Introduction to the complex octonions (Video 8/14)
ฝัง
- เผยแพร่เมื่อ 16 ธ.ค. 2024
- Video 8 of 14
Series: Division algebras and the standard model
Some short videos filmed by Vincent Lavigne
Seminar by C. Furey,
Walter Grant Scott Research Fellow in Physics
Trinity Hall, University of Cambridge
damtp.cam.ac.uk...
arxiv.org/pdf/...
arxiv.org/abs/...
arxiv.org/abs/...
www.furey.space
"So what are we going to do?" Most ultimate cliffhanger ever! I've never been on the edge of my seat for math so hard in my life! Good lord!
What ARE we gonna do? I must know!!
@@Jhopsssss OMG No one knows!!! We're doomed!!!
Well I don't know about y'all, but we're gonna make a cake
I never made it without biting. Let's find out. 1, 2, -3...
Paused JRE #1320 with Eric Weinstein to figure out wth octonions are.
Very good explaination in this video, clear and easy to understand.
Yep. Me too 👍🏻
same
Same!
same
yes. It's imaginary BS
Very well done. I even feel like I understood it. Great professor.
Bruh Sia smart af tho
Bruhh😂😭
5head Sia Pog
@@maxvc2330 God Damn u a savage my dude
HALEY WILLIAMS BUT WITH MATH
I just have to say, I was inspired by an article about your application of this to quantum physics, and now a couple years later I'm beginning to explore it to program simulations for real-world applications. Thank you Dr. Furey for your work.
Its incredible how little info there is on the subject on the general web. Thanks for sharing!
Triangles, circles, abstract writing, secret codes.
Also: white hair, blue eyes, thin tall posture and a mind wanting to push the limits of the curent status quo.
You are made of the same material as the Salem Witches!!!!
You are sοοοo lucky to have been born in our modern era.
Embrace witchcraft all you want, but to be clear, there were no witches at Salem. The elborated theory of witchcraft was a unhindged conspiracy, and it led to the slaughter of innocents. This mundanely horrific reality was known even then, hence why our legal system now has the principle of presuming innocence.
Easily some of the best intro lectures on the topics. Clear direct speaker with understanding.
Who in the world would down vote this video‽ It's a math lecture for Ganesha's sake! Did you get here by accident? Did it make you feel stupid? Well that's on you. Just don't watch things intended for smart people. There's plenty of content for the cognitively challenged. Cat videos not your thing? I hear they're rebooting the Honey Boo Boo series on TLC on the TV Lookey Box. Maybe you should try to find that on line.
Personally I really enjoyed it. Why wasn't there math instructors like her when I was in college. Concise content, clearly stated, and easy on the eyeballs. I'm sorry if I'm objectifying you, but I'm very partial to smart women, and I absolutely love that hair style of yours. Don't worry, I'm a 60 y/o, toothless old lion who loves math lectures related to E8 Lie Algebra. That's how I ended up here.
I swear, TH-cam has EVERYTHING!
xxxooo
dc
I hear you. I must admit that she made it look like too easy - I felt like she is cheating somewhere - lol.
or having a bad day... but wait the rick and morty meme....
@@winninymeanssweet1920 She's just well practiced. Has probably taught and learned this many times to be able to have an understanding of a really complex topic.
Dear Sia lover, where can I find part two? Or do you have any other research suggestions. I’m intrigued by the subject
So meant for the smart, then other smarties can help explain to Lehman's just how this is important to everyday life ? Or important to math going one step closer to figuring out the universe. If one truly gets it it can this be explained simplified to all the Lehman out there.. and Non associativity means a, counterintuitive way to use 3D !-? In (actual) order from 8D !? But the (pyramid?) she depicts here is flattened to a triangle.
These videos are amazingly well instructed. Diving into this "portal" head first.
I fell in love and learned a bit of octonions
"So what are we going to do?"
Cry softly under my desk
Jk, this is actually one of the most digestible lectures on HARD physics I've ever seen - I love how you chunk stuff up so nicely!
Thanks. Such an interesting topic with very few lectures are online.
