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UV Wizard
Registrace 10. 12. 2023
blah blah blah description this is description blah blah
Lie Theory Ramble
Lie theory is a branch of mathematics that studies Lie groups, Lie algebras, and their representations. It is named after the Norwegian mathematician Sophus Lie, who developed the theory in the late 19th century. Lie theory has deep connections with geometry, algebra, and mathematical physics, and it provides a unifying framework for understanding continuous symmetry.
Key Concepts in Lie Theory
1. Lie Groups
Lie groups are groups that are also smooth manifolds. This means that they have a group structure (with operations such as multiplication and inversion) and a differentiable structure, allowing the application of calculus. Lie groups often arise as groups of symmetries of geometric objects or solutions to differential equations.
Examples of Lie groups include:
The general linear group GL(n,R)GL(n,R), which consists of all invertible n×nn×n matrices with real entries.
The special orthogonal group SO(n)SO(n), which consists of all n×nn×n orthogonal matrices with determinant 1.
The unitary group U(n)U(n), which consists of all n×nn×n unitary matrices.
2. Lie Algebras
Lie algebras are algebraic structures that are closely related to Lie groups. They consist of a vector space equipped with a binary operation called the Lie bracket, which satisfies certain properties (bilinearity, antisymmetry, and the Jacobi identity). The Lie algebra of a Lie group can be thought of as the tangent space at the identity element, with the Lie bracket capturing the infinitesimal structure of the group.
3. Representation Theory
Representation theory studies how Lie groups and Lie algebras can be represented as matrices, making it possible to study these abstract objects using linear algebra. A representation of a Lie group or Lie algebra is a homomorphism from the group or algebra to the group of invertible matrices or the algebra of endomorphisms of a vector space.
4. Applications
Lie theory has numerous applications across various fields of mathematics and physics, including:
Differential geometry: Understanding the symmetries of geometric structures.
Mathematical physics: Studying the symmetry properties of physical systems, particularly in quantum mechanics and particle physics.
Harmonic analysis: Analyzing functions on Lie groups using tools from Fourier analysis.
Control theory: Applying Lie groups to study the controllability of dynamical systems.
Historical Development
Sophus Lie initiated the study of Lie groups in the context of differential equations and symmetries. Over time, the theory expanded and was further developed by many mathematicians, including Wilhelm Killing, Élie Cartan, and Hermann Weyl. In the 20th century, Lie theory became a central part of modern mathematics, influencing various areas of research.
Lie theory continues to be a vibrant area of study, with ongoing research exploring new connections and applications in both mathematics and theoretical physics.
Featured for the thumbnail is the 24-cell (or hyper-diamond), which exhibits F4 symmetry. F4 is one of the exceptional Lie groups, which is also related to the octonions.
Key Concepts in Lie Theory
1. Lie Groups
Lie groups are groups that are also smooth manifolds. This means that they have a group structure (with operations such as multiplication and inversion) and a differentiable structure, allowing the application of calculus. Lie groups often arise as groups of symmetries of geometric objects or solutions to differential equations.
Examples of Lie groups include:
The general linear group GL(n,R)GL(n,R), which consists of all invertible n×nn×n matrices with real entries.
The special orthogonal group SO(n)SO(n), which consists of all n×nn×n orthogonal matrices with determinant 1.
The unitary group U(n)U(n), which consists of all n×nn×n unitary matrices.
2. Lie Algebras
Lie algebras are algebraic structures that are closely related to Lie groups. They consist of a vector space equipped with a binary operation called the Lie bracket, which satisfies certain properties (bilinearity, antisymmetry, and the Jacobi identity). The Lie algebra of a Lie group can be thought of as the tangent space at the identity element, with the Lie bracket capturing the infinitesimal structure of the group.
3. Representation Theory
Representation theory studies how Lie groups and Lie algebras can be represented as matrices, making it possible to study these abstract objects using linear algebra. A representation of a Lie group or Lie algebra is a homomorphism from the group or algebra to the group of invertible matrices or the algebra of endomorphisms of a vector space.
4. Applications
Lie theory has numerous applications across various fields of mathematics and physics, including:
Differential geometry: Understanding the symmetries of geometric structures.
Mathematical physics: Studying the symmetry properties of physical systems, particularly in quantum mechanics and particle physics.
Harmonic analysis: Analyzing functions on Lie groups using tools from Fourier analysis.
Control theory: Applying Lie groups to study the controllability of dynamical systems.
Historical Development
Sophus Lie initiated the study of Lie groups in the context of differential equations and symmetries. Over time, the theory expanded and was further developed by many mathematicians, including Wilhelm Killing, Élie Cartan, and Hermann Weyl. In the 20th century, Lie theory became a central part of modern mathematics, influencing various areas of research.
Lie theory continues to be a vibrant area of study, with ongoing research exploring new connections and applications in both mathematics and theoretical physics.
