You laugh now, but just wait 3 years until this morphs into the next right-wing cult conspiracy theory…
You think one imaginary number is crazy? Just wait till you learn about quaternions. One real number and 3 imaginary numbers forming a four dimensional coordinate system. It's the basis for quantum mechanics and most video game engines. Who thinks of this shit?
Quaternions? Basis of quantum mechanics? Pretty sure that's not right at all. A lot of games use them for rotations in place of rotation matrices though I suppose.
Iirc, using quaternions for rotations let's you avoid "gimbal locking".
Quaternions are not the basis for quantum mechanics. Biquaternions have some applications in quantum field theory, but there are many areas of quantum mechanics where there's no need or space for anything above complex.
We owe "quatties" to hamilton, but there is a generalization of the process in case you're curious: https://en.wikipedia.org/wiki/Cayley–Dickson_construction
The general concept is called Spinors, Quaternions are just one representation. Here's a great video on them. In physics they're using them because they're necessary (video explains), in computer graphics we're using them because they're algorithmically convenient, very cheap to compute and ignore that whole half-spin thing. It's one of those instances where it's cheaper to compute useless information and then throw it away as opposed to avoiding to compute it.
They're also absolutely impossible to deal with when authoring stuff, as in rotating things in Blender, it's just a representation on the backend. Quaternions would avoid gimbal lock but when authoring you really rather deal with that than a 4-dimensional hypersphere.
Sounds like someone’s developing a…
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C o m p l e x
YEEEEAAAAAHHHHHH
Bro, if you don't like imaginary numbers then just don't imagine them?
I tried that but then i went and got their siblings j and k. They're threatening to burn down my plane. What do I do now?
Add another axis to your game plan.
Also mathematicians making them entirely self-consistent then using them in regular maths until we're all forced to deal with them and accept them as normal
Instead of just admitting they were wrong
But isn't it fascinating that NASA used theoretical math that didn't have an intended use by the mathmaticians that developed it years ago, but it ended up working well with orbital entry calculations?
There's a lot of theoretical math that ends up being very real.
Quaternions? They were used as intended - to represent rotation.
Actually it really looks like physic needs imaginary numbers to accurately explain reality.
https://www.sciencenews.org/article/quantum-physics-imaginary-numbers-math-reality
This was one of the points of contention with the quantum revolution of the beginning of the 1900's, schrödinger came up with the equation, which fitted like a glove for a lot of scenarios, but it had an imaginary component, which baffled a lot of people since it could imply reality uses such numbers at a fundamental level
What's really screwy is you can force light to only travel as a evanescent wave. It's completely undetectable without a second interaction, but light must transmit energy using the purely imaginary part of the complex wave.
The imaginary component definitely has some physical meaning, it's not just a useful mathematical trick.
This is why some observers have noticed that religion, 'the God of the gaps' especially, is dying and losing any use or meaning, leading to less metaphysical thought in everyday life, that math and physics especially now use metaphysical thought is the primary tool of new understanding and discovery. Which is bringing it back into everyday life.
For some it's the stock market instead of physics. Human brains are wired to invent patterns and meanings in places where there aren't any.
Mathematicians dug up quaternions. Double the imagination. They aren't Complex for comprehention.
Little known fact: the imaginary numbers are the algebraic closure of the irrational numbers.
Yes the obscure and little known fundamental theorem of algebra
Is this some joke I'm not getting? Cause yes, real numbers are the closure of irrational numbers, but imaginary numbers are just isomorphic to them.
You're thinking of topological closure. We're talking about algebraic closure; however, complex numbers are often described as the algebraic closure of the reals, not the irrationals. Also, the imaginary numbers (complex numbers with a real part of zero) are in no meaningful way isomorphic to the real numbers. Perhaps you could say their addition groups are isomorphic or that they are isomorphic as topological spaces, but that's about it. There isn't an isomorphism that preserves the whole structure of the reals - the imaginary numbers aren't even closed under multiplication, for example.
Imaginary numbers are math cope for when you're too cool to just use two numbers.
I never got why they didn't just introduce tuples in maths
They did, linear algebra and vector calculus are a thing, but complex numbers have certain properties that you don’t get with vectors and that are quite useful and worth studying.
For various math reasons you only get consistent systems with 2^n dimensions, so after complex you get quaternions with 4, then the next one that works is 8, then 16, etc. They become less useful because you lose various useful features, like you lose commutabiliy with quaternions (eg ab != ba), and every time you double you lose more things.
I know this is a joke, but wrong about what, exactly? I don't get it.
Also, and maybe this has something to do with the joke I'm not getting, the way complex numbers are motivated in school is a lie, and a stupid one. Mathematicians were perfectly comfortable with certain equations having no solutions; the problem was when their equations told them there were no solutions when they could see the solutions: the curve x3 - 15x + 4 crosses the x-axis, but Cardano's cubic formula gives up due to negative square roots. Imaginary numbers were originally no more than an ephemeral reasoning tool, and were only reluctantly accepted as entities in their own right because of how damn useful they were.
Imaginary numbers were originally no more than an ephemeral reasoning tool, and were only reluctantly accepted as entities in their own right because of how damn useful they were.
That, there, is the story of pretty much all maths. There were occasional mentions of zero and debates about whether it's a number or not in old Europe, it only became widely accepted once base 10 became popular. And people still can't agree whether the natural numbers contain it!
Jujutsu Kaisen characters pulling yet another 'binding vow' out their arse instead of learning to fight better.
It's a long standing shonen tradition of ass-pulling
Fucking pathethic, just admit you're all wrong, they even made a bullshit-number-generator to keep making up new stupid-useless-made-up-numbers that serve no purpose at all in any discipline of science, it's disgusting
And instead of admitting you can not solve a problem prove that it's impossible to solve it
“Taravangian was here”
Taravangian the next day: “What was I thinking?”
Mmmmmm lies
Like zero?
No, square root of -1. https://en.wikipedia.org/wiki/Imaginary_number
This is exactly what Lewis Carroll was saying..
1*1=2 prove me wrong mathematicians.
If you have 1 of 1 bag of apples, you have 1 bag (1x1=1).
If you have 2 of 1 bag of apples, you have 2 bags (2x1=2).
If you have 3 of 1 bag of apples, you have 3 bags (3x1=3).
And so on...
Why so serious?
"Hey, Mr. Cheadle? You're needed again."
What are these references?
