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buybuydandavis comments on Harry Potter and the Methods of Rationality discussion thread, July 2014, chapter 102 - Less Wrong
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Although people are ignorant of why it works, people casting the patronus charm know exactly what it does. It makes a silver colored animal that makes fear go away and can chase dementors.
As to conceptualization, you may well be right that it could be done without understanding the mechanism but with correct conceptualization. But, I bet most wizards don't have the right conceptualization. And worse, I bet most wizards investigating the philosophers stone have a Theory. And their theory is probably directly wrong which blocks them from being able to do it.
This does sound very likely. Although it's worth noting that there are at least a few powerful wizards who are, if not rational, at least capable of processing evidence without leaping to conclusions - we hear them described at the conclusion of Hermione's trial.