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Flat Earth Theory / Re: Some perspective on perspective
« on: May 01, 2016, 07:22:42 PM »Math is a purely logical construction; it concerns what can be deduced from an initial set of propositions. So the only way to refute a mathematical conclusion (i.e., a statement that proposition P can be deduced logically from the initial premises A, B, C,…) is to show a logical error in the proof.
An error in the proof is that parallel lines seem to converge in contradiction of theory.
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In the Elements, Euclid defined parallel lines as lines in the same plane that never meet no matter how far they are extended in either direction. So if two lines meet, by definition they are not parallel in Euclid’s sense. Saying “these two parallel lines actually touch, therefore Euclid was wrong,” is like saying “this triangle has four sides, therefore Euclid was wrong about triangles.”
Elucid was wrong about a lot of things. Look up Zeno's Paradox. The Greek model of the universe is flimsy.
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Example: You look at straight railroad tracks extending miles into the distance on a flat plain. You observe that what your brain tells you are rail lines in your field of vision meet at the horizon, and conclude that Euclid’s world view is wrong. No, you’ve just misapplied his reasoning. He never said that parallel lines will never appear to meet in your field of vision, no matter how far away they are. Now you look at the lines through a telescope, and the lines you see don’t meet any more. Hmm.
So what you seem be saying is that if lines in your field of vision actually meet as interpreted by your brain, then the lines out there, miles away, actually do meet. But that doesn’t explain why they don’t meet any more when viewed through a telescope. Nor is it consistent with our everyday observation that what looks like an ellipse turns out to be a circle when viewed from a different angle.
If the Greek models are corrupted by illusions at long distances then we must admit that there are illusions present in the subject matter and that the unsatisfactory Greek models cannot be used as a disproof of what a Flat Earth sun might or might not do.