Never studied physics, but enjoy unravelling these mysteries through the many wonderful STEM presenters on youtube. I have used your videos, on occasion, to help my four high school sons grasp a concept they were struggling with. It does work, and you are appreciated. 😁
I'm an engineering-physics major so I understand a pretty good deal of your videos. But damn, you make this type of difficult content far more accessible and easier to understand than ALOT of professors I know. Keep up the good work Jade, but don't forget to spend time with friends and family.
I am a bartender who hasn’t pursued any science education since high school 5+ years ago. I still come here and am able to follow each of these ideas without any prior context. They are fantastic, thank you for making learning free and accessible! : )
Are you any smarter than AOC? Cause thats not hard. Maybe you could replace her as youre probably more qualified anyway. And being worse than her would be near imposible
SP33DDY7 I bartend too and decided to go to school a couple years ago (been bartending for 9 yrs now) and am majoring in Physics and I must say, it’s easier said than done but when you have the passion it’s worth the effort! I’ve failed a few courses here and there too, but words of advice is it does get more difficult the longer you wait to get back into the sciences.
that's the power of a youtuber who isn't trying to prove their worth, but one who means only to simplify an idea in its most palatable form. Powerful things basics.
Once in a while, I come across people as radiant as you are which makes me tear up a bit with happiness! As someone who was on the path to being a theoretical physicist a few years back and betrayed that beautiful aspiration due to circumstances, I have a lot of love for Physics and guilt for abandoning it. It has been a lifelong belief of mine that the world need more people of Physics, and you, Ma'am, are helping to create that world by your lucid explanations of complicated physical and philosophical ideas. You have earned yourself another subscriber today:-)
5 лет назад+2
Exactly my feelings. Plus using it as inspiration for my philosophical debates with laymans! How "simply" share our understanding to the duality of complex AND simple at the same time universe.
Great, isn't she? I went on to do politics w/ sociology at uni but I still love physics. Jade has a real love for the subject and I'm glad I came across her. Just recently but now i'm a subscriber. She's collected some real groupies, unsurprisingly.
Mine too. Ever thought that everyone in life is actually 100% composed of particles that are all obeying the principle of least action? Therefore so are you and me. But thanks to a great illusion, we think we have some control. We are really all multi-dimensional vortices, obeying a higher order form of the Navier-Stokes equations.
@@lyrimetacurl0 But in order to say that we are wrong when "we think we have some control" (which you did not actually say), we must have a solid understanding of what "control" is
hey there! current physics major here. I'm taking a course on this stuff next semester and I love how simple and digestible you make everything, it really helps me build the foundational conceptual knowledge I need for these courses bc professors tend to skip over that part and go straight to the math without ever explaining the why or how. keep up the good work!
@@JonathanMandrake You ever the old laments about degrees? BS obviously is interpreted as bullshit, MS is "More of the Same" and PHD is "Piled Higher and Deeper" :-) Or... "what else has degrees? A thermometer - and you know what to do with that" Strangely enough - I discovered these words of wisdom written on the blackboard of my High School's math office in 11th grade.
- Explaining a difficult concept in an intuitive way - Stating you're not smart These are mutually exclusive Please continue with the first!! I love it
She just said she's not a "smart super-elite genius". I am not a true genius either, but I know I'm generally smarter than the majority of people (maybe including her, but I can't tell for sure). That doesn't mean that I'm any more effective at life though. I just take a different path.
@@lyrimetacurl0 Arrogance always shows who are not so smart that one thinks of about itself....The most brilliant people I have ever known have been the ones that never consider themselves as so intelligent ones.
@@GIFPES Are you saying arrogance and intelligence are mutually exclusive? Because that would require some sort of proof. Why can't a smart person be arrogant? Also, how do we define "smartness" and "intelligence"? Are they the same thing or different? Is "smartness" how much we know and "intelligence" how capable we are at learning new things (like IQ)? Would be interested to hear your thoughts.
It is really refreshing to see a physics teacher emphasize that physics is a model and we don't really know the clockworks of the universe but that doesn't stop us from modeling it. Thanks @upandatom!
Well yes we don't reallydescribe the workings, just the effects of the workings and how to predict their actions. Sometimes we try to suggest what the workings are, but it's really rather irrelevant so long as we know what they do.
That's also an important point when it comes to math: most math has clear analogs in the real world so it's easy to confuse math with the real world. In reality, math is an abstract symbolic language that has been cultivated so as to be useful for real-world purposes. Almost all concepts in conventional math find direct representation in the real world: integers, fractions, negative numbers, and so on. About the only thing that doesn't find direct representation is imaginary numbers, and that's the point at which one needs to recall that math is a useful abstraction but is not interchangeable with the real world.
My favourite memory from university was a lecturer ranting and raving about how the many worlds interpretation was an absurd interpretation of quantum mechanics, and how it was ridiculous to choose that over the Copenhagen interpretation -- and then in practically the next breath casually mention that the Copenhagen interpretation is also a non-physical mathematical tool, and not a literal explanation of reality.
Hey, I'm doing my PhD in Meteorology now and I'm been watching physics videos on RUclips since I'm a teenager. I'm sure you're one of the best. Keep the good work
Surprisingly, I found this channel in the recommendations next to one of PhysicsGirls's videos. Back then this channel had a different name that kind of sounded like "Physics Girl" (totally forgot what it was). Then some boring people pointed this out so Jade changed the name to Up and Atom. Which turned out to be a better name. Later I've seen Jade help with some Physics Girl videos (you could recognize her art style), then finally saw her on Tom Scott's channel. She's been through a great journey 😁
Re: "Physics is a model" Physics is a map, while reality is the territory. We do our best to describe the territory, and while maps can be accurate, and there are many ways to draw maps, they are distinct from the territory. Same with Physics. It's a description of what we think about reality, but it is not actually reality. It's just a map. It's just a model. Great video!
Also like maps you often have to make choices of what you want to show. A road map would be useless for someone trying to find mineral deposits etc. There are also choices about how accurate to be, the only perfectly accurate map would be the size of the area it's trying to show but well that's not a map and even then said place would be constantly changing and the map could never keep up. You can use smartphones with zoom but imagine trying to navigate highways with the map permanently zoomed into pedestrian level, you could do it but ut would be tedious and you don't need that accuracy. It's just how in physics you could use quantum mechanics to try to model large systems but it would be pointless because classical mechanics does the job just alright. And in a similar veing technically mechanical mechanics was proven wrong by Einstein but it's way easier and simpler to use for most jobs and it works.
I think it is safe to say that models are a part of the reality of consciousness, which means models are a part of reality. Another approach to that argument is that we are a part of reality, and it seems intuitive to imagine that our thoughts have validity in reality, not just an approximation of it. It's much easier to work under the assumption that everything is an approximation of reality, and it works well as long as your purpose is clearly restricted, but looking at reality as a whole, even an "approximation" is a perfect part of reality, and great value can be gained from a general contemplation of those "approximations"
*Physics Is A **_Predictive_** Model* ( *_That's Always Being Refined_* ) Once upon a time, maps were made by explorers estimates and were ridiculously inaccurate, if not completely fantastic (Here Be Dragonf). Then scientists started using tools & precise instruments (Measuring Rod, Compass, Roman Hodometer, Sextant, Portable Clock, Theodolite, Radar, Lidar, GPS, etc.) to measure out the seperate parts & different aspects of the maps. Little by little, the accuracy & resolution of our maps have gotten better. Now we can set out on a journey knowing not only how to find our destination, but also the most efficient route, the best vehicles to use for each terrain & so on - all with a level of precision down to the millimetre. We can understand that there are both parts to our maps that previous generations never even looked for and parts that the current generation has yet to know. There simplified maps which we use in our day-to-day lives & staggeringly vast & complex maps (perhaps far beyond the comprehension of all but a very few genius minds) that combine everything that we know about a territory into a singular construct. The map, & the territory it describes, grow ever closer over time, but there will always be a difference between the analogy & the reality...
A long time ago I had to demonstrate the Principle of Least Action in a Classical Mechanics II exam, one of the subjects of my doctorate. It's amazing how profound this principle is, providing the basis for several conservation laws in physics, including the strongest of all: the conservation of energy. In addition, this principle is also the basis of mathematical structures such as poisson's parentheses that later, in quantum mechanics, give rise to the mathematics of commutators... Currently, in the higher courses of Classics and Quantum that I teach at the Faculty, when I talk about conservation laws, I point directly to the principle of least action. the universe follows this principle mainly for the propagation of light... Excellent explanarion. Nicely done.
