The Simple Math Problem That Revolutionized Physics

แชร์
ฝัง
  • เผยแพร่เมื่อ 23 ธ.ค. 2024

ความคิดเห็น • 10K

  • @veritasium
    @veritasium  หลายเดือนก่อน +229

    If you enjoyed this video and want to go deeper, you'll find bonus content on Patreon, featuring the full interview with Prof. Steven Strogatz www.patreon.com/posts/principle-of-116042877

    • @volts420
      @volts420 หลายเดือนก่อน +7

      gnarly

    • @SPplayer.
      @SPplayer. หลายเดือนก่อน +5

      gnarly

    • @engincallahan2943
      @engincallahan2943 หลายเดือนก่อน +1

      I am having a very hard time understanding how they were able to integrate speed variations of light speed in different mediums into formulas at that time?
      Is this in the interview?
      Or can anybody explain please?

    • @zetta3official
      @zetta3official หลายเดือนก่อน

      I regard action as the first fundamental principle of the universe that defines spacetime as it arises from a deeper principle that we deal with all the time in physics: the potential
      Which points to an even deeper concept:
      Relationship most notably computational complexity that leads to a very promising explanation of our universe. The lagrangian ties that in beautifully.

    • @trakkaton
      @trakkaton หลายเดือนก่อน

      Make some more content with pedo-buddy Bill Gates before all he did with Epstein comes out. Add some more COVID poison injection BS before the turbo cancers really kick in. You know, $cience...

  • @3blue1brown
    @3blue1brown หลายเดือนก่อน +27140

    This was so beautiful. I was thinking of revisiting the old video I made with Strogatz about the Brachistochrone and Johann Bernoulli's solution, but this honestly does most of what I could have dreamed and so much more. Bravo!

    • @tanvirzawad
      @tanvirzawad หลายเดือนก่อน +332

      Peace be on them who follow the guidance. Nice to see you here!

    • @ModernWizardx1
      @ModernWizardx1 หลายเดือนก่อน +268

      your videos are pretty good 3b1b i always enjoy them!

    • @LearningAccount-e5x
      @LearningAccount-e5x หลายเดือนก่อน +522

      This whole STEM education space has reached completely new heights because of the likes of you guys!!! I couldn’t be more thankful. Stuff like this will be truly world changing.
      (The hologram video was epic! Long format is incredible and the little secret vlog was the cherry on top. Thanks so much for your work!)

    • @JadMustafa
      @JadMustafa หลายเดือนก่อน +44

      Indeed, surpasses the limit of education - absolutely beautiful.

    • @felix0003
      @felix0003 หลายเดือนก่อน +5

      wowie

  • @nolanthedude
    @nolanthedude หลายเดือนก่อน +6318

    One thing I adore about these videos is that they bring attention to history's forgotten heroes. Nakamura wasn't given the credit he deserved for the blue LED, and that video brought his contributions into the spotlight for millions. Now, Maupertuis has been given the spotlight and he can be recognized for his efforts alongside some of history's greatest mathematicians. If only he lived long enough to see this.

    • @entitledOne
      @entitledOne หลายเดือนก่อน +212

      Those things always make me wonder what the people who denied the inventions so hard would say now when they see how much they pushed the world forward. What would the people who insulted Maupertuis for his idea would say after they see it proven right.

    • @Player_is_I
      @Player_is_I หลายเดือนก่อน +1

      So true

    • @sottonk
      @sottonk หลายเดือนก่อน +14

      Poor Ibn Sahl

    • @TheAntira
      @TheAntira หลายเดือนก่อน +32

      I'm not sure I'd call a Nobel prize laureate a forgotten hero

    • @julioaurelio
      @julioaurelio หลายเดือนก่อน +90

      @@TheAntira The company he worked for thoughout most of his life dumped him and refused to give him the compensation he deserved. A real injustice.

  • @craiglorck
    @craiglorck หลายเดือนก่อน +14931

    Man! Euler is that superhero backup that arrives just in time when all hope is lost!

    • @threeuniquefingers
      @threeuniquefingers หลายเดือนก่อน +388

      Indeed! He was like Dr Strange in Avengers Endgame! Summoning Langarange as the ultimate support lol

    • @derroz3157
      @derroz3157 หลายเดือนก่อน +60

      U LER-NING is the real superhero :D

    • @Game_Masters
      @Game_Masters หลายเดือนก่อน +153

      14:02 I am like: Not this guy again.. I swear XD
      THE MAN - THE LEGEND

    • @tturi2
      @tturi2 หลายเดือนก่อน +21

      I've already used his stuff in solid mechanics

    • @johnimusic12
      @johnimusic12 หลายเดือนก่อน +128

      Euler = GOAT

  • @PriestofEvil89
    @PriestofEvil89 หลายเดือนก่อน +258

    Thank you Derek for making such great videos. Especially this one touched my heart. I am a mechanical engineer and I work in the field of dynamics. I have never understood why there are two ways how to get motion equations - at the university, I used Newton's second law most of the times, because it was straightforward. I did't understand, where the Lagrange's equatins came from. Now I know. And I am touched by the fact that each of those great mathematicians added a small pice of puzzle into this picture. And I feel sad for Mapertuis who died without knowing, that his theory was proven to be correct. Thanks for reminding us the important people, that were forgotten throughout the history.

    • @neektum8230
      @neektum8230 25 วันที่ผ่านมา +1

      Dumbfuc_ bro is wasting money why to donate they are generating threw yt

    • @Vordikk
      @Vordikk 23 วันที่ผ่านมา

      @@neektum8230 it's not a waste, unless you realize that YT takes 30% of donated sums. Which is A LOT. Literally any other donation service is more effective.

    • @WoodlandT
      @WoodlandT 23 วันที่ผ่านมา

      @@neektum8230Those of us with sufficient funds to do as we wish, do as we wish. See how that works?

    • @JohnVelazquez-jo3pd
      @JohnVelazquez-jo3pd 22 วันที่ผ่านมา +29

      ​@@neektum8230honestly how does it affect you? People can spend their money how they want to. The same logic could be applied and one could say that you _" _*_wasted_*_ precious moments of _*_your time_*_ to make a comment that benifits no one, when you could have used it for something more productive..."_

    • @TemporaryTemporary-y2j
      @TemporaryTemporary-y2j 22 วันที่ผ่านมา +15

      ​@@JohnVelazquez-jo3pd I agree with you. If someone wants to make a donation as a token of _appreciation,_ it's entirely up to them to do so and it's not "dumb" or "silly." No one is being forced.

  • @RENO_K
    @RENO_K หลายเดือนก่อน +15142

    "I recognize the lion by his claws" is such an epic quote
    Imagine being so legendary you don't have to sign off your letters/papers and people instantly know who wrote it

    • @joelspaulding5964
      @joelspaulding5964 หลายเดือนก่อน +246

      This is quite possible and common in art and music.

    • @ahsaasinator2840
      @ahsaasinator2840 หลายเดือนก่อน +76

      Let’s go another science banger !!!

    • @ares395
      @ares395 หลายเดือนก่อน +372

      @@joelspaulding5964 Try doing that with Science.

    • @Lucks-3
      @Lucks-3 หลายเดือนก่อน +165

      Counterpoint: “I have the most beautiful solution. Nobody has seen such a perfect solution, you wouldn’t believe it. You know it, I know it, everybody knows it. Don’t we have the best solutions?”

    • @jmalmsten
      @jmalmsten หลายเดือนก่อน +21

      That's basically how Richard Bachman was revealed. :P

  • @MrNpr
    @MrNpr หลายเดือนก่อน +2124

    I generally dont leave comments. But I felt I had to write this down. 24 years ago when I took my physics class as a first year under grad student, I was quickly introduced to the Lagrangian and Hamiltonian in a physics class with just the equations thrown around. There were books in the library which provided tons of equations but never the intuition behind them. It was assumed that the reader knew why this had to be the case. I never got back to digging this deeper as my primary area of focus had shifted to other subjects. But after so many years I am finally happy to see the beautiful thought process behind them. Really appreciate you for making such valuable and interesting content.

    • @AbyssRein
      @AbyssRein หลายเดือนก่อน +83

      Exactly!! Its degrading to teach how to use a formula without the story… the story and attempts through 4+ time periods are rich with lessons that can be applied all throughout life. Stories captivate an audience! Not formulas! Plus, you’ll only find independent thinkers at the forefront of discovery, I wonder how many greats fell short due to the rigidness of curriculum.

    • @UniverseSpeck
      @UniverseSpeck หลายเดือนก่อน +36

      I’m 100% with you. I find people tend to learn best through story telling. Not “facts”. Understanding what lead people to a current understanding is far more powerful and sticks with you. It’s harder to do and takes more time and work, but I think it serves more.

    • @erikziak1249
      @erikziak1249 หลายเดือนก่อน +5

      Same here.

    • @guigoinz112
      @guigoinz112 หลายเดือนก่อน +5

      Yeah, I need the story in order to make me abaorb the info, otherwise it’s too stale for my brain to remember😅

    • @semsuddin
      @semsuddin หลายเดือนก่อน +8

      This! Wouldn't it be much beter if all of those equations actually started as a story you'd follow through similarly as in this video? Wouldn't be much longer but way more meaningful and easier to learn and understand.

  • @caifasvaca9451
    @caifasvaca9451 หลายเดือนก่อน +1216

    The way Euler was described as a “good guy” wanting to help and explain stuff brought tears to my eyes. My old math teacher was a HUGE fan of Euler and his face would light up every time he talked about him. To the point that some students mocked him behind his back for it. That teacher was very much invested in his students and whenever someone, who had struggled with a certain concept, finally grasped it, he would be overjoyed - much more than by someone effortlessly picking things up. If you genuinely worked hard to improve, you would be rewarded with grades on the same level as the naturally “gifted” kids. Only watching this video I just realized that Euler being his personal hero most likely had more to do with Eulers personality traits and empathetic teaching approach rather than his mathematical acumen. Truly a great teacher who had a lasting impact on my life.

    • @nokta7373
      @nokta7373 หลายเดือนก่อน +66

      Sometimes all it takes is one good teacher who loves and believes in their job to set you onto a path that really defines your life. Wish we had more of those. They are rare and the system doesn't really help finding them and keeping them around.

    • @blazedinfernape886
      @blazedinfernape886 หลายเดือนก่อน +26

      We don't a lot about Euler as he lived almost 300 years ago. But judging by what we know i am pretty sure he was one the greatest mathematician of all time not just because he produced a lot(and i mean a lottttttttt) of papers but because of his personality. He was probably a very nice man. Being friends with the bernoulli's who were seen as the bad guys certainly helped. He also played with his kids and grandkids and also did math with them!
      Euler is definitely one of my favorites!

