Laplacian intuition

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  • Опубліковано 22 гру 2024

КОМЕНТАРІ • 160

  • @srgkzy1294
    @srgkzy1294 7 років тому +1208

    That voice... makes me feel safe with math

  • @ryanthomas9693
    @ryanthomas9693 5 років тому +83

    Literally got more intuition from a 5 min video than scouring through a myriad of textbooks back in my college days. It's interesting to note that the Physicists' notation for the Laplacian is nabla^2, which maybe makes it a bit more confusing because it implies it's the second order gradient or could imply the curl of gradient, etc.

    • @sumdumbmick
      @sumdumbmick 2 роки тому

      you do know that multiplication can be rendered in English as 'of', right?
      3 * 4 apples = 12 apples -> three groups of 4 apples is 12 apples
      and thus a second order derivative, which is the derivative of a derivative is validly derivative * derivative, or derivative^2. and the only difference between a generic derivative and the differential is that a nabla indicates is that it's the sum of all n partial derivatives over an n-space. so the second order differential is nabla of nabla, or nabla * nabla, or nabla^2.
      the reason it appears to be the same as the second order gradient is because it is. it's the sum of the partial derivatives... which is the second order gradient, and the laplacian, they're two names for the same thing, and thus it's actually not confusing. and curl is notated differently, since it's the cross product. if you separate it out as nabla dot nabla, then it might be ambiguous as divergence of the gradient, but with very little effort you can see for yourself that it's actually the same thing anyway, so again... what are you confused about, exactly?

    • @sumdumbmick
      @sumdumbmick 2 роки тому

      see @0:52
      he literally shows you that the laplacian is the divergence of the gradient and it remains on screen for the entire rest of the video.
      how in the world are you confused, and how did anybody like your comment that you're confused? it's not remotely confusing.

    • @notstarboard9792
      @notstarboard9792 Рік тому +4

      ​@@sumdumbmick 1) Chill out. Just because something isn't confusing to you doesn't mean everyone needs to agree.
      2) The Laplacian is not the same as a second-order gradient. The Laplacian is the *divergence* of a gradient, which gives a scalar. The gradient is a vector, so you would expect a second-order gradient to also be a vector / matrix. Ryan is right that the notation obscures the meaning of the term. Leaving it as del dot del would be a lot more clear.
      3) The eye-rolling-ness of appealing to English grammar to criticize a benign internet comment aside, multiplication and "of" are not always the same thing in this context. Let's say f(x) = x^3. The derivative of the derivative of f(x) is 6x. The derivative of f(x) times the derivative of f(x) is 9x^4. This line of reasoning is only going to get us into trouble.

    • @metheewatchakittikorn4796
      @metheewatchakittikorn4796 10 місяців тому

      I agree definitely.

  • @jlpsinde
    @jlpsinde 5 років тому +18

    This is heaven on Earth for someone like me that learned this 24 years ago and just now understand!

  • @e1123581321345589144
    @e1123581321345589144 2 роки тому +5

    I swear to god, I've been reading various pages for days to understand what this operator does. You made it cristal clear in a few minutes

  • @czarlito_
    @czarlito_ 5 років тому +107

    Welcome, all you travelers, coming from Partial Differential Equations! Praised be 3B1B!

    • @lopkobor6916
      @lopkobor6916 5 років тому +3

      I'm from the video "Divergence and Curl" ( also from 3b1b )

  • @wtflks
    @wtflks 7 років тому +516

    3blue one brown????

    • @ANJALISINGH-yp4tr
      @ANJALISINGH-yp4tr 7 років тому +33

      yup .....100% sure

    • @davidwiedemann9926
      @davidwiedemann9926 6 років тому +14

      Yes

    • @drakefire1800
      @drakefire1800 6 років тому +12

      ya dude. he is awesome. love his videos. he uses right brain thinking.