Get Cohl Furey on the Rogan podcast. Coolest name in the numbers game.
I wish I could understand this. I should probably pass a calculus class first, though. Heh.
With a little work, you can understand it. Calculus is not so important for these videos, but linear algebra is.
Thanks for the encouragement! :D
I must be partially autistic because I found this comment vaguely discouraging. Perhaps it was the inclusion of the 'z' ... hmmmmm
That's good to hear! I think I even HAVE a linear algebra textbook..
Great! Please begin a study of these (previously obscure) complex octonians and report your findings back to the rest of us, OK? (:
This is highly fascinating, my first impression is that its sort of like 3d or more multiplication. If you are on a 1d or 2 d ( like a piece of paper) and you multiply numbers of the same set, and irregardless what sequence you multiply, you get the same answer. 2(3*4) = 24 so is 2*(3)4 , but in a multidimension you get different answers?
@absoftitanium quantum mechanics--at the CENTER of this, uncertainty, lies the unified field theory. To subsume relativity and quantum mechanics within a formulation simpler and more comprehensive than either..
Space/time matter/energy
G,UV = 8T,UV all four created at the big bang. UFT quest this is the way.. As so gathered--- matter tells space time how to curve space time tells matter how to move.
It's perhaps more like rotations where if you have rotations one more than one axis, then changing the order of the rotations can have different results.
⓪
Generation Zero
diag(+1,+1,+1,+1)
❶
The first generation
diag(+1,-1,-1,-1)
❷
The second generation
diag(-1,+1,+1,+1)
❸
The third generation
diag(-1,-1,-1,-1)
❶⇔⓪⇔❸⇔❶
❶⇔⓪⇔❷⇔❶
❷⇔⓪⇔❸⇔❷
❶⇔❷⇔❸⇔❶
⓪⇔⓪
❶⇔❶
❷⇔❷
❸⇔❸
There are a total of 8 types of transitions.
There are 3 types of colored self-transitions.
The vector of the time arrow can be
macro or nonmacro.
⓪⇔⓪
Self-transitions are colorless.
I had to watch the video four times to follow the math. I am really fascinating by the professor Furey.
At 3:39 "there is already a minus here..." but that was a different grouping I do not understand how that could change the sign when comparing to another grouping/order.
It was hard to see what she was pointing to, but it was the e3(-e1) part.
Thank you so much. Stunningly efficient videos. Very helpful for in my quest to answer 'where are electrons?'.
Would be great to see this explained with a 3D animation
From eric weinstein
same
Yep
Yup
yee yuup
Diddo.
The quaternions describe movement, rotation etc. in 3D space. What dimensional space do the octonions describe movement etc. in ?
A quaternion by itself does not describe that. Quaternions are useful for conducting those operations.
So, the order of the factors does alter the product in this case. That's about all I understood.
This video, which I stumbled on first searching for info on these octonions I’d read about, made complete sense to me and made me think I could understand the rest of these lectures. As it’s turned out, not so much. I obviously have a LOT of reading to do...
What happens to primes as you move into more complex number systems?
Beauty with brains....
Could octonions be used to improve time crystals? Or helping to create, I don't know if it's too crazy, 5D crystals?
I think 5D crystals it's too crazy
1:00 thats the deathly hallows
I thought it looked familiar.
I really wish there was more info on TH-cam about octonions.
Thank you for your lecture, teacher.
Is this concept of octonions used in physics?
That cliffhanger is killing me
She can get it
SHE CAN DOE !!!!!
You know that scene in 2009's Star Trek where Vulcan children are learning math/physics/etc? Are we actually getting closer to that for real? Cause here we are, getting a brief meaningful primers on 8 dimensional mathematics and their object properties like it's no big deal.
Serious question; do you see any links between physicist Sabrina Paterski's work and your own between the fields of physics and mathematics?
Ok, but why go via Octonions? Why not just start with the Clifford algebras, they are, after all, far more natural (IMHO) than the Octonions. Is it because you will feature Octonions non-associativity later on for some of the gauge groups of the Standard Model?
