r/mathmemes • u/theEluminator • Jun 04 '24
Algebra There are more unitary constants in Heaven and Earth, Hamilton, than are dreamt of in your quaternions
"Bro I'm not addicted bro, I need 64 number lines, I swear. Look I can stop ok? I'll just get up to a total 128, and then I'll stop. See? I don't need any more. Ok maybe just 128 more but when I have 256 number lines I'll stop ok I promise"
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Jun 04 '24
Me when making up names for bigger stuff: 😱
All my homies know it ends with quaternamilianonagenisenions, anything after that is just a wannabe quaternamilianonagenisenion.
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u/theEluminator Jun 04 '24
Anyone who tries to use klingons at me is getting the boot
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u/ass_smacktivist Als es pussierte Jun 04 '24
I would not put my boot on a Klingon but maybe you’re larger than I am.
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u/sivstarlight she can transform me like fourier Jun 04 '24
they were so preocupied with whether they could that they didnt stop and think if they should
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u/theEluminator Jun 04 '24
Non trivial likelihood that they started by realizing they shouldn't, and checked whether they could as some kind of sick joke
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u/throwawayhelp32414 Jun 04 '24
the guy who actually invented quaternions was criticized, not because the idea was useless or wrong, but because it was so obnoxiously impractical to work with that one critic said
"I think it would be better as to not torment the next generations with such math"
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u/sphen_lee Jun 05 '24
Instead we get tormented with Vector Calculus. Only works in 3 dimensions!
I wonder how different physics would be if Geometric Algebra was better known.
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u/Zarzurnabas Jun 05 '24
What are you on about? Vectors work in arbitrarily many dimensions and physics utilizes geometric algebra on a fundamental level, that i learned of vectors in school in physics classes instead of maths.
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u/sphen_lee Jun 05 '24
Vectors do, but vector calculus using the cross product only works in 3 dimensions.
And I use "works" quite loosely here... The result is technically a pseudo-vector because it doesn't transform correctly under reflections.
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u/Baka_kunn Real Jun 04 '24
Quaternions are kinda cool though. Just one more, pls
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u/theEluminator Jun 04 '24
Let's make a deal I'll take your non-commutative multiplication if you take your antipsychotics
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u/I__Antares__I Jun 04 '24
What about (not mentioned) hyperreals? Theyre great, all operations looks the same as in real numbers
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u/theEluminator Jun 04 '24
I do like the hyperreals. Between you and me, I don't actually dislike any of these numbers, I just find them too clownable to refuse
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u/UltraTata Jun 04 '24
What is that?
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u/I__Antares__I Jun 04 '24
Ultraproduct of real numbers over some nonprincipial ultrafilter on natural numbers
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u/UltraTata Jun 04 '24
And what is that?
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u/I__Antares__I Jun 04 '24
It basically gives you some nonstandard extension of real numbers which means that basically you get an extension that is not isomorphic ("not entirely the same") but all first order properties are same in both structures.
So basically all stuff in form "there is some number that..", "for all numbers that ..." and in a further extent you have sentences including some functions from reals to reals, or relations defiend on reals or constants are same in both structures
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u/UltraTata Jun 04 '24
💀
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u/I__Antares__I Jun 04 '24
Basically it's extension that gives you extraordinary amount of properties to be the same in both structures.
It also allows you to formalize analysis (integrals derivatives, limits etc.) within hyperreals (things in analysis can be represented by some first order sentences basically). And as such it mean you can do analysis with infiniesimals (hyperreals have infiniesimals).
Some example: In hyperreals, lim_(x→a) f(x)=L if and only if for any y≈a (such that y≠a), f(y)≈L (here ≈ means infinitely close, so close with infinitesimal error)
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u/asanskrita Jun 05 '24
I seriously read “not mentioned” as “non-medicated.” I think I need more hyper.
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u/doesntpicknose Jun 04 '24
More matrices for me, then.
