Secular Reincarnation
Lately I've been thinking about Thomas Huxley's idea of infinite monkeys on infinite typewriters for an infinite amount of time. As the theory goes, they'd eventually recreate Shakespeare's works in their entirety simply due to random hitting of the keys. Don't argue this point, it's true. In fact, they'd not only recreate Shakespeare's works once, but would do so an infinite number of times. The same goes for every other literary work, supposing that they phonetically write out other scripts (like oriental, Cyrillic, Sanskrit, etc.)) and ignore accents that aren't available.
An easier way to wrap your head around this problem is to envision a keyboard that has pebbles being dropped on it, hitting only one key at a time and no others. Given that each key has an equally probably chance of being struck, it will produce every work if left doing this processes for unlimited time. The reason I find this example to be clearer is because most people seem to think the monkeys would have some sort of intent behind their actions, as if they're actually trying to recreate Shakespeare or whatever. This isn't the case - they're simply mashing keys and accidentally making novels.
Expanding from this, I realized that secular reincarnation is capable of happening. It is entirely possible that one or all of three things are infinite: time, space, and/or alternate dimensions. As long as one of these is unlimited, it's quite possible that when we die, our consciousness in its exact form could re-manifest somewhere else. This pulls a lot of things into question, of course. Where does consciousness rest? Is it possible to transmit it? Even if something is structurally identical, will you, as you are now, be part of it? What about a/the soul? Too many questions, really. But, it is promising for any non-religious person who's despairing at the afterlife.
To clarify where I'm coming from, probability theory states that nothing has a 0% chance of happening (aka everything has a chance greater than 0). Even if it's infinitesimally small, it will express itself somewhere in an unlimited number of trials. The real mindfuck here is if you consider omnipresent beings. If every possible combination of things must happen, then somewhere an omnipresent god must exist, and in another place it must not, which violates the first one's power. This clearly demonstrates that there is a limit to the probability curve in practice - we don't have gods walking among us and intervening, as some interventionist religions would believe.
Thus, we should refine the statement to be:
In an infinite universe, anything that is possible must happen.
Note: Do not attempt to actually create the monkey's on typewriters. Only a fucking idiot would expect to see similar results when comparing an infinite sample and an extremely small, finite sample.