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skeptical_lurker comments on Harry Potter and the Methods of Rationality discussion thread, part 19, chapter 88-89 - Less Wrong
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Harry could disassemble the world and the stars into computronium - in fact star-lifting crossed his mind when he heard the first part of the prophecy. EY stated that there would be no AI analogy, and magical intelligence amplification seems more plausible anyway.
A different route to a mini-foom is that one can make luck potions. Then gamble, get money, recruit people who know how to make potions. Now you have huge amounts of luck potion, and provided your thought process is fairly random, you will always find the right answer (e.g. opening a random book at a random page happens to provide exactly the right insight). Routes to magical IA:
Luck potions.
A thinking hat - like the sorting hat, only it uses your brainpower to help you solve problems.
Efficient use of memory charms to spread insights rapidly through a group of researchers.
Use of telepathy to create a group mind.
Potion of thinking, made of e.g. ground-up crossword puzzles.
Potion of... OH CRUD.
Buy supercomputer time to solve problems in some physical form. Melt printouts into potion. Foom.
Maybe incorporating books into the potion would give you literary skills and declarative knowledge, while computer printouts give fast computation skills? Better throw some birthday cards and essays on ethics in there too, to try and encourage friendliness :)
You mean like the Lost Diadem of Ravenclaw? which may not exist in the Rationalverse, as it's potentially OP. Especially if Harry gets his hands on it.
You know, a heavy dose of luck potion would almost justify messing with time. I still don't see any way to fake a failed ghost creation without transfiguring a witch or wizard. (Though in principle, Imperio would remove the need for a volunteer.) A few hours does not seem like enough time to grok ghosts in fullness and produce a guaranteed failure. Nor do you want any uncertainty. Never let under-determined Outcome Pump Physics decide if your plan will really preserve the appearances most efficiently, or if the Universe should create Uplifted utahraptors to stop you.