You need to be able to know that Omega has arbitrary amounts of computing power. At some point, you won't be able to tell between the capacity of two super powerful computers.
I think nearly all responses to "what would you do when faced with X" questions are confabulation and I don't think this case is especially worse than most.
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Anyway, (IMO) the point of the thought experiment isn't to reproduce your hypothetical internal state, it's to figure out without pressure what you'd want yourself to do.
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At what point does this stop making sense: Dust speck Ramsey number R(10^100,10^100) people, dust speck BB(50000) people, aleph_0 people, aleph_1 people
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