Originally posted by Guybrush Threepwood How can you be sure there are no two snowflakes the same?
Because you define 'the same' in some convenient fashion like, two entities are 'the same' if and only if they are the same entity (maybe at different times).
The question is, after all, really:
"Why are no two [distinct] snowflakes the same?"
Snowflakes can be very similar to each other, so similar, in fact, that calling them alike would be fair. They can certainly be similar enough that you would not be able to distinguish two photographs of one of them from one photograph of each.
OK, how about congruent for all of you who don't like "the same".
I don't think you can say with metaphorical certitude that no two are congruent. I think it is a matter of probability. Each time a water molecule is added, it has different ways to fit in. It would be like flipping a coin some very large number of times, and getting the exact same sequence. Make the number of flips high enough, and the odds become very low - perhaps so low that a very large number of trials has a negligible chance of producing two duplicate sequences.
How many molecules in a snowflake? How many ways are there for a molecule to be added to the structure? How does symmetry effect the probability? How many snowflakes have there been?
I have lost two friends over conversations on this idea and an argument that followed and went something like this. But MY thoughts are that if you have parallel universes where almost everything but a speck is identical, you cannot call two John's the same even if they are the same in every aspect in universes the same in every aspect except for the little speck of difference somewhere far far away from the Johns and won't bother them during their lives. Because I want to be right when I say "John lives in a universe where a certain speck far far away from John is attacking people at a very specific location." If this can't be true, then damn John and his alter ego and his ARGGH damn John. Hey, your name is John! Then if you have Johns that are different, you are going to decide on whether or not to call them the same for practical reasons. Hug John because he's wearing a fez? You'll have to examine the Johns for fezzes, if one has a fez and the other doesn't, you're going to have to call them two different things when considering hugging. Snowflakes ARE the same? I think I'm missing something.
Great replies, I love this site!
Snow flakes are a great example of the creator creating. Every single thing you see is a "one of". Each is its own creation. For two things to be the same they would have to be the same thing. Any two things contain thier own "matter". The world is full of similarities but no two items are the same.
The snow flake is a great example of this.
When I think about asking if two snowflakes can be the same I usually try to guess the chances of the person I'm talking to killing me. Hypothermia wonderland is not the best time to ask such questions as Why are no two snowflakes the same?
E being the creator don't make since. Since everything comes from E then there was no creation. Merely just converting and making the converter everything. So E is the converter. Makes perfect sense. Since we weren't created just converted like the houses we live in converted from trees. Our bodies converted by the food we eat. blah blah blah eh.
Depends on the scales you use. Before the universe (leaving out the fact that we probably can't apply logic to this period), there are no defined reference frames, so in comparison to an boundless sea of possibility and impossibility, I would think it pretty infinitessimal.