    • @afterthesmash
      @afterthesmash หลายเดือนก่อน +7

      I never had that experience as a math student, because I never had a math teacher with enough ambition to attempt to teach me something I didn't grasp almost immediately.
      Yes, the hard working dullards were awarded the same grade as I was awarded, but mostly because I was constantly forced to sit there in first gear, basically twiddling my thumbs.
      Math is endlessly full of things I would have found very difficult on first encounter at that age. But none of these things were on the dullard curriculum, so I got to sit there and goof off with my own projects and be the bright student my teachers mostly ignored.

    • @emceeboogieboots1608
      @emceeboogieboots1608 หลายเดือนก่อน +3

      This makes me think that I need to thank my old science teacher in highschool in Esperance, Mr Boyland. Not that I amounted to a great deal, but his enthusiasm for teaching and seeing us learn was awesome. At 52, I still remember him as a great educator

    • @samwilliams369
      @samwilliams369 หลายเดือนก่อน +2

      Lovely sentiment but it’s a disjustice. U don’t doctor grade lie to students that struggle more than others. You tell them the truth and try to help in anyway possible. If they don’t get it they don’t get theyllshine elsewhere. But equalling grades for different qualities of work isn’t the way teach

  • @arpanpardeshi6189
    @arpanpardeshi6189 24 วันที่ผ่านมา +22

    It would be incomplete to say its "The theory of everything".
    this itself is actually "Everything"...? Like the universe's working. No theories, no hypothesis but rather just "is". This feels like the universe's own flow state of consciousness. Its just is!!!
    Thank you so much for this video.

    • @veritasium
      @veritasium  19 วันที่ผ่านมา +4

      Thank you, that's a great way of looking at it!

    • @Lecommandant_camroun
      @Lecommandant_camroun 5 วันที่ผ่านมา +1

      Space time is a continuum
      Jesus loves you!❤✝️Repent

  • @xxvimilia
    @xxvimilia หลายเดือนก่อน +5723

    I love these math videos because its so weirdly satisfying when you introduce another famous mathematician, and I'm like, "My man Euler was in this???". Its the same kind of excitement as the portal scene in Avengers endgame.

    • @skoogy7
      @skoogy7 หลายเดือนก่อน +769

      They say that theorems are named after the second mathematician who discovered them because the first was probably Euler.

    • @robspiess
      @robspiess หลายเดือนก่อน +265

      @@skoogy7 Euler's got his thumb up in everyone's business.

    • @threeuniquefingers
      @threeuniquefingers หลายเดือนก่อน +264

      @@robspiess Euler with his thumb and Newton with his nose poking in every flippin field in math and physics lol

    • @matercan5649
      @matercan5649 หลายเดือนก่อน +56

      fr, the same mathmeticians discovered everything

    • @kallewirsch2263
      @kallewirsch2263 หลายเดือนก่อน +202

      First guesses: If it wasn't Euler, then it was Gauss.

  • @raktimaryabiswas3182
    @raktimaryabiswas3182 หลายเดือนก่อน +4092

    Waiting eagerly for the next part.
    Please take the least possible time !

    • @krishnarajput3515
      @krishnarajput3515 หลายเดือนก่อน +541

      but ironically bring the maximum action

    • @yarodi
      @yarodi หลายเดือนก่อน +16

      😂

    • @nicezombie8054
      @nicezombie8054 หลายเดือนก่อน +21

      The maximum effort so the maximum work, doesn’t necessarily necessitate the most action, but actually… make it cause the most action

    • @drttgb4955
      @drttgb4955 หลายเดือนก่อน +6

      @@nicezombie8054 Government in the equation = less action.

    • @TravisTellsTruths
      @TravisTellsTruths หลายเดือนก่อน +1

      Bam ​@@krishnarajput3515

  • @McBobtheruggaman
    @McBobtheruggaman หลายเดือนก่อน +1330

    Mechanical engineer here:
    You took us on a winding journey and brought it all back to F = ma. Subbed for life.

    • @Guy-z6o
      @Guy-z6o หลายเดือนก่อน +15

      F= (far out...or fark all) etc.) we agree.

    • @evanmika905
      @evanmika905 หลายเดือนก่อน +12

      The long and winding road

    • @JEEtube-f5g
      @JEEtube-f5g หลายเดือนก่อน +8

      ​@@evanmika905 Definitely not the road with the least action.

    • @CitroenDS23
      @CitroenDS23 หลายเดือนก่อน +17

      There's a new rickroll in town. We've all been been FMAd.

    • @cellofellow5115
      @cellofellow5115 หลายเดือนก่อน +3

      This was my favorite part of my intermediate mechanics course, except in the opposite direction. My professor would take F=ma and somehow turn it into a 2 class multi-page problem that in no way resembles the principles it had built from.

  • @david_r_munson
    @david_r_munson หลายเดือนก่อน +36

    Really started going over my head in the second half, but that’s fine. I’m a photographer with an allergy to mathematics, but I know enough to appreciate the quality of communication happening here. Well done.

    • @graememorrison333
      @graememorrison333 9 วันที่ผ่านมา +4

      Keep at it! I have a bachelors in physics and had to keep going back and over the video to 'get' it. This is by far the best explanation of the Langrangian and (Least) Action I've encountered, and so wish we had resources like this when i was studying forty years ago.

  • @SalilShahane
    @SalilShahane หลายเดือนก่อน +2767

    15:34 the smile on Derek's face when he was compared to Euler made my day.

    • @akarshiaaryan5952
      @akarshiaaryan5952 หลายเดือนก่อน +20

      😂

    • @arskiz
      @arskiz หลายเดือนก่อน +21

      Euler angles

    • @realracing3specter295
      @realracing3specter295 หลายเดือนก่อน +2

      👌

    • @ludnix
      @ludnix หลายเดือนก่อน +36

      prof Strogatz was really channeling The Dude when he said that too!

    • @Utoxin
      @Utoxin หลายเดือนก่อน +81

      My jaw literally dropped. That's one of the highest complements I think I've ever heard.

  • @kevinboles3885
    @kevinboles3885 หลายเดือนก่อน +1208

    PLEASE, I BEG YOU - continue doing collaborations with Prof. Strogatz!! The combination of TWO of the greatest "explainers" of our time is producing absolutely compelling stories!!

    • @TheMoikero
      @TheMoikero หลายเดือนก่อน +9

      At university I have heard a lecture about non linear dynamics. Based on his book. It was the best lecture I have had

    • @Kyriancdb
      @Kyriancdb หลายเดือนก่อน +2

      I agree!

    • @cocoji3214
      @cocoji3214 หลายเดือนก่อน +2

      Totally agree with you

    • @RichyRich2607
      @RichyRich2607 หลายเดือนก่อน +2

      Nice try Prof. Strogatz..nice try.

    • @xiaoyu88
      @xiaoyu88 หลายเดือนก่อน +1

      Agree.

  • @ahwe173
    @ahwe173 หลายเดือนก่อน +1796

    veritasium changed my life, from almost quitting school to mechanical engineering

    • @AlanTheBeast100
      @AlanTheBeast100 หลายเดือนก่อน +6

      Then 2B2B should be your math guide (if it wasn't).

    • @Waiter1986
      @Waiter1986 หลายเดือนก่อน

      @@AlanTheBeast100 3b1b?

    • @gustavosantiago1543
      @gustavosantiago1543 หลายเดือนก่อน +71

      @@AlanTheBeast1002 bedrooms 2 bathrooms?

    • @discursively
      @discursively หลายเดือนก่อน

      @@gustavosantiago1543 @3blue1brown

    •  หลายเดือนก่อน

      jj

  • @stefankovacevic1344
    @stefankovacevic1344 หลายเดือนก่อน +8

    This singlehandedly made me understand all the math and physics I did at university by now, mind blowing.. Those little dots are exactly what I have been missing all this time!!! Only after i switched my major have I now realised what I truly seek, it's these moments of epiphany!!!

  • @harananand
    @harananand หลายเดือนก่อน +853

    As a Mechanical Engineer I certainly knew the principles of Lagrangian and the Eulerian. I also knew Newton and Bernoulli's story. It touched my heart to learn about Euler's kindness and Maupertuis contribution. I never knew that. The human element was the most special. Thank you for sharing.

    • @arunjangir5781
      @arunjangir5781 หลายเดือนก่อน +3

      Yes, me too bro. 😅 its like revision.

    • @lawrencerisley7231
      @lawrencerisley7231 หลายเดือนก่อน +20

      As a carpenter that watches math videos - knowing little about advanced equations - when I saw the outline of his profile it piqued my interest. I said to myself, "cool, he's back. There's something special about the E man." To discover he's also kind and generous, sorta made my day. Thanks Derek.

    • @Just_A_Dude
      @Just_A_Dude หลายเดือนก่อน +26

      Maupertuis is, I feel, a guy that saw Bernoulli's work and had an intuitive vibe, but wasn't quite able to put into words correctly. People like him are invaluable for the process of discovery and creation, but hardly ever get the recognition they deserve because they're not the ones that bring it home.

    • @dangerfly
      @dangerfly หลายเดือนก่อน +8

      @@Just_A_Dude People want to feel special by worshiping special individuals when advancements are always built on top of the previous shoulders. It's shoulders all the way down...

    • @user-gr5tx6rd4h
      @user-gr5tx6rd4h หลายเดือนก่อน +1

      I have read that Gauss (according to Niels Henrik Abel, 1802 - 1829, a very short life) did not have Euler's kindness of writing clearly understandably, but rather like a sly fox who uses his tail to remove his tracks.
      Gauss: ".... Thus it follows, obviously, that ...", and you need 8 hours (or perhaps 5 days) to see the "obvious"...

  • @SochWrld
    @SochWrld หลายเดือนก่อน +1706

    Watching this from Nigeria, and it's incredible how i can have access to this quality of information for basically free. I really love the internet sometimes.

    • @nemesiswes426
      @nemesiswes426 หลายเดือนก่อน +58

      It is something every person on the planet should have access too. It is the great knowledge equalizer. Allowing anyone from anywhere to learn anything.

    • @SochWrld
      @SochWrld หลายเดือนก่อน

      @@nemesiswes426 amen to that

    • @Gpacharlie
      @Gpacharlie หลายเดือนก่อน

      @@nemesiswes426Elon is working on that.

    • @iceteazen
      @iceteazen หลายเดือนก่อน +36

      we need this kind of content to dominate most of the internet.

    • @sozzled3053
      @sozzled3053 หลายเดือนก่อน +4

      The best thing about it… you can look up the different concepts brought up in this as well. It’s the perfect source for going down the “rabbit hole”.

  • @arthurcuesta6041
    @arthurcuesta6041 หลายเดือนก่อน +1355

    I just saw another brazilian watching this video on the supermarket while waiting for his Uber. It was a somewhat old dude with his daughter. You've become massive, man. Great to see it.

    • @dpatts
      @dpatts หลายเดือนก่อน +130

      Q: How many viewers does this video have?
      A: More than a brazilian

    • @ronaldderooij1774
      @ronaldderooij1774 หลายเดือนก่อน +2

      That was a fun father (NOT).

    • @joseivan2337
      @joseivan2337 หลายเดือนก่อน

      Two Brazilians! Guilty

    • @kawafernandes7025
      @kawafernandes7025 หลายเดือนก่อน +17

      Que legal!

