JohnSidles comments on Harry Potter and the Methods of Rationality discussion thread, part 21, chapters 91 & 92 - Less Wrong
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Conspicuously absent from the canon, and from Methods of Rationality (so far) --- and absent entirely from the Hogwarts curriculum --- are two fundamental elements of rational cognition:
Therefore
Literary Remark Harry Potter would do well to reflect upon the words and fate of Captain Ahab:
Conclusion Harry Potter's quest to restore Hermione Granger may be leading him and the Hogwarts crew to a similarly disastrous fate as Ahab and the Pequod crew.
Abominable Conclusion 1: the AIs that first negotiated with humanity, thousands of years ago, to levitate objects on command, had insisted that humans speak the protocol words... Wingardium Leviosa.
AI-1: And so we have decided to grant the humans great powers
AI-2: but when we bestow our awesome power upon the puny humans they may become arrogant and forget that they are small and ridiculous
AI-1: we've thought of that, and have a solution...
Wingardium Leviosa!
Except that said humans won't develop the language where those not-words sound kind-of-sensible for a few more thousand years. And even then, most of the people in the world wouldn't get the joke. (Do French wizards cast French spells? What about the Chinese?)
Probably. Quirrell teaches at least one spell which is clearly neither of English nor Latin origin.
Excellent point, I'd forgotten about that. Ma-ha-su.
Since Eliezer does nothing accidentally, this is very strong evidence that wizards invent spells with words related to the language they speak, and that spells then have a high turnover rate that doesn't let them survive longer than their languages.
LOL --- perhaps a chief objective of the Ministry of Magic is to conceive and require obfuscating interfaces to magic! That would explain a lot!
Parallels to real-world high-school and/or undergraduate mathematical education ... are left as an exercise. :)
Both canon and HPMoR have arithmancy. In HPMoR, "Harry and Professor McGonagall had bought his textbooks from Flourish and Blotts just under the deadline. With only a slight explosion when Harry had made a beeline for the keyword 'Arithmancy' and discovered that the seventh-year textbooks invoked nothing more mathematically advanced than trigonometry." And Harry really shouldn't have exploded. Many real world Muggle schools don't get as far as trigonometry by the end of high school, and they don't have to spend any time on charms or transfiguration.
Ryvmvre unf fgngrq gung guvf vf abg na NV fgbel.
For a professional-grade comment on "muggle math" versus "Hogwarts math", see Michael Spivak's Physics for Mathematicians: Mechanics I.
To express this point another way ... how likely is it, that Harry's final understanding of magic will be non-mathematical? What grade of mathematical abstraction capabilities will Harry need to acquire?
I can't find the particular proofs of Noether theorems that your link refers to. Can you help me find them? I see no instances of the word "muggle" in Spivak's paper - in fact no index at all. Is there a different version of it? Please help, as I would greatly appreciate reading this!
Edit: I see now that the comment was referring to a book by Spivak, and that the linked PDF is only on 'elementary mechanics.'
Edit 1: Kudos to "gjm" (see above) for pointing to Spivak's page on Amazon!
Edit 2: Spivak's Hogwarts proof implicitly uses a fundamental theorem in differential geometry that is called Cartan's Magic Formula ... this oblique magical reference is Spivak's joke ... as with many magical formulas, the origins of Cartan's formula are obscure.
Amazon UK's "look inside" feature has it. I haven't checked Amazon US. Search for "Muggles"; first result (page 576) is the one.