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Andreas_Giger comments on Simulating Problems - Less Wrong Discussion

1 Post author: Andreas_Giger 30 January 2013 01:14PM

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Comment author: Andreas_Giger 30 January 2013 09:53:03PM -1 points [-]

This is obviously not about bazookas and tanks. If you want to know whether real tanks really blow up, you need real evidence. If you want to know whether CDT defects in PD, you don't. You can do maths just with logic and reason, und fortunately this is 100% about maths.

Comment author: Qiaochu_Yuan 30 January 2013 11:20:11PM 0 points [-]

You have not given me anything like a precise statement of a mathematical problem.

Comment author: Andreas_Giger 30 January 2013 11:58:35PM * 0 points [-]

Here you go:

Given a problem A which is impossible or impractical in real life, find a practical problem B (called simulation) with the same payoff matrix for which it can be proven that any possible agent will make analogous decisions in analogous states.

Solve for Newcomb or other problems at will. Bonus points for finding generalized approach.

Comment author: Qiaochu_Yuan 31 January 2013 12:01:00AM 0 points [-]

That is not a precise statement of a mathematical problem. What do "impractical" and "practical" mean? What does "analogous" mean?

Comment author: Andreas_Giger 31 January 2013 01:11:15AM * -1 points [-]

"Impractical" means that you don't want to or can't realize the problem in its original form, for example because it would be too expensive or because you don't have a prison handy and can't find any prisoner rental service.

"Practical" pretty much means the opposite, for example because it's inexpensive or because you happen to be a prison director and are not particularly bent on interpreting the law orthodoxly.

"Analogous" basically means that if you can find isomorphisms between the set of the states of problem A and the set of the states of problem B as well as between the set of decisions of problem A and the set of decisions of problem B, then each thus mapped pair of decisions or states is called analogous if analagous decisions lead to analogous states and analogous states imply analogous decisions.

Comment author: Qiaochu_Yuan 31 January 2013 01:15:20AM 0 points [-]

This doesn't sound like a mathematical problem, then. It's a modeling problem.

Comment author: Andreas_Giger comment score below threshold [+] (11 children)

Comment author: Qiaochu_Yuan 31 January 2013 01:48:47AM 1 point [-]

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.

Comment author: Andreas_Giger 31 January 2013 02:31:16AM * 0 points [-]

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 genuinely don't understand what question you're asking

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.

Comment author: Qiaochu_Yuan 31 January 2013 02:44:23AM 1 point [-]

For example my definition of analogous — what else could you possibly have expected in this context? No, don't answer that.

The question is how close you wanted the analogy to be.

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?

Okay, this is clearer.

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

I can point you to a large body of evidence that I have all of these things.

continue this thread »

Comment author: earthwormchuck163 31 January 2013 02:42:18AM 0 points [-]

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.

continue this thread »

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