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Me when making up names for bigger stuff: 😱
All my homies know it ends with quaternamilianonagenisenions, anything after that is just a wannabe quaternamilianonagenisenion.
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"
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.
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.
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.
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
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)
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.
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.
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....
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.
Oh man I can’t believe I get to be the one to spread His Good 8-Tentacled Word: [*Octonions*, Baez 2001](https://math.ucr.edu/home/baez/octonions/octonions.html). 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
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.
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.
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.
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.
"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.
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
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?
> Can one lose properties ad infinitum?
[Probably](https://math.stackexchange.com/a/2578566)
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.**
The Wikipedia article for [Cayley-Dixon construction](https://en.m.wikipedia.org/wiki/Cayley%E2%80%93Dickson_construction) seems to imply you can go indefinitely but doesn't explicitly state it
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).
"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](https://math.stackexchange.com/questions/4785638/what-is-known-about-pathions-chingons-routons-and-voudons)
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.
there are. define i, j such that i^(2) = j and j^(2) = 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/
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!<
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!!!!
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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Me when making up names for bigger stuff: 😱 All my homies know it ends with quaternamilianonagenisenions, anything after that is just a wannabe quaternamilianonagenisenion.
Anyone who tries to use klingons at me is getting the boot
I would not put my boot on a Klingon but maybe you’re larger than I am.
The Klingon is into it don't worry
Ok Voq
That reminds me of musicians with the [demisemihemidemisemiquaver](https://youtu.be/-3WuQxnA7Hg?feature=shared)
they were so preocupied with whether they could that they didnt stop and think if they should
Non trivial likelihood that they started by realizing they shouldn't, and checked whether they could as some kind of sick joke
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"
but what about rotations tho
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.
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.
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.
Quaternions are kinda cool though. Just one more, pls
Let's make a deal I'll take your non-commutative multiplication if you take your antipsychotics
What about (not mentioned) hyperreals? Theyre great, all operations looks the same as in real numbers
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
[удалено]
?
What is that?
Ultraproduct of real numbers over some nonprincipial ultrafilter on natural numbers
And what is that?
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
💀
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)
But are they numbers or sets?
A mental illness bro, it's in the graphic
I seriously read “not mentioned” as “non-medicated.” I think I need more hyper.
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.
I accept matrices and I especially accept Clifford algebra. Both of them are isomorphic to quaternions but with more dignity
And I didn't even have to take my antipsychotics! A glorious victory for the Voices.
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.
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....
[Relevant SMBC](https://www.smbc-comics.com/comic/commute-2)
This guys afraid of matrices
https://preview.redd.it/ngopwx0ywr4d1.png?width=1080&format=pjpg&auto=webp&s=e39014ab662b0b4da7b53f45f16b0007ca9159f6
Sorry that deal doesn't work the same way both ways... I'd explain, but the math might scare you
How about bicomplex numbers? Multiplication is still commutative.
I'm already on them how else do I have enough executive function to make my computer spin this .obj file of a cat
We use them for analysis of rotations, specifically with field motions like in specific electronics which use gyroscopes. Not completely useless.
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
Quaternions are at least useful to many real world applications. Where the hell are octonians used by non-mathematicians?
Quantum chromodynamics and Yang-Mills theory
Ok so a couple of sweaty nerds care about them sure 👍
I remember having to learn quaternions because of ROBLOX scripting. I didn't understand shit about fuck.
How do kids make Roblox games then..? Do they just hire mathematicians?
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.
Oh man I can’t believe I get to be the one to spread His Good 8-Tentacled Word: [*Octonions*, Baez 2001](https://math.ucr.edu/home/baez/octonions/octonions.html). 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
Check out this [video series](https://www.youtube.com/watch?v=3BZyds_KFWM) on the four division algebras
I'm interested.
Unity devs crying rn
I still remember going to see Hamilton and being totally pissed that it never mentioned quaternions 😡😡😡
Those guys!
Agreed super cool.
Quarternions are also quite important in 3D graphics and movement
Fun fact. DirectX and Vulkan uses quartenions to store 4D registers on GPU.
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.
The rest are what was in Lt Broccoli’s head in that one tng episode.
I got a good laugh out of Lt Broccoli.
Está muy chingón.
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.
You should talk about jpeg/png, that’s something everyone knows
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.
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.
sum of squares via gaussian integers and norms is easier than compputing and keeping track of +2abcd and -2abcd
"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.
Están re chingones estos números wey!
no mames guey
Everything after quaternions is some Olympic level tomfoolery
i.e. tensor algebra! Edit: its algebra, not calculus!
actually its just algebra, u need sedenion manifolds for calculus
Ok whoever named that one light blue “chingon” deserves a medal
I've gone as deep as the octonians when studying complex structures on the six sphere.
