I feel fortunate to live in a time were there are people who teach hard-to-understand concepts for free in a easy to grasp fashion. Hats off to you and thank you a lot
@hyperduality2838 Жыл бұрын
From a convergent, convex (lens) or syntropic perspective everything looks divergent, concave or entropic -- the 2nd law of thermodynamics. According to the 2nd law of thermodynamics all observers have a syntropic perspective. My syntropy is your entropy and your syntropy is my entropy -- duality! Syntropy (prediction) is dual to increasing entropy -- the 4th law of thermodynamics. Homology (convergence, syntropy) is dual to co-homology (divergence, entropy). Teleological physics (syntropy) is dual to non teleological physics (entropy). Duality creates reality. "Always two there are" -- Yoda. Points are dual to lines -- the principle of duality in geometry.
@parahumour46197 ай бұрын
Amazing video, your channel deserves more views. I would suggest having a section where you ask the viewers questions so they stop and think and end up being onboard with the understanding
@virmaq51872 жыл бұрын
As a visual learner, this video helped me tremendously. Thank you!
@jiaqi91133 жыл бұрын
Extremely good introduction!!!! It is very hard to imagine how much work put behind the video!! Thanks for your input on this!! I already worked on convex optimization problem in a research project for a few months but honestly I really don't know what is special about convex optimization. Thanks for giving us the intuition behind it!!
@hyperduality2838 Жыл бұрын
From a convergent, convex (lens) or syntropic perspective everything looks divergent, concave or entropic -- the 2nd law of thermodynamics. According to the 2nd law of thermodynamics all observers have a syntropic perspective. My syntropy is your entropy and your syntropy is my entropy -- duality! Syntropy (prediction) is dual to increasing entropy -- the 4th law of thermodynamics. Homology (convergence, syntropy) is dual to co-homology (divergence, entropy). Teleological physics (syntropy) is dual to non teleological physics (entropy). Duality creates reality. "Always two there are" -- Yoda. Points are dual to lines -- the principle of duality in geometry.
@raulsena39172 жыл бұрын
Thanks for the video, I was reading many books to understand this and you explain it plain and simple. Keep it up!
@wexwexexort11 ай бұрын
I always like to watch the visual explanations even though I know the topic quite well and to be honest, you do a really good job on both explanations and visuals.
@vats62 жыл бұрын
Woah! Thanks a lot sir, for such an intutive explaination of convexity. The best explaination I have seen on the internet so far!
@hyperduality2838 Жыл бұрын
From a convergent, convex (lens) or syntropic perspective everything looks divergent, concave or entropic -- the 2nd law of thermodynamics. According to the 2nd law of thermodynamics all observers have a syntropic perspective. My syntropy is your entropy and your syntropy is my entropy -- duality! Syntropy (prediction) is dual to increasing entropy -- the 4th law of thermodynamics. Homology (convergence, syntropy) is dual to co-homology (divergence, entropy). Teleological physics (syntropy) is dual to non teleological physics (entropy). Duality creates reality. "Always two there are" -- Yoda. Points are dual to lines -- the principle of duality in geometry.
@cmatiolli13 Жыл бұрын
Your videos are awesome. The right balance of math concepts and intuition to explain complex ideas is the perfect fit for this essential concept.
@hyperduality2838 Жыл бұрын
From a convergent, convex (lens) or syntropic perspective everything looks divergent, concave or entropic -- the 2nd law of thermodynamics. According to the 2nd law of thermodynamics all observers have a syntropic perspective. My syntropy is your entropy and your syntropy is my entropy -- duality! Syntropy (prediction) is dual to increasing entropy -- the 4th law of thermodynamics. Homology (convergence, syntropy) is dual to co-homology (divergence, entropy). Teleological physics (syntropy) is dual to non teleological physics (entropy). Duality creates reality. "Always two there are" -- Yoda. Points are dual to lines -- the principle of duality in geometry.
@imotvoksim2 жыл бұрын
The least squares example you show at 7:59 has a wrong sign as far as I can tell!.Otherwise a great video providing the intuition I was looking for, took down some notes, hopefully they finally stick and I understand this dual magic once and for all, thanks!
@VisuallyExplained2 жыл бұрын
You are correct about the wrong minus sign, thanks for watching the video carefully, and thank you for the very nice comment. I am glad the video was helpful to you. :-)
@Sirentuber Жыл бұрын
Good God. This is so beautiful and intuitively explained. Can thank you enough for this! you are the savior.
@rubenosmond820010 ай бұрын
Thank you sir. I'm having a hard time understanding this concept for my machine learning class and you helped me in a beautiful fashion. May you have great things in line.
@colin_hart2 жыл бұрын
The code samples for linear programming and least squares are swapped at 0:23. I’ve been enjoying your work. Thanks for sharing!
@VisuallyExplained2 жыл бұрын
Thanks for watching carefully, and I am glad you liked my videos. :-)
@gustavgille93232 ай бұрын
The least squares error example is beautiful!!!
@MaxWasserman13 жыл бұрын
Huge fan. Keep it up.
@SonLeTyP94963 жыл бұрын
Awesome :) cant wait to see next episode :D
@think98243 жыл бұрын
true
@jiaqint961 Жыл бұрын
I learnt so much from this video, I love you so much
@parhamzolfaghari739410 ай бұрын
Wonderful! I always wonder why the professors and teacher follow the worst method possible to teach materials.
@nashwahammoud40765 ай бұрын
That's wonderful 🎉 thanks for you
@thebifrostbridge39002 жыл бұрын
Great video. Fun fact, the autogenerated subtitles at 9:32 says: "to optimization problems with cancer friends"
@phogbinh2 жыл бұрын
God like overview of the topic. Thank you.
