March 18, 2007

Is every snowflake truly unique?

“No two snowflakes are identical” – The first thing I was ever told about snowflakes.

Being young and impressionable, I was very dazzled by it and dutifully spread the word; after which, I filed it away in that part of my brain reserved for useless but amazing facts.

The first time I experienced snow, I was 19 and much too enraptured with the actual snow to dwell on the minute details. The next, love waived all practical thoughts from my head and the last was a day of returning to missed childhoods and revelling in the excess.

The inclination to question this fact never having risen before today, a particularly lazy Sunday when snow was the thought of the day and not the catalyst for a string of new thoughts and experiences, it lay dormant and unexposed to other facts I had learnt through the years.

So, now I pose the question, “why is it that they are considered unique?”

The general argument, I believe, is that no two snowflakes are formed under the exact same conditions, i.e. temperature, humidity, wind, dust, etc. However, surely the commutations of these give you a finite number of possibilities and there are an infinite number of snowflakes, as one assumes there will always be one more snow. Even if this were not the case, have you seen the number of flakes in just one shower? The number of snowflakes must vastly outnumber the commutations.

Furthermore, no one has proven this to be fact and it is probably not possible to do so.

So, not only have I been duped as a child, but I’m part of the conspiracy in my role of ‘word-spreader’. It’s only fair that I bring my doubts to the attention of those I have plied with this misinformation.

- 22 comments by 2 or more people Not publicly viewable

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  1. In the same way all fingerprints are unique I guess…

    19 Mar 2007, 06:21

  2. Good point. Another fact to ponder on. Although, that does have the added argument of genetics – possible DNA commutations are much larger than the number of children any two people can have.

    19 Mar 2007, 12:08

  3. Chris May

    warning vague, handwavy probability theory coming up…

    It is, of course, conceiveable that there could be two identical snowflakes, in the same way that it’s conceiveable that I could flip a coin 1 million times and get 1 million heads. But it’s very unlikely.

    The number of actual snowflakes is finite. It might be very large, but if it were infinite then the entire universe would be filled with them. So really all you need to do is show that the number of permutations is much much larger than the number of snowflakes that will ever exist. Let’s have a go at coming up with a value for that

    the average rainfall per year around the globe is probably ~ 1000mm. So for every m3 of surface area, we get 106 g of water per year. The earth’s surface area is ~1015. So we get ~1021g of rainfall per year. Let’s assume that .1% of that is snow (that’s probably a big overestimate, but hey. So 1018g of snow falls each year. The earth is expected to exist for about 1010 years, so that’s a total of 1028g of snow that will fall. A snowflake weighs about a gramme, so that’s 1028 snowflakes that will ever exist.

    A snowflake made of between 0.5 – 1.5g of water then it contains ~1022 molecules of water. How many possible permutations is that? It ought to be something like 1022! (i.e. 1022 factorial) . In which case the chances of there ever being two identical snowflakes in the whole history of the world is 1028 / 1022!, which (if my creaky maths is still functional) is still about 1/ 1021! . Which is pretty near zero.

    19 Mar 2007, 12:23

  4. Firstly, I am so embarrassed that I used the wrong word for permutation! You think I’d remember that after 3 years of mathematics… In my defense, I avoided stats like the plague and haven’t seen used the word in 4 years. I’m still embarrassed.

    Mr May, I appreciate your argument and the time you must have spent on it. However, the possible permutations of the water molecules depend largely on the environment in which the snowflake is formed, is it not? Hence, wouldn’t they be much less in number, due to the environment possibly being similar? Of course, I can see how wind currents could definitely increase randomness.

    And, is that really how many snowflakes there must be in the history of the earth? Seems rather small to me… But, to be honest, I can’t find a flaw with your reasoning seeing as I don’t know anything about the numbers.

    I might have to be happy in the knowledge that I didn’t actually spread misinformation…

    19 Mar 2007, 14:03

  5. Chris May

    I reckon the estimate for number of snowflakes is about right, give or take a few orders of magnitude. Big powers of 10 always look smaller than they are; there are “only” 1040 particles in the entire universe (apparently, I haven’t counted )

    As to the finite set of conditions, I’m not sure that’s really true. Snowflake formation is one of those unstable equilibrium conditions that are very sensitive to changes in initial state (like balancing a pencil on it’s point and trying to predict which way it will fall). A very tiny difference in initial conditions (right down to air molecules bumping around via brownian motion) will affect what shape the crystals start to form in.

    19 Mar 2007, 17:12

  6. Well, that’s that, then.

    19 Mar 2007, 23:00

  7. Michael

    I think the most important factor is time!
    It can be possible that two snow flakes can molecular identical, but they cannot exist in the same place in the same time (because then they would be the identical flake!). That is why every thing on earth is truly unique, take e.g. enzygotic twins: Obviously they are identical, but they are just same.

    20 Mar 2007, 07:02

  8. I’d expect a snowflake to weigh nearer 0.1g or even 0.01g, but what’s a couple of orders of magnitude between friends? As you note, Chris, that would make no difference to your logic anyway.

