How is it mathematically possible for no two snowflakes to be alike?

Answer 1

There are 3 x 10^19 H2O molecules in a typical snowflake (http://chemistry.about.com/library/weekly/aa021503c.htm) You could think of each of them as little hexagons which pack together. For snowflakes to be identical is staggeringly unlikely. Even if you allow slight differences too small for the naked eye, there are a lot of possibilities.

Here's (http://www.its.caltech.edu/~atomic/snowcrystals/alike/alike.htm) a guy who analyzed it in great depth. His conclusion is "And thus it's unlikely that any two complex snow crystals, out of all those made over the entire history of the planet, have ever looked completely alike.".

I think a good question is how the molecules on one arm "know" how the other arms are growing - why, though any 2 snowflakes are different, the 6 "arms" on a snowflake are almost identical.

Answer 2

The "no two snowflakes are alike" is meant that - in a random sample, you won't see to snowflakes alike. It's true that in the history of snow, all over the Earth, the conditions for snow were identical (that is identical for snowflake making) and that the snowflake was formed and fell in an identical shape.

Put another way... in a single snowfall at any given place, you have an almost zero propability to find two snowflakes at look identical.

Just enjoy that there can be so many different ways to have snow!

Answer 3

Look alike, be identical. Two very different concepts. At the molecule-counting level, we can't see a difference of 30 trillion molecules stuck onto one arm of a six-armed snowflake because that's only one millionth of the flake, using sofarsogood's quote of 3 x 10^19 H2O molecules per flake. Now think of all the variations you can do with 30 trillion molecules, both in number and distribution, each one non-identical with any other but visually the same.
Although the statement that in a single snowfall you have an almost zero probability of finding two snowflakes that look identical is probably technically correct, part of that correctness stems from the fact that you could never check even one millionth of the flakes that fall; I would say the probability of two such flakes actually not falling is very small. Guessing at the numbers, there is a limited number of flake "styles" and a countable number of "features" that one would compare when assessing the lookalike property of 2 flakes. Elongated features could be considered to look identical if within, say, 2% of each other in length and 5% in width and thickness. So we might distinguish 100 styles, 1000 features per style, and 20000 different feature sizes, for 2 billion distinguishable flake shapes. Assuming an average flake weight of 3 mg, I calculate that a snowfall equivalent to one inch of rain deposits 21.8 trillion flakes per square mile, or 11000 times as many as there are distinguishable shapes. Pretty heavy odds that there'll be a visual match.
Sofar wondered about the near-identity of the arms of a flake in spite of the rarity of flake matches. I suspect that has a lot to do with the flakes' histories of formation. Each flake must travel a unique path, being turbulently mixed and tossed up and down in the cloud for many minutes before falling to earth. (The property of extreme sensitivity of a chaotic system to small differences in initial, and midcourse, conditions.) Since other flakes undergo different sequences of humidity and temperature changes, their shape reflects those differing histories, whereas the arms of an individual flake only experience very small-scale differences.

Answer 4

A snowflake is made of many, many molecules. These molecules can be arranged in so many ways that there are in effect an infinite number of arrangements.

There are 6.02x10^23 molecules of water in 18 grams. That is a really BIG number.

Answer 5

Its kind of like saying that the powerball will never have the same numbers twice.... Even though it is possible it is very unlikely to happen.

Answer 6

The mathematical Genius/Artist Who created them all only makes one of each?

Answer 7

forget the odds. Yes it is possible. It far fetched - yes. But yes it is possible. there is nothing in this world keeping it from being impossible. :)

Answer 8

yes, they all do, i certainly cant tell them apart, even if their molecules are blah, blah, something