We've all heard of an infinite number of monkeys typing out Shakespeare, but could coincidence be even stronger than that? Could the universe become populated by giant space brains? And more importantly, has it been already?
Some time ago, scientists noticed that the universe was flying apart. It was flying apart, they noticed, faster and faster. Sooner or later the stars will recede beyond the span of our view. Then our own sun will recede. Particles will be lost in an increasingly vast sea of nothing, until the nothing goes on forever. The universe will just fade out.
That kind of thinking really makes one look forward to being dead so one doesn't have to deal with all of that, but some scientists got together and thought up some the idea of a randomly-generated resurrection. Space, even as we see it now, is not as empty as it would seem. It is permeated by a field that gives rise to short-lived but spontaneously occurring particles that pop into and out of existence. And in the void that will be the future universe, this will still happen. And with an infinite amount of time to keep popping up, some of these particles will clump together to form bigger particles, and bigger ones, and so on. Sure, it's unlikely, but in such massive stretches of time and space, unlikely doesn't really matter. Not only that, but the matter that pops up won't have extreme temperatures or natural predators or any existing structures to skew chance. A marshmallow can't spontaneously form in a lava flow, because it would be melted. In a random bit of space that no particle is influencing? Maybe it would have a better shot. The matter that forms, whatever it is, could be as small as a quark or as big as a planet.
And that matter could get seriously ridiculous. Ludwig Boltzmann was a physicist at the latter half of the nineteenth century, and he put forward a theory just like this. From this argument the Boltzmann Brain argument emerged. This was the idea that random fluctuations in the universe will give rise to a self-aware mind in the chaos. Sure, it would take a while, but it's not like the universe is on a deadline or anything.
It gets weirder. As physicists kicked around this idea, the Boltzmann Brain Paradox was floated. Not only could the brains emerge from the chaos after the universe, but one could have already emerged. It could, in fact, with memories of its past life. What I'm saying is, "Hi, space brain!" What are the odds, the Paradox implies, that somehow a whole universe was formed in a Big Bang and is now winding down with all of us sentient beings observing it? Isn't that less likely than one consciousness, with a few delusions, having popped into life by chance?
While the Boltzmann Brain Paradox idea is a fun one to explore, most scientists don't buy it. Feynman famously pointed out that, even if one part of the universe could get it together and pop out a space brain, then it would be likely that the rest of the universe would still be in complete disorder. So when the brain looked around, it might be in a orderly little corner itself, but when the rest of the universe would most likely be a mess. The universe we can see is strange, sure, but it's as orderly as our corner, right out to the edges. So, sorry Boltzmann. No brains yet.