-Francois Villon, c. 1461


By Edwin D. Reilly, Jr.

For The Sunday Gazette



I write a week before Christmas day. As I adorn our tree with its last ornament, an oversize but otherwise realistic white snowflake, I look out at our lawn, as green as it was in June. And the forecast seven days out says that unless the spirits of Irving Berlin and Bing Crosby intervene, rain is much more likely than snow.

It is highly unlikely that the first Christmas was white. Christ was born in about 4 B.C., a mere 2,010 years ago, so its climate has not changed over such a short time. And we do not know that He was born in the winter, much less in a particular month such as December. One can view the dynamic seasonal advance and retreat of the snow ridge from the North Pole southward and back again at http://en.wikipedia.org/wiki/Snow. The front of maximal probable advance never reaches as far as the heart of the Middle East, so certainly not as far south as Bethlehem, a city with a Muslim majority in what is left of Palestine.

I love the hexagonal symmetry of individual snowflakes. They form miles above the earth, so soft and feathery that they take hours to flutter down to earth. When they fall in the company of similar but rarely identical flakes, unaccompanied by excessive numbers of poor little water droplets that never got promoted to the ethereal splendor of ice crystals, they share the magic power to cover even an urban landscape with a soft velvety white blanket that hides its every blemish.

Snow can cover sadness, too. I thought of leading with a quote from James Russell Lowell’s “The First Snowfall,” a childhood favorite that I can still recite. But that would be too painful, akin to listening to Judy Garland sing “Have Yourself a Merry Little Christmas” in a way that makes the listener believe that such a wish is unlikely to come true for whomever she is singing to: “Through the years we all will be together, if the fates allow.”  I tear up every time.

Instead, consider the following from a novel in which Smilla, the protagonist, a native Greenlander who emigrated to Copenhagen at an early age, uses “Smilla’s Sense of Snow” (the title of the book by Peter HØeg) to help convince the police that the acrophobic

eight-year-old Isaiah, who jumped off the snow-covered roof of a seven-story building, was being chased. Early in the book, Smilla as narrator says:


“For the first time I look at his coffin, hexagonal in form, like ice crystals. Now they are lowering him into the ground. The coffin, made of dark wood, looks so small, and there is already a layer of snow on it. The flakes are the size of tiny feathers, and that’s the way snow is; it isn’t necessarily cold. What is happening at this moment is that the heavens are weeping for Isaiah, and the tears are turning into frosty down that is covering him up. In this way the universe is covering him up, pulling a comforter over him, so that he will never be cold again.”


The only thing on my Christmas list is a new book whose large cover features a glorious photo of the most perfect imaginable snowflake (see above). The photo is credited to Patricia Rasmussen, but the book’s author is Cal-Tech physicist Kenneth Libbrecht, who has a cottage industry going in the production of snowflake books (see Amazon.com and search for “snowflakes.”) An earlier snowflake pictorial book was published in 2000 by Wilson A. Bentley.  See http://snowflakebentley.com for a portrait of this renowned “Snowflake Man” and some of his work.

My fascination with snowflakes is that of a scientist interested in art, just as an artist interested in science would be—and there are many of both types. Surely the hexagonally symmetric pattern of a snowflake with its whorls and filigreed arms is an artistically pleasing architectural edifice, even if only a few millimeters in diameter.

I almost wrote that each of a snowflake’s six arms is in a whorl of its own, but that’s not true because what one arm does as it grows through transition of contiguous water vapor to solid crystal, so do the other five, in lockstep. That, for me, is the crux of my scientific interest in snowflakes. As one arm “decides” to extend an outstretched limb of a certain length at a certain angle emanating, say, seven millimeters away from the previously formed extension, how do the other five arms “know” to do exactly the same thing?

<>Professor Libbrecht offers two theories. First, as the flake grows, identical information as to what an arm should do could be flowing, through moderated surface tension perhaps, from the hub out through each arm. Abracadabra! His second and more plausible hypothesis is that branching depends on the precise combination of temperature and pressure present in the tiny region of space engulfing the snowflake. Since the values of these attributes fluctuate slightly as the growing snowflake flutters and falls, but are essentially the same throughout the hexagonal envelope of the flake, whatever one arm does the others will too.

A third possibility, the one I like best as a computer scientist, is that a snowflake functions as a tiny cellular automaton. Information as to what a tiny (non-biological) “cell” of an arm does at any one point depends on the characteristic values of adjacent small cells, areas of identical shape—a mesh of equilateral triangles, perhaps, for a two-dimensional simulation—or volumes of identical shape, regular tetrahedrons most likely, for a three-dimensional simulation. So if the flake grows from a hexagonal seed, hexagonal symmetry is maintained until the flake reaches maturity.

Scientists have tried to make such models work, but with only limited success. To produce images of flakes of acceptable fidelity this way, one must deduce the adjacency “rules” that cause an initially empty cell adjacent to a partially formed flake to remain water vapor or to crystallize.

The necessary space eluded me, but I also wanted to tell you about “ice nine” as described by my favorite philosopher, Kurt Vonnegut. The substance is fictional, but the book “Cat’s Cradle” that describes it lies open to the right page at the Schenectady Museum. Go see it.

Kurt’s brother Bernard and his friend Vince Schaefer knew how to make it snow; how I wish they could help us on the 25th. But the fates didn’t allow it, so dreaming will have to do.


Edwin D. Reilly, Jr. lives in Niskayuna and is a regular contributor to the Sunday Gazette opinion page.