I am so in love with this video because it is not afraid to ask questions like "does a light particle really choose anything", most physics arguments make unintuitive assumptions and this video is not afraid to tackle them ❤
This channel deserves more veiws for following reasons : 1. The content is solid 2. Animations and drawings are really good and sometimes hilarious 3. She has done collabs with big and famous in this niche 4. She is beautiful and pretty
“Your videos are simply brilliant, enlightening and works of pedagogical genius ...what passion, what infectious enthusiasm - great job, keep it up” -this remark is by a theoretical physicist.
You asked for feedback and about your viewers. I'm in my 60s and only got to high school physics but I have an insatiable desire to learn and I'd rather watch an educational video than TV. I confess your smile and your accent make your videos easy to watch, but that would only hook me a few minutes. I enjoy your videos because you have interesting topics and a gift for making things very clear. You obviously are well educated but your style is very approachable. What I think is the critical factor though is your obvious passion for the subject. By far the greatest presentations are full of infectious passion that reals me in. There is nothing more tedious than an instructor devoid of passion and nothing more exciting than following an enthusiastic explanation to the next step. Your channel feeds my mind in a joyous fashion. Thank you.
Thank you for your clear verbiage and visuals. I found myself for the second time grabbing a screen capture of the math, which flashes on for a second or two. So even the math is accessible if you look.
I seriously appreciate what you do on this channel. I'm a recent CMPS graduate and I've always had an interest in Physics and Philosophy. So all the topics that you talks about really seem to hit home for me. I enjoy pretty much everything from your thought process to the illustrations that are in the presentation. Thank you for what you do!
I’m a senior in high school and I really did enjoy the video really made me think. Especially when you mentioned how nature always seems to choose the path of perfection. Really weird when you sit down and think about it. Reminds me a lot about entropy and how the world is seemingly perfectly imperfect
being in 12th grade right now, we have been studying organic chemistry for 4 months straight, and whenever something out of the ordinary happened over there, the only thing our sir told was "the theories didnt come first, the observations did, and then we moulded our theories into something or the other to fit the observations, so if you are hoping everything will fit to your intuition, then that wont be the case." and i let that sink in for the past 4 months, and now here we are understanding that the exact same goes for physics, its exciting to know that i will one day get to go deeper into all of these alternative theories, and as of now it just excites me that even i can create my own model to explain things. and your videos help me a lot, i have info about things you talk about so its never going above my heads. loved the video!
One of my favorite 'least action'-like phenomenon is simple soap bubbles. Singular bubbles, the surface tension makes them spherical. When several cling together, the faces/edges start getting more complicated shapes, but it's always the shape of 'least action' or 'lowest energy level'. Nice videos, I just discovered these and currently binge-watching. :)
I've seen thousand of Brilliant ads, but today is the first time my mind was stretched enough that I am really interested in subscribing. You really got me thinking, and at least in this video it was at the perfect level for me. I'd love to see the sources of the lectures you spend time watching too.
I didn't finish high school but loved physics and was a straight A student until year 11. I love learning in general and stumbled across your channel recently. I'd say you do an incredible job of making complex material friendly and approachable. Your animated dialogue adds to the delivery and helps with engagement. I'm certain this channel will continue to grow, serving many students of physics and broadening perspectives and understanding for many. Many thanks for the time you put into this.
I have a middle school aged daughter and your videos are very accessible and relatable for her, as well as someone like me who felt completely overwhelmed by physics class as taught back in my high school. Thanks Jade!
I think the idea behind the Lagrangian and the principle of least action is one of the ideas that blew my mind the most. I think I had to think about it for months. Well what I like in it is its simplicity. Just give me a Lagrangian, I'll tell you how your object/particle will move. For most of the physical models. It's so simple I can't tell myself it could be wrong. Moreover, the Noether theorem, as a consequence of it, represents a huge advance in my comprehension of physics. This theorem is really beautiful, and found by a woman.
Was the second thing that blew my mind most about bachelor-level classical mechanics. First was being asked to derive the equation of motion for some arbitrary rotating reference frame, getting a normal looking answer plus a bunch of garbage, checking my answer and seeing in the book, "Oh, by the way...those last three terms are sometimes called the Euler, centrifugal, and Coriolis forces." I can still remember that feeling of "Hu-whaaaaa?"
The video didn't say it explicitly, but the simplicity mostly lies in the fact that setting the derivative of the Lagrangian equal to 0 gives the equation of motion. Reason? This calculates the minimum of the Lagrangian, which is the solution by the Principle of Least Action. So, take any isolated classical physical experiment, and you can get orbits, trajectories, and other equations of motion just by setting the derivative of the Lagrangian to zero. Of course, this ignores Chaos Theory, but that is another story...
Thank you so much for this video. I m doing my masters in physics and for the first time I have lagrangian formulation of mechanics and its been 2 month, and its been chaos in my head and for the first time I could develop some imagination of what might be happening, this video was a boost that I strongly needed. Thank you so much great work.
1. This explanation was really intuitive and really helped me. Thanks! 2. It's encouraging to see videos on RUclips about Physics recorded by women. Thank you and good job!! 3. Your husband's French accent and other segments in the video made it entertaining and fun. Regarding your questions you opened to the audience: I'm a junior in my undergraduate math-physics degree so I can't tell you how accessible this is to someone without a background. Also, I don't understand the Principle of Least Action enough to chime in specifically regarding "wonders of God" vs "just a mathematical model" but I am a strong Messianic Jewish believer and a major aspect of my passion for physics, since I was first exposed to it in high school, is how the perfection of it all points to an extremely intelligent, creative, and beautiful design. Sometimes my eyes water when I read something cool in physics (or even in math) and I think that happens to me because I'm experiencing deep awe and admiration for God as a result of learning something remarkable about His creation :) Logically, there seem to be strong arguments for both sides and ultimately I don't think one can really use logic (which is a human creation anyways) to conclude anything about the existence or involvement of God in human life :) Thank you so much for making this video!
I learnt some Lagrangian Mechanics over the past couple of months, and it (sort of) culminated today, with the submission of my first ever research paper - a Lagrangian formulation for non-uniform rotor whirl prediction...
Loved the analogy between the car and light particle. The graphics are nice and simple but really helpful to understanding. I studied physics at school and at uni a bit. Didn’t continue with it but still very interested. You’re a really good teacher. Look forward to more - particularly about theories, equations, models etc that challenge us to think differently about reality. Keep it up! Thanks😊
This is one of my favorite videos about physics and science in general because your ideas are both deep and clearly stated. Newton, Lagrange, Hamilton, and Einstein are only making models, not truths. The models are good and should be trusted in the right contexts. So long as people appreciate the context in which models operate, we can make progress.
As a long-serving student of the "Feynman Lectures on Physics", I can definitely state that this was one of your "better" and more "intriguing" vids. It is a great example of applying a different model and system of equations to describe the same physical ( or, perceived physical ) phenomenon. Perhaps another vid on different but equivalent / orthogonal models for 'gravity' would also be of interest to your subscribers and audience !?! . . . " incroyable " !!!
Can't we think light the same way we think of gravity? Well, if we could see gravity, we might think of it the way we do photons. But think of photons the other way, as carriers of a field interaction that's more intense at a light source. We say photons travel in straight lines, but that's because we are a straight line away from a light source. Really, the light is a spherical gradient with the same inverse square law as gravity.
This is such a great video! I would like to see also a video on how the principle of least action leads to the symmetries of nature which are the basis of conservation laws. You are one of the best way explaining things, and I think this may be the most important and fundamental topic of all!
I was today years old when I learned that there are many, many more people in the world who are interested in science and skepticism than ever before. Please keep doing what you are doing. it is working. We are changing the world. :)
Hi Jade, I'm a bit late answering your question: I just found your video. Hope my answer is still somewhat of interest to you. I live in Belgium (bonjour à ton mari français ;-) ) where I was born in 1961. I have a university degree that involved some science (math, stats, physics, chemistry...) but was mostly geared towards economy and management. I have an extremely broad range of interests, and have been dipping back into physics in the last years, especially trying to wrap my head around quantum mechanics (though not really digging into the maths involved... :-/ ). So your videos are exactly what I need. They help me improve my understanding of physics, by providing me with an accessible interpretation of Newtonian / Lagrangian / Hamiltonian maths that I never had before. A big BIG thank you for that ! Keep at it. You're on the optimal path :-D , well at least from my perspective ;-) Cheers Gilles
Oh, Jade, you are absolutely ace! I've been watching your vids for a couple of months now and I love them. Don't worry about going too far... I did humanities and I can follow you pretty well. After all, your happy enthusiasm is deliciously infectious! Totally love your stuff! Keep it up like this and I'll keep right on watching.
