Ideally we want a theory of how to change energy into winning, not information and a prior into accurate hypotheses about the world, which is what probability theory gives us, and is very good at.
You need accurate information about the world in order to figure out how to "change energy into winning."
Jeepers. I haven't thought about this problem for a long time. Thanks.
The answer that occurs to me for the original puzzle is that Yudkowsky never proved (◻(2 = 1) -> (2 = 1)). I don't know it that is actually the answer, but I really need to go do other work and stop thinking about this problem.
This article from 2005 says that while there are some different theories about the evolution of music, there is not enough evidence yet to reach a conclusion. http://www.cns.nyu.edu/~jhm/mcdermott_hauser_mp.pdf
In another article, Geoffrey F. Miller explained that Darwin hypothesized that hominids might have included some music in their courtship, similar to birdsong, before the development of language. Darwin's theory is described pretty clearly in the refrain of "Who Put the Bomp," but you can also google the article.
G. F. (2000). Evolution of human music through sexual selection. In N. L. Wallin, B. Merker, & S. Brown (Eds.), The origins of music, MIT Press, pp. 329-360.
And since it has observable consequences, you can do science to it! Yay!
In that case, they're arguing about the wrong thing. Their real dispute is that the painting isn't what the Mongolian wanted as a result of a miscommunication which neither of them noticed until one of them had spent money (or promised to) and the other had spent days painting.
So, no, even in that situation, there's no such thing as a dragon, so they might as well be arguing about the migratory patterns of unicorns.
I think that this is what the theorem means;
If (X->Y) -> Y, then ~X -> Y (If it's true that "If it's true that 'if X is true, then Y is true,' then Y must be true," then Y must be true, even if X is not true).
This makes sense because the first line, "(X->Y) -> Y," can be true whether or not X is actually true. The fact that ~X -> Y if this is true is an overly specific example of that "The first line being true (regardless of the truth of X)" -> Y. It's actually worded kind of weirdly, unless "imply" means something different in Logicianese than it does in colloquial English; ~X isn't really "implying" Y, it's just irrelevant.
This doesn't mean that "(X -> Y) -> Y" is always true. I actually can't think of any intuitive situations where this could be true. It's not true that the fact that "if Jesus really had come back to life, Christians would be Less Wrong about stuff" implies that Christians would be Less Wrong about stuff even if Jesus really hadn't come back to life.
Also,
To anyone who wants to tell me I'm wrong about this; If I'm wrong about this, and you know because you've learned about this in a class, whereas I just worked this out for myself, I'd appreciate it if you told me and mentioned that you've learned about this somewhere and know more than I do. If logic is another one of those fields where people who know a lot about it HATE it when people who don't know much about it try to work stuff out for themselves (like Physics and AI), I'd definitely like to know so that I don't throw out wrong answers in the future. Thanks.
Making perfect, evil plots can be a great conversation starter.
I have a friend who is much better at starcraft than I am; he says that he's largely better because he's worked out a lot of things like exactly the most efficient time to start harvesting gas and the resource collection per minute harvesters under optimal conditions, and he uses that information when he plays. It works better than playing based on feelings (by which I mean that he beats me).
If you don't have way too much time on your hands, though, it's about as much fun to not bother with all of that.
Also, I notice you cited a Wikipedia page. Naughty, naughty, naughty.
You might pull together a good message just based on the original question, "what advice do you give to Archimedes, and how do you say it into the chronophone." Yudkowsky's question was designed to make us think non-obvious thoughts, after all.
"Would you be able to ask anything meaningful through the chronophone?"
(My construction might not be quite right. I'm feeling all smug and Godelian, but it's 1 AM, so I've probably missed something.)