Featured for the thumbnail is the 24-cell (or hyper-diamond), which exhibits F4 symmetry. F4 is one of the exceptional Lie groups, which is also related to the octonions.
zhlédnutí: 10
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German has long words. Beginner Duolingo
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zhlédnutí 35Před měsícem
Looking to pay $100/month for help with Roblox games. (programmer, PM, maybe builder)
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This looks awesome 🔥
GG ;D
good gameplay
uviolet lore
Honestly, making your own game engine would be a good way to learn; but in the modern era I think it’s undeniably unnecessary. Many of the industries top game engines are available for free, it just doesn’t make since to make one at this point.
Agreed. But making games from scratch, say in python, javascript, c, c++, c#, etc, is also a good exercise. It's an ok way to learn languages.
thanks..... appreciate your hard work
It's my pleasure
first
Ur 2nd
bet you cant be first on all of them
@@UViolet87 sometimes
1st
how do i change the keybind for it, my alt key is broken
idk
Looks like u missed ur French lessons today, u know what happens now
What happens Principal Skinner?
@@UViolet87 nothin really
how many total languages can u speak?
English, French, Japanese. I can usually understand Spanish, but can't speak it. I can usually read Italian. I can speak pretty basic Chinese for getting around, ordering at restaurants, etc. Priority now is German and possibly Korean.
Julemanden :)
Im close to section 3
Section 3! Wow, I just got to unit 3 now and will upload soon.
@@UViolet87 ok
This was so useful! ive been trying to learn german for a while because im in love with their literature :D im going to give pimsleur a try
Glad to hear it! Glad you found it useful! I'm learning it partly for reading math and physics texts, but literature sounds great too!
Good
Thanks!
@@UViolet87 you're welcome
Ur a noob
Indeed!
fire, what will u use this in?
idk
I don't expect editing but writing notes for yourself before recording would be cool
Thanks for the feedback
@@UViolet87 of course
I actually found this very interesting, thank you UViolet!
Good work❤
Thanks 🔥
Tu m’as donné envie d’apprendre l’allemand là (j’hésitais depuis longtemps mais mtn j’ai installé duolingo)
Bon courage! Dites-moi si tu continues à apprendre!
@@UViolet87 merci ! Oui là c’est mon 2nd jour mais je verrai si je continue car il faut que je passe plus de temps sur l’anglais …
i wouldnt suggest getting your rigs you base stuff off from the toolbox, instead use a rig that you made, it takes longer but is safer and you can customise it more
ok thx
Good luck man! Did you use duolingo to help you learn french and japanese as well or no? And if yes how much would you say it contributed?
I did not. I think Duolingo is very over-rated. It won't hurt though.
Could you please specify the number of hours per week or month you expect for $100? I would appreciate more details about the project. What exactly do you want the programmer to build? Do you have a specific game in mind? If so, what type of game are you envisioning? Also, you mentioned that the programmer could benefit by improving their skills. Could you clarify if you mean self-improvement or if there will be feedback provided on their code?
There will be feedback provided on code. Not all code, but definitely some of it. I'm leaving it up to others to specify the number of hours. The game type is not determined yet. If the individual is choosy/picky about what kind of game they want to work on, then that is still possibly fine, but they should specify it in their pitch document/message. If you have any more questions let me know. Commenting here is fine so others who may have the same question can see.
Thanks for the help yal. I think the cause of the problem is that the same modulescript is appearing in multiple places, resulting in behavior that is difficult to predict.
Make sure the serverscripts that you move over to the character model are disabled in server storage and only set Enabled to true after you move them. Im afraid your server scripts are running in server storage before they are moved.
It does seem to recommend your videos whenever you put a thumbnail with like a roblox character facing towards the screen, also nice ramble. And you clickbaited me!, this aint no devlog num 10!!!!!!!!. I subscribed for your roblox game devlog stuff and u do sometimes ramble abt roblox codin stuff which I like to listen to and when I see a math video it generally turns me off cuz of my adhd brain. Anyways hopefully you get 2k subs and do whatever you wanna do seriously ♥
Thanks for that! Yeah, I agree. The algo does seem to like that.
aa
aaaaa
maybe model is null since the player model structure could be different then the zombie.
model cant be null but the structure in the model is prolly difrfernet
Good video? Except! one problem. get back to me as soon as possible. big problem, huge! get back to me. Excellent video? But! one issue. fix it immediately. major issue, massive! fix it. Awesome video? However! one flaw. address it now. significant flaw, crucial! address it. Fantastic video? Except! one concern. resolve it quickly. serious concern, critical! resolve it. Wonderful video? But! one drawback. handle it soon. major drawback, huge! handle it. Superb video? However! one bug. correct it at once. significant bug, critical! correct it. Remarkable video? Except! one glitch. repair it promptly. major glitch, crucial! repair it. Amazing video? But! one error. rectify it immediately. big error, huge! rectify it. Incredible video? However! one problem. get back to me as soon as possible. major problem, massive! get back to me. Stellar video? Except! one issue. fix it quickly. serious issue, critical! fix it. Excellent video? But! one complaint. address it now. major complaint, significant! address it. Impressive video? However! one fault. handle it promptly. significant fault, crucial! handle it. Great video? Except! one oversight. correct it soon. major oversight, huge! correct it. Wonderful video? But! one mistake. repair it at once. big mistake, critical! repair it. Superb video? However! one error. resolve it immediately. significant error, massive! resolve it. Remarkable video? Except! one flaw. rectify it quickly. major flaw, crucial! rectify it. Excellent video? But! one inconvenience. fix it now. significant inconvenience, huge! fix it. Fantastic video? However! one issue. handle it promptly. serious issue, critical! handle it. Amazing video? Except! one bug. address it immediately. major bug, massive! address it. Great video? But! one glitch. correct it quickly. significant glitch, crucial! correct it. Stellar video? However! one problem. get back to me as soon as possible. major problem, huge! get back to me.
