## Probability of finding two snowflakes alike? Need help!

For the discussion of math. Duh.

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donkom
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### Probability of finding two snowflakes alike? Need help!

Hi there! I thought I'd pose a season question for everyone. I've been photographing snowflakes recently and I'm writing a coffee table book about my photography, and I'd like to throw some random facts in there about the subject matter...

So, here's the question:

What is the probability of finding two snowflakes identical on the molecular level if you were comparing snowflakes, two at a time, once a second, since the beginning of the universe.

Numbers you'll probably need:
roughly the number of water molecules in a snowflake: 1-2 quintillion (based on internet research and estimations)
age of the universe: 13.75 billion years (4.33907732 × 10^17 seconds)

I'm sure that there are a number of incalculable variables, but a rough idea would be a pretty nifty fact.

Anyone up for figuring this out?

the tree
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### Re: Probability of finding two snowflakes alike? Need help!

Really the question is how many ways can [however many] water molecules be arranged in a snowflake like pattern, which requires knowing more about water molecules than it does about probability.

donkom
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### Re: Probability of finding two snowflakes alike? Need help!

I agree with you there, if you want to take it further:

water forms hexagonal crystals, which is why snowflakes have 6 sides. The only reason the branches of a snowflake appear to be symmetrical is due to them forming under nearly the exact same conditions - most snowflakes are certainly not symmetrical. So, divide the problem up a bit. six asymmetrical branches, each one having roughly 1/6th of the mass of the snowflake.

I'm sure you could go even deeper into what possibilities are more or less likely, but I was trying to keep it simple.

jestingrabbit
Factoids are just Datas that haven't grown up yet
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### Re: Probability of finding two snowflakes alike? Need help!

I think that the answer to this question is pretty strongly dependent on what sort of snow crystal you are looking at. Here's two diagrams, one of which is linked to some useful source material.

If the shape of the snow is one of the simple crystals like plates or columns, then they would have a better chance to be identical. Wikipedia agrees with me and gives a much larger estimate on the number of water molecules in a snow flake.

WP on Snow wrote:It is very unlikely for two snowflakes to be exactly alike due to the roughly 1019 water molecules which make up a snowflake,[7] which grow at different rates and in different patterns depending on the changing temperature and humidity within the atmosphere that the snowflake falls through on its way to the ground united.[8] Initial attempts to find identical snowflakes by photographing thousands of them with a microscope from 1885 onward by Wilson Alwyn Bentley found the wide variety of snowflakes we know about today.[9] It is more likely that two snowflakes could become virtually identical if their environments were similar enough. Matching snow crystals were discovered in Wisconsin in 1988. The crystals were not flakes in the usual sense but rather hollow hexagonal prisms.[10]
Last edited by jestingrabbit on Tue Dec 07, 2010 4:18 am UTC, edited 2 times in total.
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Mo' Money
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### Re: Probability of finding two snowflakes alike? Need help!

That's 1019, obviously, not 1019.

jestingrabbit
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### Re: Probability of finding two snowflakes alike? Need help!

Yes, sorry, fixed.
ameretrifle wrote:Magic space feudalism is therefore a viable idea.

Cleverbeans
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### Re: Probability of finding two snowflakes alike? Need help!

What's the equivalence relation on snowflakes? Do we expect two to have the same number of molecules or is it sufficient for one to be a scaling of the other in some meaningful way?
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Thootom
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### Re: Probability of finding two snowflakes alike? Need help!

I believe snowflakes falling should all have roughly similar mass, depending on altitude, climate etc, as the snow has a required weight/mass in order to fall. Like how you see stones of the same size in groups along rivers, when the stream loses strength at a point it deposits only the stones above a certain mass, carrying the lighter material with it (in the sky the flakes wouldn't have much of a chance to gain extra mass before falling, on average).

I'm no mathematician, but because the material does have limits to it's length and breadth (panning out at 1 molecule thick and 10^19 wide at it's limit) there should be a way to formulate the possibility of finding two snowflakes exactly the same based solely on atmospheric conditions over a given area.

Though because this wouldn't take into consideration the patterns with which snow crystals form I'd expect your odds to be a fair amount higher than the predictions given.