[This is the second of the re-posted articles, from 2007.]

Wilson Bentley is famous for his phrase ’no two alike’, but what did he really mean by it? Excerpts in Duncan Blanchard’s book suggest that Bentley was usually referring to only the crystals he photographed (1).

Sometimes though, Bentley seems to be referring to all snow crystals. Maybe sometimes he meant it one way and sometimes the other; however, I wonder if he also had a third, and more profound, meaning in mind, a meaning suggested in his passage (2):

The deeper one enters into the study of Nature, the
further one ventures into and along the by-paths that,
like a mystic maze, thread Nature’s realm in every
direction, the broader and grander becomes the vista
opened up to the view.

If Nature becomes ‘broader and grander’ the deeper one looks, as he so eloquently stated, then of course every snow crystal will be unique; indeed, so too will everything else in Nature. In this meaning, ‘no two alike’ is a very condensed way of saying that Nature will always show you something new. Bentley arrived at this opinion by observing various forms of water, but he applies the idea to all of Nature. This third meaning of ‘no two alike’ reminds me of Kamo no Chomei’s opening line of his early 13th century classic of Japanese literature (3): “The river flows on unceasingly, yet the water is never the same.” Both phrases, Chomei’s and Bentley’s ‘no two alike’, can be interpreted (4) as meaning that the closer one views Nature, the more details one sees. Regardless of Bentley’s intended meaning, I prefer to think that he had this deeper interpretation in mind.

As to why, in 1901, Bentley first chose his now-popular words ‘no two alike’ instead of other phrases, like ‘all are unique’, ‘every one different’, ‘no two the same’, or some other variation, we may never know, but it is curious that George E. Ohr (1857-1918), the self-proclaimed “mad potter of Biloxi” often used the same phrase to describe his unique pottery. I’ve seen no evidence to suggest that Bentley was aware of Ohr’s phrase; indeed, it has been said that until recently nobody outside of Biloxi had heard of the mad potter either, so it may be that the phrase had been in some popular work before Ohr and Bentley used it. If a reader can find a reference to ‘no two alike’ that predates Bentley, please let me know. Compared to the other variations, the phrase Bentley chose has a certain poetic simplicity, and for all we know, he created it himself.

I also wonder why people often ask “Is it true that no two snowflakes are alike?” As far as I know, this ‘no two alike’ question is asked only of snow and not other things we look at, like roses, leaves, or pebbles. Part of the reason is that Bentley applied the phrase only to snow. But is there something special about snow that makes it the sole target of the question?

The answer may be ‘yes’; for with snow, we have just a bunch of H2O molecules locked together, plain old water turned solid, and yet the designs on the crystal have both an elaborate detail that is easy to see and an obvious symmetry that makes the pattern relatively quick to grasp. Other symmetric objects are usually simple, like ball bearings, diamonds, and starfish. However, a snow crystal, in addition to its relatively uncommon six-fold symmetry (i.e., the same when rotated by 1/6 of a turn) and its mirror symmetry about each corner, nevertheless contains a surprising intricacy and detail. When one sees a snow crystal for the first time, and sees all the fine lines and branches, one may naturally wonder if all crystals are somehow destined to look that way. Then one sees another crystal and notices right away that it is different but just as elaborate, and after seeing more crystals one is surprised that something as plain and pure as water can produce so much variety. Roses, leaves, and pebbles, in contrast, seem to lack one or more of these qualities of snow. We could examine each case in turn and try to determine exactly why we don’t ask the question of roses, leaves, or pebbles, but I think it all boils down to the fact that only the snow crystal has this element of surprise.

Finally, is there an answer to the question? Maybe, but the answer will depend on how the words ‘snowflake’ and ‘alike’ are defined. And even when these words are precisely defined, the answer may only be a probability based on some dubious assumptions. I say dubious because we still have only a very poor understanding of how snow crystals grow under ideal laboratory conditions, never mind the actual conditions in a cloud, of which, incidentally, we also have very little knowledge. Despite these limitations, we can still have fun trying to answer the question.

However, I think the more interesting question is the following: Why do snow crystals have so much obvious variety? This question is answerable. From what we now know, the best answer is that Nature has made the growth of the snow crystal to be extraordinarily sensitive to temperature and has made the clouds to have ever-changing temperatures. Or, to paraphrase Chomei, “The clouds churn on unceasingly, yet the crystal-laden air is never the same.” (5)

--JN

References and notes

1. Duncan Blanchard The Snowflake Man (McDonald & Woodward Publishing, Blacksburg, Virginia 1998).

2. Ibid, page 141. Originally from Wilson A. Bentley “The latest designs in snow and frost architecture” The American Annual of Photography vol. 20, pp. 166-170 (1906).

3. Kamo no Chomei, Hojoki [Record of the ten foot square hut] in Four Huts: Asian writings on the simple life translated by Burton Watson (Shambhala, Boston 1994).

4. Chomei instead uses the phrase as a metaphor for the lives of people and their dwellings, but the phrase can just as well be applied to natural objects like the river itself.

5. After this was first published, I studied the question in more detail after finding out how a researcher had made very fine-scale (inch-scale) measurements of temperatures and windspeeds in clouds. Some results are in a subsequent article.