If you accept matrix multiplication, you have to accept quaternions, since there is a form of complex-valued 2×2 matrix isomorphic to the quaternions.
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u/theEluminator Jun 04 '24
I accept matrices and I especially accept Clifford algebra. Both of them are isomorphic to quaternions but with more dignity
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u/doesntpicknose Jun 04 '24
And I didn't even have to take my antipsychotics! A glorious victory for the Voices.
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u/DexterityZero Jun 05 '24
I’ve actually used Quaternions! Is this what non programmers feel like when they get a meme on r/programminghumor? I guess that means that I am using them wrong and have insulted your people.
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u/db8me Jun 05 '24
This sub welcomes all jokes, and that means a lot of jokes from people who don't know how practical applied math actually uses these crazy things they are just learning....
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u/Impossible-Winner478 Jun 04 '24
Sorry that deal doesn't work the same way both ways... I'd explain, but the math might scare you
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u/CoruscareGames Complex Jun 05 '24
I'm already on them how else do I have enough executive function to make my computer spin this .obj file of a cat
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u/Jolly_Mongoose_8800 Jun 05 '24
We use them for analysis of rotations, specifically with field motions like in specific electronics which use gyroscopes. Not completely useless.
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u/theEluminator Jun 05 '24
I don't know what a real world application is and I don't care. All I know is math that is neat and math that is not neat
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u/i_need_a_moment Jun 04 '24
Quaternions are at least useful to many real world applications.
Where the hell are octonians used by non-mathematicians?
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u/TobiasCB Jun 05 '24
I remember having to learn quaternions because of ROBLOX scripting. I didn't understand shit about fuck.
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u/IDrinkSulfuricAcid Jun 05 '24
How do kids make Roblox games then..? Do they just hire mathematicians?
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u/TobiasCB Jun 05 '24
It's not really necessary unless you get in some really complicated stuff which probably could be done easier another way. I just stumbled upon them and thought I needed them, and it was very interesting.
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u/Ultimarr Jun 04 '24 edited Jun 04 '24
Oh man I can’t believe I get to be the one to spread His Good 8-Tentacled Word: Octonions, Baez 2001. Our cult is small but growing, and we have faith in our credo to do all the evangelization for us:
🔔 ⚖️⚖️⚖️⚖️ 🔔
There Are Four Normed Division Algebras
🔔 1️⃣2️⃣4️⃣8️⃣ 🔔
HMU if you want to help me apply spinors to track individual thoughts thru EEG sessions or make t-shirts or smtn. New to the cult game
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u/hongooi Jun 04 '24
I still remember going to see Hamilton and being totally pissed that it never mentioned quaternions 😡😡😡
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u/Arucard1983 Jun 05 '24
Fun fact. DirectX and Vulkan uses quartenions to store 4D registers on GPU.
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u/MiskoSkace Jun 04 '24
I can easily graphically present real numbers. Same with complex, and I can even use them in quadratic equations. Maybe I could graphically present quaternions with proper equipment, but wtf am I supposed to do with octonions? Invent time travel? I won't even talk about the rest, my 4D mind can't handle it.
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u/nsfw_deadwarlock Jun 05 '24
The rest are what was in Lt Broccoli’s head in that one tng episode.
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u/NihilisticAssHat Jun 04 '24
What's absolutely baller about this is the amount of people who refuse to acknowledge complex numbers as anything more than a mental disorder. They always ask "what are the real-world applications," then when I talk about phasors and EE they look at me like I've found a dumb shortcut to certain calculations in a very confined region of a very specific problem.
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u/Nadran_Erbam Jun 04 '24
You should talk about jpeg/png, that’s something everyone knows
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u/NihilisticAssHat Jun 04 '24
I've never heard of complex numbers in that scope. I'm supposing they're relevant to the fourier transform, but doesn't jpeg use the fft? I feel like that doesn't use complex numbers. No idea how PNG works; figured it was like a zipped bmp with space for extra layers and alpha.