I am 56, have no background in physics but find the subject fascinating. Your car and water analogy was excellent and having recently subscribed am really enjoying your videos. You pitch them well. Keep it going!
Excellent. I always wondered why the Lagrangian was like it is. Now I have a better understanding. The part I did not like about university physics was that everything was about solving problems, not really seeing the relationships. Thank you.
@@amoonra8385 are you saying you have a obligation to understand "God will" because sound like you got a pretty big ego then. "The God will is under no obligation to make sense to you" = "The Universe is under no obligation to make sense to you"
@@MouseGoat no, he is saying there is a rational Being (namely God) who created the Universe, therefore it is imbued with some of His characteristics, and one of those being "rational", the Universe has a rational sense. We being rational creatures (although obviously limited) can also understand this rational structure in the Universe, to some degree
I got my BA in physics from the University of California, Berkeley a long time ago. I spent 30 years as a mechanical engineer at the Lawrence Berkeley National Laboratory. You are doing fine with the clarity of your videos. I have always come down on the side of physics being a model of the universe. I am not much concerned about reality in any philosophical sense. If it works then use it - the engineer in me says. Knowing that uncertainty, whether in quantum mechanics or in measurements, is fundamental to what we can know experimentally convinces me that any clean statement of physics can only be a model.
After studying physics for some time now i’ve come to realize that for you to understand an explanation, you need that explanation to resonate with you. It doesn’t matter how much detail you provide if your brain doesn’t buy the premise. Thus, the best way to teach is to present multiple viewpoints of the same problem.
Rhade: the universe isn't lazy, it's so smart that it's infinitely efficient. That is a very different way of looking at the principle of least action, and probably the right way. When we are lazy we are being very inefficient.
If you look at the footpaths in mountainous areas, carved over generations, I'd bet that they represent the most efficient path from point A to point B. People (and animals) are just particles trying to use the least energy possible.
This video is great. I would like to learn more about Lagrangians. Thank you for posting this. I am an infectious disease physician with a background in physical chemistry.
I'm a college dropout,a bum from the philippines, and i enjoy watching your videos. I dont runderstand everything perfectly but i understand enough that i am able to enjoy it and be fascinated by it. You explain physics very well in a simplified yet interesting manner for simpletons like me, and you're a breath of fresh air in this time of chaos. Good job and thanks. ✌
That quote is a favorite of mine, too. I've been attributing it to George Box, who included it in an _excellent_ text book called "Statistics for Experimenters." It's particularly relevant for statistical models, but the lesson extends to all applied mathematics and arguably to mathematical physics.
I always thought of it as all models are inherently inaccurate, some are simply less inaccurate than others. Modeling the trajectory of a known mass under known conditions, can be fairly accurate while trying to model the stock market, highly inaccurate. One uses fairly straightforward physical parameters the other includes a lot of psychology.
If two different methods of modelling something both give the same results for every case they can be tested with (like the refractive index/minimum time of flight solutions for light refraction) then they're mathematically exactly the same thing. For most problems I've seen the refractive index method is much more straightforward to apply, hence it being more popularly taught. A much better example many people will have seen is using the equations of motion vs. conservation of energy to describe how masses move. Both give exactly the same results in all cases, so they're the same model, just looked at from different angles, but in this case both methods are widely used as both methods are easily applied and depending on the problem usually one method is much easier than the other. It's only when models disagree that there's any chance of devising experiments to determine whether one model is more correct than another. Often very difficult problems in one method are very easy to solve using another, which is why it's good to be familiar with as many models as possible as it makes it more likely that you can find a quick intuitive solution for new problems.
@@upandatom Probably because professors have to worry about grades and homework and a lot of them have probably been teaching for so long they forget what's it like to learn something for the first time. You clearly work on your videos devote a lot of time time to them, and because you don't have to worry about grades and meeting curriculum requirements, you can focus on the content and explaining it well. You also clearly remember what's it like to learn this stuff for the first time, so you make it simple enough that we can understand it without having a physics or math background. RUclips is great for for learning because they are lots of people like you making great videos. Yours are up there with The Science Asylum, Minute Physics, and 3Blue1Brown in terms of quality. Lots of videos explains things well, but yours and a few others stand out because of your obvious enthusiasm and enjoyment in the subject and your excellent animation.
Jade you are a total science communicator ROCKSTAR! I discovered you only. approx 48 hours ago and so wish it was much sooner.nl/.Please don’t stop you’re brilliantly understandable and just freakin greatly entertaining videos. re knowledge about how crazy crazy non-real reality is and isn’t is...nl/THANK YOU😊
i feel like there may be some context lacking in this scenario. you'll probably just confuse her... it happens to me every time. I've been following the path of least action since puberty...
or how about a math one: "Are you a circle? Because when I am within your perimeter I start to become irrational! Thus, only together can we transcend to become that which is real; you need but consign, uh, cosine yourself up to me!" "Huh? What do you mean my chances are the same as the derivative of a constant? What do I look like, a mathematician?!"
I think both Feynman's and Euler's views are true. There is a certain pattern to nature that just makes sense somehow but at the same time, for all practical purposes these are the models we've come up with for our work and we'll use them as models. We'll leave the philosophising for later, once we crack the quantum box.
As a non-cartesian individual, with average-at-best knowledge of physics, I think I can safely say : Yeah, you do make sense on your explanations. (Also, welcome to the Recluse club. We don't meet up.)
You came across as a pure, affectionate, curious, intelligent and studious 'little' girl. God bless you! Though I've most of the times struggled to understand Physics, but you DID make it easy. Thanks.
She is doing fine and for those of us with an advanced knowledge of the subject her shallow coverage is more than compensated by her bubbly positive energy.
You're such a cute couple! As someone who played with Kerbal Space Program, I was immediately intrigued by "lagrange" because Kerbal Space Program lacks Lagrange points. That's one of the first physical concepts I actually understood which isn't modelled in Kerbal Space Program.
Jade, it's not just how you explain things, which is excellent, it's that you are thinking deeply about the meaning of physics and that you see beauty in it. I find this is rare in popularisers of science who tend to be story tellers, telling the same stories over and over.
I'm an old engineer, who has prided himself in being able to do two things: solve impossible Real life problems, and to explain nearly anything. I love everything about your "way". BRAVO! Viva Feynmann!
back to the refraction example... consider the case where the light source is below the surface of the water. if the angle of incidence with the air/water boundary is greater than the critical angle, the light is totally reflected back into the water. it never makes it into the air, where (according to you) the "action" should be less. how does the principle of least action account for that?
I had a similar idea to this way back in school. Basically to explain wrt this case I believed that action that light tries to minimise is not time taken but the actual speed of transmission itself. Since the speed of light remains constant in all frames of reference so I imagined it like basically the speed of light is fixed. So since in a denser material light actually slows down physically, it actually bends in such a way that it has to travel a shorter distance inside the denser material. So OVERALL average speed of light would remain constant. Thinking about it this way can explain the thing you are talking about (total internal reflection).... If light hits a material boundary in such a an angle that it cannot makeup the constant speed by bending it simply never goes into that medium and gets reflected back.
