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On the question of the birth certificate, I feel like this is one of those things where the best facts we have state that yes, he was born in Hawaii. I question how easy it would really be to not only fake the document, but get it into all the right places to have the proper record of it. If you can create a situation where I can call up the appropriate offices in Hawaii and be confirmed that you were born there but you weren't, maybe I'd believe it.
I mean, if you want to be philosophical, you can't really trust any piece of information. Why trust anything you see or hear, ever? At some point you have to believe that some things are at least probably true.
I'm no engineer, but doesn't isn't the uncertainty principal a quantum phenomena, and therefore irrelevant at a macro scale?