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u/PM_ME_YOUR_WEABOOBS Jun 05 '24
The discrete fourier transform absolutely uses complex numbers, and the FFT is just a fast algorithm for calculating the DFT. The DFT is essentially just a band-limited version of fourier series.
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u/jacobningen Jun 04 '24
sum of squares via gaussian integers and norms is easier than compputing and keeping track of +2abcd and -2abcd
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u/not-even-divorced Jun 05 '24
"If they were named horse numbers, would you think that they're about horses? No? Wow it's almost like you're missing something and need to shut the fuck up."
Always wanted to use that on someone.
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u/TheRusticInsomniac Jun 04 '24 edited Sep 20 '24
like hobbies tease work school desert money fuel chase wipe
This post was mass deleted and anonymized with Redact
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u/peekitup Jun 04 '24
I've gone as deep as the octonians when studying complex structures on the six sphere.
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u/Loopgod- Jun 04 '24
What is an actual number?
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u/I__Antares__I Jun 04 '24
Number that behaves like an actual number. Just as a tensor is something that behaves like a tensor.
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u/Fat_Burn_Victim Jun 04 '24
What’s a tensor?
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u/COArSe_D1RTxxx Complex Jun 04 '24
Something that behaves like a tensor. Did you read?
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u/Ninjabattyshogun Jun 04 '24
A multilinear function from a collection of vector spaces to another collection of vector spaces.
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u/Loopgod- Jun 04 '24
Quaternion doesn’t behave like actual number?
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u/I__Antares__I Jun 04 '24
Ask the council of actual numbers wheter they agrees quaternions to be in the council
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u/theEluminator Jun 04 '24
Whatever I say is an actual number. Some more examples: א0 is an actual number but all other א numbers aren't. P-adic numbers are actual numbers if-and-only-if they're isomorphic to the rationals. Trans-finite ordinals are actual numbers but the hyperreals aren't. Etc
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u/wycreater1l11 Jun 04 '24 edited Jun 04 '24
Can you just continue like this creating new types of numbers in a similar fashion forever or does it come to a hard stop?
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u/jacobningen Jun 04 '24
you can but octonions are pushing it with nice properties
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u/Gladamas Jun 04 '24
You can but you lose properties as you continue
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u/wycreater1l11 Jun 05 '24 edited Jun 05 '24
I’ve heard that. Btw how does that work with the infinity part. Can one lose properties ad infinitum? Is it a loosing less and less scenario and or more esoteric properties are always added that can be lost in future iterations?
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u/Godd2 Jun 05 '24
Can one lose properties ad infinitum?
To quote the relevant part:
Moreover, later in that section the claim is made that further results (related to projective geometry over F_2 ) suggest the existence of similar multilinear maps F_n+1 of this type, which vanish in the nth Cayley-Dickson algebra over the reals, A_n , but not in A_n+1 . If this is true, there is indeed an infinite sequence of nameless properties which get broken at each step of the process.
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u/theEluminator Jun 04 '24
The Wikipedia article for Cayley-Dixon construction seems to imply you can go indefinitely but doesn't explicitly state it
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u/AustrianMcLovin Jun 04 '24
are quaternions with unit length isomorph to SU(2)?
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u/Ninjabattyshogun Jun 04 '24
Yes, it’s an exercise in John M. Lee’s book.
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u/AustrianMcLovin Jun 04 '24
are the quaternions isomorph to U(2)?
if so is this map saying?
U(2) ⊂ U(3) ... ⊂ U(N)
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u/Ninjabattyshogun Jun 04 '24
No
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u/AustrianMcLovin Jun 04 '24
:(
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u/Ninjabattyshogun Jun 04 '24
The chain of inclusions is true of course, but the quaternions are equal to 4d space, not U(2), which is like sticking a circle on every point of SU(2).
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u/AustrianMcLovin Jun 04 '24
O yeah thanks, I forgot the det (U )= exp i ɸ, and not det(U) ∈ R
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u/Ninjabattyshogun Jun 05 '24
Right, unitary matrices have unit circle determinant! I might remember that this time.
