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.
Ah, but what if we find out that there are Universal Laws of Morality which prove that being stupid is amoral? After all, a mind could exist which thinks that stupidity is morally wrong.
Ehehe.
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.
I like your suggestion to learn to learn to like things. If anyone is looking for things to learn to like, these are some nice ones.
Ligeti’s etudes (and other 12-tone music); www.youtube.com/watch?v=h0qoue0JbbU
This piece by Charles Ives; www.youtube.com/watch?v=OBU_XzWZNtc
Plays! You don’t need to buy hundred-dollar tickets to fancy Broadway shows; community theater productions are often comically horrible in movies, but I’ve only seen good ones in real life (I did just put drama in a group with Ligeti etudes and cowboy music, but not because it’s really weird).
I think I wrote an essay for a middle-school english teacher to the effect that any belief that I had in [the belief in] Santa Claus dragged my belief in [my belief in] God along as it went away (Which would have been around… when I was three or five; my parents didn’t really try very hard to convince my siblings or me that Santa actually existed).
I don’t remember a time when I believed in more than a belief in Santa, or, though my parents tried a little harder on this front, in God. My mother read to me from a kid’s bible (with stories like Noah’s Ark (the one with all the incest in it, for anyone who doesn’t know) set as poems), but I could tell she didn’t believe the stories (she probably figured she ought to make an effort, just ’cause).
Nonetheless, my father only recently began to imply outright that Santa Claus wasn’t real.
Just so you know, there are two columns of Y subscript 3s in the first joint distribution.
I heard about this study in the book Moonwalking with Einstien: the Art and Science of Remembering Everything, by Joshua Foer. Apparently there was only one test subject who seemed to have eidetic memory, and instead of doing more tests after the one that you described, the experimenter married the subject.
When John Merritt put a similar test in newspapers, nobody who wrote in with the correct answer could do the test “with scientists looking over their shoulders.”
Foer, Joshua. Moonwalking with Einstein: the Art and Science of Remembering Everything. New York: Penguin, 2011. Print.
Now cryonics are starting to sound like a religion; if you are an interesting person, and have a good enough reputation, then someone will bother to reanimate you and you will live forever. I like it.
Sorry, I didn’t mean to do that, and I don’t know how it happened.
This isn’t entirely relevant, but it’s a good story, so… I recently heard from one of my mom’s friends that my fifth grade teacher won the lottery, and continued teaching afterward. This makes me very happy, because he’s a fantastic teacher (he has a reputation, actually, for making his classes really fun, like using remote-control cars for an Oregon Trail activity), and, as has been mentioned on this site, a lot of people don’t end up being very happy once they’ve one the lottery. I’m glad Mr. Lesh was smart enough to keep teaching his class, which he obviously loved doing.
Teehee… “Men are from Mars...”
The mention of music and evolution sent me off on a tangent, which was to wonder why human brains have a sense of music. A lot of music theory makes mathematical sense (the overtone series), but it seems odd from an evolution standpoint that musicianship was a good allele to have.
I think, based on everyone’s level of discomfort with this problem, that if there were an experiment wherein people in one group were asked a question like this, but on a much smaller scale, say, “torture one person for an hour or put a speck of dust into the eyes of (3^^^3)/438300,” or even one second of torture vs (3^^^3)/1577880000 (Obviously in decimal notation in the experiment) specks of dust, and in the second group, people were told the original question with the big numbers, people in the first group would choose the torture more often and much more quickly and confidently.
I say this because people are quite uncomfortable having to choose to torture someone for 50 years, even if it isn’t necessarily as bad as the other option.
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.)