If you have a set of scales and you have a thing that shows on the scale that it weighs two, and another if that thing, that also shows on the scale that it weighs two, and you weigh both together you still see that it weighs five. That's the point.
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Replying to @phyphor @Gent_Sausage
The argument has never been to crumple up arithmetic and throw it in the trash and replace it with a completely new number theory The argument is that the number theory "we all learned as kids" maps onto physical reality in various complicated, subjective ways
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But the whole 2 grams + 2 grams = 5 grams is absolutely false. Putting two objects on a scale is not addition or arithmetic. Addition would be weighing each one separately and then adding the weights + uncertainty of each measurement
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Yes It is a statement about how naive faith in addition without considering the process by which real quantities get turned into numbers in the real world (measurement) can fail
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If you just naively take a bunch of separate measurements and add them up on paper you get a "correct" answer (2+2=4) that is actually worse than the answer you get if you weigh them all together (5)
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I get what you’re saying but “weighing things together” is not addition. You could just glue those things together and they become one thing that is being measured as 5 grams. Addition would be, “I have 2 measured weights, here is the sum”
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It means whatever the person talking finds it useful to mean Carr went on to bring up stuff that people say as a joke -- "1+1=3", when it's two animals that mate and have an offspring, "1+1=1", when one of them kills and eats the other -- but it reflects a deeper truth
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One of the things I find beautiful about pure math is that it’s objective and straightforward. Bringing in real-world examples of things that “appear to be math” and then proclaiming it to be objective math is silly, unnecessary, and confusing.
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But that's the whole point! Math is beautiful in that sense BECAUSE it's divorced from empirical truth Its self-evident "truths" work the way they do because you're comparing something you imagined to something else you imagined
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Math automatically becomes "messy" when applied to the real physical world That act of application is messy, it's subjective, it inevitably introduces error and bias Significant digits, error bars, ceci n'est pas un cinq
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This may be a trivial truth but it's a deep and important one, precisely because it's one that people VERY FREQUENTLY forget (the laughable aphorism "Numbers don't lie")
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