    That said, is there no more scientific proof? Given that snowflakes are held to always form in regular patterns, often with three-, six-, ten-fold symmetry, and usually without any significant third-dimensional size to them, I don’t think it’s valid to assume there are (number-of-molcules factorial) permutations. That would only be true if every flake was made of the same number of molecules, and a standard shape ‘grid’ to fit them into.

    I think it would be concluded that two snowflakes were effectively identical if they were discovered to have the same shape but had a couple of hundred molecules in transposed positions (how would you tell?), or even missing entirely. The myth/maxim is really about shape – unless you get into the semantics, like Michael did, in which case you can definitely conclude that no two flakes will ever be identical.

    like balancing a pencil on it’s point and trying to predict which way it will fall

    Down! :-)

    20 Mar 2007, 14:13

  9. I thought it was a given that I didn’t mean “same place, same time”.

    20 Mar 2007, 14:27

  10. Chris May

    I think it would be concluded that two snowflakes were effectively identical if they were discovered to have the same shape but had a couple of hundred molecules in transposed positions

    Yeah, that’s certainly true. I was hoping that a chemist would come a long and offer some more accurate explanation of what the available configurations for a snowflake are :-)

    However, I’d still be pretty confident that the number is some large power of the number of molecules (which means it will easily trump the total number of snowflakes). IIRC snowflake crystals are fairly fractal, so I think there must be a large number of possible configurations that have a different shape.

    20 Mar 2007, 17:23

  11. National Geographic, source of all knowlege and priddy pictures, last week informed me ‘that no two snowflakes look exactly alike is fairly common knowlege’ and included some stunning magnfied pictures of the different shape types that are formed under different condidtions. i want the job of Kenneth Libbrecht, Ontario, who grows snowflakes under artificial conditions. Surely there can be no more satisfying job than creating snow, source of all childhood joys.

    21 Mar 2007, 14:25

  12. anon

    I think you would have been much more duped as a child if you had been told there was a Father Christmas or tooth fairy.

    21 Mar 2007, 14:43

  13. Snowflakes never look like the snow you might see when it’s snowing. I don’t think what we usually see is snowflakes at all, not like here for instance…

    22 Mar 2007, 23:42

  14. Peter

    Fingerprints are not associated entirely with DNA, identical twins have different fingerprints. It’s more to do with the development of the fingers during early growth, which can be affected by a number of different factors and is largely random.

    Also, my mate fat chris did his PhD on snowflakes, so it’s probably something to do with fractal growth.

    23 Mar 2007, 09:02

  15. You can do a PhD on snowflakes?!? What have I done?!?

    23 Mar 2007, 11:10

  16. Peter

    You can do one in Warwick with the theory group, it’s more on fractals than just looking at snowflakes really though.

    26 Mar 2007, 17:33

  17. Fractals are a very interesting field of mathematics, and can be used to model lots of natural phenomena, but snow is not one of them. This is because matter is not infinitely divisible; i.e. if you zoom in close enough to a snowflake pattern, to inspect further detail of the pattern, you eventually end up looking at atoms.

    I would imagine that group theory would be a more useful mathematical tool for studying the intricacies of a snowflake. All symmetries and transpositions can be represented as elements of a group, so if we predefine the size of the average snowflake (in particles) we can identify the group concerned. It is then a mere matter of classifying that particular group (expressing as product groups, identifying subgroups, etc) before we can deduce the number of possible distinct snowflakes, where distinct is taken to exclude all symmetries.

    That in turn, should imply that the probability of seeing two similar snowflakes in the same place at the same time is negligible.

    14 Apr 2007, 20:37

  18. Marty

    Obviously we need a project like the genome project where we have machines that catch snowflakes, sorts and photographs them, and then stores and compares the images to find snowflakes that are identical. In the past we haven’t had the technology to do such a task, now we can!
    I think we ought to bust this myth once and for all. We just need a Google or Bill Gates to sponsor this important project.

    15 Apr 2007, 02:53

  19. Ski Lover

    And then we have context – say we could find two snowflakes which were identical at the molecular level, consider their difference were one to be found drifting across your off-piste run whilst skiing in the Alps and the other was found to be about to melt in an instant as it fell towards a gritted path in shoreditch.

    Still the same? Or has the context changed their value?

    05 May 2007, 13:11

  20. Ski Lover, in my opinion, they would be the same. I am only talking about size and shape, so if they are identical on a molecular level, that’ll do me.

    I should work on my clarity. I figured it was obvious that I didn’t mean 2 identical flakes in the exact same place. That would be rather silly and impossible.

    Marty, I’m not sure people would see the usefulness of such a database, but let me know if you get it going. It doesn’t snow much here, but I can do my bit. :0)

    05 May 2007, 13:26

  21. Wonderer

    But what really makes them all different? I mean, yes they are all different because they are all formed under different conditions, as it was stated, but I mean really?

    20 May 2007, 15:48

  22. My meaning was that they have different structures, hence they are different.

    20 May 2007, 18:44

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