Cohl Furey sounds like a goddamn new Marvel character, but actually she's a mathematical physicist. Can that really be her name? As a novelist, I feel reality is cheating by being so fucking dramatic:https://www.quantamagazine.org/the-octonion-math-that-could-underpin-physics-20180720/ …
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I think the key word is “number”. What’s a number? Is the ring Z_p numbers (where p is prime)?
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Which I recognize is pretty redundant with your subsequent tweets that went into the true statement that Quanta mangled, but eh
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By the way, no one has ever explained "i" to me in a way that makes sense. I think my calculus teacher was just like "'i' stands for imaginary, OK?" and then grunted and went back to staring out the window.
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OK super short version why someone would care: Mathematicians like to solve equations. They really like it. It's a big deal. Now one super important class is the polynomials, stuff like: x - 1 = 0 2x^2 + x + 4 = 0 18x^3 - x^2 + 1 = 0
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It turns out that not every polynomial equation can be solved using regular numbers. For instance, x^2 - 4 = 0 is easy to solve (2 and -2 both work), but x^2 + 1 = 0 can't be solved at all. (x^2 can't be negative, so x^2 + 1 is always positive)
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Mathematicians like to do endruns around a stuff like this, by pretending there's a solution and giving it a name. Like, let's just _pretend_ there's a number, call it 'i', so that i^2 + 1 = 0, in other words i^2 = -1. Just create it out of thin air and see what happens.
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Ha, OK.
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The correct statement is insanely fiddly and I don't know how you'd do it in a popular science article, but Quanta usually finds a way and this is disappointing.
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Popularizing science with a lot of math in it is a heroic task... people underrate spokesmodels like Sagan and that Tyson chicken guy because they're celebrities, but it ain't easy.
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. Banned in Sweden. SubGenius, Zhuangist, white-hat troll. Defrocked mathematician. Brain problems.