# (Ln(*x*))^{3}

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4:51pm on Monday, 14th March, 2011:

## Infinite

Rant

I heard three physicists on the radio this morning talking about possible universes, and they seemed to agree that if the current universe is finite and there are an infinite number of universes, then there are an infinite number of other universes identical to this one.

The explanation they gave was by way of an analogy. If you take a pack of cards and shuffle it, you get the same cards in a different order. If you shuffle it enough times, though, eventually you'll get the same order as you had to start with. Shuffle it an infinite number of times, and you get an infinite number of repetitions.

I don't buy this. Sure, you're guaranteed to get an infinite number of repetitions of at least one card ordering, but in theory you could get the same ordering every single shuffle, even if you did it an infinite number of times. Just because there are an infinite number of universes, that doesn't mean there are an infinite number of universes just like this one — ours really could be unique.

I remember being told at school that the sequence of digits in the mathematical constant pi contained every finite sequence of digits an infinite number of times. This meant that if you converted them into coloured squares, you could build photographs of any size that showed every object in existence from every conceivable angle. That sounds great, but how do we know that? It might be that after a finite number of digits, pi stops containing the number 9.

The same "contains all possible finite sequences of digits" argument applies to the mathematical constant e, too. OK, so how many times do you have to multiply pi by 10 and discard the tens column before you get e? An infinite number? Because until you do, you can't say the same thing about both of them.

I'm sure there's some mathematics that explain all this, but we need a better example than shuffling cards for it to make sense...

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Copyright © 2011 Richard Bartle (richard@mud.co.uk).