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Psy-Kosh comments on Harry Potter and the Methods of Rationality discussion thread, part 7 - Less Wrong
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Haven't really thought about it until now, but I'll assume that Finite is a brute-force method requiring strength proportional to the original spell to cancel (so a Transfiguration that takes minutes would require a mass casting to cancel, perhaps) and sometimes won't work at all, while specialized counter-jinx just works if the caster has sufficient strength to cast it.
Depends... if the original spell took time/effort due to it being, well, for lack of a better word "delicate", then finite should work easily on it, while a simple spell that you can just pump more and more power into should require a really strong finite to cancel.
At least, that's how I'd imagine it.