    • @alial-ansari8815
      @alial-ansari8815 5 років тому +6

      Yes that’s him 😂👌🏻❤️

    • @lLlILILw
      @lLlILILw 4 роки тому +4

      He did say in an interview that he taught in khan academy or something before youtube

  • @ummwho8279
    @ummwho8279 8 років тому +46

    You guys are amazing, thank you for publishing these! Multivariable calc is so much more understandable now!

  • @oscarsharkslayer
    @oscarsharkslayer 6 років тому +34

    I could never understand Laplace operators at school. I hated them. Today, my 7 year old kid looks at this video and says: "it is simple, why did you not understand?". Yes! This is a new wave of learning. Thank you Sal and thank you Blue Brown. You redefine learning!

    • @heavennoes
      @heavennoes 3 роки тому +4

      as a 10 yr old, he makes everything hyper - simple.

    • @suveermanj1001
      @suveermanj1001 Рік тому +8

      My son just got out of my wife's womb guys and he also said it's so easy,...thanks Obama.

    • @funkdrunk
      @funkdrunk Рік тому +1

      ​@@suveermanj1001are you mocking? the statement? And Obama at the same time? Kids have a knack to find their own interpretation of stuff presented in visual form. Perhaps they forget in a day, but they comprehend more than adults think

    • @DaBestNub
      @DaBestNub 11 місяців тому +3

      Dunning Kruger effect go crazy

    • @funkdrunk
      @funkdrunk 11 місяців тому

      @@DaBestNub Dunning Kruger effect MYTH go crazy

  • @MattiLargeWorld
    @MattiLargeWorld 4 роки тому +4

    The intuition for the laplacian is exquisite I am very glad that you’re getting a ton of recognition.

    • @funkdrunk
      @funkdrunk 11 місяців тому

      with your young face you risk getting some detractors here. Check some neighboring comments for Dunning or Obama. Hilarious. I agree with the intuition part. First time in my life I understand that stuff! :)

  • @Luisgar1234
    @Luisgar1234 2 роки тому +2

    I was saying today why doesn’t 3blue have a video on laplace… one trip to the search bar later and I found this hidden gem.

  • @harshchikorde9495
    @harshchikorde9495 8 років тому +24

    please make a vedio on LAPLACE TRANSFORM

  • @mahsanafisi2937
    @mahsanafisi2937 4 роки тому +4

    Thank you soooo much for amazing illustration and for making it so easy to understand.

  • @quantaali543
    @quantaali543 5 років тому +3

    superb ... finally, I understand the concept of gradient, divergence and Laplace's equation.

  • @victorvalencia6466
    @victorvalencia6466 5 років тому +4

    3blue1brown should voice all math videos on the internet

  • @eduardoandrescontrerasrome6703

    Omg god, this video is sublime. I am currently taking an Electromagnetism class so we constantly use this concepto of the Laplace equation but I never really understood what it meant.

  • @vector8310
    @vector8310 3 роки тому

    When I click on a Khan Academy video I pray it's a 3B 1B. Ghee was born for this.

  • @othmaneelhanchi4451
    @othmaneelhanchi4451 5 років тому +3

    Brilliant explanation !

  • @pavi512k
    @pavi512k 5 років тому +2

    Please make a video on laplacian operator in spherical and cylindrical coordinates

  • @priyocoutinho
    @priyocoutinho 2 роки тому

    Nice explanation...it will help us get a picture of what we are doing when we solve laplacians...

  • @jh2519
    @jh2519 4 роки тому +1

    Awesome, this helps with my electrical prospecting class.

  • @inquisitiverakib5844
    @inquisitiverakib5844 2 роки тому +1

    solid concept
    lucid explanation 😍😍

  • @chrysostomoschadjiminas6217
    @chrysostomoschadjiminas6217 4 роки тому

    Since we are talking about the direction of steepest descent instead of ascent, shouldn't the gradient vectors point the opposite direction? Shouldn't the sources be sinks and vice versa?

