[DoctorBeaver (OP)]

This question is prompted by us having had 4 inches of snow in an hour last night.

How can it ever be proven that no 2 snowflakes are identical? There may have been 1 fall somewhere a few million years ago that was identical to the 1 that landed on my nose last night; no-one can ever prove that isn't the case. So why does everyone claim they are unique?

[neilep]

I agree with Dr Beaver.

I remember seeing a snowflake a few years ago that looked remarkably the same as one I saw this morning !

[DoctorBeaver (OP)]

If they said that no 2 Cornflakes were the same, I might be inclined to agree  []

[neilep]

Well, after spending literally ...seconds....rustling around our Cornflake box...I am in total concurrence yet again with the remarkable Doctor Beaver.

[DoctorBeaver (OP)]

& cows. They're all different. But they don't fall from clouds  []

P.S. After a good cowfall, make cowmen and throw cowballs at each other!

[neilep]

Surely you are jesting !!.....pull the udder one !!! ...............*groan*

[paul.fr]

The no two snowflakes are the same tale is a myth, Wilson A. Bentley is responsible for it.

at the age of 19, he became the first person to photograph a single ice crystal, by fixing a microscope to a camera.

He took over 5,000 “photomicrographs” of individual snowflakes. He is quoted as saying that he had “never seen two snowflakes alike”.And so the no two snowflakes myth/tale began.

[Bored chemist]

A typical snowflake weighs something like a miligram. That's about 6E20 hydrogens. About i in 6000 of those are heavy hydrogen, so picking hydrogens randomly as you assemble the snowflake you have a (roughly) 5999 out of 6000 chance of picking the right one. Sounds like pretty good odds until you think about doing it 600000000000000000000 times. I'm sorry but my calculator won't handle numbers that small.
That gives the chance of getting the hydrogens correctly placed. Now think about the fact that of those vanishingly small number of snowflakes with the hydrogens in the right places, a similarly small fraction will have the oxygen isotopes correct.
Of that tiny fraction of a tiny fraction, only those that are the right shape (again a tiny fraction) are identical.
Strictly, that doesn't prove that there are not 2 the same,  but it does give some idea of how unlikely it is.

[chris]

Why would the location of a heavy hydrogen make a difference to the appearance / structure of a snowflake? Presumably H2O is the same shape as DHO or D2O (where D = deuterium, heavy hydrogen).

Chris

[JimBob]

The space in the crystal lattice of a snow flake is of a given size for all the unbound water. Deuterium in a crystal takes up more space so the water molecule is of a different size.

[Bored chemist]

The point is not that the effect is visible, or even observable by other means; just that if they are different they are not the same.

[DoctorBeaver (OP)]

A typical snowflake weighs something like a miligram. That's about 6E20 hydrogens. About i in 6000 of those are heavy hydrogen, so picking hydrogens randomly as you assemble the snowflake you have a (roughly) 5999 out of 6000 chance of picking the right one. Sounds like pretty good odds until you think about doing it 600000000000000000000 times. I'm sorry but my calculator won't handle numbers that small.
That gives the chance of getting the hydrogens correctly placed. Now think about the fact that of those vanishingly small number of snowflakes with the hydrogens in the right places, a similarly small fraction will have the oxygen isotopes correct.
Of that tiny fraction of a tiny fraction, only those that are the right shape (again a tiny fraction) are identical.
Strictly, that doesn't prove that there are not 2 the same,  but it does give some idea of how unlikely it is.

But set that against the number of snowflakes that fall every year. Or against the total number of snowflakes that have fallen since the earth formed. I would say that makes the odds of identical snowflakes having occurred pretty damned high. Think about it, if something has a 1:1,000,000 chance of occurring it doesn't sound very likely. But if there have been 10E100 chances of it occurring then it is quite likely that it has occurred.

[Bored chemist]

I did think about the number of snowflakes that have ever fallen - it's not very big.
If the odds had been better than 1 in a googol my calculator should have coped.
I didn't bother trying to get a reliable estimate of the probabillity because there are estimated to be fewer tha a googol particles in the known universe. The number of snowflakes is clearly less than this.
Lets make a couple of aproximations. First off, rather than 1 in 6000 we might as well use 1 in 1000- this is never going to be a precise calculation.
That makes the calculation 0.999 to the power 600000000000000000000.
Lets just try a few numbers and see how the odds vary.
.999 ^ 3 is about .997
.999 ^ 10 is about .99
.999 ^ 100 is about .904
.999 ^ 692 in pretty near 0.5
so, by the time you were putting in the 692nd atom you would have a roughly 50:50 chance of having got the "wrong" atom somewhere in the snowflake.
Add another 692 atoms and theres a 50 50 chance one of these is wrong so, overall you have a 25% chance of getting all the atoms right.
Another 692 and the odds are down to one in 8 of a perfect copy.
By the time you have done this 10 times your odds are about 1 in 1024 of having the right atom in each place.
OK so that's how lucky you need to be with the first 6920 atoms
The next lot of 6920 atomstake the odds to one in about a million.
Each further 6920 makes it roughly another thousand fold more unlikely that you have the atoms all correct.
By the time you have used all 600000000000000000000 atoms you have added another 3 zeros to the odds 600000000000000000000 / 6920 times
The odds against getting all the atoms right is of the order of 1 followed by 86 thousand million million zeros.

That's just the hydrogens; then there's a comparable set of odds for the oxygen isotopes. Then think about all possible arangements in space (ie the numbet of possible ways to stick the atoms together).
The earth weighs something like 6*10^27 grammes or enough, if the entire earth were made into snowflakes, enough for about 6*10^30 snowflakes of 1mg each.
You are trying to compare 2 numbers, one has 30 digits the other has  more than 85 thousand million million digits.
The number of possible combinations is so huge that it wouldn't matter much if you made snowflakes from something as much bigger than the earth, as the earth is bigger than a snowflake.
That's just the hydrogens; then there's a comparable set of odds for the oxygen isotopes. Then think about all possible arangements in space (ie the numbet of possible ways to stick the atoms together).
Trust me, I did think about the number of snowflakes. []