Why is there no one talking about quaternions for roblox
They are complicated to understand. Even the documentation only mentions them in a couple places and doesn't even try to explain them.
@@UViolet87 That's fair but you would expect some advanced scripter guy to have a 5 hour video on CZcams explaining them, except I have to go and read a book. 😂
@@WillPhilCollins You might expect that, true. The thing is, quaternions are a special topic. Someone smart can read about them and think about them for 200 hours and still not properly understand them. Even great physicists back in the days of Hamilton struggled to understand quaternions (I think the great James Clerk Maxwell, who was the first to put together the full laws of classical electromagnetism struggled with them). Hamilton was the inventor and primary proponent of them while he was alive and I have to say I really hate his writing style because he is very grandiose and puts in all kinds of unnecessary extra garbage into his prose (philosophical stuff included) that doesn't need to be there. In fact, I'm sure Hamilton himself didn't even fully understand them in terms of how they fit into a larger context (the larger context wasn't developed at the time). Quaternions fit into larger contexts of spinors, Clifford algebras, octonions, and the so-called normed division algebras. If you play with them, you realize that they fit into some kind of hyperbolic geometry. I know that this hyperbolic part of things is well known about them because I have seen it in writing in a couple places about Clifford algebras, but the authors just sort of casually mentioned it and didn't go into detail. I'm sure it's out there somewhere in the literature. The quaternion algebra is also isomorphic to Mobius transformations, which is another deep and profoundly interesting topic. There are also the so-called dual quaternions (unfortunate name imo). So there are quite a lot of things to say about quaternions. But you can avoid all that complicated context and gain a decent understanding of them on their own, but the geometry in reality is in fact complicated to understand. It is essentially the same geometry as that of spinors in elementary quantum mechanics, except that quantum mechanics has "phase invariance" that plays a role and is a bit complicated to understand in its greater full context (that would be gauge theory or gauge invariance). Anyway, anyone who can get a really good understanding of quaternions has themselves a start for studying particle physics and special relativity, though they are not necessarily mentioned in those studies. Particle physics has a much more complicated SU(3) symmetry (which is a super set of the quaternion algebra as it is isomorphic to SU(2) symmetry) and one really should study Lie theory, though. Sorry if I'm going overboard here with too much info, but this is the kind of rabbit hole that quaternions suck people like me into.
@@UViolet87 Yeah I guess they are really interesting. Was probably never going to use them I was just curious.
UV WIZARD i have a question! about your video! please get back to me soon is very question!
What is the question?
@@UViolet87 i fogor
That's painful to watch
i miss tyou
no views in 36 minutes you really fell off
bro where ia the skibidi toilet
stumbled upon this video in my recommendations for some reason, and im glad i did! the way you explain stuff is interesting and easy to process, good stuff my guy!
i asked whats your discord over a month and half ago
True. You can find it by looking at my recent games in roblox. It's in the social media links for my games such as the Rocket Fight games. I don't think yt will let me post links yet bc my channel is too new still.
btw actually it was 12 days ago!
Mate what's your discord link?
Very nice
So nice
new sub :D
UViolet, there is no correlation between any changes you make to the game and the like/dislike ratio, its because your advertising it and players play it, and they think its a bad game, because it is. Honestly, you very rarely make a game that I personally enjoy playing. Most of your games have no objectives or reason to play. I'm not trying to be mean, but I'm trying to be honest, so hopefully you'll improve. I don't think you should be spending any money to advertise the games you are currently creating.
I know it's a bad game, but how do you explain the ratio going from 80% likes to less than 50? There should be an explanation for it.
@@UViolet87 You spent more money on ads, therefore more people saw the ads, therefore more people were exposed to the bad game and disliked it
That does not explain a change in percentage. @@LuckmanWasHere
oo wow i am a roblox dev as well can i help you build your new game? i can kinda build not that great but i can help
there's a discord somewhere. maybe find that and then we can go from there
your game is so bad just delete it lol
lol
more mire more
13:20 earthquake T.T
"Ok, I'm back" hahahaha
"polynomials are not the same as apples, bananas, and carrots" 💀
can u tutotr alculuis e,
Depends how serious you are about it
should stream
Thanks
nice, I suck at maths very much and thanks for letting me know the amount of things you can do with maths