    • @aboriani
      @aboriani หลายเดือนก่อน +48

      @@ronaldderooij1774 If you raise your kids to be dumb, then yes, but my 11 years old daughter and 6 years old boy LOVE watching this and other science channels with me...

  • @dannyrose42
    @dannyrose42 หลายเดือนก่อน +4

    I love how you mentioned the problem of "an intuitive way to think about action". In Ted Chaing's "The Story Of Your Life" (the one the movie Arrival is based off) they use the idea of "action" to show just how different the aliens are cognitively especially with respect to time. Specifically they describe how "action" is intuitive for them and instantaneous metrics like velocity and acceleration are considered abstract to them. Always loved that.

  • @st0rysphere
    @st0rysphere หลายเดือนก่อน +1148

    Veritasium has now surpassed the quality of netflix docementaries. Really one of the best videos on math i have ever seen. Well done Ve. Cant wait for part 2

    • @Neverforget71324
      @Neverforget71324 หลายเดือนก่อน +13

      Agree. A few years they did a reboot of "Cosmos" ... The production quality of these videos is at least as good as the Cosmos series.

    • @jmalmsten
      @jmalmsten หลายเดือนก่อน +11

      Netflix docus really have fallen lately. Moving more and more towards the formats of cable TV to desperately stretch out every single minute of content 3-6 times longer than necessary.

    • @jerrysoncallado8709
      @jerrysoncallado8709 หลายเดือนก่อน +7

      Im still waiting for the part 2 of their video about Thermite, and now Derek is making me wait for the part 2 of Action. They better release these sequels soon because im loving it

    • @Patterner
      @Patterner หลายเดือนก่อน +5

      too bad for netflix my first thought will always be "black Cleopatra"

    • @andrewandrus3296
      @andrewandrus3296 หลายเดือนก่อน +3

      Imo these have always been better

  • @DataIsBeautifulOfficial
    @DataIsBeautifulOfficial หลายเดือนก่อน +21607

    Physics is just old guys arguing over who invented the best shortcut.

    • @lulairenoroub3869
      @lulairenoroub3869 หลายเดือนก่อน +1239

      "The difference between science and screwing around is writing it down"
      -A guy Adam Savage was hanging around with. Then Adam Savage.

    • @JeffreyBenjaminWhite
      @JeffreyBenjaminWhite หลายเดือนก่อน +175

      fastest shortcut ;.)

    • @lazyphoton
      @lazyphoton หลายเดือนก่อน +261

      True, but that's also because nature takes the best shortcut too!

    • @XILikeTrainsX
      @XILikeTrainsX หลายเดือนก่อน +186

      So trackmania

    • @Truth4Lyf
      @Truth4Lyf หลายเดือนก่อน +59

      Math also uses this same principle

  • @Kampamba
    @Kampamba หลายเดือนก่อน +426

    I’m a practicing mechanical engineer of 6 years now. Nearly 30 years old. In 2014 I discovered Veritasium and Smarter Every Day when deciding what to study. I cannot explain how instrumental these videos have been to my life. Thank you so much Derek!! Humanity is better off because of you

    • @elementalist1513
      @elementalist1513 หลายเดือนก่อน +2

      Im in school for engineering, but we haven't talked about this topic at all. Would this principle apply to classes like Dynamics and make it easier for me😅

    • @offabender2719
      @offabender2719 หลายเดือนก่อน +2

      ​@@elementalist1513You do generally cover it, idk in how much depth, it depends on your course structure and discipline.
      But if you ever take an advanced dynamics subjects you'll encounter them especially for shafts and machines with linkage mechanisms. Although nowadays most of this stuff is taught in conjunction with computational methods not strictly rigours math (at least where i study eng).

    • @thegr8malachite370
      @thegr8malachite370 หลายเดือนก่อน +1

      2 of my favorite science channels! add tom scott to that and we're set 😊

    • @patinho5589
      @patinho5589 10 วันที่ผ่านมา

      It really helps give an overview and context to what is out there in these fields. I was the top of my class in maths, but I had no idea about what is out there overall..
      If I had done, I might have continued with maths. Being keen to at least catch up on what the likes of Euler figured out.

  • @tubester358
    @tubester358 หลายเดือนก่อน +5

    I really appreciate that you still keep the sponsor segments at the end of the video instead of randomly bringing it into the middle of the content like most TH-camrs nowadays, and it's a clearly separate segment. I'm totally fine with them that way.

  • @funnyname7773
    @funnyname7773 หลายเดือนก่อน +625

    As a first year physics student, these types of videos are incredibly valuable! I legitimately cannot explain how incredible it is to walk the line of simple explaination vs specificity and detail that you and your team walk perfectly. Thank you so much, it makes me so happy that there are science educators such as yourself following in Euler's footsteps, teaching with empathy, clarity, and clear passion!

    • @leviathan5207
      @leviathan5207 หลายเดือนก่อน +4

      The video is interesting for sure, but it is technically little more than a history lesson. I wager you would not be able to solve even the simplest of problems using the fucntion you probably just saw for the first time in your life, after watching this video. Calling him a teacher for giving you a history crash course on a single formula is a disservice to anyone who is actually teaching, I think.

    • @funnyname7773
      @funnyname7773 หลายเดือนก่อน

      @@leviathan5207 While I understand where you are coming from, I never meant to undermine or disparage classical teachers and educators with my praise of Veritasium. Rather, and this was unstated, so there would have been no reason to assume this, I meant to call attention to the benefit of having various avenues and angles to education.
      To be sure, I am pursuing physics first and foremost because I had a fantastic high school physics teacher who ignited my initial passion and you are most definitely right, I likely would not be able to solve most simple problems using the function without help. However, I do not think that the value that Derek and his team provides is that of immediate practical application of the mathematical concepts they cover. Rather, as stated by many other people much smarter than myself, by teaching the history and rationale behind these mathematical concepts, one can make sense of them outside of just calculus and algebra.
      Additionally, I am calling Veritasium a teacher because, over the past couple years, I have learned a lot from this channel. I think that classical teachers are incredibly valuable (and often undervalued by most people), but I do not think one has to teach in a school to be an educator.

    • @emm6064
      @emm6064 หลายเดือนก่อน +18

      @@leviathan5207 my father tried to teach me to drive stick without explaining the principles behind it ("just do what I say when I say it"). Fortunately, he was a fast-hand on the emergency brake and I got to autograph the the skidmarks in our driveway. 🙂 Mom took over after that and learning what was happening in the engine as I pressed pedals kept that from happening again. Knowing _why_ helped me learn about "how".
      Having a conceptual underpinning and an understanding of how a concept was _developed_ gives you a framework to attach all the specific mathematical details to; something that simply throwing the final equation at you wouldn't provide. Context matters.

    • @aitsfni
      @aitsfni หลายเดือนก่อน +16

      ​@@leviathan5207 I am also pursuing a physics degree. I'm in third year. While a large part of physics is, indeed, knowing how to solve formulae for solutions, simply knowing how to plug in numbers/manipulate an expression pales in importance compared to actually understanding the concept at hand. Where the equation comes from, what each term means, why certain cases yield certain solutions, etc.. Without this knowledge you are no longer doing physics, just math. Videos like this are invaluable when it comes to forming intuitive foundational understanding of these topics. Setting it all against the backdrop of the real history of the development of these concepts and ideas surely helps connect everything together. Also, Derek is Ph.D. in education research. I'd wager he knows more than most when it comes to education.

    • @funnyname7773
      @funnyname7773 หลายเดือนก่อน

      ​@@emm6064 Wow, what an eloquent way of putting it, thanks!

  • @vitofodera3615
    @vitofodera3615 หลายเดือนก่อน +388

    I'm a PhD physicist and I'm very grateful to you for this video. I'm amazed, I still have goosebumps. Best explanation I've ever seen. And all physicists and engineers know how difficult it is to understand this topic the first time during college, and you made it so easy. What an amazing trip it was!

    • @hyperduality2838
      @hyperduality2838 หลายเดือนก่อน +5

      Potential energy is dual to kinetic energy -- gravitational energy is dual.
      The Lagrangian is dual to the Hamiltonian synthesizes the principle of least action,
      The equations of motion (predictions) minimize the action in quantum mechanics.
      The Schrodinger representation is dual to the Heisenberg representation -- quantum mechanics is dual.
      Action is dual to reaction -- Sir Isaac Newton.
      "Aways two there are" -- Yoda.
      The equations of motion are predictions -- syntropic!
      Syntropy (prediction) is dual to increasing entropy -- the 4th law of thermodynamics!

    • @kilmer009
      @kilmer009 หลายเดือนก่อน +6

      As someone deeply interested in science but with zero qualifications, this video made my eyes water (from the mental torture). Every time I think I'm intelligent, I think of physicists and advanced mathematicians who not only understand this stuff but even improve upon it, and it brings me right back down to earth.

    • @saganandroid4175
      @saganandroid4175 หลายเดือนก่อน

      Now explain it to us.

    • @matthewboyd8689
      @matthewboyd8689 หลายเดือนก่อน

      I get the Einstein explanation (if you can't say it simply enough for a child to understand you don't know it well enough) but I'm glad there are people enjoying the parts after the 10% of the equation I can understand.
      Sometimes it reminds me of Ai and their increasing understanding of things most don't understand, and I watch math videos for fun so Ai scaring me says something when most people hate math.

    • @BristleHiffyn
      @BristleHiffyn หลายเดือนก่อน

      @@matthewboyd8689 lessons in the Bible are important.Numbers 25
      New International Version
      Moab Seduces Israel
      25 While Israel was staying in Shittim, the men began to indulge in sexual immorality with Moabite women, 2

  • @ctoid
    @ctoid หลายเดือนก่อน +7495

    It's truly an Eureka moment when all the things just came out to be F=ma

    • @happygood18
      @happygood18 หลายเดือนก่อน +375

      Yeah, my mind was blown. I did not expect that!

    • @steffenbendel6031
      @steffenbendel6031 หลายเดือนก่อน +156

      Actually, forces do not describe all of physics. They are mainly a helper in classical mechanics. But you can not describe interference effects with forces. And in Langrangian mechanics you do not have explicit forces.

    • @csgas0
      @csgas0 หลายเดือนก่อน

      @@steffenbendel6031🤓

    • @Unmannedair
      @Unmannedair หลายเดือนก่อน +104

      But it never does describe f=ma... That's just a very special case. F=dI/dt.... di/dt only equals ma for cases where mass is constant.

