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!
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!)
"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
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?”
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.
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.
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.
@@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...
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"...
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.
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.
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.
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.
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.
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.
@@ronaldderooij1774 If you raise your kids to be dumb, then yes, but my 11 daughter and 6 years old boy LOVE watching this and other science channels with me...
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.
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.
Not one single channel on RU-vid 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!
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.
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.
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.
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.
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.
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.
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.
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
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😅
@@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).
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
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.
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
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
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.
@@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
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.
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.
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.
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
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.
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!
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.
@@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.
@@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.
@@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.
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!
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.
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.
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
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
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 🤯🤯
<a href="#" class="seekto" data-time="772">12:52</a> When you are so wrong that your close friend wrote an entire book just to ridicule you for how blasphemous your work is
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.
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.
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
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) <a href="#" class="seekto" data-time="1310">21:50</a>
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
<a href="#" class="seekto" data-time="1712">28:32</a> 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 🤯.
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.
@@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.
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
Love the video! Adding a key or writing in the for the variables in these equations is one thing that would help me and probably others understand a bit better in those sections.
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!
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
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!!
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 RU-vid channel like this that helps me explaining Physics to my kids. Thank you Veritasium.
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.
@Veritasium Thank you so much for this wonderful video! As someone who studied this in my first year of grad school, I find myself smiling ear to ear as I see your brilliant presentation!
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.
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
Beautiful video, just as beautiful as the concept itself. I was emazed by the power of variational calculus in physics applications back in university and still am to this date. It also reveals many insights in geometry
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.
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.
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.
@@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?
@@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.
In my final year of Engineering degree, I took a course called Interfacial Phenomenon. There we study how different fluid interfaces interact with one another. In that one such problem involved finding the height and the radius of curvature of fluid inside a capillary tube. We were introduced to Lagrangian differential equation mentioned in the video. I didn't have intuitive understanding of it back then. It was kind of a Eureka moment for me when I was watching this video. The puzzle finally falling into place. That' why I love veritasium !!
Notice how you needed to have knowledge of outside info to be able to have that moment? Most don't have that, and those who do not are almost all not going to be looking into secondary sources of information on the topic; this is their only introduction and lesson.
I felt the massive shock when you say I have to wait for another video. Truely, watching that one equation poped in everywhere made me shout. Really Great!!!! Can't wait >>>>>>>>>>>>>>
Bro <a href="#" class="seekto" data-time="1570">26:10</a> is like the coolest thing ever I haven't done math and physics in a while but I like the subjects even thought they don't usually apply to my life anyhow being able to follow the video and understanding f =ma is just something I didn't expect that this equation will do like whaAT???
As a Physicist, I LOVED that class at University! Definetely waiting for the next part, about the UV Catastrophe and so on, that would be awesome to watch!
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!
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.
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.
Condensed into 30 minutes. Yeah, I'm sure someone without background knowledge understood the topic, there are plenty of comments from people like you. But there are even more from people who simply just memorized an extremely short summary that leaves out so much that should and would be covered in an actual class.
I loved this video. The sounds, the background music, the knowledge, the quality, the delivery. Truly a masterpiece. I honestly felt like I was watching a revelation of immense proportions. THANK YOU!!
Same here. In fact, I think I'm lost even a bit earlier: "So if you took a tiny step to the left or the right, the value of the function basically doesn't change". What does that mean? So does the value change or not? I think it does, I don't see why it wouldn't. And then, if you were to change the path of least action by "adding a tiny bump here or flattening it out there", why "the action basically shouldn't change"? It seems obvious to me that it would change. They even say a few moments later that "any other path must have more action". So why this altered path doesn't have more action? I would really appreciate an explanation.
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.❤❤❤
I'm always blown away by the quality of your videos. The animation, the story telling, and the science itself, it's all top tier. I'm really happy that someone as capable as you, is covering these important topics with such care and respect. You are bringing all of this information to millions, and that's amazing!
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! :-)
Fun fact : <a href="#" class="seekto" data-time="1423">23:43</a> the plant behind him with the pink flowers are extremely toxic, if you happen to eat/bite any part of the plant including the flower or the leaves, you’ll die 💀
Okay its not that deadly, i mean for more than 20 years we had one indoor in our family home, avarage family life, not a single dog or family member died, so wont kill you overnight, just dont eat it 😂
@@matwinchest3r Correct, the really deadly grows around my area. Called "la manzanita de la muerte" in my native language; the manchineel tree is so deadly that just sitting near it will get you sick and leaning up on it possibly dead. Poison sumac and ivy aren't a joke either but "la manzanita" is way worse.
