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Decius comments on [HPMOR][Possible Spoilers] Gedankenexperiment: Time Turner Meta-Informational Relativity - Less Wrong
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I don't accept that "strong evidence-based arguements" is a meaningful phrase in the presence of a counterfactual premise. If there was introduced some kind of unexplained techno-babble that wasn't consistent both internally and with the entire story (including the exchange rate of magical currency), it would simply be pushing 'magic' up or down the meta-scale.
The (reletivivistic) speed of a broomstick is roughly equal to the speed of the Earth, which almost has measured relativistic effects (GPS satellites in LEO observe relativistic effects from their orbital velocity, but their orbital velocity is inherently greater than any sustained orbital velocity on the surface).
And the math doesn't have to be done in-universe. Can you estimate the mathematical complexity of turning into a cat, getting your tail stepped on, and then returning to human form with a bruised coccyx? In a world where magic acts this way, it makes sense for physics to be a cultural phenomenon as well.
I have conferred with a few of my most trusted rationalist friends, It seems we agree that you conceive of a "magic" being separate from "physics" in a way which we have collectively edited you of our cognition.
I really must emplore you to read the sequence Highly Advanced Epistemology 101 for Beginners. It argues strongly for why Mathematics and Physics/Causality is the only way of talking "meaningfully" about the universe.
Also, you are veering dangerously close to my trolling pattern matching algorithm's threshold.
Given the object-level information I have about the universe of HPMOR, I assign a significant probability to the possibility that the universe there does not follow Mathematics as we can conceive of in this universe. With the meta-level knowledge I have, I an certain that it will not be confirmed to be the case, and that magic will have the properties needed for the plot without having any epicycles which are not foreshadowed far enough in advance. It is currently too late to foreshadow anything new.
Your algorithm has the risk of false positives and false negatives; you can reduce the false results by improving the algorithm, or you can shift the threshold to reduce one and increase the other.