    • @liamweavers9291
      @liamweavers9291 หลายเดือนก่อน +44

      Would it not be more accurate to say force is a function of mass and acceleration?
      Newton's second law, F = ma, is traditionally seen as a static equation describing force as the product of mass and acceleration. However, life and complex systems are inherently dynamic, requiring a reinterpretation of this law as an interdependent relationship where force, mass, and acceleration are mutually dependent functions over time (defined as Einstein's Co-ordinate Time or the speed of light). Just as the electromagnetic field arises from the interactions of electrical and magnetic activities derived from matter and energy, Force dynamically interacts with mass and acceleration, creating a continuous feedback loop. External perturbations to a system's electromagnetic field influence its internal dynamics, and vice versa, through a process of field alignment at various levels. When matter and energy interact to produce information, or when information is applied to affect matter and energy, the resulting changes occur instantaneously across different field alignments. For example, information interactions at the matter and energy level generate electromagnetic interactions that, in turn, influence the information within the electromagnetic field itself. On a larger scale, the Earth's electromagnetic field interacts with that of the human body, affecting its internal dynamics and maintaining homeostasis-a state of equilibrium. This dynamic version of F = ma, measured continuously over a constant time frame, emphasizes the continuous, reciprocal relationships that sustain complex, living systems, illustrating how fundamental forces and properties are interconnected through time to maintain stability and balance.

  • @chaoticlue
    @chaoticlue 24 วันที่ผ่านมา +1

    I am an electronics engineer trying to switch to a career in Physics. For that, I need a fundamental understanding of basic Physics and while I was well equipped with the Physics involving Newton and others; Hamiltonian and Lagrangian mechanics is something that is only taught to Physics majors. The first time I saw the equations, I naturally thought, why would someone go such great lengths instead of just using F=ma. I got the answer to that and much more thanks to this video. Can't wait for Part-2!

  • @Lukav1
    @Lukav1 หลายเดือนก่อน +493

    This is such a great transition:
    Mapertui is bullied - depressing music playing
    Euler mentioned - Boss battle music starts playing 🔥🔥🔥

    • @LuisSierra42
      @LuisSierra42 หลายเดือนก่อน +5

      Epic fight ensues

    • @One.Zero.One101
      @One.Zero.One101 หลายเดือนก่อน +5

      It's like when the battle theme starts playing in Final Fantasy.

    • @Beeblebrox6868
      @Beeblebrox6868 หลายเดือนก่อน +6

      I like the idea of Euler as final boss - that works

    • @gidoskales5517
      @gidoskales5517 หลายเดือนก่อน

      😂😂

  • @fernandoizaurieta7270
    @fernandoizaurieta7270 หลายเดือนก่อน +541

    I'm a theoretical physicist, and I'm astonished by how precise and well-presented the video is. It reminded me of the wonder I felt as an undergraduate attending beautiful lectures on classical mechanics. Thank you for creating such wonderful material for everyone on TH-cam.

    • @asjordan0yt
      @asjordan0yt หลายเดือนก่อน +2

      Here, here.

    • @isodoubIet
      @isodoubIet หลายเดือนก่อน

      Shouldn't a theoretical physicist know that the central claim of the video is completely wrong?

    • @Dragrath1
      @Dragrath1 หลายเดือนก่อน +1

      @@isodoubIet If you have data to "prove" that the principal of least action is wrong then do so but until then this forms the principal foundation of not just all of classical mechanics but the Feynman path integral and quantum field theory i.e. the standard model of particle physics. The burden of proof always falls onto the claimant when the weight of all human progress and knowledge in physics is at the heart of the subject.

    • @isodoubIet
      @isodoubIet หลายเดือนก่อน +2

      @@Dragrath1 The principle of least (stationary) action is not wrong... _in classical physics._ It doesn't apply in quantum mechanics. In fact, quantum mechanics is what you use to prove exactly in which sort of situations the principle is a good _approximation._ The video goes so far as to state that quantum mechanics can be replaced by the least action principle, which is categorically nonsense.
      "but until then this forms the principal foundation of not just all of classical mechanics but the Feynman path integral and quantum field theory i.e. the standard model of particle physics"
      That is nonsense. Pop quiz! Explain in your own words how dimensional regularization is used to treat infinities arising from loop diagrams, why that doesn't present any conceptual problem for the theory, and why dimensional regularization is advantageous when compared with more simplistic schemes like cutoffs.

    • @Dragrath1
      @Dragrath1 หลายเดือนก่อน

      @@isodoubIet I thought you were trying to say the principal of least action was wrong, and yes the mechanical form of the action breaks down in quantum mechanics but the Feynman path integral shows quantum systems still follow the principal within probability or state space. I don't think you can really say that the Feynman path integral isn't part of the principal foundation of the standard model given that Feynman diagrams which are a computational tool for calculating these systems of possible interactions depend on this theoretical framework At this point though I think there is good evidence that this is a consequence of deeper more fundamental rules with Wolfram's computational emergent model of physics as a consequence of Turing complete computational constraints simultaneously iteratively acting on some informational system looks promising if they can come up with a solution for computing the continuous domain of dimensionalities which appear to be natural in that framework.

  • @DevRajyaguru-lx8pi
    @DevRajyaguru-lx8pi หลายเดือนก่อน +675

    A beautiful mix of history, physics, math, music, emotions and story telling. I am just blown away !
    I remember terry tau's quote at this point that, we should teach our children the history behind the things, how it came and how much effort went to bring it in the form it is today. If we don't appreciate history then there is no way we can appreciate it's true essence.
    Thank you Derek and the team for their amazing efforts in STEM.

    • @Neverforget71324
      @Neverforget71324 หลายเดือนก่อน +31

      100 percent agree. I was always frustrated in college because I felt I was never "catching on" quickly enough... only to find out years later that the knowledge we were taught in one semester took humanity hundreds of years to figure out.

    • @chattiezzz
      @chattiezzz หลายเดือนก่อน +5

      couldn't agree more!!

    • @kirkbotingress3690
      @kirkbotingress3690 หลายเดือนก่อน +9

      I hated history class because it seemed to be about learning these dates and names of dead people. Nowadays I love history because I can ignore exact dates and focus on the reasons and motivations of those people that came before me

    • @aseemlimbu7672
      @aseemlimbu7672 หลายเดือนก่อน +1

      @@kirkbotingress3690 Loved the way you put it.

    • @btf_flotsam478
      @btf_flotsam478 หลายเดือนก่อน

      It's worth noting that the history of a field is often more understood by those in its field than most historians. As a mathematics person, I have already heard of the Maupertuis, Voltaire and Frederick the Great drama from a biography of Leonard Euler, and have discussed the history of probability with professors while doing my honours thesis.

  • @ChanelCoco555
    @ChanelCoco555 24 วันที่ผ่านมา +5

    20:44 “the energy of different paths has to be the same”
    Is in direct contradiction with
    23:11 “while with Hamilton’s principle, the energies can differ, but the time has to be the same between paths”
    In deriving the equation you seem to make use of the energies between paths being the same, hence allowing you to drop out a term, however later on you suggest that the energy can vary across paths. Which one is it? If the former, doesn’t that mean that we’ve only shown that the least action principle applies only for situations when the energy across all possible paths is the same, which is pretty restrictive? And if the latter, how can you justify the delta E term dropping out in the derivation?

    • @lisarene1543
      @lisarene1543 20 วันที่ผ่านมา

      I was pondering exactly the same and imagined someone else might already have raised this contradiction in a comment so started scrolling down the comments. Has the question been answered?

    • @ChanelCoco555
      @ChanelCoco555 20 วันที่ผ่านมา

      @ I haven’t seen it answered no

  • @Fallkhar
    @Fallkhar หลายเดือนก่อน +664

    Euler truly was a legend. In his later years he unfortunately started going blind but would still continue to do maths by feel, writing it down, for a few more years.

    • @jbangz2023
      @jbangz2023 หลายเดือนก่อน +21

      And also very generous by giving merits to other discoverers.

    • @pizzainc.1465
      @pizzainc.1465 หลายเดือนก่อน +5

      Writing blind be like: 1̷̤̬̲͍̩̞͔̩̉+̴͉̼̜̹̼͑͛̌͛̂̓̐͌̍̀͝1̶̧̫̦̭͚̳̖̂̓̃̀͂̊͝͝=̴̡̦̖̖̟̜̠͚̦̪̦̣̳̎͊͜2̸̨̛̻͍̺̄̒̍͒̽̀̐̓̈́̚͘͝͝

    • @Blitterbug
      @Blitterbug 22 วันที่ผ่านมา +4

      ... he also took time out to make my favourite physics toy

    • @popop143
      @popop143 22 วันที่ผ่านมา +5

      Yeah, I know Isaac Newton might be the most famous one, but Euler arguably has the widest and most contributions in math and physics

    • @douglaswilkinson5700
      @douglaswilkinson5700 5 วันที่ผ่านมา

      @@popop143 And still there was a problem with Mercury's orbit around our Sun. Predicting it's precession correctly only became possible with Einstein's General Theory of Relativity.

  • @roodog1
    @roodog1 หลายเดือนก่อน +857

    I took a class called theoretical mechanics, where we learned most of this. What was explained to me over 10 weeks was described infinitely more beautiful in this 30 minute video. I’m tearing up just thinking about it. Your channel is absolutely incredible for bringing math and physics to the average person, and even making the people familiar with the material think about it in a new way. Thank you

    • @G36-999
      @G36-999 หลายเดือนก่อน +9

      damn literally same here

    • @backspace345
      @backspace345 หลายเดือนก่อน +10

      Last semester theoretical mechanics ended for me. I thought Lagrange's mechanics was just yet another way to describe moving things, except even more generalized and even more boring. I still do find it unintuitive, and i was genuinely hoping to see how this pops up somewhere else, but sadly we must wait for another video.

    • @Luicatus
      @Luicatus หลายเดือนก่อน +4

      ​@@backspace345
      Funny
      Lagrangian Mechanic saved me in my first Semester of theoretical physics. Could not get the hang out of classical Mechanik, but this gave me at once a tool set, i could appy.
      Esp. Double Pendulums (practical example: swinging bell)
      That and the Maxwell Equations are still the only parts of theoretical physics I like as a applied and Experimental physicist
      Even 20 year later and out of the scientific world

    • @gd1037
      @gd1037 หลายเดือนก่อน +12

      Personally, watching this 30 min video made me wish I had time to study the subject over a 10 week course. These videos are nice to learn about the history of physics, but if you don't study the math behind it you don't really understand any of it. You just accept an answer for the correct one.

    • @manuel0578
      @manuel0578 หลายเดือนก่อน +9

      No it doesn’t. You’re not going to be able to do any calculations yourself after watching this video.

  • @StarFury2
    @StarFury2 หลายเดือนก่อน +564

    16.5M subscribers, and still not afraid to show entire formula deriving process using calculus! Bravo!

    • @DanKaschel
      @DanKaschel หลายเดือนก่อน +49

      I wish he'd taken the time to impart a bit more intuition to those of us who haven't done calc in a long-ass time. But I'm certainly glad the rigor is there for those who can fully appreciate it.

    • @jackkerouac1523
      @jackkerouac1523 หลายเดือนก่อน +2

      Gay comment

    • @DanKaschel
      @DanKaschel หลายเดือนก่อน +26

      @@jackkerouac1523 oh noooo incel doesn't like the comment nooooo

    • @PMA65537
      @PMA65537 หลายเดือนก่อน

      partial calculus

    • @douglaswilkinson5700
      @douglaswilkinson5700 26 วันที่ผ่านมา

      However the formula is not quite correct. It must be adjusted when dealing with relativistic velocities such as cosmic rays that travel at almost c.