+THeMin100 - ok, here's your fundamental error. you start with, "Since the speed of light remains constant in all frames of reference..." that's NOT A FACT. there is ZERO direct experimental evidence to support it. let go of all the BS you were taught. free your mind and think for yourself, NOT in mathematics, but in CONCEPTS. if you can handle the calculus, i recommend to you "Old Physics for New" by Thomas Phipps, which gives a thorough and absolutely indisputable deconstruction of SRT, and exposes ALL of the fundamental flaws and egregious blunders saint einstein made. or just stick to the dead religion of scientism. your choice. "Einstein's relativity work is a magnificent mathematical garb which fascinates, dazzles, and makes people blind to the underlying errors. The theory is like a beggar clothed in purple whom ignorant people take for a king. It's exponents are brilliant men but they are metaphysicists rather than scientists." -- Nikola Tesla besides his 1905 paper on the photoelectric effect (which was no great conceptual leap in itself but merely put together in a fairly obvious way ideas previously conceived by others), einstein's only other significant contribution was that he believed QM and especially the Copenhagen interpretation was fatally flawed. remember, CONCEPTS come FIRST, and math follows. with the photoelectric effect, einstein did that. with SRT and GRT, he substituted "thought experiments" for actual physical observations. that's why they are wrong. even worse, today it's TOTALLY back-asswards. "scientists" have forgotten reality doesn't have to abide by equations. equations have to be consistent with reality. we use them when they work, and IGNORE them when they don't. fr'instance, how would you solve this problem? ignoring aerodynamic drag, how long does it take a rock to hit the ground when dropped from a height = s? you would rearrange s = 1/2at^2 and solve for t, but doing that you get t = ±√2s/a and plug in the values of s and g. but you get TWO answers. you IGNORE the answer of NEGATIVE TIME, because you "know" THERE IS NO SUCH THING IN REALITY, even tho the equation tells you there is. that simple example is lost today. today, abstract mathematicians who have NEVER conducted a single experiment in a lab pose as physicists. just because someone can derive an equation, DOES NOT MEAN that it automatically must describe REALITY. "A mathematician may say anything he pleases, but a physicist must be at least partially sane." -- J. Willard Gibbs "Insofar as mathematics is certain, it does not apply to reality. Insofar as it applies to reality, it is not certain." -- Albert Einstein "Today's scientists have substituted mathematics for experiments, and they wander from one equation to the next, and end up with a structure that has no correspondence with reality. [They] think deeply instead of clearly. A man must be sane to think clearly, but it's possible to think deeply and still be quite insane." -- Nikola Tesla
@@johnmichael1594 Uh but there is experimental evidence?? And infact in use. Do you use GPS? If you do then do read up how the satellites are synced up. Although satellite communication is not my area of expertise, I am however a communication engineer and do know the basics. We heavily use SRT equations for syncing satellites and ground stations along with different satellites in different orbits. It's necessary because the speed and the lower gravity at which satellites operate and our rate of data communications makes it necessary to mitigate the time dilation effects and the Einstein equations works there beautifully. Now you also missed the point of the video, I am not denying that relativity no matter how useful or accurate is just a model just like every other mathematical model. But what I am saying is relativity only doesn't work in one area i.e at the quantum level where both theories disagree on micro gravity. Apart from that case nowhere was relativity found to be not satisfied. There was uncertainty yes but no definite proof of relativity being wrong. Also just because something is not intuitive and doesn't follows common sense doesn't mean that it cannot fully model the things that actually happen. I am up for a whole new model but for me to accept that it must be objectively better than relativity in some sense. And also have the practical utility that relativity has. I like to keep and open mind man.
+TheMin1000 - that is evidence that clocks on satellites run at different rate than earthbound clocks. THAT'S ALL. there are an infinite number of theories that would account for that. any connection between the OBSERVATION of clock speeds and the speed of light ARE CONJECTURE. do you even understand the DIFFERENCE between facts and theories? READ THE BOOK. or close your mind and worship at the altar of scientism.
@@johnmichael1594first give just "*one*" of those "*infinite*" number of theories that you are talking about. Second if you had read my whole comment you'd have known that I said the same thing about it being a conjecture/ mathematical model... But it doesn't matter to me if it's what's REALLY happening because the things we have i.e the model that we have is being used for last half of the century and the equations it gives agrees with observable phenomenon and has been put into good use and gets us actual results. So why would anyone Change it for something completely new, you know the phrase that "if it ain't broke then don't fix it". You may come up with a better/different model but at the end of the day it's gonna be just that man, a model. I don't believe we as humans can ever completely know the true objective nature of the universe as it's filtered through our own brain and there will come a point where our brain's resolution wouldn't be enough to capture some of the finer details. So yeah I can say the same thing about any theory you make and call it's just a model/conjecture and there will be more than one ways to look at it just like Newtonian mechanics in the video. I leave the making of better models to those who are smarter then me and want to completely sacrifice their life to science. That's why I became and engineer and not a scientist... And I wish you luck, tell me when you get the Nobel prize for your model. Also bro please understand what science is. Science is not a religion, there is no alter to worship in science. One day suddenly something may be found that shakes our theories to the ground. And you know what scientists are going to do then? They are going to admit being wrong and try develop a new model taking into account the new things that were observed. Smaller theories keep changing and made better everyday. In science we don't get fixed into one mindset that's why there are peer reviews in science. If you are really about disproving the general relativity then you know what the scientists would say? They'd say you are welcome to try. If you can give and actual mathematical proof it will be peer reviewed and accepted because a theory that disproves relativity is going to be ground shattering and very important milestone. I urge you to do that instead of acting superior by looking down on the work done by many. Also do read about the scientific process. Facts and theories are inherently related. It's very logical. First you observe a phenomena/facts actually happening then you create a hypothesis i.e you try to give an explanation of why the thing you saw happening, happened. Then You experiment/test your hypothesis by trying out different test cases to see if your hypothesis can account for all conditions, if it can it becomes a theory until someone finds something that breaks it. If it can't then you go back to step two to create a new hypothesis. So you see it's only after confirming with experimentation that a hypothesis becomes a theory. I.e facts have a lot to do with it.
Could we see it through model of Copenhagen interpretation model also that is, like a Quantum object it chooses all the possible paths but the one that become reality to us, is the only one which follows the laws of least action. Is it could also be the case? Please also share your precious view on it so that I could become more clear about it. Once again thanks for another enlightening video.😊😊keep it up.👍👍
While studying QED, I ran into a problem. My professor suggested that I write Dr. Feynman for his help. He wrote back and told me just to use the model and not to get caught up in any physical interpretation. It has been a guiding principle for me ever since. My copy of his lectures has a special place in my library.
What if things take all paths, and the shortest path, is the one realised by the particle, or the path of highest probability? Edit: I think the principle of least action makes me wonder if life in the universe is inevitable as the fastest way for the universe to increase entropy with less action. Especially intelligent life, we can process and waste a lot of usable energy and increase the universes total entropy.
In 1933, Paul Dirac discerned the quantum mechanical underpinning of the principle in the quantum interference of amplitudes (en.wikipedia.org/wiki/Principle_of_least_action)
This is essentially the Feynman path integral formulation or "sum over histories". Except it is not necessary to collapse the wave function as that is a feature of interaction with a larger system. What it does mean is that you add together the probability amplitudes of the all the possible paths, which interfere with each other to produce the amplitude of the most likely path. Amazingly, this probabilistic treatment works out the same as the principle of least action. (Although maybe not so amazing as quantum action is at the heart of the Schrodinger equation).
But if it doesn’t become reality until the wave function collapses, then the ones that didn’t collapse it weren’t real, were they? And how can something that’s not real take a path? The path isn’t even real. You’ve done something really important, here, which is to show that QM, to a much higher degree than NM, is just a model. It’s not a description of reality, but only a way of calculating outcome probabilities.
@@dialecticalmonist3405 I don’t get ur point? If the original comment is right then that shouldn’t matter wether it was measured before or after which is why I said “always”
I conclude that I have a problem with keeping attention for any more than a moment. I have always felt this for most part of my life, in school, around people, while reading, thinking, etc. Right now, I understood the idea Jade tried to explain us in this video, I understood the examples as well - but the thing is, I have watched this video at least 5 times and did not have any context what of what was going on, earlier. New dots have connected now. Thank you.
Hi Jade, I have an arts background and find your physics presentations lively and interesting. I am now in my 60s and choose to broaden my topics of learning to include science related presentations yours are refreshing, Thank you, Lewis
We're in a simulation and the person who made it wants to minimize the power needed to calculate all this. Plain and simple, mistery solved, gimme my nobel.
or how about this: we dont actually exist we are what it is to be 'nonexistent', and what all we think is existence is merely the ground state for nonexistence.
I might have cried at the end... I wish my professors had your same approach, this care for our understanding of the topic and concepts warmed my heart. I hope you get to reach as many people as possible and show them how amazing physics is and how anyone can learn it
Seems like your question about physics being a model is closely related to the question of why is math so good at describing reality. So, for me, the question boils down to: is math discovered (in this case physics would point to truths about the world) or invented (here, physics is just a model)? IMO, this is the most interesting question in the world... is math simply a language or is it THE language.
If information is a carrier of existence then we are unavoidably inventing models of it. If information is actually what existence is made out of, then we are discovering it. And this is of course not an answer to your most interesting question, but it is my personal most interesting question. I don't expect either of us getting an answer in our lifetimes, for better or for worse.
Exactly lol. The moment I learned electrons go back to their ground state, I was like these guys sure seem lazy. Of course optics and QM confirmed this further
Very, very interesting issue. Nowadays I tend to think that physics, chemistry and all forms of science are models. They are ways in which we make phenomena understandable to ourselves and we use them because they work for us to calculate and predict the behavior of matter and energy for instance. Of course, we are yet to discover many nuances, facts and phenomena that might have been unobserved so far but do have effects that appear to us as anomalies of flaws in current models. Dark matter for instance, is a concept which results from observing gravitational acceleration in universe at rates that do not match observable matter. The current model takes us to think that there is some matter that we cannot see by using the available technology. But that we might discover some other causes which lead to update or change the model is a possibility. Excellent video, Jade 😀👍
Helloooooo there is a little message for you after the ad at 11:04 🤗
Great having you as a physics model 😁😘
Understood perfectly, and I didn't study Physics at university - definitely accessible to me at least!
