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:
mathematics, and
artificial intelligences (AIs)
Therefore
Postulate 1 “Magic” is the name that witches, wizards, and muggles alike give to the practice of manipulating physical reality by negotiation with agents that are (artificial? primordial? evolved? accidentally created?) intelligences.
Postulate 2 “Magical Spells” is the name that witches, wizards, and muggles alike give to an evolving set of protocols for negotiating with an existing community of (mysterious) intelligences. These protocols are designed to minimize the risks and harms associated to the practice of magic, by concealing the physical origins of magic.
Postulate 3 The chief organizing objective of the Hogwarts curriculum is to preserve the social fictions that are associated to Postulates 1 and 2.
Postulate 4 Harry Potter is regarded as dangerous because he seeks to evade the restrictions associated to Postulates 1, 2, and 3, by inquiring into the true nature of magic and its actions.
Literary Remark Harry Potter would do well to reflect upon the words and fate of Captain Ahab:
“All visible objects, man, are but as pasteboard masks. But in each event — in the living act, the undoubted deed — there, some unknown but still reasoning thing puts forth the mouldings of its features from behind the unreasoning mask. If man will strike, strike through the mask! How can the prisoner reach outside except by thrusting through the wall? To me, the white whale is that wall, shoved near to me. Sometimes I think there’s naught beyond. But ’tis enough. He tasks me; he heaps me; I see in him outrageous strength, with an inscrutable malice sinewing it. That inscrutable thing is chiefly what I hate; and be the white whale agent, or be the white whale principal, I will wreak that hate upon him. Talk not to me of blasphemy, man; I’d strike the sun if it insulted me. For could the sun do that, then could I do the other; since there is ever a sort of fair play herein, jealousy presiding over all creations. Ohg abg zl znfgre, zna, vf rira gung snve cynl. Jub’f bire zr? Gehgu ungu ab pbasvarf.”
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.
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?)
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.
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.
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.
Regrettably, tgb, even the redoubtable Google Books does not provide page-images for Spivak’s Physics for Mathematicians: Mechanics I. The best advice I can give is to seek this book within a university library system.
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:
mathematics, and
artificial intelligences (AIs)
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.