@user-nm3mn1ir2z Жыл бұрын
great video! What program did you use to make this fantastic visualization?
@ZhanCaitao2 жыл бұрын
Great video!
@ian.ambrose Жыл бұрын
Yes! New Blender tutorial!
@jameskirkham50193 ай бұрын
Amazing video thank you
@jsalca523 жыл бұрын
Shokran kathir!
@lilialola123 Жыл бұрын
AMAZING visualizations, thank you
@LuisLascanoValarezo Жыл бұрын
7:59 Formula is key for interviews and in Machine Learning
@think98243 жыл бұрын
very interesting and useful. thanks a lot
@chinmaydhole40012 жыл бұрын
mind blown! thanks a lot for this video
@mandystritzke33393 жыл бұрын
Great explanation!
@_soundwave_9 ай бұрын
What about convex in terms of geometry? What about all three definition of convexity with that of geometry?
@AJ-et3vf Жыл бұрын
awesome video. thank you
@fabricetshinangi50422 жыл бұрын
Amazing video, thank you for the explanation
@VisuallyExplained2 жыл бұрын
Glad it was helpful!
@fabricetshinangi50422 жыл бұрын
Yes it is very insightful. I'm actually optimizing a Non linear cost function (with more than 6 variables) using newton raphson method. And my hessian matrix must be >=0
@sateeshk33472 жыл бұрын
Great Video, thank you for the effort and time in creating the same.
@VisuallyExplained2 жыл бұрын
My pleasure!
@federicobarra36552 жыл бұрын
amazing explanation! keep it up!
@Tibug Жыл бұрын
These videos are marvelous(!) but you need a better mic.
@benjaminbenjamin88342 жыл бұрын
I appreciate this video but there was nothing related to primal and dual concepts in this video?
@rylanschaeffer32483 жыл бұрын
You have an extra negative at 7:59, I think.
@VisuallyExplained3 жыл бұрын
Correct! I will compile a list of typos and add it to the description. Thank you!
@olivier306 Жыл бұрын
beautiful
@VivekYadav-ds8oz5 ай бұрын
I don't get how h(x)
@VisuallyExplained4 ай бұрын
-e^x is not convex
@tomwassing3 жыл бұрын
Absolutely amazing video! Great visualisation and explanation of the topic. I found it pretty difficult to find any interactive and visual content, thank you! I just finished my computer science bachelor and I find a great interest in these types of problems, could you recommend me an introductory book?
@VisuallyExplained3 жыл бұрын
Awesome! Convex Optimization by Boyd and Vandenberghe is really good. The first author has his lectures on youtube as well if you're interested.
@hyperduality2838 Жыл бұрын
@@VisuallyExplained From a convergent, convex (lens) or syntropic perspective everything looks divergent, concave or entropic -- the 2nd law of thermodynamics. According to the 2nd law of thermodynamics all observers have a syntropic perspective. My syntropy is your entropy and your syntropy is my entropy -- duality! Syntropy (prediction) is dual to increasing entropy -- the 4th law of thermodynamics. Homology (convergence, syntropy) is dual to co-homology (divergence, entropy). Teleological physics (syntropy) is dual to non teleological physics (entropy). Duality creates reality. "Always two there are" -- Yoda. Points are dual to lines -- the principle of duality in geometry.
@werdasize2 жыл бұрын
Really nice! But one thing I didn’t understand was at 5:02 ish. You say that the intersection of those support planes is the convex set.. but in your example, isn’t the intersection of the planes just a bunch of connected lines? Not sure if I understood correctly.
@werdasize2 жыл бұрын
Or is it that there exists an infinite set of unique such planes whose intersection is the surface of the convex set? Even then, still not sure how to recover the interior.
@VisuallyExplained2 жыл бұрын
Great observation. The intersection of the hyperplanes themselves could be empty. It is the intersection of the corresponding half spaces that gives the convex set.
@werdasize2 жыл бұрын
@@VisuallyExplained makes perfect sense then, thanks!!
@osamazaheer64302 жыл бұрын
great. Thanks
@aswathik4709 Жыл бұрын
6:51 is the lhs f(x)?
@dempstert27122 жыл бұрын
At 3:12, did you mean to say hᵢ(x)≤ 0 and -hᵢ(x) ≥ 0 ? Such that the overlap of the two functions is linear?
@VisuallyExplained2 жыл бұрын
"hᵢ(x)≤ 0" and "-hᵢ(x) ≥ 0" are actually the same thing.
@wokeclub18442 жыл бұрын
Great video!! Can Someone please explain How at 3:11 the equality Can be considered as those two inequalities?
@VisuallyExplained2 жыл бұрын
sure, let's take an example. The equality x = 1 is equivalent to x >= 1 and x
@blueberry235 ай бұрын
❤
@hyperduality2838 Жыл бұрын
From a convergent, convex (lens) or syntropic perspective everything looks divergent, concave or entropic -- the 2nd law of thermodynamics. According to the 2nd law of thermodynamics all observers have a syntropic perspective. My syntropy is your entropy and your syntropy is my entropy -- duality! Syntropy (prediction) is dual to increasing entropy -- the 4th law of thermodynamics. Homology (convergence, syntropy) is dual to co-homology (divergence, entropy). Teleological physics (syntropy) is dual to non teleological physics (entropy). Duality creates reality. "Always two there are" -- Yoda. Points are dual to lines -- the principle of duality in geometry.
@sygmermartins60822 жыл бұрын
very nice :)
@VisuallyExplained2 жыл бұрын
Thank you! Cheers!
@korayyy4402 жыл бұрын
>Potato shape >Makes an egg
@Throwingness Жыл бұрын
Who named the friggin things 'primal' and 'dual'? It's confusing. 'Primal' is fine. 'Dual' makes it sound like we're dealing with two more of something. As we have three now.