Never studied physics, but enjoy unravelling these mysteries through the many wonderful STEM presenters on youtube. I have used your videos, on occasion, to help my four high school sons grasp a concept they were struggling with. It does work, and you are appreciated. 😁
@@csredmond518 wow that's lovely to hear!
I'm an engineering-physics major so I understand a pretty good deal of your videos. But damn, you make this type of difficult content far more accessible and easier to understand than ALOT of professors I know. Keep up the good work Jade, but don't forget to spend time with friends and family.
I am a bartender who hasn’t pursued any science education since high school 5+ years ago. I still come here and am able to follow each of these ideas without any prior context. They are fantastic, thank you for making learning free and accessible! : )
SP33DDY7 Yes it’s great. I’m a 43 year old who was told not to do Physics GCSE as I wasn’t good enough but I really like learning about it.
Are you any smarter than AOC? Cause thats not hard. Maybe you could replace her as youre probably more qualified anyway. And being worse than her would be near imposible
SP33DDY7 I bartend too and decided to go to school a couple years ago (been bartending for 9 yrs now) and am majoring in Physics and I must say, it’s easier said than done but when you have the passion it’s worth the effort! I’ve failed a few courses here and there too, but words of advice is it does get more difficult the longer you wait to get back into the sciences.
that's the power of a youtuber who isn't trying to prove their worth, but one who means only to simplify an idea in its most palatable form. Powerful things basics.
@@dvaVivyYou mean you wish Brilliant made learning free and accessible,
or do you mean you wish Brilliant had bartending courses?
Once in a while, I come across people as radiant as you are which makes me tear up a bit with happiness! As someone who was on the path to being a theoretical physicist a few years back and betrayed that beautiful aspiration due to circumstances, I have a lot of love for Physics and guilt for abandoning it. It has been a lifelong belief of mine that the world need more people of Physics, and you, Ma'am, are helping to create that world by your lucid explanations of complicated physical and philosophical ideas. You have earned yourself another subscriber today:-)
Exactly my feelings.
Plus using it as inspiration for my philosophical debates with laymans!
How "simply" share our understanding to the duality of complex AND simple at the same time universe.
@ It is always amazing to know that there are kindred spirits out there:-)
Great, isn't she? I went on to do politics w/ sociology at uni but I still love physics. Jade has a real love for the subject and I'm glad I came across her. Just recently but now i'm a subscriber. She's collected some real groupies, unsurprisingly.
@@ModernSocialist True:-)
I AM 65 nd atended physic clas 42 years go/ kept on rading Russian popular science books and am still interested in understanding the stuff!
Seems like my social life also obeys the principle of least action
Mine too. Ever thought that everyone in life is actually 100% composed of particles that are all obeying the principle of least action? Therefore so are you and me. But thanks to a great illusion, we think we have some control. We are really all multi-dimensional vortices, obeying a higher order form of the Navier-Stokes equations.
You are not alone
my toilet obeys the principle of least flushing
You must put more time and energy into it
@@lyrimetacurl0 But in order to say that we are wrong when "we think we have some control" (which you did not actually say), we must have a solid understanding of what "control" is
hey there! current physics major here. I'm taking a course on this stuff next semester and I love how simple and digestible you make everything, it really helps me build the foundational conceptual knowledge I need for these courses bc professors tend to skip over that part and go straight to the math without ever explaining the why or how. keep up the good work!
Speaking as someone who got a BS in physics decades ago, and who had a career as a CS prof -- amazingly clear and lucid presentation. Thanks!
As I know Bachelor of Sciemce as B. Sc., i frist thozght of Bull Shit instead of Bachelor of Science, so you had me on a loop for a few seconds😂
@@JonathanMandrake sorry, didn't mean to confuse!
@@JonathanMandrake You ever the old laments about degrees? BS obviously is interpreted as bullshit, MS is "More of the Same" and PHD is "Piled Higher and Deeper" :-) Or... "what else has degrees? A thermometer - and you know what to do with that"
Strangely enough - I discovered these words of wisdom written on the blackboard of my High School's math office in 11th grade.
hi, i am goind down the same path, with physics and cs after that, can you recommend? what kind of jobs do you do?
I really like your style of teaching physics, keep up the good work!
thank you!
I think the same
I gree
I agree. keep up the good work.
- Explaining a difficult concept in an intuitive way
- Stating you're not smart
These are mutually exclusive
Please continue with the first!! I love it
She just said she's not a "smart super-elite genius". I am not a true genius either, but I know I'm generally smarter than the majority of people (maybe including her, but I can't tell for sure). That doesn't mean that I'm any more effective at life though. I just take a different path.
@@lyrimetacurl0 ...the path that minimizes action! badum-tsh!
@@lyrimetacurl0 Arrogance always shows who are not so smart that one thinks of about itself....The most brilliant people I have ever known have been the ones that never consider themselves as so intelligent ones.
@@GIFPES Are you saying arrogance and intelligence are mutually exclusive? Because that would require some sort of proof. Why can't a smart person be arrogant?
Also, how do we define "smartness" and "intelligence"? Are they the same thing or different? Is "smartness" how much we know and "intelligence" how capable we are at learning new things (like IQ)? Would be interested to hear your thoughts.
@Evi1M4chine Yes, that's what is called "proof" in real life.
It is really refreshing to see a physics teacher emphasize that physics is a model and we don't really know the clockworks of the universe but that doesn't stop us from modeling it. Thanks @upandatom!
Well yes we don't reallydescribe the workings, just the effects of the workings and how to predict their actions. Sometimes we try to suggest what the workings are, but it's really rather irrelevant so long as we know what they do.
That's also an important point when it comes to math: most math has clear analogs in the real world so it's easy to confuse math with the real world. In reality, math is an abstract symbolic language that has been cultivated so as to be useful for real-world purposes. Almost all concepts in conventional math find direct representation in the real world: integers, fractions, negative numbers, and so on. About the only thing that doesn't find direct representation is imaginary numbers, and that's the point at which one needs to recall that math is a useful abstraction but is not interchangeable with the real world.
My favourite memory from university was a lecturer ranting and raving about how the many worlds interpretation was an absurd interpretation of quantum mechanics, and how it was ridiculous to choose that over the Copenhagen interpretation -- and then in practically the next breath casually mention that the Copenhagen interpretation is also a non-physical mathematical tool, and not a literal explanation of reality.
Guess that's why a lot of great Physicists and Mathematicians were also Philosophers.
Hey, I'm doing my PhD in Meteorology now and I'm been watching physics videos on RUclips since I'm a teenager. I'm sure you're one of the best. Keep the good work
"I am open to have my mind changed."
Beautiful.
One like for the "Pierre de Fermat" in French :D
3:08 weird flex but ok.
One dislike for Leibneees. /jk
But then the pronunciation of Aristotélēs :D :D :D
I’m glad Tom had you make a video on his channel otherwise I wouldn’t have discovered this wonderful channel!
as in Scott?
@@lyrimetacurl0 yea
Well that came full circle
Surprisingly, I found this channel in the recommendations next to one of PhysicsGirls's videos.
Back then this channel had a different name that kind of sounded like "Physics Girl" (totally forgot what it was).
Then some boring people pointed this out so Jade changed the name to Up and Atom. Which turned out to be a better name.
Later I've seen Jade help with some Physics Girl videos (you could recognize her art style), then finally saw her on Tom Scott's channel.
She's been through a great journey 😁
Re: "Physics is a model"
Physics is a map, while reality is the territory. We do our best to describe the territory, and while maps can be accurate, and there are many ways to draw maps, they are distinct from the territory. Same with Physics. It's a description of what we think about reality, but it is not actually reality. It's just a map. It's just a model.
Great video!
Also like maps you often have to make choices of what you want to show. A road map would be useless for someone trying to find mineral deposits etc. There are also choices about how accurate to be, the only perfectly accurate map would be the size of the area it's trying to show but well that's not a map and even then said place would be constantly changing and the map could never keep up. You can use smartphones with zoom but imagine trying to navigate highways with the map permanently zoomed into pedestrian level, you could do it but ut would be tedious and you don't need that accuracy. It's just how in physics you could use quantum mechanics to try to model large systems but it would be pointless because classical mechanics does the job just alright. And in a similar veing technically mechanical mechanics was proven wrong by Einstein but it's way easier and simpler to use for most jobs and it works.