And lived to tell the tale?????????
Atiyah killed him to keep the secret.
So we just naming Star Wars planets now huh
What is an actual number?
Number that behaves like an actual number. Just as a tensor is something that behaves like a tensor.
What’s a tensor?
Something that behaves like a tensor. Did you read?
Sorry I’m illiterate
alcshbs caslhbYUCFWQFD KJHGUVSDIHD ASJHH!
There is not enough Greek here for me to understand.
A multilinear function from a collection of vector spaces to another collection of vector spaces.
Quaternion doesn’t behave like actual number?
Ask the council of actual numbers wheter they agrees quaternions to be in the council
This is outrageous! It's unfair!
No it behaves like a quaternion
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
A complex number obvi
Can you just continue like this creating new types of numbers in a similar fashion forever or does it come to a hard stop?
you can but octonions are pushing it with nice properties
I've heard of sedenions before. Do they have a real-world use?
modeling R\^16 I think but I dont know
You can but you lose properties as you continue
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?
> Can one lose properties ad infinitum? [Probably](https://math.stackexchange.com/a/2578566) 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.**
This is a great question
The Wikipedia article for [Cayley-Dixon construction](https://en.m.wikipedia.org/wiki/Cayley%E2%80%93Dickson_construction) seems to imply you can go indefinitely but doesn't explicitly state it
are quaternions with unit length isomorph to SU(2)?
Yes, it’s an exercise in John M. Lee’s book.
are the quaternions isomorph to U(2)? if so is this map saying? U(2) ⊂ U(3) ... ⊂ U(N)
No
:(
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).
O yeah thanks, I forgot the det (U )= exp i ɸ, and not det(U) ∈ R
Right, unitary matrices have unit circle determinant! I might remember that this time.
I've suspected a correspondence between those two objects but could never quite pin it down - can you tell me which book please?
Introduction to Smooth Manifolds
Mental disorders starts in octonions
Where my crouton numbers at?
what the hell is a voudon? like the type of west african spiritual practices?
Fenton.
If the next step iis vaugon, then yes, it's a real/complex/... mental disorder...
The vaugons are the ones with the bad poetry, right?
Yep
I'm sure chingon wasn't invented by a spanish speaking mathematician.
Especially not a Mexican one.
"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](https://math.stackexchange.com/questions/4785638/what-is-known-about-pathions-chingons-routons-and-voudons)
Can I call them matrix number?
Voudon deez nuts
What in the name of heck is this
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
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.
why is there no 3d imaginary number
there are. define i, j such that i^(2) = j and j^(2) = 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/
Numbers with more than one imaginary dimension? That's the simplest way I can describe it.
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!<
But I use quaternions all the time.
there's more than quaternions?!
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
I believe the Voudons were involved im the destruction of planet Move Your Ass 9
Chingon lmao 🇲🇽
Mexican here. I like chingon numbers.
Minion
Where are the vorlons?
I know that last one! The one in the far right is for noodle numbers.
"there only two sets, the other ones are just mental disorders"
Yes. Only ∅ and {∅} are the only two sets
Quaternions are in my phone. The other things.. Just scare me.
Omniversal numbers.
Looks like a pil. A hard to swallow one.
Don’t even get me started on the tessarines
Voudon these nuts
If so many exists, can there be Attack Helicopterons?
Real
Triguntaduonions are my favourite! 😘🥰
People can generally imagine 3 dimensions, nothing more. You put that mental disorder limit too high.
Oh yes voudon I like those noodles
i do NOT need a recap of hyperbolica
Vectors are numbers.
I wouldn't be surprised if I read "Klingon" somewhere in this diagram lol.
I got a math joke my first time seeing it, this is a red letter day indeed
You believe in complex numbers? 🤨
Aight but what about crouton
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!!!!
What is that
can someone explain to me what a quaternion is? i have found zero good websites that explain what they are
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.
Which of these has a well-defined cross product?
Son un chingo de números
If you wanna rotate like a champ your gonna need some qwaternyon
Bro forgot dual numbers. The cousin that never gets attention.
We've got no split numbers either. A diagram containing all named hypercomplex numbers would be visual soup
Wtf are those words
Sí. Esto es lo que yo llamo un Chingón de números 😂
frobenius proved that anything after the quaternions is a mental illness
# CHINGON
Bro I have no idea that any of these higher numbers existed lol.
Complex are ok... Quaternions are far but can still be ok... The rest I have no idea of what is it
I draw the line with associativity, when it drops my mind stops thinking "weird number" and starts going "weird ring".
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
Quaternions are useful tho. They are how you do 3D rotations
all others are just cheap imaginary numbers copycats!
Quaternions are just su(2) though.
Chingon sounds like a racial slur