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MaoShan comments on Rationality Quotes March 2012 - Less Wrong
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If you find a right triangle with sides (2.9, 4, 5.15) rather than (3,4,5), are you ever entitled to reject the Pythagrean theorem? Doesn't measurement error and the non-Euclidean nature of the actual universe completely explain your experience?
In short, it seems like you can't empirically check the Pythagorean theorem.
Peer review. If the next two hundred scientists who measure your triangle get the same measurements from other rulers by different manufacturers, you'd be completely justified in rejecting the Pythagorean theorem.
My challenge to you: go out and see if you can find a right triangle with those measurements.
Sure, how about a triangle just outside a black hole.
That was a quick trip. Which black hole was it?
You're completely justified in rejecting Euclid's axioms. You're not at all justified in rejecting the Pythagorean theorem.
Upvoted for your excellent demonstration of peer review ;) I stand corrected.