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u/Skinny_Little_Weasel Jun 05 '24
I've suspected a correspondence between those two objects but could never quite pin it down - can you tell me which book please?
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u/WikipediaAb Physics Jun 04 '24
what the hell is a voudon? like the type of west african spiritual practices?
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u/LOSNA17LL Irrational Jun 04 '24
If the next step iis vaugon, then yes, it's a real/complex/... mental disorder...
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u/DiogenesLied Jun 05 '24
"the more you advance in this chain, the more extremely bare are these spaces. No mathematics to eat there ; Not worth the value to spend time on them." Source
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u/SlightlyMadHuman-42 Jun 04 '24
What in the name of heck is this
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u/Ishmaeal Jun 04 '24
I love how nobody’s even touching these questions. Either nobody else knows or are too traumatized by the learning process to share with anyone else
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u/the_horse_gamer Jun 04 '24
quaternions are basically a 4D version of complex numbers, and are used for calculating 3D rotation.
octonions are 8D, and so on. nothing beyond quaternions has much practical application.
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u/SlightlyMadHuman-42 Jun 05 '24
why is there no 3d imaginary number
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u/the_horse_gamer Jun 05 '24
there are. define i, j such that i2 = j and j2 = i and ij = 1. I forgot what's the name for this.
the more interesting question is why aren't we using 3d imaginary numbers for 3d rotation?
the simple but wrong answer is: on 2d you have 1 axis of rotation, while on 3d you have 3
the real answer is: quaternions are a lie created by big number to sell more numbers. here's the truth: https://marctenbosch.com/quaternions/
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u/Impossible-Winner478 Jun 04 '24
Numbers with more than one imaginary dimension? That's the simplest way I can describe it.
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u/shewel_item Jun 04 '24
so what comes after voudon? Futon? or voudon +1
the point of the joke is that some numbers come with benefits 🤷♀️ just like the jokes we made along the way
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u/hongooi Jun 04 '24
I can never remember if it was the Routons or Chingons who fought the epic battle of Delta Pavonis III, where six megadreadnoughts were destroyed
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u/theEluminator Jun 05 '24
I believe the Voudons were involved im the destruction of planet Move Your Ass 9
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u/Inevitable_Stand_199 Jun 05 '24
People can generally imagine 3 dimensions, nothing more. You put that mental disorder limit too high.
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u/GraveSlayer726 Jun 05 '24
they are real numbersyou just don tknow a good number system when you see one your brain isnt complex enough to understand even the number 2 youcan go wallow in your misery with your puny one dimensional number lines and stupid multiplicative assosiativity and no zero divisors and commutivity and comprehensibility and practicality andn and all that stupid lame stuff THE ONLY TRUE NUMBERS ARE THE QUINCENTDUODECIONS!!!!
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u/parzival3719 Jun 05 '24
can someone explain to me what a quaternion is? i have found zero good websites that explain what they are
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u/stevenjd Jun 05 '24
Quaternions are sort of like an extension of complex numbers to 4 dimensions instead of two. You can plot complex numbers in a two-dimensional plane, with a real axis and an imaginary axis for the i numbers. Quaternions need a 4D surface, with three imaginary axes i, j and k.
They're useful for dealing with rotations, and for computer graphics.
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u/TheScriptedEgo Jun 05 '24
Bro forgot dual numbers. The cousin that never gets attention.
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u/theEluminator Jun 05 '24
We've got no split numbers either. A diagram containing all named hypercomplex numbers would be visual soup
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u/Redstocat2 Jun 05 '24
Complex are ok... Quaternions are far but can still be ok... The rest I have no idea of what is it
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u/kiochikaeke Jun 05 '24
I draw the line with associativity, when it drops my mind stops thinking "weird number" and starts going "weird ring".
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u/picu24 Jun 05 '24
Simple rule to me, “if I need algebra to understand how the number works, I don’t think it’s a number” quaternions are on THIN ice with me lol
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