3Blue1Brown - 2018-09-06
How to think about this 4d number system in our 3d space. Brought to you by you: http://3b1b.co/quaternion-thanks Part 2: https://youtu.be/zjMuIxRvygQ Interactive version of these visuals: http://3imaginary1real.com Quanta article on quaternions: https://www.quantamagazine.org/the-strange-numbers-that-birthed-modern-algebra-20180906/ The math of Alice in Wonderland: https://www.newscientist.com/article/mg20427391-600-alices-adventures-in-algebra-wonderland-solved/ ------------------ If you want to contribute translated subtitles or to help review those that have already been made by others and need approval, you can click the gear icon in the video and go to subtitles/cc, then "add subtitles/cc". I really appreciate those who do this, as it helps make the lessons accessible to more people. Music by Vincent Rubinetti: https://vincerubinetti.bandcamp.com/album/the-music-of-3blue1brown ------------------ 3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted on new videos, subscribe: http://3b1b.co/subscribe Various social media stuffs: Website: https://www.3blue1brown.com Twitter: https://twitter.com/3blue1brown Reddit: https://www.reddit.com/r/3blue1brown Instagram: https://www.instagram.com/3blue1brown_animations/ Patreon: https://patreon.com/3blue1brown Facebook: https://www.facebook.com/3blue1brown
Explaining 4D objects using 3D shapes in a two dimensional screen to my 1D brain 😁
Comment of the day award!! Thumbs up
Good joke, exactly like one i heard on that A.I comedy channel explaining dimensions...
@Lost Montanelas Sciencephile
mine's 0D
4D aliens somewhere are using this video as a reference to better explain 6D spaces, ...
Rambo Or understand how linguistics break down into colors, the more complex the language the more colors. Bet they understand our field of vision and how we perceive them and can stand right next to us without us even knowing by using the opposite order of proper color perspective, “cool to warm, warm to cool” now imagine the words with multiple axis on your screen and give just that section depth.
@YeetusDeletus SixtyNineFourTwenty Yes, this video is about explaining quaternions. But he mentioned it multiple times, that these are useful to describe 3D rotations. If you wanted to rotate in 3D with just three dimensions, you would have to make it with a matrix, which can be way longer for a computer to work with, than a "single equation", that is in 4D, but can represent a 3D rotation.
They’d probably explain 5D using that. I mean, remember what Monika said, we aren’t 2D creatures
CartooNinja somehow, I’ll love again
Laplace just rolled over In his alternate reality 5D grave smh
You know it's going to be a bumpy road when you don't understand the 1 dimensional analogy lol
You know it's going to be a non-linear line when you don't understand what a dimension is lol
@shrdlu oh oh, i understand. misinterpreted your original comment, sorry lol. thought you were just being a cock. now who's the cock hehe. it's me
nice one haha
because it is poorly explained, this is not a good video to learn about quaternions
@dirt man what's a better video?
Now it's 3Imaginary1Real...
Imaginary Blues for a brown and PHysical Reality
@Leif The term 'infinity' does not represent a 'place' on the line. If you add one to it, it remains infinity. If you multiply it by 100, it will still remain infinity. It is a concept, that is hard to work with in most cases. But if we're at this point, we should consider, that - if we interpret the line as a circle with infinite diameter, then it's center is also in infinity, only perpendicular to the 'other' infinity.
@Kuma Ahito i said the same thing..i literally said infinity is not a point on the line..so you don't need to corrext me because that is mwhat i said..and I'm not sure what you mean by other infinity..I get if a circle has ibfibte diameter you will never touch the circumference so that's one infinity..but do you mean the center is another infinty because if you were to start at the circumference and head towards the center you will never reach it?
@Leifyeah, dunno why i answered to your comment, i was pretty tired... Sry lol
@ffggddss 3 blue-eyed grandfathers and 1 brown-eyed grandmother
when you portray the audience or students as the pi symbol, are you saying that they are irrational students?
Lol
@Taurui so you eat too much pi, you get round ? Make sense.
