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Subbak comments on Harry Potter and the Methods of Rationality discussion thread, part 28, chapter 99-101 - Less Wrong
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Comments (365)
Eliezer: I got the math joke.
Explanation and implementation (spoiler if you haven't spotted the joke yet): http://tinyurl.com/hpmor100mathjoke
(But this only covers the first half of the joke; I had not heard of the second half before!)
If you want to play with a (rather tame, since it doesn't always use its regeneration powers) Bucholz Hydra, here's a link for you: http://www.madore.org/~david/math/hydra.xhtml
For my part, I knew about hydra games and had forgotten the name, but the context made it fairly obvious that this was a joke about the hydra being so hard to kill that you can't prove you do it with only Peano arithmetic.
I have defeated the hydra! (I had to cut off 670 heads). Feels like playing Diablo.
670? Lucky. I finally bested it after 1750-ish, yesterday. Once I hit 1000, I thought, "Why am I doing this? What am I proving?" and then I started clicking again.
1750? I forced myself to give up and get back to work somewhere around the 6500 mark.
(I had decided, somewhere around 1000 or so, to try out the strategy of preferring to cut normal rather than dire heads when possible. Maybe that's a bad idea)
I worked top-to-bottom, without change. If a new branch grew higher than my previous cuts, I focused it immediately. I know there's an optimal way, but I'm not quite clever enough to think of it.
Well, for this applet the optimal strategy might depend heavily on how exactly its tameness is executed, which isn't very enlightening.
Edit: Derp, I tried out top-to-bottom and got it in 572. Definitely better than left-to-right or normals-first-ltr.
I used top-to-bottom, but dires first on each level, and that seemed to work consistently pretty well.