I think it is safe to say that models are a part of the reality of consciousness, which means models are a part of reality. Another approach to that argument is that we are a part of reality, and it seems intuitive to imagine that our thoughts have validity in reality, not just an approximation of it. It's much easier to work under the assumption that everything is an approximation of reality, and it works well as long as your purpose is clearly restricted, but looking at reality as a whole, even an "approximation" is a perfect part of reality, and great value can be gained from a general contemplation of those "approximations"
you are onto something except what are you getting at? what is the territory like ??
From now on, I am using this description for science.
Thanks S.Death, very cool!
*Physics Is A **_Predictive_** Model*
( *_That's Always Being Refined_* )
Once upon a time, maps were made by explorers estimates and were ridiculously inaccurate, if not completely fantastic (Here Be Dragonf).
Then scientists started using tools & precise instruments (Measuring Rod, Compass, Roman Hodometer, Sextant, Portable Clock, Theodolite, Radar, Lidar, GPS, etc.) to measure out the seperate parts & different aspects of the maps.
Little by little, the accuracy & resolution of our maps have gotten better. Now we can set out on a journey knowing not only how to find our destination, but also the most efficient route, the best vehicles to use for each terrain & so on - all with a level of precision down to the millimetre.
We can understand that there are both parts to our maps that previous generations never even looked for and parts that the current generation has yet to know. There simplified maps which we use in our day-to-day lives & staggeringly vast & complex maps (perhaps far beyond the comprehension of all but a very few genius minds) that combine everything that we know about a territory into a singular construct.
The map, & the territory it describes, grow ever closer over time, but there will always be a difference between the analogy & the reality...
A long time ago I had to demonstrate the Principle of Least Action in a Classical Mechanics II exam, one of the subjects of my doctorate. It's amazing how profound this principle is, providing the basis for several conservation laws in physics, including the strongest of all: the conservation of energy. In addition, this principle is also the basis of mathematical structures such as poisson's parentheses that later, in quantum mechanics, give rise to the mathematics of commutators... Currently, in the higher courses of Classics and Quantum that I teach at the Faculty, when I talk about conservation laws, I point directly to the principle of least action. the universe follows this principle mainly for the propagation of light...
Excellent explanarion.
Nicely done.
I am so in love with this video because it is not afraid to ask questions like "does a light particle really choose anything", most physics arguments make unintuitive assumptions and this video is not afraid to tackle them ❤
You do a “Feynman” job of explaining ideas in Physics. Keep adding to, while I am catching up.
Nice comment, Fyneman was known for being an excellent teacher, and his lectures are still used and referred to heavily.
Jade anytime you and Mr Feynman are on the same page is a good thing.
I am so gonna use that sorry for stealing that pun ;)
I just learnt it yesterday in the university! And you made a video :D
😊
This channel deserves more veiws for following reasons :
1. The content is solid
2. Animations and drawings are really good and sometimes hilarious
3. She has done collabs with big and famous in this niche
4. She is beautiful and pretty
“Your videos are simply brilliant, enlightening and works of pedagogical genius ...what passion, what infectious enthusiasm - great job, keep it up”
-this remark is by a theoretical physicist.
wow thank you :)
You asked for feedback and about your viewers. I'm in my 60s and only got to high school physics but I have an insatiable desire to learn and I'd rather watch an educational video than TV. I confess your smile and your accent make your videos easy to watch, but that would only hook me a few minutes. I enjoy your videos because you have interesting topics and a gift for making things very clear. You obviously are well educated but your style is very approachable. What I think is the critical factor though is your obvious passion for the subject. By far the greatest presentations are full of infectious passion that reals me in. There is nothing more tedious than an instructor devoid of passion and nothing more exciting than following an enthusiastic explanation to the next step. Your channel feeds my mind in a joyous fashion. Thank you.
Thank you for your clear verbiage and visuals. I found myself for the second time grabbing a screen capture of the math, which flashes on for a second or two. So even the math is accessible if you look.
I seriously appreciate what you do on this channel. I'm a recent CMPS graduate and I've always had an interest in Physics and Philosophy. So all the topics that you talks about really seem to hit home for me. I enjoy pretty much everything from your thought process to the illustrations that are in the presentation. Thank you for what you do!
I’m a senior in high school and I really did enjoy the video really made me think. Especially when you mentioned how nature always seems to choose the path of perfection. Really weird when you sit down and think about it. Reminds me a lot about entropy and how the world is seemingly perfectly imperfect
being in 12th grade right now, we have been studying organic chemistry for 4 months straight, and whenever something out of the ordinary happened over there, the only thing our sir told was "the theories didnt come first, the observations did, and then we moulded our theories into something or the other to fit the observations, so if you are hoping everything will fit to your intuition, then that wont be the case." and i let that sink in for the past 4 months, and now here we are understanding that the exact same goes for physics, its exciting to know that i will one day get to go deeper into all of these alternative theories, and as of now it just excites me that even i can create my own model to explain things. and your videos help me a lot, i have info about things you talk about so its never going above my heads. loved the video!
This video should be the opening video at the start of every Lagrangian Mechanics 101 course conducted on the planet !
Simple, yet Deep and Brilliant.
One of my favorite 'least action'-like phenomenon is simple soap bubbles. Singular bubbles, the surface tension makes them spherical. When several cling together, the faces/edges start getting more complicated shapes, but it's always the shape of 'least action' or 'lowest energy level'.
Nice videos, I just discovered these and currently binge-watching. :)
I've seen thousand of Brilliant ads, but today is the first time my mind was stretched enough that I am really interested in subscribing. You really got me thinking, and at least in this video it was at the perfect level for me.
I'd love to see the sources of the lectures you spend time watching too.
Wish I had teachers like you when I was in school. Regret for having missed such interesting ways of perceiving all natural phenomena.
I didn't finish high school but loved physics and was a straight A student until year 11. I love learning in general and stumbled across your channel recently. I'd say you do an incredible job of making complex material friendly and approachable. Your animated dialogue adds to the delivery and helps with engagement. I'm certain this channel will continue to grow, serving many students of physics and broadening perspectives and understanding for many. Many thanks for the time you put into this.
I have a middle school aged daughter and your videos are very accessible and relatable for her, as well as someone like me who felt completely overwhelmed by physics class as taught back in my high school. Thanks Jade!
"Camelot!" "Camelot!" "Camelot!" "It's only a model." "Shhhhhh!"
Who are you who is so wise in the ways of science?
I think the idea behind the Lagrangian and the principle of least action is one of the ideas that blew my mind the most. I think I had to think about it for months. Well what I like in it is its simplicity. Just give me a Lagrangian, I'll tell you how your object/particle will move. For most of the physical models. It's so simple I can't tell myself it could be wrong.
Moreover, the Noether theorem, as a consequence of it, represents a huge advance in my comprehension of physics. This theorem is really beautiful, and found by a woman.
Was the second thing that blew my mind most about bachelor-level classical mechanics. First was being asked to derive the equation of motion for some arbitrary rotating reference frame, getting a normal looking answer plus a bunch of garbage, checking my answer and seeing in the book, "Oh, by the way...those last three terms are sometimes called the Euler, centrifugal, and Coriolis forces."
I can still remember that feeling of "Hu-whaaaaa?"
The video didn't say it explicitly, but the simplicity mostly lies in the fact that setting the derivative of the Lagrangian equal to 0 gives the equation of motion. Reason? This calculates the minimum of the Lagrangian, which is the solution by the Principle of Least Action. So, take any isolated classical physical experiment, and you can get orbits, trajectories, and other equations of motion just by setting the derivative of the Lagrangian to zero. Of course, this ignores Chaos Theory, but that is another story...
Thank you so much. No formal education past high school and this was completely understandable. I desperately seek more stuff like this video.
Thank you so much for this video. I m doing my masters in physics and for the first time I have lagrangian formulation of mechanics and its been 2 month, and its been chaos in my head and for the first time I could develop some imagination of what might be happening, this video was a boost that I strongly needed. Thank you so much great work.
1. This explanation was really intuitive and really helped me. Thanks!
2. It's encouraging to see videos on RUclips about Physics recorded by women. Thank you and good job!!
3. Your husband's French accent and other segments in the video made it entertaining and fun.
Regarding your questions you opened to the audience:
I'm a junior in my undergraduate math-physics degree so I can't tell you how accessible this is to someone without a background.
Also, I don't understand the Principle of Least Action enough to chime in specifically regarding "wonders of God" vs "just a mathematical model" but I am a strong Messianic Jewish believer and a major aspect of my passion for physics, since I was first exposed to it in high school, is how the perfection of it all points to an extremely intelligent, creative, and beautiful design. Sometimes my eyes water when I read something cool in physics (or even in math) and I think that happens to me because I'm experiencing deep awe and admiration for God as a result of learning something remarkable about His creation :)
Logically, there seem to be strong arguments for both sides and ultimately I don't think one can really use logic (which is a human creation anyways) to conclude anything about the existence or involvement of God in human life :)
Thank you so much for making this video!
