Naked Science Forum
General Science => Question of the Week => Topic started by: Adam Murphy on 24/05/2021 16:14:04
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Alan sent us this message about snowflakes:
"I have heard it said many times that no two snowflakes are the same. Given the billions and billions of them that have fallen to Earth, this really does seem unlikely. Since nobody has looked at them all, would you agree with me that the only thing to be said with any certainty, is that no researcher has ever found two the same?"
What do you all think?
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I've never really been able to successfully capture snowflakes. But they come in a few different varieties. At times one gets big fluffy ones. And other times, small ones, perhaps more like a low density hail. Generally all very much 3 dimensional. And, I generally don't see the symmetry that 2 dimensional flakes are represented as. Especially the amorphous big fluffy flakes.
And, of course, one sees the familiar splat of them on a car's windshield.
Then one gets into a question of what is sameness.
Is it general morphological features, or does one get down to a single molecule?
If one takes Avagadro's number: 6.0221409 x 1023... 8) 602,214,090,000,000,000,000,000
Ok, so a mighty big number. But, what is that really measuring? The number of molecules in a mole.
Take the molecular mass (H2O)... so, O:16 + 2x H:1 = 18, and one gets that many molecules in about 18 grams per mole of water. (18.01528 g/mol)
So 18 grams would be a mighty big snowflake. And, they would obiously vary a lot in size. So, perhaps 1/100 or 1/1000 of a mole depending on the size of the snowflake.
So, at 1/1000 of a mole, one still has 6.0221409 x 1020 molecules (602,214,090,000,000,000,000).
That would be a lot of different snowflakes.
Oof... :o
That is just calculating the number of ways a single molecule could be different (in identical sized snowflakes).
But, really, it can be any or all of the water molecules could be in a different place...
So, a factorial problem.
6.0221409 x 1020 !
Now that becomes a really big number!!!
But, perhaps that isn't calculating quite what one wants.
Snowflakes would be somewhat constrained by the crystalline structure of water. So, internal to the crystal, the water molecules would be generally constrained. It is only on the surface where the constraints are loosened. Does the water molecule exist? Branch point? Are there a couple of possible orientations?
So the number of choice points gets reduced, and it becomes a density/surface problem. Nonetheless, it is still a LOT of different configurations on the molecular level.
Likely any chance for identical flakes would not be those big fluffy ones, but small low density hail.
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Clifford's post is a brilliant example of modern science at its best.
Superb in analytical detail. Though not answering the OP's question. For understandable reasons.
Personally, I'd bet that identical snowflakes do occur, perhaps quite frequently.
But there are too many ephemeral snowflakes for Science to ever prove it.
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Clifford's post is a brilliant example of modern science at its best.
Superb in analytical detail. Though not answering the OP's question. For understandable reasons.
Personally, I'd bet that identical snowflakes do occur, perhaps quite frequently.
But there are too many ephemeral snowflakes for Science to ever prove it.
You may prefer a more detailed study.
https://www.thenakedscientists.com/forum/index.php?topic=6511.msg67939#msg67939
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Oh, man, I forgot about Deuterium and Tritium, and various Oxygen isotopes. Not particularly common, but there will be a few in that mole. And that doesn't count other contaminants. A nucleation particle? What about a few rogue hydrogens giving H3O+ and OH-?
When one starts calculating factorials... the numbers get really really big.
But, that is calculating the number of different possible snowflakes.
In a sense, this is also the birthday problem. (https://medium.com/i-math/the-birthday-problem-307f31a9ac6f)
We know that there are 366 different unique birthdays (ignoring the year). But, it doesn't take 367 students to have two with the same birthday. In a class of 30 students, there is about a 75% chance that two will have the same birthday.
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The classic experimental publication is "Snow Crystals" by Bentley and Humphries, who spent many happy hours in Vermont photographing snowflakes and frost. They selected some 2500 images from many, many more and certainly never found two alike.
Even if you found two structures with the same underlying fractal symmetry, they would almost certainly not have the same number of molecules.
But beware. A searching question in the 1966 Natural Sciences Tripos Part II Crystallography was "The average photograph of a snowflake is more symmetrical than a photograph of an average snowflake - discuss."
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The reason that a snowflake looks fairly symmetrical is because all sides of the same crystal took the same path through the varying temperature, pressure and humidity profile inside the cloud.
But these dynamic environmental conditions are not precisely uniform across the width of a snowflake.
- So is even 1 "arm" of a snowflake identical to the other arms?
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Perhaps "all snowflakes are unique" has a similarity to another popular saying "lightning never strikes twice in the same place".
Does anyone know what's at the back of it?
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"lightning never strikes twice in the same place".
It strikes things like the Eifel Tower fairly regularly.
In a sense, this is also the birthday problem.
We know that there are 366 different unique birthdays (ignoring the year). But, it doesn't take 367 students to have two with the same birthday. In a class of 30 students, there is about a 75% chance that two will have the same birthday.
Except in this case there are vastly more days in the year than students.
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Perhaps "all snowflakes are unique" has a similarity to another popular saying "lightning never strikes twice in the same place".
Does anyone know what's at the back of it?
It's demonstrably untrue. I have a friend who has been struck by lightning twice. Even if the "place" moves from one country to another (in Dave's case Norway to England) if your name is on the ticket, it will find you.
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To get struck by lightning once, may be regarded as a chance misfortune.
To get struck twice, looks like some kind of heavenly signal that Dave is marked out for a special destiny.
Has he experienced any further omens or portents of what that destiny might be?
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Possibly as a result, he had the most amazing Afro hairstyle for a man born with a straight Caucasian thatch. And a belief that resurrection was only needed by the sort of wimps who died in the first place. So his destiny may well have been as a permanent model for hairdressers and soul bands.
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There is a lovely book by (mathematician) Prof. Ian Stewart called "What shape is a snowflake?" In it he explains more or less (if I remember correctly) that the hexagonal symmetry of snowflakes is due to the shape of the water molecule so that property is always present, but the exact shape depends on the exact conditions encountered by the snowflake on its descent, temperature, pressure, wind, dust etc. Since it is highly unlikely that 2 conditions will be identical, it is highly unlikely that 2 snowflakes will be identical. But no one has seen them all to make sure.
Clara
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Alan sent us this message about snowflakes:
Hi Alan! & Thanks for such an Intriguing question.
🙏
"I have heard it said many times that no two snowflakes are the same.
Yes.
❄️
Given the billions and billions of them that have fallen to Earth, this really does seem unlikely.
Yes.
❄️
Since nobody has looked at them all, would you agree with me that the only thing to be said with any certainty, is that no researcher has ever found two the same?"
Yes.
❄️
What do you all think?
P.S. - Probability is Longer than Infinity, Only when you count the Alphabets used to describe them.
♾️
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Thanks everyone for your input, we've now published our answer to this question, and you can find it here:
https://www.thenakedscientists.com/podcasts/question-week/every-snowflake-unique
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"I have heard it said many times that no two snowflakes are the same. Given the billions and billions of them that have fallen to Earth, this really does seem unlikely. Since nobody has looked at them all, would you agree with me that the only thing to be said with any certainty, is that no researcher has ever found two the same?"
What do you all think?
I believe that every single structure no matter what it is has its own unique shape size weight. Even a man made object let's say a steel ball bearing one may say it is made to exacting standards well the answer to your question lays their standards imply within a degree of tolerance so perfection is a concept, not a fact.