  • @tonytya
    @tonytya หลายเดือนก่อน +229

    I attended a university lecture which covered Multi DOF Dynamic Systems, the Euler-Lagrangian Equation, and Double Pendulums this morning as a Mechanical Engineering student. Was completely baffled and confused about the theory behind all of it. Coming home exhausted at the end of the day watching this piece of art just made me tear up. Such an amazing coincidence that this video was released today. The moment everything came to F=ma was such an Eureka moment too! Thank you Derek.

    • @kzeich
      @kzeich หลายเดือนก่อน +1

      It's beautiful

    • @tatsga
      @tatsga หลายเดือนก่อน +3

      I just had 8 weeks of my first course of mechatronics in technical university and this video was some what eye opening. I have been struggling with concepts of virtual work etc used in very hard and tidious matrice calculations used in equations of motion on multibody systems.

    • @whatTheblue
      @whatTheblue หลายเดือนก่อน +3

      Only if uni teachers were like this!!!

    • @cleon_teunissen
      @cleon_teunissen หลายเดือนก่อน +1

      As you mention: F=ma can be recovered from Hamiltion's stationary action. But then you go: hang on, mathematically that means that F=ma has already been in there all along. So: is it possible to go the other way round? Is it possible to *start with F=ma, and in all forward steps arrive at Hamilton's stationary action? Indeed that is possible. (It is common for mathematical relations to be valid in both directions.)
      The path from F=ma to Hamilton's stationary action has two stages:
      - Derivation of the work-energy theorem from F=ma
      - Demonstration that in cases where the work-energy theorem holds good Hamilton's stationary action will holds good also.
      My point is: it is possible to introduce Hamilton's stationary action in such a way that confusion is avoided.
      In case you are interested:
      The path from F=ma to Hamilton's stationary action is available on my website. A link to my website is available on my youtube profile page. (I can't give a direct link; comments with a link in them disappear, presumably due to false positive anti-spam.) On my website use the navigation column to go to the 'Hamilton's stationary action' article.
      For me finding the forward path (from F=ma to Hamilton's stationary action) was a Eureka moment.

  • @manuelapollo7988
    @manuelapollo7988 หลายเดือนก่อน +264

    Fun fact: in quantum physics, in the famous formula E = hv, h is dimensionally an action, in fact Planck himself used to call h elementary quantum of action. All of this is so beautiful, that one of the most important constant in physics is in fact action. And, in a way, h is THE LEAST action possible.

    • @lysenko_nikolay
      @lysenko_nikolay หลายเดือนก่อน +6

      comment for promoting the comment! Magical!

    • @mayankkmr77
      @mayankkmr77 หลายเดือนก่อน +3

      This is amazing. Makes me rethink and re-intuit myself on how the world works. Largely based my model of the world on laws of thermodynamics. Increases my understanding and reverence for Plank's Constant. Whooh!

    • @edd8914
      @edd8914 หลายเดือนก่อน +3

      Yep, the action is a quantum phase angle

    • @Lecommandant_camroun
      @Lecommandant_camroun 5 วันที่ผ่านมา

      Yup, h is in Joule-Seconds
      Jesus loves you!❤✝️Repent

  • @mariamabdallah-u5x
    @mariamabdallah-u5x หลายเดือนก่อน +16

    Your video deeply moved me, I have been wanting to go back to learning physics for a while now and your video reminded me of the sense of wonder I had in my freshman year. Thank you for creating something so special, I can’t wait for future videos like this one!

    • @veritasium
      @veritasium  19 วันที่ผ่านมา

      Thank you! That's amazing to hear, we have a part 2 to come in the near future so stick around for that!

  • @TheMarkEH
    @TheMarkEH หลายเดือนก่อน +1

    It's heartwarming to see that listening to clever people discuss mathematics/physics attracts 16M subscribers on TH-cam. Thank you for developing this channel which I, as a non-mathematician, find insightful, interesting and entertaining.

  • @blu_sevn
    @blu_sevn หลายเดือนก่อน +396

    As a physics student in the 3rd semester this is a brilliant video to watch...literally goosebumps all the time. It is so satisfying to see what u have learned being illustrated in such a way. Just WOW really

    • @ashleymorrissey101
      @ashleymorrissey101 หลายเดือนก่อน +7

      I've been out of my engineering school for over a decade, but this video brought me back to my youth, lol I don't remember how to do all this math anymore but I recognize it and I think of my friends that went into math and physics

    • @realracing3specter295
      @realracing3specter295 หลายเดือนก่อน +3

      i always get goosebumps when i read about all those mathematicians, as they always somehow related to/connected another great mathematician, which i had no idea belonged to his timeline... and also contributed to the theory 🤯🤯

    • @Pleasing_view
      @Pleasing_view หลายเดือนก่อน +1

      Have you done Mathematical Physics yet?

    • @blu_sevn
      @blu_sevn หลายเดือนก่อน +1

      @@Pleasing_view just theoretical physics

    • @acron7559
      @acron7559 หลายเดือนก่อน +5

      I am a computer science student, i have a special place for physics, even though I left it for 4 years. This video revives those good ol' days.

  • @ShikharMishra-ih5bb
    @ShikharMishra-ih5bb หลายเดือนก่อน +81

    I remember back in school when I was taught snell's law, I was absolutely not ready to accept it as it is, because I realised that its just an observation and not an explanation of why it is the way it is. So many many years later, you filled in a missing gap in my head that I had forgotten about. Very very grateful !!

    • @bangscutter
      @bangscutter หลายเดือนก่อน +5

      Basically for most of school, science is taught "this is just the way it is", because the proof is beyond the conceptual ability of the average kid. Even at tertiary level, most professors focus on teaching the content and not really go into the rigorous proof of why things are the way they are.

    • @bernhardtrian7471
      @bernhardtrian7471 29 วันที่ผ่านมา +1

      @@bangscutter because education isn't layed on that. Time is money. We only need a good foundation to later choose on our own life paths, wether you become an engineer, doctor, teacher, politican or millions of other things. This is the beauty of life. Its a sandbox in it self. As long as you are happy with yourself, don't harm others and cooperate in a way, even if you isolate yourself, you accomplished life fully. Even tho our society relies on reproductio, optimization and arguably beeing well with health till the end (till we have found out the formula to live on this planets/universe infinitely :) )

  • @gabberwhacky
    @gabberwhacky หลายเดือนก่อน +226

    24:44 I appreciate that you don't shun away from showing derivations. Makes it much more enjoyable for the average physicist

    • @madamred3793
      @madamred3793 หลายเดือนก่อน +18

      King of confusing for the laymen though😂. Imaging trying to understand this with highschool level understanding of math, I'm no genius in the subject so it was hard to say the least.

    • @madamred3793
      @madamred3793 หลายเดือนก่อน +3

      But he did a great job of explaining ngl

    • @gabberwhacky
      @gabberwhacky หลายเดือนก่อน +14

      @@madamred3793 I think that wasn't really the purpose. by showing a wall of equations for 5 sec, you don't expect anyone to read it except of sb who hits the pause button and goes through all of it slowly.

    • @Krazykahaan
      @Krazykahaan หลายเดือนก่อน +5

      ​@@madamred3793same man. I mean, ik basic differentiation and integration, some standard values, but the derivation for F = ma that he showed made me realise I should watch this a couple years later

    • @veritasium
      @veritasium  หลายเดือนก่อน +56

      We debated how to do this. We wanted to show all the math in case someone wanted to step through it, but we didn’t want to get bogged down in it and lose people so this was our compromise.

  • @MegaMathnerd
    @MegaMathnerd หลายเดือนก่อน +1

    Two thoughts: First, our daughter Cleo Abram recommended your channel, and it's outstanding! Optimizing an explanation is itself a problem to be solved. Occam's razor calls us to craft our explanations in a way that requires the fewest elements or assumptions -- a principle of least complexity. You are a master at finding that path through often highly complicated topics. Second, I hope the next video will take the principle of least action into quantum mechanics and Feynman's path integral.

  • @MasterReady12
    @MasterReady12 หลายเดือนก่อน +280

    Initially I was skeptical of the clickbaity title and the intro, but just after 3-4 minutes I was so *indulged* in it that I forgot to increase the video resolution to 1080p like I always do. Only later I realised that I watched 30 minutes of video that I was not going to watch.
    This is a testimony to how great this video is.

    • @Egan466
      @Egan466 หลายเดือนก่อน +5

      I have a plugin that auto set to highest quality all videos because TH-cam doesn't like anything above 1080p

    • @ElusiveEel
      @ElusiveEel หลายเดือนก่อน +3

      Same for me. I was going to watch this anyway because Veritasium always delivers, but I thought I'd put it to later and store the tab for a later day.
      But I saw a math equation, was intrigued and kept watching for a bit, then it was so interesting that pausing wasn't even on my mind.

    • @ryukiiprimer5383
      @ryukiiprimer5383 หลายเดือนก่อน +5

      You should watch Derek's video on clickbait and why his video's title and thumbnail seem clickbaity when you'll actually get what you see.

    • @HunsterMonter
      @HunsterMonter หลายเดือนก่อน

      It sound like clickbait, but it's true. Literally all of modern physics are derived from either lagrangian or hamiltonian mechanics, both of which are founded on the principle of stationary action

    • @cherriberri8373
      @cherriberri8373 หลายเดือนก่อน

      If only that skepticism lead you to look deeper. Or even, I don't know, at any citations given?
      Should be very telling if you're already *actually* skeptical and not just waiting to be lead into whatever plays next on the screen.
      Or keep learning info you can memorize and regurgitate irregardless of factual relavence, that's easier anyway.

  • @Beryllahawk
    @Beryllahawk หลายเดือนก่อน +117

    My son sent me to watch this. I'm already subscribed but so frequently when it's physics I get a bit wary, I'm very much not a maths person. You start throwing equations across the screen and my mind often just quits right there, lol. But this was fascinating. When he told me the name of the principle I blinked at him and said "You mean conservation of energy?" and he started hopping up and down going "NO! That's just the thing! Augh, go watch it Mom!"
    SO here I am! And I see what y'all are saying. Interesting to think about and I look forward to the next one!

    • @meghanto
      @meghanto หลายเดือนก่อน +3

      this is so nice to see! thank you for watching and sharing his enthusiasm!

    • @DJTubeFactory
      @DJTubeFactory หลายเดือนก่อน +1

      Welcome. The next video will be interesting.

  • @notenoughmonkeys
    @notenoughmonkeys หลายเดือนก่อน +447

    They should make a movie about this, Least Action Hero.

    • @vids7983
      @vids7983 หลายเดือนก่อน +6

      You talking about anime earth? Haha

    • @garybaldrick
      @garybaldrick หลายเดือนก่อน +14

      @@vids7983I think it’s either a reference to the movie Last Action Hero or the title of their sex tape.

