Let's take a Turing machine, Bob, that can test whether a certain Turing machine would accept a given input. Bob will accept if the other machine accepts, and reject if the other machine rejects. It can't ever figure out if it was never stopping, thus it can't really decide the language of Turing machines.

But going a step further, Bob by definition replicates all Turing machines. Let's say that Bob is Turing machine 666 for the hell of it. There's also the Anti-Bob, a Turing machine that's the compliment of Bob, saying yes when Bob says no, and no when Bob says yes. So as Bob says yes if the machine accepts the input, Anti-Bob says hell no.

So does the Anti-Bob accept the Anti-Bob? Assuming that the Anti-Bob is machine 668 (the bloke next door), we're really accepting if it accepts Turing machine 668. The Anti-Bob accepts machine 668 if and only if Bob says that machine 668 does not accept machine 668. So machine 668 accepts machine 668 if and only if Bob says that machine 668 does not accept 668.

That's whack shit.

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