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cousin_it comments on What a reduction of "probability" probably looks like - Less Wrong
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About your first question: I use "randomness" in a sense that doesn't have anything to do with unpredictability. It only relies on observed long-run statistical properties: limiting frequency, stddev, law of large numbers, frequencies of substrings... For example, the binary expansion of pi works fine for my purposes (if pi is a normal number), even though it's perfectly predictable by an algorithm.
About your second question: LW is one of my ways to avoid losing my grasp of English :-) And I'm still waiting for my chance to use "As you know, Bob" like Shalizi did.
About your third question: I don't think anthropic hypercomputation is the big blocking issue. After all, our brains don't seem to use quantum computing, even though it's available here in 2-world and offers significant speedups on problems like database lookups which sound pretty damn important! My idea is rather that the 3-world and friends are too crazy to support any life at all.
Okay, but then you shouldn't say that failing to know the sequence is not a property of his ignorance. If pi works here, then not knowing the next digit is indeed a fact about your ignorance (specifically, ignorance of the result of a known procedure).
Edit: nevermind, I had misread that: yes, it makes sense to that that the agent is ignorant of the result, but that the randomness is not a fact of that agent's ignorance.
Yes, but that's still part of the anthropic argument for the Born rule, just on the other end of boundary.