It's because the mantissa of "2 grams" isn't visible, it's below the level of precision being measured, therefore the quantities get rounded down separately and get rounded up when combined It's not really that hard
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Replying to @arthur_affect
Rounding errors don't alter the underlying fundamental math. 2.49+2.49 =4.98 still
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Replying to @Gent_Sausage
Yeah but because you can't see at that level of precision you don't know what those numbers are
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Replying to @arthur_affect @Gent_Sausage
It doesn't even need to be that close to 2.5 2 1/3 pretty clearly rounds to two. And two lots of that clearly rounds to five.
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Replying to @Gent_Sausage @arthur_affect
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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This was @kareem_carr's broader point, that when you see an apparent absurdity like "2+2=5" your impulse should be to ask "What do you mean by that? Why are you saying that?" and not just get mad and act superior
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Replying to @arthur_affect @phyphor and
Anyone with a basic knowledge of pedagogy would tell you it’s far more important to help the student find the flaws in their own process. Just saying the answer is wrong literally does nothing to help kids learn. That this even needs to be explained is astonishing
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