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I suppose the difference is knowing to put the number into your bit string interpreter. Whether that be a computer program or the physical universe.
It's kind of like the arguments for "you can't copyright a number". Well sure, but when you stick .mp3 on the end it isn't just a number any more - it now tells you that you should interpret it.
Agreed, but then, I still disagree with Eliezer when he says that when you generate 2^N possible bitstrings of size N, "you wouldn't expect this procedure to generate any people or make any experiences real". If I can generate all these strings in the first place, I could just as easily feed each one to my person-emulator, to see which of them are valid person-strings. Then I could emulate these people just as I emulate meat-based people whose brains I'd scanned.