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ygert comments on Harry Potter and the Methods of Rationality discussion thread, part 28, chapter 99-101 - Less Wrong
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How come? They were not saying things that make no sense, if that is how hydras operate in that world...
That (the mathematical hydras related to ordinal arithmetic) can't possibly be how hydras operate in that world. Wizards don't know ordinal arithmetic, they only go on experience, and experience would tell them that a hydra with more than a few heads is impossible to kill. The mathematical existence of success is irrelevant when it takes longer than the age of the universe.
These are wizards. They can do, if not quite everything, a lot that we consider impossible or insanely hard. Maybe hydras have the magic property that they "stop time" nearby. For anyone near a hydra, time seems to freeze, at least until the hydra is dead. So if they can kill the hydra, the world pops back to normal with not a second past since the hyda attacked, but if not, they just get eaten.
This is a powerful attack/defense mechanism for the hydra, as the hydra's opponent must spend eon upon eon fighting it to win, and almost all give up before then.
At least, that is how I imagine Eliezer would write it if that kind of hydras appeared in canon and Eliezer had to come up with a reasonable explanation to it. Many things "don't make sense". How can dragons fly? They are to big to reasonably do so. But an intelligent author can "fix" things, and give a reasonable explanation.
Eliezer did that a lot to certain things from canon, and such is the correct attitude for facing a fictional thing you deem "impossible".
In that case, fighting hydras is something that any decently curious Wizard should attempt as a matter of course. Even if you're spending most of your effort watching the hydra, it still gives you a long time to think. No way (unless that's part of the hydra's spell) that you're coming out of that experience the same person!
Well over periods of time that long, you might come out of it a new person who differs from the old one by being bugfuck crazy.