Infinite Improbability

If you took an absolutely titanic-sized bag of randomly unsorted letters and numbers and proceeded to draw them out, one by one, laying them in long threads of letters – what is the chance that you would accidentally assemble the collected works of Shakespeare, perhaps Tolstoy’s Anna Karenina, Orwell’s 1984 or the Tibetan Book of the Great Liberation? Or all of them?

This is a question that has been asked before, in a different way: an infinite number of monkeys hammering away on an infinite number of typewriters is as a matter of logical necessity bound to eventually write everything that has been or ever will be written. Not much of a realistic prospect except that some models of hyper-inflationary (i.e. “Big Bang”) Cosmological model suggest that our Universe may very well be infinite in spatial extent.

A curious mathematical fact of infinity is that it can have sub-components (sets) that are the same size as the whole infinity. Difficult to wrap our minds around but demonstrably true. (Consider that the infinite sequence of natural numbers 1,2,3,… can be paired off in one-to-one correspondence with the even numbers, or the multiples of 3 or 7 or 327, or square numbers, and so on.)

An even more mysterious result – tying together the monkeys and the infinite sub-sets: in an infinite Universe, anything that can happen will happen and will happen an infinite number of times. So, this includes you reading this, me, the room where you are, the planet, this galaxy and all the possible permutations and configurations of all these (infinitely many) things.

Is this Universe infinite? We might never know but it is fascinating to consider that of all the possible, probable worlds that we might have found ourselves in – we are in this one and that there may be an infinite number of identical worlds, even if we will never know it.

Dredged out of vast electrochemical pools of improbability and entropy, the long threads of causal facts that have led to this moment also seem very unlikely but are nothing near infinite. Still, I don’t think we ever stop to acknowledge the utter improbability of any of this even existing in the first place.

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