This was an amazing introduction to Lie theory. It would be wonderful if you could attach the links you have mentioned at the end in the video description.
What would you like to have exemplified numerically? There are quite a few things in this course. If you tell me a concrete topic I can make a numerical example
@@joansola02 may be just a very simple 2d ekf slam with 1 landmark, nothing fancy, sometime just able to see numbers being manipulated is less intimidating i think. Now that i have read the actual paper i'm more familiar of how it works, but i think it will still be useful for others
Thanks for this comment. Let me try to explain why you did not find any reference to Geometric Algebra. I tried to use as few mathematical concepts as possible to make LT understandable and useful for roboticists. Myself, I am not a mathematician and I do not use the theoretical corpus of Geometric Algebra, I just use its tools. I can do so comfortably because I find these tools intuitive, and so I do not need to go into the theory or formalization of them. For example, the notion of the Manifold as a smooth hyper-surface that I use here is enough, because it gives enough intuition. Therefore, I did not use the concepts proper ro Riemanian manifolds either. With Lie theory is different: from all I could read, I could find no intuitions to help me understand. The result of trying to make LT intuitive is this video.
lol, I've seen tons of videos on Lie Theory but this is the first time it has clicked. Why are mathematicians so terrible at conveyance that it has to be done effectively by engineers and compsci guys?
Thanks! I also think mathematicians have a problem for communicating their ideas clearly! Maybe it's a matter of the Bourbakists, which discarded all intuition in favor of cold and obscure axioms. The Bourbakists follow Bourbaki, a mathematician that never existed: ca.wikipedia.org/wiki/Nicolas_Bourbaki
@@joansola02 Bourbaki is not responsible for the current formulation of Lie theory, and mathematicians aren't collectively bad at teaching their craft. Engineers using math to solve problems, they tend to use just enough to get shit done, and they focus on the process of concrete calculations. Have you ever watched a physicists take an integral? (; They use of tons of delicate math to develop model of physical systems with total reckless abandon, and aren't overly concerned with justifying why they work and what their fundamental properties are. They sweep so much detail under the rug, I can't digest physics books about math theory I understand well, because it's just cryptic one liners and handwaving. Mathematicians are burdened with legitimising what they do with proofs, and things become technical messy and myopic by necessity, it's their job. I use engineering books as well to get me up to speed with a subject or programming some simulation, but in the end I'm turning back to a mathematical treatment of the subject to equip me with some theory to gain real leverage on a problem.
@@7177YT Absolutely no aim of arguing here, I agree with what you say. And I totally respect mathematicians. My comment is more a humorous act fruit of some frustration, sure. I do think, however, that sometimes we confuse proving with explaining. In the particular context of Lie theory, I found too much proofs and too little explanations. Or to say it otherwise, the explanations tend to be axiomatic, built from a whole lot of previous bricks, and they look like proofs to me, but I do not understand them. Removing 90% of the jargon and still being able to explain the concepts would be very much appreciated. And while this can be said of all disciplines of knowledge, I feel it is particularly true for math. But again, it´s just an uninformed opinion. Just my experience.
@@joansola02 Got you! I agree! Lie theory in the form it is tought today feels a bitdisconnected from problems it was created to solve and asks you to just accept a lot of technical machinery up front without showing the merrit of it all.
Not just for roboticist. I find this video is very intuitive for a theoretical physicist like me
Where has this talk been the past 5 years of my life lol thank you so much
This is the exact level of explanation I've been looking for. Thank you very much.
Fantastic content. Finally a succinct explanation in layman terms about Mr. Lie. Thank you for posting!
Very informative, probably the best video on Lie group I ever watched, thanks a lot
Nice and neat! Especially with beamer so that it's easier for audiences to understand your idea. Thank you for sharing.
This was an amazing introduction to Lie theory. It would be wonderful if you could attach the links you have mentioned at the end in the video description.
Absolutely amazing video!
Thank you for sharing this.
Great video. Thank you for posting it.
This was excellent! Thank you!
Aoplied Lie. That's a novelty. Thanks!
thank you so much, lie theory is so large, it's really hard to extract just enough information for robotic application
i'd like a video called 'lie theory for an old astrophysics grad who forgot everything from 30yrs ago'...
Excellent!
Great Video!!!!!!!! Very informative
i really need numerical example to know what to do with the operators
What would you like to have exemplified numerically? There are quite a few things in this course. If you tell me a concrete topic I can make a numerical example
@@joansola02 may be just a very simple 2d ekf slam with 1 landmark, nothing fancy, sometime just able to see numbers being manipulated is less intimidating i think. Now that i have read the actual paper i'm more familiar of how it works, but i think it will still be useful for others
How can I get related slides?
Thank you.
amazing... thx
Hi Joan, Do you know about Geometric Algebra?
Not really!
Great😀
I see no mentions of geometric algebra in a presentation that discusses the concepts it thoroughly generalizes. 😉
Thanks for this comment. Let me try to explain why you did not find any reference to Geometric Algebra.
I tried to use as few mathematical concepts as possible to make LT understandable and useful for roboticists. Myself, I am not a mathematician and I do not use the theoretical corpus of Geometric Algebra, I just use its tools. I can do so comfortably because I find these tools intuitive, and so I do not need to go into the theory or formalization of them. For example, the notion of the Manifold as a smooth hyper-surface that I use here is enough, because it gives enough intuition. Therefore, I did not use the concepts proper ro Riemanian manifolds either. With Lie theory is different: from all I could read, I could find no intuitions to help me understand. The result of trying to make LT intuitive is this video.
lol, I've seen tons of videos on Lie Theory but this is the first time it has clicked. Why are mathematicians so terrible at conveyance that it has to be done effectively by engineers and compsci guys?
Thanks! I also think mathematicians have a problem for communicating their ideas clearly! Maybe it's a matter of the Bourbakists, which discarded all intuition in favor of cold and obscure axioms. The Bourbakists follow Bourbaki, a mathematician that never existed: ca.wikipedia.org/wiki/Nicolas_Bourbaki
@@joansola02 Bourbaki is not responsible for the current formulation of Lie theory, and mathematicians aren't collectively bad at teaching their craft. Engineers using math to solve problems, they tend to use just enough to get shit done, and they focus on the process of concrete calculations. Have you ever watched a physicists take an integral? (; They use of tons of delicate math to develop model of physical systems with total reckless abandon, and aren't overly concerned with justifying why they work and what their fundamental properties are. They sweep so much detail under the rug, I can't digest physics books about math theory I understand well, because it's just cryptic one liners and handwaving. Mathematicians are burdened with legitimising what they do with proofs, and things become technical messy and myopic by necessity, it's their job.
I use engineering books as well to get me up to speed with a subject or programming some simulation, but in the end I'm turning back to a mathematical treatment of the subject to equip me with some theory to gain real leverage on a problem.
@@7177YT Absolutely no aim of arguing here, I agree with what you say. And I totally respect mathematicians. My comment is more a humorous act fruit of some frustration, sure.
I do think, however, that sometimes we confuse proving with explaining. In the particular context of Lie theory, I found too much proofs and too little explanations. Or to say it otherwise, the explanations tend to be axiomatic, built from a whole lot of previous bricks, and they look like proofs to me, but I do not understand them. Removing 90% of the jargon and still being able to explain the concepts would be very much appreciated. And while this can be said of all disciplines of knowledge, I feel it is particularly true for math. But again, it´s just an uninformed opinion. Just my experience.
@@joansola02 Got you! I agree! Lie theory in the form it is tought today feels a bitdisconnected from problems it was created to solve and asks you to just accept a lot of technical machinery up front without showing the merrit of it all.