  • @EssamSat
    @EssamSat 5 років тому +34

    Anybody here from 3blue one brown PDE video ?

  • @thevegg3275
    @thevegg3275 6 років тому +1

    Wrt the vectors representing the gradient...are these colored differently to represent magnitude of the vectors? Is it also a convention to use longer vectors to represent vectors with larger magnitudes? I prefer color coding since the smaller and more numerous the vectors are, the better the visualization of what they represent. Changing length of vectors would take up space which could be better used to increase the count of vectors used.

  • @dkoz8321
    @dkoz8321 Місяць тому

    I got all that. Tottally understood everything!

  • @vinbo2232
    @vinbo2232 4 роки тому +1

    Thank you, great intuitive explanation

  • @technosapien330
    @technosapien330 8 місяців тому

    this man is getting me through grad school

  • @JohnVKaravitis
    @JohnVKaravitis 3 роки тому

    Difference between Laplace and Poisson equations? One equals zero, the other does not, right?

  • @BAD_LS
    @BAD_LS 7 років тому +2

    Well explained, so far! Even for a german, thanks!

  • @BatistaR0X
    @BatistaR0X 7 років тому +64

    Instead of expecting Khan, this guy sounds like 3blue1brown?

    • @error.418
      @error.418 7 років тому +4

      yep, that's 3b1b

    • @biggbuck9535
      @biggbuck9535 6 років тому

      In fact, it is the same guy 3blue1brown. He decided to do khan just for a bit outside of his patreon channel

    • @That_One_Guy...
      @That_One_Guy... 4 роки тому +1

      @@biggbuck9535 He worked at khan academy before doing his channel

  • @yeungpakming
    @yeungpakming 3 місяці тому +1

    I was thinking oh no 3b1b didn't make a video about laplacian, maybe i should just check out this video... nice

  • @hanyiliu3332
    @hanyiliu3332 2 роки тому +1

    This is amazing.

  • @user-or7ji5hv8y
    @user-or7ji5hv8y 4 роки тому +1

    What a great explanation. Thank you

  • @mitalpattni1977
    @mitalpattni1977 6 років тому +1

    Please do a video on spectral clustering or graph theory!

  • @Gaming_station93
    @Gaming_station93 3 роки тому

    No copyright issue from 3blues1brown?

  • @anonymoustraveller2254
    @anonymoustraveller2254 7 років тому +10

    Oh my god! You really exist.

  • @fahim1943
    @fahim1943 3 роки тому

    Revisiting all of this cause its beena while I didnt touch Multivariable Calc and its still so fascinating and I realised how much I discovred more even if I watched this already time ago

  • @bunkerputt
    @bunkerputt 6 років тому +2

    I just love talking about the Laplacian. It's such an edgy subject.

  • @williamlee0
    @williamlee0 4 роки тому

    Will the learner notice that you would have to flip the blue blanket inside-out for the water droplet analogy to make sense? Water does not flow uphill to pool at the peak of a hill.

  • @tahaabujrad7806
    @tahaabujrad7806 7 років тому

    What this has to do with L(f(t))=integral from 0 to inf of e^-st*f(t)

  • @kvamshi4561
    @kvamshi4561 5 років тому +5

    Those who're wondering whether this guy is 3Blue1Brown guy..
    Hell yes! He is the same guy left khan academy and doing his own videos

    • @axelmeramas976
      @axelmeramas976 4 роки тому +1

      he didn't left khan academy, is still working

    • @kvamshi4561
      @kvamshi4561 4 роки тому

      @@axelmeramas976 OK

  • @dudewhat9329
    @dudewhat9329 4 роки тому +2

    this is awesome, thank you :D

  • @CGKittenz
    @CGKittenz 4 роки тому +1

    finally understood this!

  • @BraaiEngineer
    @BraaiEngineer 4 роки тому

    Link so follow-up video, please?

  • @ProfeARios
    @ProfeARios 5 років тому +1

    Great lesson!!!