What a touching story!! I am no science person but I have watched your vidoes for years and recognise Euler's name. What a kind and talented guy!! 🎉 This video also shows the mountainous backlash could be faced by true pioneers. My heart aches for Maupertuis. 😢
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 ^^
I love the timing of the video, recently I was looking into Lagrangian mechanics just for fun and I understood the formulas and how to solve basic problems but I couldn't figure out the intuition behind the proofs/derivations. Truly one of the best videos made by you, thanks Veritasium!
While watching this video, I felt like I was a guest in a lecture that I knew nothing about prior, yet still managed to walk out amazed and full of knowledge. Guys, thank you so much for making these... tbh I can't call them simply videos, but short movies. Like another dude pointed out, this felt like watching the latest season of Cosmos and it was incredible, to say the least
<a href="#" class="seekto" data-time="1538">25:38</a> This is why I love math. When it was revealed that under all of that derivation and derivation results in an equation that we're all too familiar with, I just gasped.
Because every formula or equation you know is just the simplification of its integral and derivative. Or in the quote of a famous Mathematician "Simplicity is hidden beneath the mask of Calculus"
This is all just beautiful how everything turns out to be. And damn these short documentaries are getting levelled up everytime. Respect and applaud to Veritasium.
I enjoyed maths and physics as a kid, did it all through high school, and even did an entire engineering degree 15 years ago, and I've never even heard of "action" as a quantity until today, amazing! I wonder why, as it seems like the general solution for many of the concepts I studied.
@@thatdude_93 I would leave out the bit part. It IS more complicated than what you do in high school, period. Variational calculus is in many ways different than standard calculus. There are analogies that can make it at least a little easier to digest, but you really can't work with it as with derivatives. The great example of that is when you try to tackle second order action, where you can't use any trick like integration by parts or something, and you need to seriously work with second order variation, which is a function, not a differential and that makes things much much harder. Besides, action is not the only variational problem you can do. Also, this guy said he studied engineering at college, and most of the engineering majors do not take much math beyond calc 1,2,3. So naturally, he wouldn't have the math for that, although I would argue that a decent professor can teach you without you knowing variational calculus.
that's weird, I was from electrical engineering that has nothing to do with mechanics but i remember being introduced to principle of least action somehow
Lagrangians are also used all over in finance (my field) - portfolio optimization problems and much more. Although I took a shitload of physics and math classes, perhaps this was all the wrong way to go - Veritasium and many other content creators for math and physics (and other sciences) have done so much more to improve my understanding of so many concepts. Maybe these videos should be a mandatory part of the syllabi of many high school and college courses! Ty Derek!! ❤
This is an amazing way to explain The Principle of Least Action! Considering that it serves as the basis for Analytic Mechanics, which is to this day the preferred formalism of classical mechanics (and what Quantum Mechanics ended up going with), this video has TREMENDOUS value!!
I learned this principle a year ago at uni, got extremely excited about it, surly listened to lots of physicists speaking about its importance and and explaining its depth, and of course read the Feynman lecture of it. still, you have added a lot to my knowledge about it. thank you !
<a href="#" class="seekto" data-time="1020">17:00</a> I think there is an intuitive way to action. Imagine you are sitting next to a door(side opposite to the door ). We usually (as far as it's not necessary) don't close the door by putting force near the hinge (imagine the door is half open) *Now if you think we are just saving energy by that not action* Then I want to argue the secondary case Case 2 Now you are sitting on the chair at the same place you are most likely to close the door by applying force near the hinge because knob is too far I want to argue about the fact that you may save energy by standing up and closing the door with little energy but you will use more force and do it even if you feel pain in your hand. I think that is action's intuition Becoz a man with a diff. body like ectomorph (rather than endomorph) chose to stand up and close Slite slim and muscular man may have diff. Approch
It's the best video on RU-vid describing *action* in a proper way. All the writers of the so called "classical mechanics " Books must include this journey to reach the concept of action. I am really very thankful to you sir.
My wife is related to William Rowan Hamilton. We were married in the town of Killyleagh Northern Ireland. We stayed in Killyleagh castle which is still owned by Hamiltons. Great video as always
In a world where everything seems to be trending towards flat design, I adore the expressive sketched style of animations in these videos. Thanks Veritasium!
I think I may have been waiting for this video for nine years. In one of my systems engineering courses in school we were shown THAT the lagrangian works, but not why. I asked the professor, and he basically scoffed asking, "did you just ask me, 'why are we learning this?'" No, I was genuinely curious WHERE this new tool came from. We were taught for literal years at this point how to solve these problems with vector diagrams and calculus, then all of a sudden here's this tool you can plug and chug and it'll just magically work. Where the hell did THAT come from? Why is it equivalent to solving these problems more rigorously? Is it just a fancy wave of the hand? Fantastic explanation on describing this piece to the puzzle.
