What is the strangest math that turned out to be useful?
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Donut mathematics is the name of the field; I literally named it.
The writings on it are dense and only available in Russian and Mandarin Chinese. Further I provided the name of an author on the subject.What would you call the purposeful prevention of English/French/German/etc translations of the material?
The phrase "donut mathematics" was not in your earlier comment. You literally did not name it.
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I'm studying EE in university, and have been surprised by just how much imaginary numbers are used
wrote on last edited by [email protected]EE is absolutely fascinating for applications of calculus in general.
I didn't give a shit about calculus and then EE just kept blowing my mind.
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It's imaginary numbers. Full stop. No debate about it. The idea of them is so wild that they were literally named imaginary numbers to demonstrate how silly they were, and yet they can be used to describe real things in nature.
I don't really get 'em. It seems like people often use them as "a pair of numbers." So why not just use a pair of numbers then?
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A math discovery unmotivated by research in other fields; just discovering math to see if it works out
With that as the definition I would say Boolean Algebra.
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12 is the most based number in that respect IMO.
But then...hey, we use that for hours!
and in parts of the world for inches to a foot. pretty useful for carpentry for example
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I don't really get 'em. It seems like people often use them as "a pair of numbers." So why not just use a pair of numbers then?
Because the second number has special rules and a unit. It's not just a pair of numbers, though it can be represented through a pair of numbers (really helpful for computing).
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A complex number is just two real numbers stitched together. It's used in many areas, such as the Fourier transform which is common in computer science is often represented with complex numbers because it deals with waves and waves are two-dimensional, and so rather than needing two different equations you can represent it with a single equation where the two-dimensional behavior occurs on the complex-plane.
In principle you can always just split a complex number into two real numbers and carry on the calculation that way. In fact, if we couldn't, then no one would use complex numbers, because computers can't process imaginary numbers directly. Every computer program that deals with complex numbers, behind the scenes, is decomposing it into two real-valued floating point numbers.
That's not quite accurate because the two numbers have a relationship with each other. i^2 = - 1, so any time you square a complex number or multiply two complex numbers, some of the value jumps from one dimension to the other.
It's like a vector, where sure, certain operations can be treated as if the dimensions of the vector are distinct, like a translation or scale. But other operations can have one dimension affecting the other, like rotation.
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I don't really get 'em. It seems like people often use them as "a pair of numbers." So why not just use a pair of numbers then?
wrote on last edited by [email protected]I totally get your point, and sometimes it seems like that. Why not just use a coordinate system? Because in some applications the complex roots of equations is relevant.
If you square an imaginary number, it's no longer an imaginary number. Now it's a real number! That's not something you can accomplish with something like a pair of numbers alone.
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It's imaginary numbers. Full stop. No debate about it. The idea of them is so wild that they were literally named imaginary numbers to demonstrate how silly they were, and yet they can be used to describe real things in nature.
wrote on last edited by [email protected]I mean, quaternions are the weirder version of complex numbers, and they're used for calculating 3D rotations in a lot of production code.
There's also the octonions and (much inferior) Clifford algebras beyond that, but I don't know about applications.
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I don't really get 'em. It seems like people often use them as "a pair of numbers." So why not just use a pair of numbers then?
wrote on last edited by [email protected]They also have a defined multiplication operation consistent with how it works on ordinary numbers. And it's not just multiplying each number separately.
A lot of math works better on them. For example, all n-degree polynomials have exactly n roots, and all smooth complex functions have a polynomial approximation at every point. Neither is true on the reals.
Quantum mechanics could possibly work with pairs of real numbers, but it would be unclear what each one means on their own. Treating a probability amplitude as a single number is more satisfying in a lot of ways.
That they don't exist is still a position you could take, but so is the opposite.
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I'm studying EE in university, and have been surprised by just how much imaginary numbers are used
From what I've seen that's one example where you could totally just use trig and pairs of numbers, though. I might be missing something, because I'm not an electrical engineer.
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I mean, quaternions are the weirder version of complex numbers, and they're used for calculating 3D rotations in a lot of production code.
There's also the octonions and (much inferior) Clifford algebras beyond that, but I don't know about applications.
Yeah but aren't quaternions basically just a weird subgroup of 2x2 complex matrices?
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There have been a number of Scientific discoveries that seemed to be purely scientific curiosities that later turned out to be incredibly useful. Hertz famously commented about the discovery of radio waves: “I do not think that the wireless waves I have discovered will have any practical application.”
Are there examples like this in math as well? What is the most interesting "pure math" discovery that proved to be useful in solving a real-world problem?
wrote on last edited by [email protected]Strangest? Functional analysis, maybe. I understand it's used pretty extensively in quantum field theory, although I don't actually know firsthand.
That's a body of mathematics about infinite-dimensional spaces and the operations on them. Even more abstract ways of defining those operations exist and have come up as well, like in Tseirlson's problem, which recently-ish had a shock negative resolution stemming from quantum information theory.
There's constructions I find weirder yet, but I don't think p-adic numbers, for example, have any direct application at this point.
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Oh god, the cringe.
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From what I've seen that's one example where you could totally just use trig and pairs of numbers, though. I might be missing something, because I'm not an electrical engineer.
You can, they map, but complex numbers are much much easier to deal with
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Does this count? Because it really is wtf.
Don't put that cursed shit on mathematicians, lol.
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The following aren't necessarily answers to your question, but he also mentioned these, and they are way too funny to not share:
The Hairy Ball theorem
Cox Ring
Tits Alternative
Wiener Measure
The Cox-Zucker machine (although this was in the 70s and it's rumored that Cox did most of the work and chose his partner ONLY for the name.
)Based Cox.
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There's no such thing as a Nobel Prize in economics. Economists got salty about this and came up with the Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel, and rely on the media shortening it to something that gets confused with real Nobel Prizes.
I mean, it's endorsed by the same people. He has a page on their website and everything.
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Look up Wassily Wassilyevich Leontief
Are you talking about the input-output thing? It assumes each sector produces exactly one thing, and is agnostic of growth, change and multiple non-equal possibilities existing. I'm skeptical.
It's not really covered up, either.
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Yeah but aren't quaternions basically just a weird subgroup of 2x2 complex matrices?
wrote on last edited by [email protected]Would that make it less true? Complex numbers can be seen as a weird subgroup of the 2x2 real matrices. (And you can "stack" the two representations to get 4x4 real quaternions)
Furthermore, octonions are non-associative, and so can't be a subgroup of anything (although you can do a similar thing using an alternate matrix multiplication rule). They still show up in a lot of the same pure math contexts, though.