I relate to the angry one, it makes me feel complete seeing my pi buddy pissed off at math.
No, they’re transcendental students. Pi is transcendental.
No, it’s because they love pie
Me at 2230: alright I have a busy week in front of me so I need to sleep now
Me at 0300: hehe yes qatrnons
bruh i thought u were talking about years
Hello fellow European citizen however the nature in which you express the time puts you within the military ranks.
@Zero Six Most people express time that way. Most people in Europe don't even know what conventions are used in the miltary.
17:49
I see what you did there. 3.14 159 265 358 979 323 846 264 338
Ohkk good catch
(Golden ratio weeps in offense)
When you don't know what digits to use
I (pun not related) commented the same thing lol
There is a joke in there about all the numbers he's picking in any video actually being decimals of pi
I think Lord Kelvin was onto something when he said quaternions are an "unmixed evil".
Why?
“It might feel weird to talk about two circles being perpendicular to each other, especially when they have the same center, the same radius, and they don’t touch each other at all…”
I understand each word in that sentence individually, and that’s it.
maybe they existed in different times
I saw something like this on acid
30 mins is not long but imagine I watch this over and over and over again. It doesn't get boring and I still have something to learn. Now I am 3.5D being.
haha yeah I feel like watching this more than once is a good idea, especially that last part
Keep watching it until you become 4D
A fractal among us!!!
me: has math test tomorrow
youtube recommendations:
me: Excellent
raise your hand if you’re linus
A hand is a 2D shape for Linux so I just raise a thumb up
I'm so far behind with this I feel like Linus is a god in comparison
I am Pony the Pointlander
linus's definitely smarter
Idk how, up doesn't exist in my world.
13:39 - How to confuse both flat-earthers and sphere-earthers
BAHAHAHAHAHAAH
what?
Wake up America, the earth is a sphere projected on a plan.
youtube: hey how about your screen becomes a 2d projection of a 3d projection of a 4d plane
me:
me:
me:
me: go on
Googly Eye I
and this is all on a 2-d screen...
Ah man. That's luxury. I watch it on one blinking led....
Yeah and also using our 2D vision with just an illusion of 3D :D
@Bartek Bartek so you watch it in 1-D. Shame. I watched it as a live-staged play
@Bartek Bartek 🤣🤣🤣
Imagine sitting in front of a red LED and counting the number of times it switches on and off (along with a stopwatch) and using that binary code, visualize the 4d crap he is showing.
17:56
All these 4 directions are PERPENDICULAR to each other...
Somehow...
Brain.exe has stopped working
@David yeah YouTube is intemporal!
@Un Perrier well damn. You got me there.
:-D lol!!
lol
@Spooky that's deep bro.
I feel like I learned something
My mind was blown
but I still don't know how quaternions work
Repeat and practise if you need to actually understand and work with it :)
I found excercises http://run.usc.edu/cs520-s12/quaternions/quaternions-cs520.pdf, under "quaternions"
Since I found this I lost the need for sleeping pills.
dude lost me at you should empathize with him, he was already over my head...
Over your head? In 4d space, you mean.
"One which you'll understand at the end of this video" , heh nah
This is going to become THE standard reference for learning quaternions!
No
No, it won't. To be honest, this wasn't a great video -- no real motivation was introduced for having a pair of rotations for each quaternion, and the reference to the stereographic projection, while nice, doesn't really introduce any new ideas either. The correct motivation for understanding quarternions comes from tensors and bivectors, or alternatively from trying to generalise complex algebra to three dimensions.
Paul
Nope, nobody is going to learn quaternions from this; 3B1B is more along the lines of providing an tipping-point, as it were, for those who already have developed a substantial body of preliminaries in a topic, but are stuck on some critical lack of insight.
tubeist- dan I'm not sure I agree. Surely you get much more out of it if you are already a bit familiar with the topic, but I have never heard of quarternions before, but also feel that I understood (as far as my 3D based mind lets me) and learned something.
