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Qiaochu_Yuan comments on Simulating Problems - Less Wrong
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I am a graduate student in mathematics, and I can point you to large quantities of evidence that hypothesis A is false. I recognize that the tone of my previous comments may have been unnecessarily antagonistic, and I apologize for that, but I genuinely don't understand what question you're asking. If you don't care enough to explain it to me, that's fine, but you should take it as at least weak Bayesian evidence that other people also won't understand what question you're asking.
It's not the antagonistic tone of your comments that puts me off, it's the way in which you seem to deliberately not understand things. For example my definition of analogous — what else could you possibly have expected in this context? No, don't answer that.
I believe I have said everything already, but I'll put it in a slightly different way:
Given a problem A, find an analogous problem B with the same payoff matrix for which it can be proven that any possible agent will make analogous decisions, or prove that such a problem B cannot exist.
For instance, how can we find a problem that is analogous to Newcomb, but without Omega? I have described such an analogous problem in my top-level post and demonstrated how CDT agents will in the initial state not make the analogous decision. What we're looking for is a problem in which any imaginable agent would, and we can prove it. If we believe that such a problem cannot exist without Omega, how can we prove that?
The meaning of analogous should be very clear by now. Screw practical and impractical.
As an aside note, I don't know what kind of stuff they teach at US grad schools, but what's of help here is familiarity with methods of proof and a mathematical mindset rather than mathematical knowledge, except some basic game theory and decision theory. As far as I know, what I'm trying to do here is uncharted territory.
The question is how close you wanted the analogy to be.
Okay, this is clearer.
I can point you to a large body of evidence that I have all of these things.
Close enough that anything we can infer from the analogous problem must apply to the original problem as well, especially concerning the decisions agents make. I thought I said that a few times.
Does that imply it is actually clear? Do you have an approach for this? A way to divide the problem into smaller chunks? An idea how to tackle the issue of "any possible agent"?
I'll give you a second data point to consider. I am a soon-to-be-graduated pure math undergraduate. I have no idea what you are asking, beyond very vague guesses. Nothing in your post or the proceeding discussion is of a "rather mathematical nature", let alone a precise specification of a mathematical problem.
If you think that you are communicating clearly, then you are wrong. Try again.