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Perhaps I've been watching too much of the BBC Horizon Program, but I think I understand his rationale.
The primary influencing factor here, is the assertion that in an Infinite Universe, anything which is possible, no matter how small the probability, will eventually happen ... and has already happened, infinitely many times over.
They spend a lot of time on the infinite monkey/Shakespeare's works thing and come to the conclusion that the monkey will succeed. Then, there will also be infinite monkeys typing randomly, ad infintum, as well. No matter how small the probability of it happening, because of the influence of the concept of infinite expanse and time, it will all eventually happen.
If one accepts this paradigm (of a truly infinite universe), then a duplicate world to our own, which is certainly possible, will exist. I'd say this is a prediction of assured existence .. it all comes from infinite mathematics (not that I've attempted any such proofs, specifically ...).
Its all about taking infinity to the extreme.
Cheers
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