I have done mind-excursions into 4D before, though (read Flatland, watched Matt Parker's 4D videos,...).
His videos are becoming canon. It's on the top of many schools' and universities' "recommended watching" lists. Him and Kahn Academy, of course.
i almost cried out of mathematical joy when i found that 4d explanations, could make sense when related to lower ones.
I understand you.
I'm watching this for the 3rd time and I'm slowly getting it.
Dang, my brain hurts, and that's a thing. But I understand it so hey that's another thing.
easy: imagine it as a 3d arc with it's half-angle projected on all three coordinate planes, with another half stored in 4-th component
Legends say that Linus is still figuring out what Grant taught him.
Hello Mr.Grant Sanderson, I have a question and you are my last hope. WHAT is the most basic Math prerequisites to understand Quaternions??
I am an Iraqi refugee living in Turkey, I tried to finish my education but because of the war in Syria and Iraq, I had to drop out of college several times in my life.
But I didn't regret that because it led me to discover my self. Eventually, I found my passion and it is programming, so I learned from the internet and I manage to make an android game. for me, it's very cool but I had to use Quaternions to make the NPCs face the direction of the player, and I wanted them to slerp to that orientation over time so it looks realistic.
I tried many many times to understand quaternions but I couldn't, so in the end, I manage to make the effect I wanted by using a method made by other people but I couldn't really understand what it's doing. please show me the way. after 4 years in different universities and 4 years of waiting I finally will continue my education in Turkey as a computer programmer its 2-year program like a community college in the USA but I feel this is what I want so I learned Turkish and I feel I am ready to this new life.
But I can't get over Quaternions I just feel I need to understand them inside out is something that really bugs me
so I decided to revise all the math that I studied over the years but even then I don't think I will understand them really well because I don't understand the vector math as well, like the dot product and the cross product.
please give me a pathway to understanding this topic and consider me someone who only know the basic arithmetic.
my best regards
@Dave Olifent thank you for your advice I will start from their
Quaternions are in the really advanced end of math, on the same level as tensor analysis, so make certain you get a very firm grip on the less advanced topics like complex numbers, complex functions and the like before you take the leap into this topic. 3b1b is very good at explaining his topics so keep following his videos and do some practical stuff on the sites that he recommends, before looking outwards and doing some work of your own, it is really worth it and you can be certain that your journey will be an interesting one.
@Henrik Thor Thank you for taking the time and response to my question I started to follow the khan academy curriculum from the basic stuff to the complex numbers so far its the best resource to refresh my memory and learn new things about math after I finish studying complex numbers, complex functions I will try to understand Quaternions because its a really fascinating thing . I hope in the end I will at least have an interesting journey and enjoy the proses of learning new things thank you so much for your advice.
@zeyad jy So, how it is going? How close are you to understanding it? If you did, can you try to explain us in a way you wanted to be explained to yourself. Thanks!
Eric Weinstein brought me here
23:08
"Any plane that you see here represents the projection of a sphere somewhere up on the hypersphere which passes through -1"
The only idea that I could honestly almost understand
Now it's time to explain quaternions to Linus
@Aditya Singh i read this in linus' voice
I can't get into Linus' or Felix's shoes
Unfortunately linus wear socks and sandals and felix have no legs 😥😥😥
I wish this man was my mentor. I’ll be the first one going to college from my family, and my counselor fails to help me out...
26:00 onwards, that's actually a beautiful visualization for why spinors have to be rotated twice for an identity operation.
Yep. My brain just exploded when I saw a sphere invert into itself.
Actually, I guess not invert. But it rotates into itself, looks normal, but is inside out. boom
OMG, I'd never heard of FOIL, that would've been so helpful.
Yes, this video was well worth half an hour of my life. I'm starting to really get intuition into how quaternions work. I'll definitely watch it again after I've slept on it. Keep up the awesome work !
Hey Jean it's me, Eric (from TI). Small world, really!
I didn't get everything but it humbled me quite a lot to imagine that someone invented it thanks to a bridge.