Thank you for asking this; I couldn’t disagree more! Suppose we were to go the route of Clifford algebras. We would then be stuck with the problem of having to choose our physical Clifford algebra from the infinite number of Clifford algebras possible. How could we make that choice? At least with the normed division algebras over R, we know that there exist only 4 of these algebras - and the idea would be to make full use of all four of them. One would then need to justify why these division algebras are special.
Later on in the videos, you will see that the left action of the complex octonions on themselves generate the Clifford algebra CL(6). So in the end the octonions do lead to a natural choice of Clifford algebra.
Finally, I would mention that people sometimes feel as if the octonions are somehow foreign or unnatural. The reason they often state is the octonions’ non-associativity. However, non-associativity is not such a compelling reason to exclude them from physical models - especially when one realises that Lie algebras and Jordan algebras are both non-associative, and they are pervasive in physics.
The octonions do indeed seem natural, in the sense that they can provide some well-known group representation structure found in particle physics. This is shown quite concretely in the remaining videos of this series.
Cohl Furey : That answers a question I had, thanks. Just stumbled into this one, which was a really nice start on these octonion thingies I’ve been hearing about lately. (A friend of mine actually asked me if I’d heard of this new theoretical physics thing!) I think I’d better go back and start from chapter one, though... Thank you so much for taking the time to do these!
Why is e4 times e2 e1
Am I the only one who thinks that looks like the symbol of the deathly hallows?
I also wish I could understand this. Fascinating.
Why do we need complex octonions to lead to a Clifford algebra again?
SO WHAT ARE WE GONNA DO?????
Two things:
1) I can tell this is answering a question that has been burning in me for a long time, but it's going to take a lot of math background for me to catch up. I get operators in the QM sense, I get quaternions and octonions and complex, I know a bunch of geometric algebra, I just don't quite get "algebras" and "ideals" and other pure math stuff. Anyway thanks a million for sharing this on TH-cam, it's extremely interesting.
2) Hottest woman alive. Are you single?
I suggest getting into some number theory stuff if you have some background with calculus. I'd say it's about as interesting as geometry because you can find some crazy patterns, although most of it probably being conjectures rather than proofs. I suggest looking at some of Ramanujan's work, Riemann's hypothesis, and blackpenredpen.
@@PimpMatt0 thanks!
Now I understand everything!
so what are we gonna do! amazinggggggggg. First thing would be to define a category that is non Clifford algebra and then define a relation between them
Interesting. I wonder . . . every basis you add to signature, you get the possibility of Mobius structures in subspaces to it. Analogous to blades in a geometric product. Then again, on the physical side, you have things like black holes, which are two-dimensional structures in a space of signature +3+0. For higher dimensions, then, you get a tree of Mobius structures, cascading down the dimensions. So . . . drop the time signature, leaving things non-timely, and you get photons? Or drop a directional dimension, you get what?
Which makes you wonder... if Maxwell solved his equations with quarternions, and Steinmetz did something similar using imaginary numbers and algebra to analyze transient electrical impulses, could adapting a specfic geometric shape in 3d down from a higher dimensional state using octonion based mathematics to get the geometry and the timing of the pulse right, and then using radiant impulses, could humans develop the next generation of hyper efficient electric motors or other advanced propulsion devices based on exotically wound coils in not so quite intuitive geometries? Especially when the coils are dropped into an electrolytic solution and the kinetic energy of the fluid is used to spin up a dynamo. Or as electric analogs of our current combustion based on multistage axial or radial turbine engines. Like a Schauberger-esque style hybrid plasma powered, magnetodielectric, inertia cancelling motor by stirring up the flow of energy in a certain geometry so that it manifests the additional energy that we can capture or use from these higher dimensions that we normally cannot access down into our normal 3 spatial dimensional + time reality that we humans are all familiar with. Basically unlocking a percieved overunity effect by tapping into something that is always there but we are just not normally aware of.
