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Addenda:
From the reader's perspective, it doesn't appear that that's what we are supposed to believe (though I'm still wondering...), so I'm tentatively guessing that the mechanism of magic is some kind of technology, and that the in-story universe has the same laws as this one. It does seem implausible that an ancient civilization could have invented technology advanced enough to be indistinguishable from this kind of magic, but that could be different in an alternate history, and it still seems less implausible than any set of physical laws that would actually make this kind of magic a normal, natural thing that a non-industrial civilization could invent/discover.
We are supposed to be wondering why magic works at all, right? It doesn't seem like Eliezer to expect us to be satisfied with an Inherently Mysterious phenomenon at the center of the story, even if it's a story based on someone else's fictional world that already had that feature... but I don't know, maybe it's a demonstration that, no matter how ridiculous the rules are, rationality will still allow you to win.
But I'm still hoping that magic will be explained at some point, and I'm still looking for clues about it.
I think magic will be explained as an addition onto physics: a new "force" is involved, but still behaves in an intelligible way. I can't imagine how the MoR series would explain the magic exhibited thus far as coming from current physical understanding.
Unless the magicians control quantum wavefunctions directly, or something like that. Or Harry is a brain in a vat.
Or if Harry figures out that he's in a story.
What kind of evidence would convince you that you were in a story?
The events in a story fit into a narrative. If I were in a story, I might be able to make especially accurate predictions by privileging hypotheses that make narrative sense. Dumbledore did this on an intuitive level, and it is the reason for his success.
This is basically an attempt to formalize genre savviness.
And of course, if you really were in a story and tried it, story logic dictates that you would almost certainly end up being wrong genre savvy
If something totally crazy seemed like it was about to happen and the world was at stake, like a technological singularity was about to occur or something, and I was called to work for the team of great minds that were trying their hardest to stop the destruction of the entire universe, dropping out of high school in the process, and meeting a beautiful girl who had been living literally a few houses down from me for the last 4 years without my knowing about it, who just so happened to be doing an essay on transhumanism for her English class and would just love to interview someone who was doing work for the Singularity Institute.
Oh wait...
If I started hearing the narrator's voice
I'm not sure, considering the number of different kinds of story there are even in our world, and especially considering that entities which could create our world will probably have sorts of fiction we haven't thought of, and may have sorts of fiction we can't think of.
However, Eliezer may come up with something which would plausibly convince Harry.
I think something like "brain in a vat" is the best inference from observing magic. [EDITED to add: of course I mean after getting very good evidence against deception, insanity, etc.]
More precisely: if you find evidence that something deeply embedded in the universe is best understood at something like the level of human concepts -- it matters what words you say, whether you really hate someone else as you say them, etc. -- then you should assign more probability to the hypothesis that the-universe-as-it-now-is was made, or at least heavily influenced, by someone or something with a mind (or minds) somewhat like ours. That could be a god, a graduate student in another universe with a big computer, superintelligent aliens or AIs who've messed with the fabric of reality in our part of the world, or any number of other things.
In a manner of speaking this is obviously correct for the Potterverse (either Rowling's or Yudkowsky's): in that universe, magic works; and indeed that universe was designed by an intelligent being or beings, namely Rowling or Rowling+Yudkowsky. It probably doesn't work "internally" for the original Potterverse -- I've no idea whether Rowling has any particular position on whether within the stories the world should be thought of as created by intelligent beings -- but I'm guessing that it does for Eliezer's.
I'm not convinced that concluding one is in a simulation is really the best bet here. A simulation would have a terrible amount of trouble specifying these effects. If for example, I have a simulation for say just our local system, how the heck are the people running the simulation easily going to be able to specify emotional states or the like? The only possible explanation I can have for this is that the simulation was originally started with humans having certain (simulated) brain structure and that structure is the type of structure that wizards have. Other humans can't do it because their structure isn't of the type the simulation recognizes to trigger magic.