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.
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 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.
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. :-)
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
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.
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.
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.
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 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.
As a visual learner, this video helped me tremendously. Thank you!
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
Thanks for the video, I was reading many books to understand this and you explain it plain and simple. Keep it up!
Good God. This is so beautiful and intuitively explained. Can thank you enough for this! you are the savior.
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.
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.
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.
The least squares error example is beautiful!!!
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. :-)
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. :-)
Huge fan. Keep it up.
Awesome :) cant wait to see next episode :D
true
Wonderful! I always wonder why the professors and teacher follow the worst method possible to teach materials.
That's wonderful 🎉 thanks for you
Yes! New Blender tutorial!
I learnt so much from this video, I love you so much
God like overview of the topic. Thank you.
Amazing video thank you
Great video. Fun fact, the autogenerated subtitles at 9:32 says: "to optimization problems with cancer friends"
Great video!
AMAZING visualizations, thank you
Shokran kathir!
great video! What program did you use to make this fantastic visualization?
Great explanation!
mind blown! thanks a lot for this video
very interesting and useful. thanks a lot
awesome video. thank 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
amazing explanation! keep it up!
What about convex in terms of geometry? What about all three definition of convexity with that of geometry?
Great Video, thank you for the effort and time in creating the same.
My pleasure!
beautiful
These videos are marvelous(!) but you need a better mic.
I don't get how h(x)
-e^x is not convex
great. Thanks
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!
I appreciate this video but there was nothing related to primal and dual concepts in this video?
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!!
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.
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.
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
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.
❤
6:51 is the lhs f(x)?
very nice :)
Thank you! Cheers!
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.
>Potato shape
>Makes an egg
This is some serious gourmath shit.
zbian
Bhai please be accurate
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7:59 Formula is key for interviews and in Machine Learning