# Unlikely things in an infinite universe

I was reading Hitchhiker’s guide yesterday, and they had an interesting section in there in which, to paraphrase, the author said this:

Virtually nothing is manufactured anymore, because in an infinite universe, most anything anyone wants grows naturally somewhere.

This got me thinking. The logic seems solid enough… as improbable as anything seems, if there is a non-zero chance of it occurring, than in an infinite universe, it will occur… so do VW bugs grow on some planet somewhere?

But how do we know that the universe is infinite? Most stuff I’ve read recently seems to give it a definite size.

The answer seems to be yes (so long as the occurence is physicallty possible). See the last three paragraphs before the list of references here.

This is probability a question that I always forget the answer to:

If you flip a coin over and over literally forever, is it IMPOSSIBLE that heads will NEVER come up, or just unlikely to the extreme?

It’s not impossible, but the probability is 0. Keep in mind, though, that the probability of any single sequence of flips in this scenario is 0.

Is the probability actually 0, or does it approach zero? (It’s been long time since calc, which I never learned well to being with)

It’s actually 0.

Yes, but the statistics also say that it will take an infinite number of explorers an infinite amount of time to find them, so you’re better off just building what you need.

In this particular case, the problem is compounded by the fact that VW Bugs are a legume (at least on all the known worlds where they’ve been found). The only time they get spotted by satellite is when the natives use their husks as yard art.

If you flip it an infinite number of times the probability is actually zero.

However, you can’t, so it isn’t. You can approach an infinite number of times, so the probability will approach zero.

Nicely explained dlack and ultrafilter, thanks.

In an infinite universe… yes.

But as has been pointed out, you’re infinitely unlikely to find that planet. Which is where Douglas Adam’s idea rather fails. And if you did find it, you’re likely to have to transport it an infinite distance back home. Which is further than any other VW has travelled before.

I suppose you might be able to narrow your chances a little if you’re not fussy about the colour.

They don’t actually grow—they’re being assembled by an infinite number of monkeys with an infinite number of monkey wrenches, right next door to the monkeys that are typing Shakespeare.

An infinite universe can repeat the same finite forms infinitely, so an infinite universe may NOT necessarily contain VW bugs growing somewhere.

This seems like a pretty big if. How would you know ahead of time whether there is a non-zeo chance of something occurring?

Note that in an infinite list of random real numbers, the probability of any particular real number (like 1 or pi) ever showing up is 0.

That’s why I like integers.

I think the odds of VW bugs growing on some planet in an infinite universe is the same as flipping a quarter (Regular US Washington/Eagle quarter) an infinite number of times and having it ever land banana side up. There may be an infinite number of chances but it isn’t going to happen unless there is a mechanism for it to happen within the laws of physics.

So, in an infinite universe, assuming that all parts of it have random atoms moving around through the interstellar space, wouldn’t there be a fully-assembled 747 somewhere out there that happened randomly?

it takes more than a random collection of atoms to make a 747. Even if all the correct atoms were in one region what would bring them together? The mass of a 747 doesn’t have enough gravity to do that and if it did it wouldn’t make a 747 shape. Notice any cube shaped planets? Even if all the atoms bumped together in the right places there would be nothing to hold them together. I still think that an infinite universe does not mean that every object imaginable must exist in it. We’d just end up with a lot of stuff similar to what we see in our on region of our galaxy with extremely small odds of finding a jupiter size planet with rings made out of pipe cleaners.

It should be pointed out that everyting in the universe, including VWs and 747s is the result of random activity at the quantum level. No?

No, it could happen. Start with a nebula which happens to contain some aluminum, magnesium, iron, titanium, and whatever other elements you need for a 747. That’s not too bad; all of the aluminum etc. which we use to make 747s was in a nebula at some point. Now, have a gentle collision between two atoms, which results in them sticking together. OK, that happens all the time in nebulae. And now, and here’s the kicker, repeat that same process about 10[sup]32[/sup] times, with each one just happening to involve the exact sort of atom you need, at the exact right spot on the growing atom-clump. The end result? A 747. Improbable in the extreme, certainly, but not impossible.