This is my favorite channel these days. Thank you for your amazing work!
Your videos are perfect for me. Love extending my physics knowledge with what has been learned since I graduated and taught physics. Thank you!
This woman seems to be made entirely of charisma.
She lost it when she pulled her french hubby out of her hat.
I loved all the other parts though.
She has the best accent
I look at her up and down, see a strange lass with lots of charm from bottom to top.
Or maybe she is made of fake auto-generated comments. I cannot believe people still fall for this in 2019.
@@zackfair54
Fall for what?
I learnt some Lagrangian Mechanics over the past couple of months, and it (sort of) culminated today, with the submission of my first ever research paper - a Lagrangian formulation for non-uniform rotor whirl prediction...
Far and away you make things easier to grasp, Jade. You are doing quite well. Your enjoyment is contagious.
Loved the analogy between the car and light particle. The graphics are nice and simple but really helpful to understanding. I studied physics at school and at uni a bit. Didn’t continue with it but still very interested. You’re a really good teacher. Look forward to more - particularly about theories, equations, models etc that challenge us to think differently about reality. Keep it up! Thanks😊
This is one of my favorite videos about physics and science in general because your ideas are both deep and clearly stated. Newton, Lagrange, Hamilton, and Einstein are only making models, not truths. The models are good and should be trusted in the right contexts. So long as people appreciate the context in which models operate, we can make progress.
As a long-serving student of the "Feynman Lectures on Physics",
I can definitely state that this was one of your "better" and more
"intriguing" vids. It is a great example of applying a different
model and system of equations to describe the same physical
( or, perceived physical ) phenomenon. Perhaps another vid
on different but equivalent / orthogonal models for 'gravity'
would also be of interest to your subscribers and audience !?!
. . . " incroyable " !!!
Can't we think light the same way we think of gravity? Well, if we could see gravity, we might think of it the way we do photons. But think of photons the other way, as carriers of a field interaction that's more intense at a light source. We say photons travel in straight lines, but that's because we are a straight line away from a light source. Really, the light is a spherical gradient with the same inverse square law as gravity.
Watching this 3 year old video and I've got to say - still relevant, perfect level, highly enjoyable. Glad you kept going 😊
Using Lagrangian Mechanics in continuum mechanics right now and this is such a nice, brief and comprehensive introduction to the concept. Thank you!
I suck in math, I studied biology. Your videos are super accessible and fascinating!! I can't stop watching :D
Love the topic! Lagrangian and Hamiltonian mechanics are way underappreciated by the non-physicist lot.
This is such a great video! I would like to see also a video on how the principle of least action leads to the symmetries of nature which are the basis of conservation laws. You are one of the best way explaining things, and I think this may be the most important and fundamental topic of all!
I was today years old when I learned that there are many, many more people in the world who are interested in science and skepticism than ever before. Please keep doing what you are doing. it is working.
We are changing the world. :)
Hi Jade, I'm a bit late answering your question: I just found your video. Hope my answer is still somewhat of interest to you.
I live in Belgium (bonjour à ton mari français ;-) ) where I was born in 1961. I have a university degree that involved some science (math, stats, physics, chemistry...) but was mostly geared towards economy and management. I have an extremely broad range of interests, and have been dipping back into physics in the last years, especially trying to wrap my head around quantum mechanics (though not really digging into the maths involved... :-/ ).
So your videos are exactly what I need. They help me improve my understanding of physics, by providing me with an accessible interpretation of Newtonian / Lagrangian / Hamiltonian maths that I never had before. A big BIG thank you for that ! Keep at it. You're on the optimal path :-D , well at least from my perspective ;-)
Cheers
Gilles
_"...I'm going to try to convey to you the gravity of this statement."_
*Wow, that's HEAVY...😝*
In my current Space-Time, I'd say that's deeper than a black hole.
"There's that word again. 'Heavy'. Is there something wrong in the future with the earth's gravitational pull?" ^^
Oh, Jade, you are absolutely ace! I've been watching your vids for a couple of months now and I love them. Don't worry about going too far... I did humanities and I can follow you pretty well. After all, your happy enthusiasm is deliciously infectious! Totally love your stuff! Keep it up like this and I'll keep right on watching.
You are such a good teacher!! Thank you Up and Atom.
I am 56, have no background in physics but find the subject fascinating. Your car and water analogy was excellent and having recently subscribed am really enjoying your videos. You pitch them well. Keep it going!
Excellent. I always wondered why the Lagrangian was like it is. Now I have a better understanding. The part I did not like about university physics was that everything was about solving problems, not really seeing the relationships. Thank you.
Your intuition are the best way to explain things... you're completing your motive
"The Universe is under no obligation to make sense to you" -Neil deGrasse Tyson
Yes, it is by God will.
@@amoonra8385 are you saying you have a obligation to understand "God will"
because sound like you got a pretty big ego then.
"The God will is under no obligation to make sense to you" = "The Universe is under no obligation to make sense to you"
@@MouseGoat I dont understand sir?
@@MouseGoat no, he is saying there is a rational Being (namely God) who created the Universe, therefore it is imbued with some of His characteristics, and one of those being "rational", the Universe has a rational sense. We being rational creatures (although obviously limited) can also understand this rational structure in the Universe, to some degree
@@MouseGoat hahahaa good point, you bridged two ideas very elegantly.
I got my BA in physics from the University of California, Berkeley a long time ago. I spent 30 years as a mechanical engineer at the Lawrence Berkeley National Laboratory. You are doing fine with the clarity of your videos.
I have always come down on the side of physics being a model of the universe. I am not much concerned about reality in any philosophical sense. If it works then use it - the engineer in me says. Knowing that uncertainty, whether in quantum mechanics or in measurements, is fundamental to what we can know experimentally convinces me that any clean statement of physics can only be a model.
After studying physics for some time now i’ve come to realize that for you to understand an explanation, you need that explanation to resonate with you. It doesn’t matter how much detail you provide if your brain doesn’t buy the premise. Thus, the best way to teach is to present multiple viewpoints of the same problem.
This was such a fine explanation, thanks for this jade!
The Universe is lazy, especially when you're looking at it.
Rhade: the universe isn't lazy, it's so smart that it's infinitely efficient. That is a very different way of looking at the principle of least action, and probably the right way. When we are lazy we are being very inefficient.
Lol
Even a supernova?
If you look at the footpaths in mountainous areas, carved over generations, I'd bet that they represent the most efficient path from point A to point B. People (and animals) are just particles trying to use the least energy possible.
This video is great. I would like to learn more about Lagrangians. Thank you for posting this. I am an infectious disease physician with a background in physical chemistry.
I came across your video yesterday. They are so good that i keep watching every video after another for 1 - 2 hours!
I'm a college dropout,a bum from the philippines, and i enjoy watching your videos. I dont runderstand everything perfectly but i understand enough that i am able to enjoy it and be fascinated by it. You explain physics very well in a simplified yet interesting manner for simpletons like me, and you're a breath of fresh air in this time of chaos. Good job and thanks. ✌
A speaker at a conference I attended made a wonderful comment: All models are wrong. But some models are useful.
That quote is a favorite of mine, too. I've been attributing it to George Box, who included it in an _excellent_ text book called "Statistics for Experimenters." It's particularly relevant for statistical models, but the lesson extends to all applied mathematics and arguably to mathematical physics.
And some models are just really beautiful but not that useful
does that include underwear models?
I always thought of it as all models are inherently inaccurate, some are simply less inaccurate than others. Modeling the trajectory of a known mass under known conditions, can be fairly accurate while trying to model the stock market, highly inaccurate. One uses fairly straightforward physical parameters the other includes a lot of psychology.
This is awesome! I would love to see a similar conceptual explanation of Hamiltonian mechanics.
Thank you Jade, for nobody had taught me refraction like this. Why is this not taught in school and colleges?
It's taught in colleges but not very well/thoroughly unfortunately (that is my experience anyway)
If two different methods of modelling something both give the same results for every case they can be tested with (like the refractive index/minimum time of flight solutions for light refraction) then they're mathematically exactly the same thing. For most problems I've seen the refractive index method is much more straightforward to apply, hence it being more popularly taught.
A much better example many people will have seen is using the equations of motion vs. conservation of energy to describe how masses move. Both give exactly the same results in all cases, so they're the same model, just looked at from different angles, but in this case both methods are widely used as both methods are easily applied and depending on the problem usually one method is much easier than the other.
