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by jasode
4225 days ago
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>Not really. You don't generally benefit from proofs being correct. We benefit from Pythagorean's Theorem (a proof) every day. We can use it calculate distances without physically laying down a tape measure to derive distances across oceans or even outer space. We can also use it to calculate distances of 2 points inside of video game scenes or a "distance" inside matrices. If two sides of a triangle is 3 and 4, we can deduce the other side is 5. We don't need to look it up in a reference book of past recorded observations. (E.g. the previous 1000 years of recorded observations show that the measurement will be 5 but we better check it again today just in case it's different. The existence of proof-theorem allows us to skip that.) Anyways, the idea of "math proofs" is still useful even though there can be disagreement on what "proof" is.[1] > I understood you correctly. Actually you didn't because I had originally wrote "disagreements of terminology" but I went back and edited it a few minutes later for brevity to just "disagreements" because I thought it was a cumbersome and long-winded sentence. I thought the previous context to OP made the qualifier "terminology" redundant. But...leaving it out lead to even more confusion. Anyways, The wide-ranging and sometimes even contradictory interpretations of terminology (such as "garbage collection") is not a convincing enough reason to dismiss "garbage collection" as pointless. That's what the OP was using as his ammunition and it's wrong. [1] http://en.wikipedia.org/wiki/Computer-assisted_proof#Philoso... |
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The problem of "proof" didn't exit back then. What is proof? What looks like correct reasoning to me, that's what it is! And that was like a fine definition for every sane for a very, very long time. Have you read Kant's "Critique of Pure Reason"? It was way later that Pythagoras, Kant was obviously quite smart man and his reasoning was pretty solid for his time. Now it's nonsense. Because Euclidean geometry was considered the only possible back then, and Kant indeed believed it's the only possible. Then some 100 years later it just appeared out of nowhere. That's when a problem of "proof" and "formal reasoning" was actually started to be considered. And only really became a problem after Goëdel. The whole math you use every day by making cell-phones, building atomic reactors and launching rockets to the Moon was mostly invented before that by people who weren't so concerned by proofs, the central object of mathematics today.
Similarly, you use just some formula you was taught at one point, and some semi-intuitive rules by which you can derive other formulas from it and don't really care about proofs. And although you without doubt have heard about Lobachevsky and Riemann and even Klein, and heard of "Erlang" (even if it's just a name of programming language to you) you don't really think much about Pythagorean's Theorem's proof and what it's built on, you use some computational methods you've been taught and what seems like "correct reasoning" to you. Actually, you even reinforced that by your examples, because there's many more ways to calculate a "distance" inside matrices or in a video game (and on plain Earth it's more based on physical properties you care for and would be fine even if only "proved" empirically). Because "distance" is not derived from Pythagorean Theorem, distance is defined and is one of key properties of some geometry. That is, you define geometry by introducing formula of how distance is calculated.