  • @trip_on_earth
    @trip_on_earth 3 роки тому

    please make a video on your channel 3b1b of Laplace transform

  • @pratikbari1714
    @pratikbari1714 7 років тому +1

    Great explaination

  • @batuskovichuman6886
    @batuskovichuman6886 4 місяці тому

    All my beloved teacher

  • @manojkumar-cb3wf
    @manojkumar-cb3wf 4 роки тому

    i kindly request you to arrange the videos order wise .

  • @yizhang7027
    @yizhang7027 3 роки тому +1

    Why am I in tears after understanding this

  • @cory99998
    @cory99998 3 роки тому +1

    Ty, im going to try to create a 2D gravity / space-time simulation using this

  • @Raptured_and_back
    @Raptured_and_back 6 років тому

    Not kind of. It is a minimum if f '' > 0 and maximum if f '' < 0, be it a local or extreme.

  • @AmeerulIslam
    @AmeerulIslam 6 років тому

    is there any relationship between laplacian and laplace transform?

  • @OnlyOneesWhoKnow
    @OnlyOneesWhoKnow 6 років тому

    Hello, Thank you so much!
    How would I intuit the Bi-Laplacian ? What's the gradient(3) of the divergence(2) if the divergence(2) of the gradient(1) characterizes already if a point is on a pedestal or in a gap?

  • @dastran2731
    @dastran2731 7 років тому

    what about f(x,y,z) intuition?

  • @AssassinGrudge
    @AssassinGrudge 8 років тому

    is this difference from the laplace transform because i was trying to understand the spherical harmonic. but instead of searching for Laplacian function i searched the laplace transform and i spend like 2 days learning it is it a waist ?

  • @MoeSalamaIbrahim
    @MoeSalamaIbrahim 5 місяців тому +1

    POV: you've stayed here because of 3Blue1Brown's very own Grant Sanderson and his soothing voice.

  • @leguminosa9
    @leguminosa9 6 років тому

    but why is the gradient is toward the top of hill? shouldn't it converge to the goalie instead?

    • @robitybopity
      @robitybopity 6 років тому

      Martin Johnsons I believe the gradient points toward the steepest point, or the greatest rate of spacial change

  • @murphy98969
    @murphy98969 5 років тому

    When laplacian of function is zero what it mean???

  • @jobhiojkp
    @jobhiojkp 6 років тому

    Does anyone say del anymore, instead of nabla? Or is that from another generation?

  • @annashchukina3768
    @annashchukina3768 3 роки тому

    thank you so much

  • @अण्वायुवरीवर्त

    I'll be really greedy this time,
    What is the software that u used
    Plzz seems like a fun way to learn things (intuitively)

    • @Pogosoke
      @Pogosoke 5 років тому

      Lawliet L i think he Programms it himself, same with the animations on his channel

    • @reemashrestha9718
      @reemashrestha9718 4 роки тому

      In 3B1B, he uses Manim: an open-source code that he created himself.

  • @Lonczakt
    @Lonczakt 6 років тому

    Anyone know what software was used to make the graph

  • @NEO-z2y
    @NEO-z2y 3 роки тому +1

    Grant you're grand❤

  • @murphy98969
    @murphy98969 5 років тому

    Where i can get this software ????

  • @amandhakal8939
    @amandhakal8939 2 роки тому

    So, to conclude,
    "At lowest point of any field, laplacian gives maximum value and at highest point of any field, lapacian gives minimum value",
    am I right?

  • @benjaminbrady2385
    @benjaminbrady2385 5 років тому +2

    I recognise Grants voice anywhere!

  • @sergiolucas38
    @sergiolucas38 2 роки тому

    great video, yhanks :)

  • @MP-cv6if
    @MP-cv6if 3 місяці тому

    3 blue 1 brown???

