Mathematicians dug up quaternions. Double the imagination. They aren’t Complex for comprehention.
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.
You laugh now, but just wait 3 years until this morphs into the next right-wing cult conspiracy theory…
God I hate that this is an entirely plausible scenario.
Nah, I’m pretty sure they avoid maths like it’s dark magic
And there you have the conspiracy theory. Now all we need is to somehow tie it back to The Jews™
I heard that Albert Einstein knew some math…
Well we did use it to carve runes into a rock and then convince said rock to think
Look at what mathematicians have been asking your respect for.
“Hello, I would like i potatoes”
How can we trust science when they say things like that?
i-anon
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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
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
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?
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.
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.
Oops my bad, it’s been a while. I thought the Hamiltonian used quaternions, but I guess that’s just complex numbers.
The Hamiltonian using Hamilton’s numbers? Now I think about it it is a bit silly that two entirely separate yet highly propinquitous concepts have such similar names. Physics really went downhill once humans started writing it down.
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”.
Perfect, we really needed some more anti-science bullshit
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I’m just saying it’s not as funny a joke as you are
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Whoa there. I detest this post as much as you do, but there’s no need to start throwing out baseless accusations. @Summzashi@lemmy.one isn’t funny at all.
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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
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.
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.
One definition of the complex numbers is the set of tuples (x, y) in R^(2) with the operations of addition: (a,b) + (c,d) = (a+c, b+d) and multiplication: (a,b) * (c,d) = (ac - bd, ad + bc). Then defining i := (0,1) and identifying (x, 0) with the real number x, we can write (a,b) = a + bi.
Ok, that’s actually quite interesting
Yup, you’ll notice the only thing distinguishing C from R^(2) is that multiplication. That one definition has extremely broad implications.
For fun, another definition is in terms of 2x2 matrices with real entries. The identity matrix
1 0 0 1is identified with the real number 1, and the matrix
0 1 -1 0is identified with i. Given this setup, the normal definitions of matrix addition and multiplication define the complex numbers.
“Taravangian was here”
Taravangian the next day: “What was I thinking?”
Mmmmmm lies
And instead of admitting you can not solve a problem prove that it’s impossible to solve it
Sounds like someone’s developing a…
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C o m p l e x
YEEEEAAAAAHHHHHH
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
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.
Don’t read into it too much.
If I’m not meant to think about it until understanding emerges, then that means it should be immediately understandable without thinking. It is not.
It is, actually
The numbers are imaginary, thus theyte not real, thus the math magicians (not gonna undo autocorrect there) are wrong and refuse to admit it because they insist imaginary numbers are real
Don’t apply actual knowledge of what imaginary numbers are for this exercise
Ok, so this is a “joke” which is only funny to people who do not understand the context, and moreover jump to insane, unsubstantiated conclusions rather than expending an infinitesimal measure of effort to understand something they haven’t seen before. It’s active mockery of the very concept of being open to new ideas.
No, the joke plays on the two meanings of “imaginary” - one being “made up, not real”, and the other being the mathematical construct. The fact that you don’t get it doesn’t make it mockery, it just means you don’t get it.
Sometimes it’s better to just accept that you don’t get the joke and move on.
I might not find a joke funny, or I might not have the necessary context to appreciate it; that’s “not getting” a joke. If it’s possible to have too much context to appreciate a “joke”, it’s at the expense of people who know more than the audience.
Bruh, who cares.
Stop complaining.
It might seem harmless, but the purpose of a joke is to draw a distinction between those who get it and those who don’t, fostering a sense of community. In this “joke”, the in-group is people who don’t know something; the community ideal fostered there is that knowledge is undesirable, that anything that seems unintuitive to the uninformed mind is inherently ridiculous. The “joke” has no effect if it doesn’t do this. Entertaining the idea without challenge is dangerous.
That’s where you’re wrong. The joke is based around a play on words: the generally accepted definition of imaginary, and a math term. Thus, the in-group for this joke are people familiar with the common definition of imaginary, and familiar with the fact that “imaginary numbers” is a term used by mathematicians. The joke being that, if they use the term “imaginary numbers”, then someone came up with numbers that don’t fundamentally exist, and they were only used to cheat out an answer to a difficult problem. Of course, in math this isn’t the case, the numbers most definitely exist. To me it just seems like you’re trying to be a pompous know-it-all and ruin people’s fun, but you can’t even do that correctly because you didn’t understand what the joke even was.
Grow up dude.
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!
Hah. Church tried to ban it because it was “associated with illegal money trading”, I remember that. What is it about maths that makes non-mathematicians think themselves qualified to judge matters they don’t understand?
They did five minutes of research on
the interneta stone tablet so their opinion is just as valid.
Like zero?
No, square root of -1. https://en.wikipedia.org/wiki/Imaginary_number
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 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.
Our theories fit reality only to some extent. Which is why they patch them with dark unicorns, even though it doesn’t help much.
Imaginary numbers are no more imaginary than real numbers. The name trips a lot of people up. If you want to call imaginary numbers “dark unicorns” then you really should say the same thing of the numbers 1, 2, and all other numbers as well.
The problem is they fit TOO well. We struggle to get either relativity or QM to deviate significantly close to their “realms”. However, neither predicts the existence of the other, and are incompatible in basic ideas about reality.
Basically, we know they don’t align, but we can’t access the middle area, and we can’t find any useful cracks to pry at within the accessible areas. It’s been driving physicists up the wall for decades.
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
“Imaginary” is just a misnomer. Descartes basically ran a smear campaign against them.
That’s actually a good point I had never considered! In a way you could consider that “negative numbers are imaginary as well”
And that’s never something I considered. You can’t see a negative amount of apples. Must be imaginary!
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.
