Analytic continuation is about saying "Okay, so if you take out everything that you're not allowed to do that absolutely by the rules cannot give you an answer, can you find something about it that *does* give you an answer"
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(Hell, the ancient Greeks, who believed you could not in fact do that, were still pretty lax traffic cops and didn't *enforce* not doing that because they didn't have the rigor, which is why Archimedes was allowed to discover a limit-based method for approximating pi)
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But it's always more interesting to just ignore him and keep walking anyway I mean what's the worst that can happen? You try to say something makes sense but everyone just looks at it a while and goes "Nah this is stupid" and moves on? You gotta at least try
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