Convexity and The Principle of Duality

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  • Опубліковано 26 вер 2024

КОМЕНТАРІ • 76

  • @snailscout9383
    @snailscout9383 2 роки тому +89

    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
      @hyperduality2838 Рік тому +1

      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.

  • @jiaqi9113
    @jiaqi9113 3 роки тому +13

    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
      @hyperduality2838 Рік тому

      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.

  • @virmaq5187
    @virmaq5187 2 роки тому +5

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

  • @parahumour4619
    @parahumour4619 9 місяців тому +1

    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

  • @raulsena3917
    @raulsena3917 3 роки тому +6

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

  • @Sirentuber
    @Sirentuber Рік тому

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

  • @vats6
    @vats6 2 роки тому +2

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

    • @hyperduality2838
      @hyperduality2838 Рік тому

      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.

  • @wexwexexort
    @wexwexexort Рік тому +1

    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.

  • @cmatiolli13
    @cmatiolli13 Рік тому +2

    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
      @hyperduality2838 Рік тому

      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.

  • @gustavgille9323
    @gustavgille9323 3 місяці тому

    The least squares error example is beautiful!!!

  • @rubenosmond8200
    @rubenosmond8200 11 місяців тому

    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.

  • @imotvoksim
    @imotvoksim 2 роки тому +3

    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
      @VisuallyExplained  2 роки тому +3

      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. :-)

  • @colin_hart
    @colin_hart 2 роки тому +2

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

    • @VisuallyExplained
      @VisuallyExplained  2 роки тому +1

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

  • @MaxWasserman1
    @MaxWasserman1 3 роки тому +5

    Huge fan. Keep it up.

  • @SonLeTyP9496
    @SonLeTyP9496 3 роки тому +4

    Awesome :) cant wait to see next episode :D

  • @parhamzolfaghari7394
    @parhamzolfaghari7394 11 місяців тому +1

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

  • @nashwahammoud4076
    @nashwahammoud4076 6 місяців тому

    That's wonderful 🎉 thanks for you

  • @ian.ambrose
    @ian.ambrose Рік тому

    Yes! New Blender tutorial!

  • @jiaqint961
    @jiaqint961 Рік тому

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

  • @phogbinh
    @phogbinh 2 роки тому

    God like overview of the topic. Thank you.

  • @jameskirkham5019
    @jameskirkham5019 4 місяці тому

    Amazing video thank you

  • @thebifrostbridge3900
    @thebifrostbridge3900 2 роки тому

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

  • @ZhanCaitao
    @ZhanCaitao 2 роки тому +1

    Great video!

  • @lilialola123
    @lilialola123 Рік тому

    AMAZING visualizations, thank you

  • @jsalca52
    @jsalca52 3 роки тому +1

    Shokran kathir!

  • @박시연-m2m
    @박시연-m2m Рік тому +2

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

  • @mandystritzke3339
    @mandystritzke3339 3 роки тому +1

    Great explanation!

  • @chinmaydhole4001
    @chinmaydhole4001 2 роки тому

    mind blown! thanks a lot for this video

  • @think9824
    @think9824 3 роки тому +4

    very interesting and useful. thanks a lot

  • @AJ-et3vf
    @AJ-et3vf Рік тому

    awesome video. thank you

  • @fabricetshinangi5042
    @fabricetshinangi5042 3 роки тому

    Amazing video, thank you for the explanation

    • @VisuallyExplained
      @VisuallyExplained  3 роки тому

      Glad it was helpful!

    • @fabricetshinangi5042
      @fabricetshinangi5042 3 роки тому +2

      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

  • @federicobarra3655
    @federicobarra3655 2 роки тому

    amazing explanation! keep it up!

  • @_soundwave_
    @_soundwave_ 11 місяців тому

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

  • @sateeshk3347
    @sateeshk3347 2 роки тому

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

  • @olivier306
    @olivier306 Рік тому

    beautiful

  • @Tibug
    @Tibug Рік тому +1

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

  • @VivekYadav-ds8oz
    @VivekYadav-ds8oz 6 місяців тому

    I don't get how h(x)

  • @osamazaheer6430
    @osamazaheer6430 3 роки тому

    great. Thanks

  • @rylanschaeffer3248
    @rylanschaeffer3248 3 роки тому +2

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

    • @VisuallyExplained
      @VisuallyExplained  3 роки тому +2

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

  • @benjaminbenjamin8834
    @benjaminbenjamin8834 2 роки тому

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

  • @werdasize
    @werdasize 2 роки тому +1

    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
      @werdasize 2 роки тому

      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
      @VisuallyExplained  2 роки тому +1

      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
      @werdasize 2 роки тому

      @@VisuallyExplained makes perfect sense then, thanks!!

  • @tomwassing
    @tomwassing 3 роки тому

    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
      @VisuallyExplained  3 роки тому +1

      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
      @hyperduality2838 Рік тому

      @@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.

  • @Throwingness
    @Throwingness 2 роки тому

    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.

  • @wokeclub1844
    @wokeclub1844 2 роки тому

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

    • @VisuallyExplained
      @VisuallyExplained  2 роки тому

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

  • @dempstert2712
    @dempstert2712 2 роки тому

    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
      @VisuallyExplained  2 роки тому

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

  • @blueberry23
    @blueberry23 6 місяців тому

  • @aswathik4709
    @aswathik4709 2 роки тому

    6:51 is the lhs f(x)?

  • @sygmermartins6082
    @sygmermartins6082 2 роки тому

    very nice :)

  • @hyperduality2838
    @hyperduality2838 Рік тому

    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.

  • @korayyy440
    @korayyy440 2 роки тому

    >Potato shape
    >Makes an egg

  • @eneserdogan34
    @eneserdogan34 2 роки тому

    This is some serious gourmath shit.

  • @tsunningwah3471
    @tsunningwah3471 2 місяці тому

    zbian

  • @himanshuverma298
    @himanshuverma298 6 місяців тому

    Bhai please be accurate

  • @tsunningwah3471
    @tsunningwah3471 2 місяці тому

    jnnjjjjjj

  • @tsunningwah3471
    @tsunningwah3471 9 місяців тому

    瘁jknj

  • @LuisLascanoValarezo
    @LuisLascanoValarezo Рік тому

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