And then that leads to the next question... if someone was capable of doing such a thing should they even bother since the defense industry is most likely going to be sticking your patent application into the list of 5500+ secret patents under the 1951 invention secrecy act and you will not be compensated for it and probably not even legally allowed to even work with models you built of your own intellectual property without a very high level security clearance. And if it's a real serious leapfrog of a technological breakthru, do they even put it on that list or is it whisked away to an even more secure and less known vault of secrets? Thanks Uncle Sam for raining on my parade and killing my desire to build a vtol electric propulsion based spaceship... although it still might be worth it if I were to just to keep it on the dl and use it to avoid traffic on the freeway! Plus you could use it to make some good money 'cause good luck trying to pull over someone running a drug smuggling operation out the back of their UFO! 🤣 🛸💰💸💉💊🚬
Anyway I am getting off topic now but how funny would it be if it turned out that those Navy Electro optical sensor videos of the Tic Tac UFO were really just the next gen tactic of Columbian Cocaine smuggling in mini submarines being adapted by Chinese intelligence officers sneaking bags and bags of fentanyl and the best Chinese massage therapists over to bribe their ring of opioid dependent and/or sex addict industrial spies with! Lol! 🤣
The things that float thru my mind... 😂 that's what I get for watching Chain Reaction on Amazon Prime the other day!
Does this imply "spin" ?
Where is video 7 of 14????
The Octonions song ! blend.io/louisfredericlessard/octonions
I may be really high, but is that the all seeing eye she just drew?
Yes, you are
Good Will hunting type stuff
Am I the only one who didn't come here from watching Weinstein on JRE? I was just curious as to what octonions were, because I heard them mentioned somewhere, sometime and I've always liked the word. I think I'll go watch Weinstein now..
Me. I heard about them when looking up mathematicians when I was trying to find out the difference between Newton's method and Euler's method. I was like wow they're applicable to robotics and wanted to know more. Sadly no one really understands this.
This is freaking me out. Non-associative algebra???? I am speechless.
I'm wondering why they invent new numbers while Matrix is there?
Matrices are overrated
The diagram lowkey kinda looks like shes trying to summon something
@sean ogara well that explains why i cried when i see the actual math part
I don't understand what having complex coefficients has to do with this, octonians are non-associative with real coefficients.
A vampire who does math?
need more likes
thank you time dialation as a function graphed ever just wanted yo say it
Yeh imma stick to just complex numbers
You don't have whiteboards at Cambridge?! I wish she spoke just a little slower for us folk born in the country.... and maybe go to the local office supplies shop and get a whiteboard.
Eric Weinstein’s call to adventure brought me here
the sound of the board is owful 😖
wtf are we going to do though?!
yes that's exactly what I was thinking too hmmmm
Ended in a cliffhanger.
Why am I here I'm in 10th grade but I heard about these from Vi Hart and I have No IdEa WhAtS gOiNg On
Can someone please tell me what are the prerequisites for these lectures. I am just an AI researcher that even loves this type of content. I think even if my 100 billion neurons fire at the time same time, then I may not be able to make sense of it for a long time.
Estoy enamorado 🥰
Lol I really thought I would understand any of this at 1am, smoking weed.. and hating/failing math since infancy.
Same
But that's crazy right
Ummm...what?
,....I wish I were smart.
ERIC WEINSTEIN!
Ok thanks for explaining imaginary letters as numbers and not really explaining anything. How can j times k equal i, and k times j equal -i? I can make up stuff too...lol
Think of i for example as a 90 degrees rotator on a plane where the horizontal axis is the real numbers. rotating 1 twice gets u at -1 so i*i = i^2 = -1
If u are not comfortable with all these i j k u can use matrices or clifford algebras to think about them
You're so pretty
Why am I here
I to listened to JRE with Eric Weinstein and ended up here
Nah this hard ima be a garbage collector then
Bend it.
what am i doing here i don‘t even study this shit
Cliff hanger not cool at all. We tryna stop skynet over here.
Here because of Eric Weinstein
So I just want to say thank you for researching this!! I was born on 8.8.88 and I followed an intuitive trail to you today. I love all things 8 or infinity. 🤍✌️♾✨