  • @kossanmoo9931
    @kossanmoo9931 6 років тому

    why wouldn't the water flow downwards following the gravity (:

    • @vectracris1
      @vectracris1 6 років тому +1

      Because the water example was just an analogy so that he could explain and make us visualise better, with the help of the blue lines, not an actual example of how gravity works

  • @nomanruhani5626
    @nomanruhani5626 2 роки тому

    oh, look who I got, mr grant

  • @michaelhaggerty569
    @michaelhaggerty569 7 років тому

    what program did you use to make this?

    • @robertwilsoniii2048
      @robertwilsoniii2048 6 років тому

      Michael Haggerty He wrote his own software from scratch. If you want to learn the skills to build something like this, you can take Stanford’s cs106ab and cs107 via UA-cam.

  • @nautiyogi8386
    @nautiyogi8386 5 років тому

    Amazing ! Amazing !

  • @weeborghini4016
    @weeborghini4016 2 роки тому

    are u bluebrown?? u sounds similar

  • @arjunmenonkandanat6328
    @arjunmenonkandanat6328 8 місяців тому

    Is this Grant Sanderson ?

  • @mingxi1055
    @mingxi1055 9 місяців тому

    heat equation intuition

  • @richardwborge
    @richardwborge 5 років тому +2

    I recognize this voice :)

  • @marcosviniciusrodriguescos8118
    @marcosviniciusrodriguescos8118 4 роки тому

    thank's man!

  • @subtlethingsinlife
    @subtlethingsinlife 5 років тому

    3 blue1 brown , I know the voice ... Happy

  • @DracoRenaissance
    @DracoRenaissance 8 років тому

    idea: Sal does the audio, another the animations and graphs and prettiness, a third the math

  • @stevewhitt9109
    @stevewhitt9109 Рік тому

    3Bu1Bn miss you at Khan

  • @joluju2375
    @joluju2375 5 років тому

    As intuitive as expected. Was it on purpose you didn't use the word "concavity" ?

  • @Revan176
    @Revan176 5 років тому

    You haven't plot the laplacian too :'(

  • @masterj2245
    @masterj2245 4 роки тому

    Good

  • @drewm-r7249
    @drewm-r7249 7 років тому +3

    Omg is this the 3blue1brown guy!?!??!

  • @Graywolf116
    @Graywolf116 3 роки тому +2

    So the laplacian is the divergence of a gradient? It'd be so much easier if they just said *that* instead of slapping someone's name onto it.

  • @jasonpapadopoulos7732
    @jasonpapadopoulos7732 6 років тому +10

    3BLUE1BROWN YEAHHHHHH

  • @victorserras
    @victorserras 6 років тому +5

    3Blue1Brown in da house

  • @rio_agustian_
    @rio_agustian_ 3 роки тому +1

    Blanket of nightmare

  • @NSLikeableHuman
    @NSLikeableHuman 5 років тому

    3b1b army reporting!

  • @ConstructionGuy
    @ConstructionGuy 8 років тому +1

    1st?

  • @rawlayer999
    @rawlayer999 3 роки тому

    Voice is same as of 3blue 1brown

  • @neallucas
    @neallucas 8 років тому +1

    I guess.

  • @rat_king-
    @rat_king- 2 роки тому

    No Pi people? What? 3 Blue 1 Brown....

  • @DracoRenaissance
    @DracoRenaissance 8 років тому +2

    calligraphy hurts my eyes

  • @ManojKumar-cj7oj
    @ManojKumar-cj7oj 4 роки тому

    Oh my goodness

  • @seandafny
    @seandafny 6 років тому

    Wait a minute !! I know you !! And you are no sal khan !!!

    • @seandafny
      @seandafny 5 років тому

      Lol 1 year to forget not bad

  • @stipepavic843
    @stipepavic843 8 років тому +1

    thx alooooottt XD

  • @helper_bot
    @helper_bot 2 роки тому

    this sounds like Grant. Is this Grant? aha.

  • @akhilan1
    @akhilan1 6 років тому

    TEACH ME