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
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.
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!!
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.
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.
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
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.
I enjoyed this video like participating in an exciting show program. I didn't even have to stress my brain to visualize such complex concepts like multivariable functions.
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.
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.
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!
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. :-)
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.
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.
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.
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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
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?
@@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.
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.
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.
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
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.
Good God. This is so beautiful and intuitively explained. Can thank you enough for this! you are the savior.
Thanks for the video, I was reading many books to understand this and you explain it plain and simple. Keep it up!
As a visual learner, this video helped me tremendously. Thank you!
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!!
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.
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.
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
Woah! Thanks a lot sir, for such an intutive explaination of convexity. The best explaination I have seen on the internet so far!
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.
Brilliant! Wish these concepts were explained in this intuitive way during my PhD.
I enjoyed this video like participating in an exciting show program. I didn't even have to stress my brain to visualize such complex concepts like multivariable functions.
The code samples for linear programming and least squares are swapped at 0:23.
I’ve been enjoying your work. Thanks for sharing!
Thanks for watching carefully, and I am glad you liked my videos. :-)
Your videos are awesome. The right balance of math concepts and intuition to explain complex ideas is the perfect fit for this essential concept.
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.
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.
Awesome :) cant wait to see next episode :D
true
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!
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. :-)
Huge fan. Keep it up.
I learnt so much from this video, I love you so much
The least squares error example is beautiful!!!
God like overview of the topic. Thank you.
Great video. Fun fact, the autogenerated subtitles at 9:32 says: "to optimization problems with cancer friends"
Yes! New Blender tutorial!
AMAZING visualizations, thank you
great video! What program did you use to make this fantastic visualization?
mind blown! thanks a lot for this video
Great explanation!
Wonderful! I always wonder why the professors and teacher follow the worst method possible to teach materials.
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.
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.
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.
@@VisuallyExplained makes perfect sense then, thanks!!
Great video!!
Can Someone please explain How at 3:11 the equality Can be considered as those two inequalities?
sure, let's take an example. The equality x = 1 is equivalent to x >= 1 and x
very interesting and useful. thanks a lot
amazing explanation! keep it up!
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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?
"hᵢ(x)≤ 0" and "-hᵢ(x) ≥ 0" are actually the same thing.
You have an extra negative at 7:59, I think.
Correct! I will compile a list of typos and add it to the description. Thank you!
Great video!
That's wonderful 🎉 thanks for you
Amazing video, thank you for the explanation
Glad it was helpful!
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
7:59 Formula is key for interviews and in Machine Learning
Shokran kathir!
I appreciate this video but there was nothing related to primal and dual concepts in this video?
6:51 is the lhs f(x)?
What about convex in terms of geometry? What about all three definition of convexity with that of geometry?
I don't get how h(x)
-e^x is not convex
awesome video. thank you
Amazing video thank you
Great Video, thank you for the effort and time in creating the same.
My pleasure!
Local minima will be global minima what about local maxima? Will it also be global maxima?
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?
Awesome! Convex Optimization by Boyd and Vandenberghe is really good. The first author has his lectures on youtube as well if you're interested.
@@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.
beautiful
These videos are marvelous(!) but you need a better mic.
great. Thanks
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.
very nice :)
Thank you! Cheers!
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.
>Potato shape
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This is some serious gourmath shit.
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