the stories from Lewis Carroll, or listen to the canons and fugues from Johannes Sebastian Bach.
Perhaps most importantly, symmetry intrigues us; it stimulates our thinking and drives us onward in our quest to understand. Anno 2015, symmetry underlies many of the revolutionary concepts of modern physics and chemistry. As Steven Weinberg (Nobel laureate in Physics) recently exclaimed, symmetry provides a key to Nature’s secrets. It unlocks the door to a profound understanding of the physical world and all the wonders it entails.
Not surprisingly then, I got bitten by the symmetry bug as well, and spent my entire PhD hunting for hidden symmetries in the periodic table of chemical elements. If all goes well, the results of my quest should appear in book form early this summer!
But I'm getting off track. From all its myriad manifestations in Nature — the rotational symmetry in flowers, helical symmetry in seashells, spiral symmetry in the Pinwheel galaxy, and cubic symmetry in salt crystals — it's the hexagonal symmetry of snow crystals I like the most! And it's with a short post on snowflakes that I would like to start the New Year.
Kepler and the six-cornered snowflake
It was a cold and snowy winter day in 1611, when the German mathematician and astronomer Johannes Kepler (1571–1630) crossed the Charles Bridge in Prague. A snowflake, born inside an icy cloud high above the city, had journeyed all the way down, to land on Kepler’s coat. Mesmerized by its sheer beauty and perfect symmetry, Kepler marveled: Why do single snowflakes, before they become entangled with other snowflakes, always fall with six corners? Why not with five or seven corners? And how could such marvelously complex structures emerge (literally) out of thin air? It was a simple enough question, but one that no one had ever answered.
Not long after, Kepler offered his friend, Johannes Matthäus Wackher von Wackenfels, a charming little booklet by way of New Year’s present. The pamphlet was modestly sized, counting a mere 24 pages, and was titled De Nive Sexangula (On the Six-Cornered Snowflake). Kepler knew that no two snow crystals are alike, but he realized they all shared the same hexagonal symmetry. Kepler of course had no way of knowing what scientists know today about the dynamics of snow crystal formation. (Did you know, for instance, that it takes about a 100 000 droplets to create one snowflake? Or that snowflakes are classified in a staggering 121 different shape-based categories?) Nonetheless, Kepler had some really original observations to make about the six-fold rotational symmetry of snowflakes, and his essay would ultimately help the science of crystallography emerge.
At this time of the year, I can only encourage you to snug comfortably in your sofa in front of the fire place, with a warm cup of (Arabica) coffee, and delight in reading Kelper’s timeless pamphlet. The English translation is available here and the Latin original here.
Grow your own snowflakes!
Living in Belgium, we never know whether we'll be blessed with a White Xmas or not. But did you know you can easily grow your own snow crystals at home? The snow guru Ken Libbrecht, an astrophysicist at the California Institute of Technology, has been growing snowflakes in his lab for years, and he claims all you need is an empty plastic bottle, some styrofoam cups, a kitchen sponge, a piece of nylon fishing line, a paper clip, and some dry ice. Find out how he does it here.
Deck the halls with science-y-snowflakes
There’s more I want to share about snowflakes. During this festive period, many children and adults have fun making paper snowflakes by folding a piece of paper several times, cutting out a pattern with scissors and then unfolding it. So can you imagine my joy when Symmetry Magazine came up with three templates for paper snowflakes, featuring Albert Einstein, Marie Curie and Erwin Schrödinger?!
The Albert Einstein template features Einstein’s characteristically asymmetric haircut, with a classic snowflake in the middle.
Maria Sklodowska Curie — famous for her discovery of radioactivity and for winning the Nobel Prize not once, but twice (!!) — has a snow crystal featuring her own image, with radioactive Erlenmeyers in between.
Finally, and perhaps not too surprisingly, Erwin Schrödinger’s snowflake features both the great scientist and his famous cat (whose tail is in a superposition of being both at the left and at the right). It’s a pity though that Schrödinger’s design has only four-fold rotational symmetry, as compared to the correct six-fold symmetry of the other ones.
Here’s a picture of the snowflakes I cut out; not too bad, isn't it?
￼So, here’s your chance to make your own geeky Winter Wonderland. Check out this video for instructions, download and print the PDF templates, and start fiddling with paper and scissors! Good luck and a happy happy New Year to you all!
Did you know that ...
the largest snowflake on record measured 38 cm wide and 20 cm thick. It was observed in Montana in 1887 and was described by witnesses as being "larger than a milk pan."
chionophobia means fear for snow.
it is a myth that Eskimos have 100 different words for 'snow'.
the average snowflake has a top speed of 1.7 metres per second.
Jepsen, K. "Deck the Hall with Nobel Physicists." Symmetry Magazine (16 December 2014)
Libbrecht, K. The Art of the Snowflake. MN USA: Voyageur Press, 2007. [This book contains some of the best snowflake photographs taken by the snow guru, Ken Libbrecht. With more that 500 photographs, full of detail, this is a great coffee table book.]
Libbrecht, K. The Snowflake: Winter's Secret Beauty. MN USA: Voyageur Press, 2003. [This popular-science book tells the story of snowflakes: how they grow, why they all have hexagonal symmetry, why they appear in so many different shapes, etc.]
Kepler, J. The Six-Cornered Snowflake. Philadelphia: Paul Dry Books, 2010. [English translation of Kepler's De Nive Sexangula.]
Libbrecht, K. Ken Libbrecht's Field Guide to Snowflakes. MN USA: Voyageur Press, 2006. [This book describes the different shapes of snowflakes, how snow crystals grow and form, and how to go outside and look yourself for snowflakes.]