There's a really awesome thread at Reddit called "What's the most mind-blowing fact you heard/read in your life?" where commenters are posting well... that.
It's a great read! But there are a few here and there that are a bit undeserving of the title, because they are just wrong :-)
Here are a couple from the beginning of the thread (it's got over 4000 posts now).
"There has been no evidence suggesting the universe is not finite. If we assume the universite is infinite, then it is certain that every single possible combination of events has happened somewhere in the galaxy. In an alternate area, all of human history is the same, except you don't decide to post this thread. With certainty."
Beyond confusing the galaxy with the universe, let's think this a bit.
It's funny, but I remember reading something like "if the universe is infinite then everything that is possible has certainly happened somewhere" in a cheap scify booklet maybe 30 years ago.
In that story, that reasoning was used to justify a naked cyclops that walked in space, IIRC. It was found by a starship called SKY-11111. If anyone has read that story, he has my simpathy (I should write about how hard it was to read scifi when I was a kid, beggars can't be choosers!)
But the problem here is just a basic misunderstanding of probability.
Let me explain with an example: Consider the odds of someone spending a year flipping a fair coin and getting "heads" every time. That's something very unlikely. Let's call that probability P1.
Now, let's consider the probability of "there has never ever been a person that flipped a fair coin for a year getting only 'heads', and there never will be", and call that P2.
Now, if the universe is large, P1 will grow. As there are more people, there is a larger chance of someone deciding to waste a year and then there is a tiny chance of him being incredibly ... (well, not lucky, see how he spent his year!) but let's say, consistent? And getting heads all year.
What the heck, let's say P1 is now 50%, so it's not even unlikey.
But that means P2 is also 50%, since it's true exactly as often as P1 is false.
Now, which one of these two things will happen "With certainty"? See? Likely is not the same as sure, unlikely is not the same as impossible, and adding an infinity doesn't do the trick here.
So, really, even if the universe is infinite, and even if it were crowded with people, there are lots and lots of things that are never going to happen.
I find that more mindblowing than the original, but that's just me.
Here's a simpler one:
If you took all of the silver the Spanish mined from Cerro Rico, you could build a bridge from Potosi, Bolivia, to Spain. If you took the bones of all the Indians (about eight million) who died in the mines, you could build another bridge back to Potosi from Spain. Cerro Rico has been so thoroughly mined that there is an entire mountain next to it of the rubble extracted from it. The Indians call this second one "the mountain that weeps."
Here I am guessing he is greatly overestimating the amount of silver extracted from Cerro Rico.
Spain is roughly 8800km away from Cerro Rico. A 2-meter wide path, 20cm thick would mean 3520000 cubic meters of materials. That's much much less than a bridge would use.
Cerro Rico is about 4800 meters tall.
So, this means the material for that path would be enough to build a column with square base 27 meters wide, and as tall as Cerro Rico, of pure silver.
That would be, considering silver has a specific weight of 10490... 36924800000000 kilograms of silver. That is... well, that's a lot of silver.
How much silver? Well, in dollars, that would be $27508976000000000
In any case, the thread is great fun, and everyone who has, say, a young kid should read bits of it ... with a skeptic eye open ;-)