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Two Snowflakes May Be Alike After All
An anonymous reader writes "LiveScience is reporting that it may be possible for two snowflakes to be alike after all. For anyone who studies probability, this seems reasonable, given that the article mentions that 10^24 snowflakes fall in any given year. The article contains links to fascinating snowflake pictures. From the article: 'A typical snow crystal weighs roughly one millionth of a gram. This means a cubic foot of snow can contain roughly one billion crystals ... "It is probably safe to say that the possible number of snow crystal shapes exceeds the estimated number of atoms in the known universe," Nelson said. Still, while "no two snowflakes are alike" might hold true for larger snowflakes, Nelson figures it might ring false for smaller crystals that sometimes fall before they have a chance to fully develop. "How likely is it that two snowflakes are alike? Very likely if we define alike to mean that we would have trouble distinguishing them under a microscope and if we include the crystals that hardly develop beyond the prism stage--that is, the smallest snow crystals," Nelson said.'"
...and of course, I can't find it... a scientist published a picture of two identical snowflakes in, I'm almost sure, Science or Nature. And, no, I'm not talking about Snowflake Bentley. It was a byproduct of some kind of meteorological research, they were flying a plane through clouds where snow was being formed, and, as you'd expect, if two flakes of snow form under virtually identical conditions you end up with two virtually identical flakes.
I think this was in the 1990s.
It made the mainstream news at the time.
"How to Do Nothing," kids activities, back in print!
What goes up must come down. (suspected true)
Lightning doesn't strike the same spot twice. (obviously false (ouch!))
A watched pot never boils. etc...
This is like numerology. You take a bunch of squishy data (aphorisms) and attempt to rigorously evaluate them.
I am reminded of Charlie Brown's answer to the question "How many angels can dance on the head of a pin?" His answer: Eight if they're skinny, four if they're fat.
Don't trust anyone under thirty.
how many lego combinations are possible
To simplify the question, we could consider just these classic bricks. By different combinations we'll understand fully connected arrangements, with no regard to combinations of colour, rotations, or symmetries. I suppose that Legos can connect with a single corner, correct me if I am wrong.
Le(1) = 1
Le(2) = 17
Then, for one of the combinations in Le(2), there are 18 ways to add the third piece. The problem seems to be barely tractable now without the aid of at least lego pieces and a piece of paper, but I'll make bold assumptions. If Le(n) grows at least as fast as 10^n (and my gut tells me that it grows much faster), then measly 100 pieces will give you a quantity that dwarfs the number of particles in the known universe.