    • @RolandoGarza
      @RolandoGarza หลายเดือนก่อน +1

      Would the villains stumble and hit their face on Least Action Hero's fists?

    • @Gogeta70
      @Gogeta70 หลายเดือนก่อน +5

      @@RolandoGarza Yep, their faces would find the quickest path to his fist, every time.

    • @-unclebuck-
      @-unclebuck- หลายเดือนก่อน +2

      @@vids7983 Last action hero is a movie.

  • @marko511d
    @marko511d 2 วันที่ผ่านมา +1

    This was the most interesting video I've watched in years. I'm just an average guy that worked in the lumber industry his whole life , but always had an interest in math. Thanks for this.

  • @pedrocasella1327
    @pedrocasella1327 หลายเดือนก่อน +352

    I just did an undergraduate research about Lagrangian in manifolds, and now I have to create a poster about it. Thank God. for this video right now!!

    • @PetraKann
      @PetraKann หลายเดือนก่อน +4

      So you were asleep in class for all those years?

    • @Gokuk-oq3uk
      @Gokuk-oq3uk หลายเดือนก่อน +7

      @@PetraKannwodent this video make his task easier

    • @roulzhq
      @roulzhq หลายเดือนก่อน +1

      Bozhe moi

    • @rasmusturkka480
      @rasmusturkka480 หลายเดือนก่อน

      @@PetraKann yes, studying is for nerds who don't know anything

    • @PetraKann
      @PetraKann หลายเดือนก่อน +1

      @@rasmusturkka480 listening and paying attention is not

  • @PrajwalDSouza
    @PrajwalDSouza หลายเดือนก่อน +303

    One thing missing? Connection to Noether's theorem.
    It is right there. Variation of momentum over space (Lagrange) vs variation of energy differential over time (Hamiltonian)
    21:50

    • @perorenchino2036
      @perorenchino2036 หลายเดือนก่อน

      Convert to hinduism

    • @hata6290
      @hata6290 หลายเดือนก่อน +22

      maybe next video

    • @toinfinityandbeyond2023
      @toinfinityandbeyond2023 หลายเดือนก่อน +18

      Hi Sir... I am Pranetha(remember from CFAL 2021 batch,druhan and pannaga's classmate in case you dont remember)....because of you I am still watching veritasium...currently in NITK final year ....hope you are doing great

    • @PrajwalDSouza
      @PrajwalDSouza หลายเดือนก่อน +3

      @@hata6290 yes. I realised that towards the end. Hope the video goes deep into this topic.
      Also, especially symmetries.

    • @PrajwalDSouza
      @PrajwalDSouza หลายเดือนก่อน +6

      @@toinfinityandbeyond2023 Hey Pranetha. :)
      Ofcourse I remember. :)

  • @niccolozanotti
    @niccolozanotti หลายเดือนก่อน +97

    Physics graduate here. You brought back a lot of good memories from my analytical mechanics course. I wasn't really able to appreciate the beauty of the principle besides its mathematical elegance. What you (and Strogatz) are doing with these videos is truly a gift to humanity. Thanks

  • @timepass4783
    @timepass4783 11 วันที่ผ่านมา

    Having learnt Lagrangian and Hamiltonian Mechanics just recently as a Physics major makes me appreciate this even more! its crazy how you could sum up my whole semester's worth of content into 30 minutes..

  • @priyobayuramadhan1284
    @priyobayuramadhan1284 หลายเดือนก่อน +380

    28:32 I remember when I was doing highschool physics olympiad, we treat Lagrange equations as some short of legendary weapon to handle meticulous oscillation problem 😂, because it is so hard to get the equation correctly using newtonian method. But we never knew why does it work and where does it came from. My mind has been blown 🤯.

    • @J.E.E.DESTROYER
      @J.E.E.DESTROYER หลายเดือนก่อน +2

      Very cool 😎😎

    • @fredericharmand
      @fredericharmand หลายเดือนก่อน +18

      It is easy to understand why this works. In the Langrange formula, the potential V is the cause and the energy of motion, the kinetic energy T, is the effect. The difference between the two must be zero all along the integration path, otherwise it means that we have missed either a cause or an effect, or both. Basically, the philosophy is that for every cause there is at least an identified effect.
      It is like the Newton law F is the cause and the acceleration is the effect, both are equal.
      The problem is that the Lagrangian assumes instantaneous transmission of causality, which is why it does not work in relativity. In Relativity the causality takes its share.

    • @Player_is_I
      @Player_is_I หลายเดือนก่อน +1

      Lol, now it is when it makes sense right

    • @sanidhyapratapsingh-h7d
      @sanidhyapratapsingh-h7d หลายเดือนก่อน +2

      @@fredericharmand what does "instantaneous transmission of causality" mean, and what's different in relativity when this doesn't work.

    • @fredericharmand
      @fredericharmand หลายเดือนก่อน +2

      @@sanidhyapratapsingh-h7d "Instantaneous transmission of causality" means that there is no delay between a cause and the corresponding effect on a body. This is not the case in relativity.

  • @jamesmiller1770
    @jamesmiller1770 หลายเดือนก่อน +225

    Not one single channel on TH-cam can give you such detailed, contextualized and informative, yet so easy to follow and beautifully arranged video on what would seem to be just another part of curriculum you would go through in school or university. This makes me want to learn more about this topic, physics and everything in general which means this channel has achieved the true meaning of teaching. Inspiration and imagination. Kudos!

    • @DanKaschel
      @DanKaschel หลายเดือนก่อน +8

      3B1B. And that channel knows its audience better, imo.
      This was a cool video though.

    • @the_spicy_orange
      @the_spicy_orange หลายเดือนก่อน +1

      @@DanKaschel 😂 That's who I was gonna say.

    • @nephi246
      @nephi246 หลายเดือนก่อน +2

      Kursgesagt is amazing like that too

    • @mugnuz
      @mugnuz หลายเดือนก่อน +1

      @@nephi246 kurZ*

    • @nephi246
      @nephi246 หลายเดือนก่อน

      @@mugnuz Kurzgesagt*

  • @aseemlimbu7672
    @aseemlimbu7672 หลายเดือนก่อน +109

    The most beautiful thing about Science and Mathematics is you can just say "I don't know" for the thing which you really don't know and it doesn't impact your stature.

    • @JoshuaNorton
      @JoshuaNorton หลายเดือนก่อน +6

      Ah, no. That's actually really far down the line. From my experience in university, the freshmen do like to play out the historic tropes of quarreling scientists fighting for each shred of credit. There are a lot of loner types entering maths and physics who are on a mission to show that they are the smartest.
      The way I experienced it, the physics course is deliberately structured to socialize such types of students towards a team spirit.

    • @user-gr5tx6rd4h
      @user-gr5tx6rd4h หลายเดือนก่อน +3

      @@JoshuaNorton That must be AMERICAN students, I guess!

    • @DanKaschel
      @DanKaschel หลายเดือนก่อน

      ​@@user-gr5tx6rd4hmy friend, you have much to learn of human nature

    • @MyNameIsSalo
      @MyNameIsSalo หลายเดือนก่อน +1

      @@JoshuaNorton I studied physics in Australia and didn't get any of that. No one really cared how smart you were or how well you did, people just wanted to get through the day and hit up the bars. Also like half of the students were asians that only spoke broken english and kept to their own social groups, and that is half of an already very small class because not many people take physics. The asians were always good to get answers from if you can communicate with them though, much smarter than us and none of us even cared or tried to compete. We just wanted to pass

    • @neileyre6019
      @neileyre6019 หลายเดือนก่อน

      If only more people said “I don’t know” rather than trying to come up with something that sounds like they do know, but only waffling and sounding like they are stupid, the world would be a better place and it would save a whole lot of time. There is absolutely nothing wrong with saying “I don’t know”

  • @memerofblaviken6326
    @memerofblaviken6326 21 วันที่ผ่านมา

    Hot damn, this was absolutely amazing. It was like watching a movie! I don’t think I’ve ever seen physics presented in this way. The music, the visuals, the editing, the voiceover, it’s all just the right mix of dramatic, entertaining and informative. Hearing about the big names dropped in the story (like Euler) legit made me feel like I was watching one of those MCU movies where a recognizable character comes back to save the day. And the way it all connects, and knowing that it’s not just a story and that the nature of our world connects this beautifully, all of it is just… Damn!

  • @ALJCpalaeozoic
    @ALJCpalaeozoic หลายเดือนก่อน +50

    I studied this as a third year physics undergraduate and you've really captured how at first it seems like pointless pushing algebra around until suddenly a profound revelation hits you. Our mind-blowing moment was the professor going on to show how you could picture every possible path between two end points as waves with neighbouring paths destructively interfering everywhere apart from along the true path where dS = 0, where the paths would be in phase. All of a sudden a ball moving under Newtonian motion looked a lot like a quantum mechanics. Eagerly waiting to see where this goes in the next video!

    • @solconcordia4315
      @solconcordia4315 หลายเดือนก่อน

      Maybe it should be dS = h instead of dS = 0.
      Euler might have made the initial error which led to the disagreement between quantum theory and relativity.
      The two may very well be in the analogous positions as the Rayleigh-Jeans and Wiens law formulas in the Blackbody radiation spectrum distribution plot. Both are accurate within the domain of applications but cannot bridge the gap. General relativity uses space-time continuum but quantum theory uses discretum of eigenvalues. Maybe space-time continuum of general relativity is incorrect but quantum theory's discretum of quantum states in the energy-momentum discretum is correct.

  • @skindalal1189
    @skindalal1189 หลายเดือนก่อน +4656

    This Comment is for Maupertuis.

    • @FScott-m1n
      @FScott-m1n หลายเดือนก่อน +220

      _pours one out for Maup_

    • @lordbunbury
      @lordbunbury หลายเดือนก่อน +96

      I did it all for the Maupie

    • @kilgorezer
      @kilgorezer หลายเดือนก่อน +3

      hi

    • @mattmccallum2007
      @mattmccallum2007 หลายเดือนก่อน +45

      If you say his full name in a dark room four times fast…… you giggle

    • @henrikebbesen1838
      @henrikebbesen1838 หลายเดือนก่อน +67

      The unit [kg*m**2/sec] of m*v*s ought to be called a Maupertuis, 1 Ma.

  • @kilimanjarocruz660
    @kilimanjarocruz660 หลายเดือนก่อน +32

    For me, one of the best introductions (albeit a bit old-fashioned at times) to the principle of least action is Landau and Lifshitz's volume on Mechanics. They also properly give Mapertuis his share of the credit. Also interestingly, they go on to explore how the equations change when you relax the constraints a bit (for instance, by not fixing the final point) and what this teaches us and how to use it. Simply marvelous.

    • @richardchapman1592
      @richardchapman1592 หลายเดือนก่อน

      Not specifying the endpoint is an interesting concept. It must allow ranges of answer that likely produce probability distributions. Odd way to get towards wave functions and their quantisations.

