No two snowflakes...

Technically, we are talking about permutations not combinations -- but either way, the count is finite. It's just an expression of probability. It's sort of like saying that the probability of a random number between 0 and 1 equals 0.5 is zero (although not quite the same, because here the probability is zero precisely because the count is not finite).

Nature tends not to spit out unique cases. There is usually something else very similiar (apply this concept to Earth...).

It's just the same as - no two humans are alike. It is possible that two humans will be born that are exactly the same, but the chance is so small that it may as well be non-existant.

Funny enough, I was asking myself the same question recently, while out on a run.
Since I did not have enough information in my head on how snowflakes are formed, I did not get too far on the number of permutations.

However, I did conclude, that if it was true, it was impossible to prove it.
It it was false you'd have to find two snowflakes that are exactly the same, and that's very unlikely even though it might be possible...

It's the same with fingerprints, isn't it?
They say that no two prints are the same.
But to prove it, you'd have to compare all fingerprints there are, and all there ever were, and on top of it all there will be in the future.
IMPOSSIBLE!

Well, I think my run came to an end at this point!

[quote="aperson"]Nature tends not to spit out unique cases. There is usually something else very similiar. [/quote]

For one, this remains to be proven.
How many trees/sunflowers/rocks/etc. that are the same have you seen, yet?
And secondly very similar <> the same

I sould have said: No two snowflakes are identical. Because all snowlfakes are the same.

It is a good point that this statement cannot be tested, but one thing occurs to me. If we define location and time to as aspects of the snowflake along with it's symmetric design, no snowflakes are identical. If not, there may be two identical snowflakes.

[quote="Cyracuz"]If we define location and time to as aspects of the snowflake along with it's symmetric design, no snowflakes are identical. If not, there may be two identical snowflakes.[/quote]

That is true, I don't think people generally asking this question, or making this statement will take this into account.
I would quite like to get back onto the question on how many possible permutations there are.

Take this one for an example

Are all the little 'limbs' at 60-degree angles?
Are all pieces a certain length or multiple thereof?

If it's a no to both questions, I think there would be so many permutations, that it's likely there are more than snowflakes.
Which still would not be a proof, of course, just the statement, that it is theoretically possible for no two snowflakes ever to have been identical!

And anyway, how many snowflakes ever existed?

The construction of a snowflake is nearly a random process, the only thing that makes it ordered is the polar nature and structure of the water molecule. A snowflake contains over 180 billion molecules. There are only a finite number of stable ways for the molecules to attach themselves, I don't know how many ways that is....let's say it is N, based on that the number of different possible snowflakes is roughly N^180000000000. Even if N=2 (which is way too small), this number is so big that you could probably jam pack the entire galaxy full of unique snowflakes.



We can't prove that 2 like snowflakes have ever existed, although it would be possible to make a statistical guess, but we can prove that it is not impossible for 2 like snowflakes to exist.

Interesting

So the saying about the snowflakes is nothing more than just that.

Btw
What is the 'polar nature and structure' of the water molecule? Is this the same thing that makes water from droplets??

A molecule that has a strong positive charge on one side and a negative charge on the other is said to be polar.

The nucleus of an atom contains protons (+ charge) and neutrons (no charge) so the nucleus is positive. The electrons which surround the nucleus have negative charge and generally shield the interior charge so that the molecule is stable / neutrally charged.

In a water molecule, an oxygen atom is bonded to 2 hydrogen atoms. The hydrogen atoms are covalently bonded to the oxygen meaning that they share electrons. This reduces the shielding of the nucleus of the hydrogen atoms because the electrons are "busy making the bond" so to speak.

So, the side of the molecule with hydrogens is more positive than the opposite side of the molecule where the oxygen is shielded by a higher density cloud of electrons, making that side negative.

The charges also determine the shape of the molecule, because the atoms are held into some stable shape due to internal attractions and repulsions.

Since like charges repel and opposite charges attract, the structure that water molecules can connect together to form a larger object depends on the charges on each side.

Thanks for the explanation, stuh.

Anytime