Granite Geek: No Two Snowflakes Are Alike, And Here's The Math To Prove It

Feb 24, 2015

The beautiful building block that makes up those baffling behemoths known as snow piles.
Credit Alexey Kljatov via Flickr/CC - http://ow.ly/JBzMe

After spending weeks and weeks surrounded by snow piles that are several feet high, it’s easy to forget that those huge piles are made of tiny snowflakes. And no two snowflakes are alike – or at least that’s what we’ve all heard.

David Brooks writes the weekly Granite Geek science column for the Nashua Telegraph and GraniteGeek.org. He ventured forth into the snow to get some answers – and he joined All Things Considered with some of what he’s learned.

Before we get into snowflakes, it’s worth noting that you talked with a researcher at a US Army Corps of Engineers facility that studies snow – and there are a lot of really weighty topics in snow research.

This is what they call CRREL for the Cold Regions Research and Engineering Lab. It's up in Hanover, and they study, as the name implies, all sorts of cold-related stuff. They're really interested in things like how does the Army make its equipment work better when it's in polar regions. That's the kind of thing they started out doing, but the research they do has extended enormously.

A big area of research right now is trying to measure how much moisture is in snow - the same two feet of snow can be quite different. We've had some really light, fluffy stuff that you can shovel with a broom, often times. And the amount of moisture in that is fairly small, even though it's two feet high. If you're in a region like out west, which counts on melting snowpack in the summertime to provide some of your water, you want to know how much moisture is in there. That's the kind of geeky research they do out there.

Now for the snowflakes: when you started to look for answers on this, did you think the old adage was true, or did you think "no two snowflakes are alike" was just a story everybody told?

Come on, I'm an objective journalist, and I always approach things quietly and - no, of course I wanted to tear it down. I didn't think it was true - I thought it was stupid! I thought I'd be rubbing my hands with glee, saying I'll get to debunk it and show how smart I am. That's why I called CRREL, and ended up talking to Zoe Courville, a research engineer there. She pointed me to, and eventually I found, this lovely paper that came out in 2006. (Here's a PDF link to the paper - start on page 286 to read more.)

What a couple researchers did was they calculated all the ways that a snowflake can grow. They're only talking about what you and I consider snowflakes - the six-arm star things called stellar dendrites. There's other shapes of snowflakes as well. But just looking at that, they conclude that the number of possible snowflake shapes is 10 raised to the 10 raised to the 13 power, which is a one followed by 10 trillion zeroes - a number so much larger than any conceivable anything that could exist in the entire universe combined that you just can't even begin to think about it.

They then tried to estimate how many total snowflakes have fallen in the history of the world, and they came to the conclusion that only - and I love the word only - 10 to the 40th power, so a one followed by 40 zeroes. That many stellar dendrite snowflakes have fallen in the history of the world.

Now 10 to the 40th power is, again, a number so staggeringly monstrous that nothing humans or the entire solar system would ever encompass a number that large. But despite that fact, 10 to the 40th is so much smaller than 10 to the 10th to the 13th power that they conclude that the odds of any two snowflakes having been formed exactly the same are zero.

So, therefore, yes: each snowflake is unique.

The question that's been on my mind thinking about this is, does knowing that each one of the tiny little stellar dendrites that makes up our enormous snow piles make the work of moving those piles any less aggravating?

Um, let me think about that... I believe the answer is no.

I notice you didn't have to call CRREL to get that answer.

I did not.