  • @anakinlapierre-tate4127
    @anakinlapierre-tate4127 หลายเดือนก่อน +1

    I got chills when it became F=ma . One always had a big interest in physics but never finished my highschool diploma and couldn't continue pursuing physics. In high school classes we never went over action so this was one of my favourite videos you've ever released. Learned lots in this one thank you.

  • @ethanboulter2883
    @ethanboulter2883 หลายเดือนก่อน +44

    Please never stop making videos! You and your team make some of the best science communication content out there. Veritasium provides the education that public schools fail to do.

  • @matercan5649
    @matercan5649 หลายเดือนก่อน +287

    The animation in these videos keep getting better and better, I love it.

    • @nclsb142
      @nclsb142 หลายเดือนก่อน

      Yeah It's a great addition to the content 😊

    • @theairaccumulator7144
      @theairaccumulator7144 หลายเดือนก่อน +1

      Am I tripping? It feels like I've seen this exact video before. Years and years ago on 3B1B. Did they just recycle the whole script and animations?

    • @cherriberri8373
      @cherriberri8373 หลายเดือนก่อน

      Yes, just let that production value keep convincing you to never be skeptical of watching these videos.

  • @marvelwizalamu598
    @marvelwizalamu598 หลายเดือนก่อน +115

    Words cannot fully express how much this channel has transformed my perspective on learning. There are times when I feel completely lost with the concepts he talks about, yet instead of feeling intimidated, I’m inspired to watch the video multiple times and seek additional sources to deepen my understanding. The passion and effort he puts in helping people understand makes me not feel like I'm too dump to understand such complex concepts; instead, it sparks curiosity and a genuine hunger to extend my knowledge.
    I really appreciate you team Veritasium

    • @mikec.8604
      @mikec.8604 หลายเดือนก่อน +5

      same for me !

    • @mikeyb7263
      @mikeyb7263 หลายเดือนก่อน +3

      The twinkle in Einstein's eyes was no accident.

  • @AryanVerma-ql3js
    @AryanVerma-ql3js หลายเดือนก่อน

    I swear I felt goosebumps when the equation of least action turned out to be equivalent to Newton's Second Law. And when you said that the man who vehemently defended Maupertuis was... Euler! And then Lagrange came in and I was ready to shout in excitement. Seriously, this way of explaining is so superior to how we're actually taught that it's not even laughable. Now I'll be eagerly waiting for the next part of this video. I LOVE it when completely different phenomena turn out to have the same principle behind them which no one could've guessed; yet someone did.

  • @kagazuki
    @kagazuki หลายเดือนก่อน +533

    I'm watching this pretending I understand it.

    • @j.antonioespinoza5485
      @j.antonioespinoza5485 หลายเดือนก่อน +5

      Ah, you are a self determined learner. Nice 👍

    • @FloopyNupers
      @FloopyNupers หลายเดือนก่อน +2

      Do better

    • @MrSindala
      @MrSindala หลายเดือนก่อน +18

      I faced reality at 17:37 and quit.

    • @rdkhatch
      @rdkhatch 29 วันที่ผ่านมา +7

      Over my head for sure

    • @Cvfdsx
      @Cvfdsx 21 วันที่ผ่านมา +3

      😂 I'm right behind you😂

  • @AffectiveApe
    @AffectiveApe หลายเดือนก่อน +31

    This was so stellar! Extremely well presented! These history of physics problems are so important, because we usually take them for granted and want to focus on the fanciest new findings, but there is such beauty in these more foundational findings! Also, Steven Strogatz is a class act and a treasure of a science communicator. Bravo!

  • @wissamkadamani
    @wissamkadamani หลายเดือนก่อน +7

    I really love it when I watch a veritasium video, because one of 2 things happen:
    1) The content is completely new to me extremely exciting to learn
    2) I already know most of what's about to be said and I'm pausing and predicting what Derek will say next. It gives me a new perspective with some wholesome details, and a nice ego boost.
    This was one of the latter, and it's an absolute masterpiece of production value.
    FLAWLESS

  • @SaadKhan-yd7ss
    @SaadKhan-yd7ss หลายเดือนก่อน

    I feel like paying at least a course fee of around $3,000 of a Mechanic course just to watch this video. The amount of effort made to edit and make it viewer-friendly is simply amazing. Good Job guys!

  • @benjamincraig7198
    @benjamincraig7198 หลายเดือนก่อน +60

    This video made me pick my Feynman lecture series book back out. The mathematics of all this is calculus of variations. I taught myself this once, and it was one of the most profound insights I’ve ever had mathematically. Thanks Derek, you are truly this days Feynman in terms of making complex concepts approachable and fun!

    • @דודקופלוביץ
      @דודקופלוביץ หลายเดือนก่อน +5

      Expect Feinmann to make an appearance in the sequel video.

    • @ivanjelenic5627
      @ivanjelenic5627 หลายเดือนก่อน

      As the previous comment to your comment said, you wouldn't want to miss the next video then.

    • @wag-on
      @wag-on หลายเดือนก่อน

      Definitely a path integral on its way.

    • @THEMathHacker-121
      @THEMathHacker-121 หลายเดือนก่อน

      Definitely getting QED vibes here

  • @deanjericevic8912
    @deanjericevic8912 หลายเดือนก่อน +28

    Teaching school physics for over 30 years I love how you have embellished the maths & physics with the history of those men who contributed to the theory’s development. A coruscating delivery; your presentation makes it so interesting that there would be so many more physicist & mathematicians by teaching that way.
    These optimisation problems solutions are found in the "Calculus of variations". Like a chain hangs freely its shape is derived as a hyperbolic cosine curve or a hole drilled through the earth from one side to the other & a ball dropped through it to minimize time is a cycloid. The shortest distance between 2 point! Yes, one of the simplest problems takes such complex maths technique to solve it!

  • @AdithiaKusno
    @AdithiaKusno หลายเดือนก่อน +123

    When Veritasium summarized Physics Grad first semester in half hour! Impressive work, you literally summarized the first semester of Physics Grad lecture series in one video. As Richard Feynman said great teacher knows how to communicate complex subjects in the least amount of action. Impressive! Even second semester on Thermodynamics, third semester on Electromagnetism, and fourth semester on QED would be extra episodes on least action principle topics. I am guessing eventually Veritasium might show how the least action principle works on Einstein's General Relativity. It's TH-cam channel like this that helps me explaining Physics to my kids. Thank you Veritasium.

    • @cherriberri8373
      @cherriberri8373 หลายเดือนก่อน +1

      Your first sentence should be a giant red flag to you.
      If you are capable of critical thought, so much info being compressed into 30 minutes should be a red flag that the info is at minimum, incomplete.

  • @ecoscinat
    @ecoscinat 9 วันที่ผ่านมา

    This video is extraordinarily elegant. A marvellous fusion of history, mathematics and physics, all narrated without skimping on technical details but maintaining an engaging tone for all. A wonderful lesson in how well this type of science communication can be done. Huge congratulations to all.

  • @muhammadsheheryaarghayas2968
    @muhammadsheheryaarghayas2968 หลายเดือนก่อน +14

    This has to be the best and most expansive crossover ever. Spanning over centuries of eras, involving almost every major mathematician, uniting various branches of maths to solve multiple problems over many fields, creating a unique new unit which sparks innovation for an entirely new and uncharted area of physics. BRILLIANT! I was legit fanboying over the entry of every mathematician and the reveal at the end equating to Newton's Second Law of Motion had me actually pause the video to really scream and grasp the mind blowing connection. Amazing work by Derek and the amazing Veritasium team. As always, awesome work and thank you for this masterpiece.

  • @bernard0camp0s
    @bernard0camp0s หลายเดือนก่อน +37

    Man, seeing what all these geniuses were up to way back when, sometimes in their spare time, is truly humbling.

    • @ultraokletsgo
      @ultraokletsgo หลายเดือนก่อน +1

      My understanding is they were fighting off bears a lot of the time.

  • @SnackPack913
    @SnackPack913 หลายเดือนก่อน +35

    I remember this blowing my mind when we learned about it as a physics undergrad. These days I forgot most of this but had always thought if it as “lagrangian mechanics” since it used the lagrangian. But now I distinctly remember a chapter on Hamiltonian mechanics. Man I miss those days where ever single lecture just completely blew your mind. I suffered through learning math just so that I could have the tools to learn more physics

  • @Lotschi
    @Lotschi หลายเดือนก่อน

    How is it possible to obtain more understanding while having breakfast than during a 90 minutes lecture.
    You put so much effort in transmitting the topics in an understandable way. I really appreciate that.

  • @oberlurch-handimations8628
    @oberlurch-handimations8628 หลายเดือนก่อน +178

    The thing I love the most about science is that it's like a cooperative undertaking spanning thousands of years

    • @iPlayDotaReligiously
      @iPlayDotaReligiously หลายเดือนก่อน +3

      Agree

    • @Argoon1981
      @Argoon1981 หลายเดือนก่อน +26

      Indeed, even Newton said "If I have seen further than others, it is by standing upon the shoulders of giants.", so no important mathematician, physicist or scientist (or natural philosopher, how they used to be called) has single handily invented or discovered anything from scratch, all discoveries in physics has been a human group effort.

    • @aldrinmilespartosa1578
      @aldrinmilespartosa1578 หลายเดือนก่อน +3

      @@Argoon1981 man, imagine these poeple who are separate in time in the same room.

    • @samagraarohan2513
      @samagraarohan2513 หลายเดือนก่อน +3

      cooperative for only as long as no one brings up a challenge to the views

    • @donmacquarrie9161
      @donmacquarrie9161 หลายเดือนก่อน +4

      Giants standing on the shoulders of Giants....

  • @prithvibharadwajmellacheru1121
    @prithvibharadwajmellacheru1121 หลายเดือนก่อน +16

    I've experienced bliss by the end of the video. Feels like it filled a small void in me that was present from the time I started using the Lagrangian formulation at school, as I was busy on the practical applications but never really took time to explore the reasoning.
    Thank you Veritasium

  • @Zibonnn
    @Zibonnn หลายเดือนก่อน +11

    Veritasium's most impactful aspect is Derek and his team's storytelling and visual presentation. I'm not a math person, and I never have been, but you still keep me watching your videos from start to finish! If I had a math teacher who could explain like this, I’d probably be good at math.

  • @cratesurprise1259
    @cratesurprise1259 8 วันที่ผ่านมา +1

    Dear Derek, you are truly a legend and I recommend your channel to all the students I encounter.

  • @TheThoughtfulInsight
    @TheThoughtfulInsight หลายเดือนก่อน +9

    When I studied these topics during my college major, they didn’t impact me the way they do now. I’m just flabbergasted at how simply you explained such a complex problem in modern mechanics-it blew my mind!

