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ikrase comments on Harry Potter and the Methods of Rationality discussion thread, part 19, chapter 88-89 - Less Wrong
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Hmmm. How large is Hogwarts? It's non-Euclidean, but it's Euclidean enough for Quirrel to shortcut by blowing up walls in a quasi-straight line.
Given Quirrel's rarely used but significant ability to blow stuff up, I think that once he reached steady state he could blow up several cubic meters of masonry per second for a good few meters per second rate of travel.
Alternatively, Quirrel's Potterdar gives him a direction sense that follows a geodesic.