Convexity and The Principle of Duality

[@snailscout9383]

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]

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.

[@parahumour4619]

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

[@virmaq5187]

As a visual learner, this video helped me tremendously. Thank you!

[@jiaqi9113]

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]

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.

[@raulsena3917]

Thanks for the video, I was reading many books to understand this and you explain it plain and simple. Keep it up!

[@wexwexexort]

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.

[@vats6]

Woah! Thanks a lot sir, for such an intutive explaination of convexity. The best explaination I have seen on the internet so far!

[@hyperduality2838]

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]

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]

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.

[@imotvoksim]

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!

[@VisuallyExplained]

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]

Good God. This is so beautiful and intuitively explained. Can thank you enough for this! you are the savior.

[@rubenosmond8200]

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_hart]

The code samples for linear programming and least squares are swapped at 0:23. I’ve been enjoying your work. Thanks for sharing!

[@VisuallyExplained]

Thanks for watching carefully, and I am glad you liked my videos. :-)

[@gustavgille9323]

The least squares error example is beautiful!!!

[@MaxWasserman1]

Huge fan. Keep it up.

[@SonLeTyP9496]

Awesome :) cant wait to see next episode :D

[@think9824]

true

[@jiaqint961]

I learnt so much from this video, I love you so much

[@parhamzolfaghari7394]

Wonderful! I always wonder why the professors and teacher follow the worst method possible to teach materials.

[@nashwahammoud4076]

That's wonderful 🎉 thanks for you

[@thebifrostbridge3900]

Great video. Fun fact, the autogenerated subtitles at 9:32 says: "to optimization problems with cancer friends"

[@phogbinh]

God like overview of the topic. Thank you.

[@user-nm3mn1ir2z]

great video! What program did you use to make this fantastic visualization?

[@ZhanCaitao]

Great video!

[@ian.ambrose]

Yes! New Blender tutorial!

[@jameskirkham5019]

Amazing video thank you

[@jsalca52]

Shokran kathir!

[@lilialola123]

AMAZING visualizations, thank you

[@LuisLascanoValarezo]

7:59 Formula is key for interviews and in Machine Learning

[@think9824]

very interesting and useful. thanks a lot

[@chinmaydhole4001]

mind blown! thanks a lot for this video

[@mandystritzke3339]

Great explanation!

[@_soundwave_]

What about convex in terms of geometry? What about all three definition of convexity with that of geometry?

[@AJ-et3vf]

awesome video. thank you

[@fabricetshinangi5042]

Amazing video, thank you for the explanation

[@VisuallyExplained]

Glad it was helpful!

[@fabricetshinangi5042]

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

[@sateeshk3347]

Great Video, thank you for the effort and time in creating the same.

[@VisuallyExplained]

My pleasure!

[@federicobarra3655]

amazing explanation! keep it up!

[@Tibug]

These videos are marvelous(!) but you need a better mic.

[@benjaminbenjamin8834]

I appreciate this video but there was nothing related to primal and dual concepts in this video?

[@rylanschaeffer3248]

You have an extra negative at 7:59, I think.

[@VisuallyExplained]

Correct! I will compile a list of typos and add it to the description. Thank you!

[@olivier306]

beautiful

[@VivekYadav-ds8oz]

I don't get how h(x)

[@VisuallyExplained]

-e^x is not convex

[@tomwassing]

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]

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]

@@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.

[@werdasize]

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.

[@werdasize]

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.

[@VisuallyExplained]

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.

[@werdasize]

@@VisuallyExplained makes perfect sense then, thanks!!

[@osamazaheer6430]

great. Thanks

[@aswathik4709]

6:51 is the lhs f(x)?

[@dempstert2712]

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?

[@VisuallyExplained]

"hᵢ(x)≤ 0" and "-hᵢ(x) ≥ 0" are actually the same thing.

[@wokeclub1844]

Great video!! Can Someone please explain How at 3:11 the equality Can be considered as those two inequalities?

[@VisuallyExplained]

sure, let's take an example. The equality x = 1 is equivalent to x >= 1 and x

[@blueberry23]

❤

[@hyperduality2838]

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.

[@sygmermartins6082]

very nice :)

[@VisuallyExplained]

Thank you! Cheers!

[@korayyy440]

>Potato shape >Makes an egg

[@Throwingness]

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.

[@eneserdogan34]

This is some serious gourmath shit.

[@tsunningwah3471]

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[@tsunningwah3471]

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[@tsunningwah3471]

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[@himanshuverma298]

Bhai please be accurate