Un Perrier thanks to a bridge and lots and lots of drinking.
Also, quaternions avoid gimbal lock unlike when representing rotation with 3 parameters
👍
Me: (using Unity, with quaternions being an essential part of their rotation system) I am the creator of the universe
Also me: wait wtf is a quaternion
They're not called complex numbers for nothing...
22:00
"The number -1 is sitting off at the point of infinity, which you can easily find by walking in any direction."
Ah, so simple.
That hit me too. If I'm lost, just walk to infinity, which is 1
Maybe the best way to picture this is trying to represent the Earth in a map. Take the world map at UN's logo, for example. It's centered on North Pole, where is South Pole? It is actually the whole outer circle. The only difference is that to represent this idea correctly the Southern Hemisphere should tend towards infinity. North Pole dimensions would be underscaled, Equator would scale correctly, South Pole would be increasingly higher in scale as lattitude grows. New Zealand would look millions of times bigger than Siberia.
Infinity isn't a number, though, so that bit got me confused, but I believe I understood the idea.
It's kind of like how, no what what direction you walk in, you can see the horizon. I like his north/South Pole analogy better though.
my mind: so you are saying that... this point is infinetly far away.. "krrrrrrrrrzzzzz".... and infinitly big??!! ---> my mind: explodes
I've watched this video several times since it came out and holy crap I finally understand it. Wow. Just freaking amazing. Really excellent explanation.
I swear... after I'm done with my BS degree... I'm gonna dive into maths more because this stuff is beautiful. Even if I can't understand most of it...
Your bachelor sciences degree?
@Rohan Shettygot 1 more year left at uni... yes, BS in CS to be exact... currently struggling with it because my maths background is not that strong
I see Linus is already starting to imagining things by aiming his eyes in 2D space ツ
28:45
You said “as mathematicians would say..”. What do you consider yourself as? If not a mathematician.
"one you will understand by the end of this video"
Wow, some confident statement right there buddy 😂😂
@Josh Sims this was better than the video. thank you
I actually kinda do now... and it won't be possible without the narrator's genius and the precise animations.
@Josh Sims Thanks a lot mate. Seeing it as 3 perpendicular circles forming a sphere themselves makes much sense!
"one you will understand by the end of this video"
I don't think you fully appreciate how simple I am, buddy :D
Yeah, I'm gonna have to watch this video a couple more times to actually understand it fully...
14:57 Hmm it's so amazing!The visualisation of the projection of a sphere on a flat plane. It makes me feel i am inside the sphere,and everything's rotating around me,and that visual is then projected on my flat screen in a game or something :P
Just an interesting note for you all: your vision/perspective is a (notable) example of a real-world stereographic projection.
Parallax is "infinity."
14:27 looks like a texture map.
Perfect. You can imagine the "Camera" rotating around the surface of a 4D sphere, while looking at the "Equator". Spot On.
as if complex numbers weren't complex enough
Excellent explanation and graphics.
The only thing missing is a practical application.
Can I use this to simplify my robot's kinematics?
Can it be used with other projections, eg Azimuthal Equidistant, to simplify coordinate systems or expose unseen relationships in complex data sets?
Presentation reminds me of the book Visualizing the Fourth Dimension
can I use it to find my keys when I'm drunk?
If I ruined the (441 likes, 7 replies) by making it 8 replies, why not make it (442 likes, 8 replies) as well?
@Shambo Saha you like trolling on the internet, man.
@Un Perrier Why do you think so?
Alex Lanoux - 2019-07-18
Math: i is as complex as it gets
Math: jk
JJCUBER - 2020-01-06
I saw this joke, left, then came back an hour later realizing just how genius this joke was lmao!
Isaac White - 2020-01-10
I cannot stop laughing help
Calen Crawford - 2020-02-17
OOH!!! I just got it!
Samuel Mackrill - 2020-02-26
Nope, you just imagined it was.
Someone New - 2020-03-22
Such a pun!