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."

—Moth­er­sRape­Horn

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."

—tofketv

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 ;-)