Here are some weird, true things I've learned about the world:
1) Each breath you take shares about 5 air molecules with Hitler's last breath. The equation to verify that yourself (assuming Hitler's last breath has evenly mixed with the rest of the atmosphere by now) is:
Number of shared molecules = volume of lungs / volume of atmosphere * molecules inhaled per breath
Those three numbers are (roughly): 1 liter, 5 * 10^21 liters, and 3 * 10^22 molecules
If that bothers you, feel free to replace "Hitler" with "Gandhi" or "Jesus." If it doesn't bother you, replace "breath" with "glass of water" and "Hitler" with "dinosaur pee."
2) It's possible to cut a sphere into 5 pieces and rearrange the pieces to make two spheres as big as the original. Google the Banach-Tarski paradox. The catch is that the cuts are bizarre, infinitely complex cuts, so you can't do it in real life. I don't get it, but it's true.
3) You can say with absolute certainty that at least 2 non-bald people in New York City have exactly the same number of hairs on their head. The argument centers on the fact that people have about 100,000 hairs, which is fewer than the ~8 million people in NYC. For more details, google the pigeonhole principle.
I also suspect that there *have* been two snowflakes that have been (almost) exactly alike, but that's just me being crazy.