  • @Miftahul_786
    @Miftahul_786 หลายเดือนก่อน +103

    25:53 I can’t lie.. I may or may not have gotten goosebumps

    • @plwadodveeefdv
      @plwadodveeefdv หลายเดือนก่อน +5

      dam right when there's an emotional crescendo in the music? that's crazy

    • @marwanfakhradin2543
      @marwanfakhradin2543 หลายเดือนก่อน

      I certainly did

    • @PinkeySuavo
      @PinkeySuavo หลายเดือนก่อน

      To be honest I wasn't shocked. I won't ever call myself to be smart, but I looked at this this way: if we initially use some formulas, isn't it normal that we can manipulate it to the already known equations? The "m*a" already popped out in integral, just "a" was written in terms of second derivative of displacement.
      I just think it's kind of rewriting the same thing in different terms. If you take a look at 24:45, they started with (1/2)*mV^2. It is already strictly connected to F=ma.

    • @Miftahul_786
      @Miftahul_786 หลายเดือนก่อน +1

      @ Yeah yeah I get that it’s just beautiful to see it in its final form and with the crescendo of the music it was just 🤌🏼

  • @HeisenbergFam
    @HeisenbergFam หลายเดือนก่อน +572

    You know its deadly serious when Veritasium says "we are approaching spooky teritory"

    • @0Senzuu
      @0Senzuu หลายเดือนก่อน +2

      😂😂😂

    • @DrDeuteron
      @DrDeuteron หลายเดือนก่อน +8

      "spooky" is such a loaded term in physics.

    • @giovanni_vaz_cardoso
      @giovanni_vaz_cardoso หลายเดือนก่อน +2

      ​@@DrDeuteronEinstein effect.

    • @dVTHoR
      @dVTHoR หลายเดือนก่อน +4

      I think this was a meant to be a really funny double meaning line, since in real life we are very close and approaching Halloween. If not, that is a hilarious coincidence.

    • @naejelangelogonzales6623
      @naejelangelogonzales6623 หลายเดือนก่อน

      Ghosts are explained by physics from this video right now😊

  • @huzaifahundercover
    @huzaifahundercover 27 วันที่ผ่านมา

    As a Mechanical engineer this sas enlightening. Honestly for the first time I understand Lagrangian mechanics. I mean I understood the need of it from a total utility point of view. But I never understood how and why it worked in contrast to you analyzing mechanics problems via forces. Amazing stuff.

  • @arktic3140
    @arktic3140 หลายเดือนก่อน +13

    The principle of least action genuinely is one of the most underrated theories when it comes to explaining general relativity. Thank you so much for exposing more people to this theoretical masterpiece ^^

  • @troik
    @troik หลายเดือนก่อน +38

    I started watching Veritasium 13 years ago about a Slinky dropping and we're now here with pretty complex formulas (for me), I feel like Derek is giving us a STEM degree without us even noticing. I learned so much in these 13 years. Thank you.

    • @cherriberri8373
      @cherriberri8373 หลายเดือนก่อน

      You need to stop implicitly trusting people simply because they appear to know what they're talking about and have a higher production value.
      Veritasium does not make very trustworthy claims.

    • @philipingram1563
      @philipingram1563 หลายเดือนก่อน +1

      Such a mental journey, awe inspiring...

    • @dog4me
      @dog4me หลายเดือนก่อน

      @@cherriberri8373what is bro smoking?

    • @DootyDuck
      @DootyDuck หลายเดือนก่อน

      @@cherriberri8373 im not saying you are wrong with the advice about not trusting people just because they appear trustworthy, but could you give me an example of Veritasium making untrustworthy claims?

    • @Tjeran
      @Tjeran หลายเดือนก่อน +1

      ​@@cherriberri8373what claims specifically is it you don't find trustworthy? Everything Derek presented here is either historical facts where you can look up the sources on every single person, or pure physics.
      The few times Derek has made bold claims without all the facts laid out, there has been an outcries from physicists in the comments. The fact that the comments are full of praise is because all the physicists watching recognize all the facts and are blown away by the genius way of presenting it.
      I dare you to point out a single factual error in this video.

  • @MrAnshulji
    @MrAnshulji หลายเดือนก่อน +164

    Gripping screenplay ✔
    Cinematic background score and camera angles ✔
    Cameos by renowned (but dead) mathematicians ✔
    Three-act structure, with the introduction of Euler's character placed perfectly at the mid-point of the video ✔
    Spooky Halloween theme for the season ✔
    Post-credit scene hinting at a sequel ✔
    Forget blockbuster Hollywoood flicks, instead this video should be released in theatres and sent in film festivals!!

    • @thehardistdifficulty1050
      @thehardistdifficulty1050 หลายเดือนก่อน +5

      We need more like you good person ❤🎉 math and science are everything ❤️ 💖

    • @LynxUrbain
      @LynxUrbain หลายเดือนก่อน +4

      And what a cliffhanger at the end !

  • @DocScoot
    @DocScoot 16 วันที่ผ่านมา

    Thanks for this video! I took a nonlinear dynamics course with Prof. Strogatz about 20 years ago, seems like he hasn’t aged a day, so fun to hear from this amazing teacher again!

  • @natetrice8194
    @natetrice8194 หลายเดือนก่อน +79

    Literally did the cycloid problem in my intermediate mechanics class yesterday. The timing is crazy!!

    • @paulbizard3493
      @paulbizard3493 หลายเดือนก่อน +5

      ... They are among us ...

    • @adnan7698
      @adnan7698 หลายเดือนก่อน +9

      You mean the timing is optimal?

    • @aqibramzan9742
      @aqibramzan9742 หลายเดือนก่อน

      Me too

    • @Flesh_Wizard
      @Flesh_Wizard หลายเดือนก่อน

      ​@@paulbizard3493amogus

  • @lidellaleice7571
    @lidellaleice7571 หลายเดือนก่อน +8

    As a person with a BS in physics, this video healed something in me. Beautifully explained. Loved it!

  • @jamescutler428
    @jamescutler428 หลายเดือนก่อน +48

    Ok. THIS might be the best veritasium video I’ve ever seen.
    THANK YOU 🙏
    This is probably the coolest thing I’ve ever learned about physics. I had no idea what a Lagrangian was before this! The explanation was phenomenal. You deserve an award. Including for the background music and the cliffhanger.
    Again, THANK YOU THANK YOU THANK YOU

    • @RichyRich2607
      @RichyRich2607 หลายเดือนก่อน +2

      I've seen better

    • @qzawxs
      @qzawxs หลายเดือนก่อน

      ​@@RichyRich2607that's what she said.

  • @mike200017
    @mike200017 หลายเดือนก่อน +1

    Back in the day, as a Mechanical Engineering intern, I had to figure out the dynamics equations for a rather oddly shaped air-gap machine (aka an electromagnet moving a piece of iron to activate a mechanism). This was for me the first (and only) time that starting from Hamilton's Principle was the most effective way to solve the problem. When I handed my solution to a rather old physicist who worked in that R&D department, he nearly fell out of his chair, filled with joy at seeing an OG mathematical solution from first principles being used in such a practical application. That said, 99% of the time, the Lagrangian method is the way to go (outside undergraduate courses, I don't think I've ever used the "Newtonian" way, with free-body diagrams and figuring out the forces at play).

  • @akhasshativeritsol1950
    @akhasshativeritsol1950 หลายเดือนก่อน +12

    I love Strogatz! I was fortunate enough to take his class on nonlinear dynamics and chaos, it was the most interesting class I'll pretty much never use!

  • @jd2757
    @jd2757 หลายเดือนก่อน +7

    Reminds me of one particularly interesting physics lecture in which my professor started with Heisenberg's Uncertainty Principles, which were reasonably easy to imagine, and performed the derivation to produce E=MC^2. The professor's intention, revealed at the last moment, made me wish I could see it all again. In light of my rather low-grade mathematical talents, I remain immensely grateful for your catalog of scientific delights... available to me on repeat... and to many others as an inspiration to remain ever hungry and thirsty for such knowledge. Your channel is a blessing and a gift. 🙏

    • @mismis3153
      @mismis3153 หลายเดือนก่อน

      Do you still have that derivation ?

  • @erthane
    @erthane หลายเดือนก่อน +45

    god these are my favourite types of veritasium videos (e.g the video about the invention of imaginary numbers and the video talking about black holes) where they explain maths/physics but also fuse lore and story into it, so immersive and entertaining, keep it up! :-)

    • @walaraubo
      @walaraubo หลายเดือนก่อน +6

      Sometimes I come back and rewatch those. I’ve probably seens the Gödel/Hilbert video 10 times

  • @danielwagner1280
    @danielwagner1280 23 วันที่ผ่านมา

    The principle of least action is presented in a much more cohesive way than at university. You immediately understand the actual physics behind the theory, how it was invented and why it is useful, all without any confusion or unnecessary digressions.
    Thank you very much!

  • @johnchessant3012
    @johnchessant3012 หลายเดือนก่อน +94

    14:01 Euler!!

    • @Weeksmistro
      @Weeksmistro หลายเดือนก่อน +12

      Euler came in and said: “On your left.”

    • @ngcool4112
      @ngcool4112 หลายเดือนก่อน

      Oiler

    • @somethingforsenro
      @somethingforsenro หลายเดือนก่อน +2

      when euler's on your side, you know you're right. god damn

    • @Nuss-j4s
      @Nuss-j4s หลายเดือนก่อน

      -0:01 HeisenbergFAM!!

    • @Nuss-j4s
      @Nuss-j4s หลายเดือนก่อน

      btw, why has Euler both eyes in the video?

  • @noddynorthside
    @noddynorthside หลายเดือนก่อน +69

    How satisfied would not Mr Maupertuis be, were he still alive, if he could see the principle of least action applied to highest degree of dignity to which it is susceptible.❤❤❤

    • @AyoolaLadapo-hg7vs
      @AyoolaLadapo-hg7vs หลายเดือนก่อน +2

      I wonder who Not Mr Mapertuis is?

    • @AyoolaLadapo-hg7vs
      @AyoolaLadapo-hg7vs หลายเดือนก่อน

      @@noddynorthside Just a joke bro😂🤲

    • @noddynorthside
      @noddynorthside หลายเดือนก่อน

      @@AyoolaLadapo-hg7vs 😅😅

    • @WhiteChocolate74
      @WhiteChocolate74 หลายเดือนก่อน

      But he was a Frenchman. They have no dignity

  • @markus9147
    @markus9147 หลายเดือนก่อน +12

    I love these types of math/physics history videos. They really put in perspective that we are standing on shoulders of giants.
    They also make me nostalgic about the time I was learning these things in college for the first time.

    • @TherapyGel
      @TherapyGel หลายเดือนก่อน

      It also really humanizes these figures, at least for me.
      We were all taught that Newton was a genius and the impact of Euler's work. But hearing about the social dynamics between these people and their relationships really brings them down to earth and reminds you that they were just people. Brilliant, yet flawed people.

  • @themorrigan3673
    @themorrigan3673 25 วันที่ผ่านมา

    I am in awe where in school i just learn them through memorization but this channel brings these equations to life. The feelings of those who authored them to those who defended it and the journey it takes to take the form it has in the textbook that I am reading. thank you for this.