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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Replying to @AnnKSterzinger
"Proof surfaced in 1898 that the reals, complex numbers, quaternions and octonions are the only kinds of numbers that can be added, subtracted, multiplied and divided." Quanta's math coverage is usually very good but this is ouch wrong
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Replying to @St_Rev @AnnKSterzinger
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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Replying to @AnnKSterzinger @TWakalix
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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It turns out that if you do this, and just throw it in the bag with your regular ordinary (real) numbers, two things happen. First, the new system of ("complex") numbers is pretty easy to work with. Every complex number just looks something like 2 + 3i or 22/7 - i.
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...ie, every complex number can be written as a + bi, where a and b are real numbers. Once you do this, something happens that mathematicians get really excited about: _every polynomial equation now has a solution_. This is a *big deal*.
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Remember that we only tried to invent a solution for one particular equation, x^2 + 1 = 0. By doing that, we somehow get solutions for _all_ of them. We made things more complicated, but we can suddenly do a lot more. And that's why complex numbers are important.
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This is so important that it's actually called the Fundamental Theorem of Algebra!
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. Banned in Sweden. SubGenius, Zhuangist, white-hat troll. Defrocked mathematician. Brain problems.