It's only when models disagree that there's any chance of devising experiments to determine whether one model is more correct than another. Often very difficult problems in one method are very easy to solve using another, which is why it's good to be familiar with as many models as possible as it makes it more likely that you can find a quick intuitive solution for new problems.
@@upandatom Probably because professors have to worry about grades and homework and a lot of them have probably been teaching for so long they forget what's it like to learn something for the first time. You clearly work on your videos devote a lot of time time to them, and because you don't have to worry about grades and meeting curriculum requirements, you can focus on the content and explaining it well. You also clearly remember what's it like to learn this stuff for the first time, so you make it simple enough that we can understand it without having a physics or math background. RUclips is great for for learning because they are lots of people like you making great videos. Yours are up there with The Science Asylum, Minute Physics, and 3Blue1Brown in terms of quality. Lots of videos explains things well, but yours and a few others stand out because of your obvious enthusiasm and enjoyment in the subject and your excellent animation.
Read optics by Ajoy Ghatak
And Feynman lectures . It is explained in those books.
I found my new favorite channel. These yourube educators may one day change our current education system by making knowledge more accessible.
Jade you are a total science communicator ROCKSTAR! I discovered you only. approx 48 hours ago and so wish it was much sooner.nl/.Please don’t stop you’re brilliantly understandable and just freakin greatly entertaining videos. re knowledge about how crazy crazy non-real reality is and isn’t is...nl/THANK YOU😊
My new pickup line is, “Are you real or are you a model?”
heheh, that's good
i feel like there may be some context lacking in this scenario. you'll probably just confuse her... it happens to me every time. I've been following the path of least action since puberty...
Non sequitur
or how about a math one: "Are you a circle? Because when I am within your perimeter I start to become irrational! Thus, only together can we transcend to become that which is real; you need but consign, uh, cosine yourself up to me!"
"Huh? What do you mean my chances are the same as the derivative of a constant? What do I look like, a mathematician?!"
@@Blox117 true slayer right there...
I think both Feynman's and Euler's views are true. There is a certain pattern to nature that just makes sense somehow but at the same time, for all practical purposes these are the models we've come up with for our work and we'll use them as models. We'll leave the philosophising for later, once we crack the quantum box.
As a non-cartesian individual, with average-at-best knowledge of physics, I think I can safely say : Yeah, you do make sense on your explanations.
(Also, welcome to the Recluse club. We don't meet up.)
Found it really helpful in understanding Lagrangian as a 1st-year Physics major ... thank u thank u
You came across as a pure, affectionate, curious, intelligent and studious 'little' girl. God bless you! Though I've most of the times struggled to understand Physics, but you DID make it easy. Thanks.
Jade!
Congrats in advance for 100k!
Comment for after the ad: You're doing just fine. Keep going.
She is doing fine and for those of us with an advanced knowledge of the subject her shallow coverage is more than compensated by her bubbly positive energy.
You're such a cute couple!
As someone who played with Kerbal Space Program, I was immediately intrigued by "lagrange" because Kerbal Space Program lacks Lagrange points. That's one of the first physical concepts I actually understood which isn't modelled in Kerbal Space Program.
The Principia mod adds n-body mechanics.
yeah they only use spheres of influence in base game
Great video. The statement "physics is a model", resonates so much with me and puts me at ease with endless number of paradoxes out there.
Jade, it's not just how you explain things, which is excellent, it's that you are thinking deeply about the meaning of physics and that you see beauty in it. I find this is rare in popularisers of science who tend to be story tellers, telling the same stories over and over.
I'm an old engineer, who has prided himself in being able to do two things: solve impossible Real life problems, and to explain nearly anything. I love everything about your "way". BRAVO! Viva Feynmann!
back to the refraction example... consider the case where the light source is below the surface of the water. if the angle of incidence with the air/water boundary is greater than the critical angle, the light is totally reflected back into the water. it never makes it into the air, where (according to you) the "action" should be less. how does the principle of least action account for that?
I had a similar idea to this way back in school. Basically to explain wrt this case I believed that action that light tries to minimise is not time taken but the actual speed of transmission itself. Since the speed of light remains constant in all frames of reference so I imagined it like basically the speed of light is fixed. So since in a denser material light actually slows down physically, it actually bends in such a way that it has to travel a shorter distance inside the denser material. So OVERALL average speed of light would remain constant. Thinking about it this way can explain the thing you are talking about (total internal reflection).... If light hits a material boundary in such a an angle that it cannot makeup the constant speed by bending it simply never goes into that medium and gets reflected back.
+THeMin100 - ok, here's your fundamental error. you start with, "Since the speed of light remains constant in all frames of reference..." that's NOT A FACT. there is ZERO direct experimental evidence to support it. let go of all the BS you were taught. free your mind and think for yourself, NOT in mathematics, but in CONCEPTS. if you can handle the calculus, i recommend to you "Old Physics for New" by Thomas Phipps, which gives a thorough and absolutely indisputable deconstruction of SRT, and exposes ALL of the fundamental flaws and egregious blunders saint einstein made. or just stick to the dead religion of scientism. your choice.
"Einstein's relativity work is a magnificent mathematical garb which fascinates, dazzles, and makes people blind to the underlying errors. The theory is like a beggar clothed in purple whom ignorant people take for a king. It's exponents are brilliant men but they are metaphysicists rather than scientists." -- Nikola Tesla
besides his 1905 paper on the photoelectric effect (which was no great conceptual leap in itself but merely put together in a fairly obvious way ideas previously conceived by others), einstein's only other significant contribution was that he believed QM and especially the Copenhagen interpretation was fatally flawed.
remember, CONCEPTS come FIRST, and math follows. with the photoelectric effect, einstein did that. with SRT and GRT, he substituted "thought experiments" for actual physical observations. that's why they are wrong. even worse, today it's TOTALLY back-asswards. "scientists" have forgotten reality doesn't have to abide by equations. equations have to be consistent with reality. we use them when they work, and IGNORE them when they don't. fr'instance, how would you solve this problem? ignoring aerodynamic drag, how long does it take a rock to hit the ground when dropped from a height = s? you would rearrange s = 1/2at^2 and solve for t, but doing that you get t = ±√2s/a and plug in the values of s and g. but you get TWO answers. you IGNORE the answer of NEGATIVE TIME, because you "know" THERE IS NO SUCH THING IN REALITY, even tho the equation tells you there is. that simple example is lost today. today, abstract mathematicians who have NEVER conducted a single experiment in a lab pose as physicists. just because someone can derive an equation, DOES NOT MEAN that it automatically must describe REALITY.
"A mathematician may say anything he pleases, but a physicist must be at least partially sane."
-- J. Willard Gibbs
"Insofar as mathematics is certain, it does not apply to reality. Insofar as it applies to reality, it is not certain."
-- Albert Einstein
"Today's scientists have substituted mathematics for experiments, and they wander from one equation to the next, and end up with a structure that has no correspondence with reality. [They] think deeply instead of clearly. A man must be sane to think clearly, but it's possible to think deeply and still be quite insane."
-- Nikola Tesla
@@johnmichael1594 Uh but there is experimental evidence?? And infact in use. Do you use GPS? If you do then do read up how the satellites are synced up. Although satellite communication is not my area of expertise, I am however a communication engineer and do know the basics. We heavily use SRT equations for syncing satellites and ground stations along with different satellites in different orbits. It's necessary because the speed and the lower gravity at which satellites operate and our rate of data communications makes it necessary to mitigate the time dilation effects and the Einstein equations works there beautifully. Now you also missed the point of the video, I am not denying that relativity no matter how useful or accurate is just a model just like every other mathematical model. But what I am saying is relativity only doesn't work in one area i.e at the quantum level where both theories disagree on micro gravity. Apart from that case nowhere was relativity found to be not satisfied. There was uncertainty yes but no definite proof of relativity being wrong. Also just because something is not intuitive and doesn't follows common sense doesn't mean that it cannot fully model the things that actually happen. I am up for a whole new model but for me to accept that it must be objectively better than relativity in some sense. And also have the practical utility that relativity has. I like to keep and open mind man.
+TheMin1000 - that is evidence that clocks on satellites run at different rate than earthbound clocks. THAT'S ALL. there are an infinite number of theories that would account for that. any connection between the OBSERVATION of clock speeds and the speed of light ARE CONJECTURE. do you even understand the DIFFERENCE between facts and theories? READ THE BOOK. or close your mind and worship at the altar of scientism.
@@johnmichael1594first give just "*one*" of those "*infinite*" number of theories that you are talking about. Second if you had read my whole comment you'd have known that I said the same thing about it being a conjecture/ mathematical model... But it doesn't matter to me if it's what's REALLY happening because the things we have i.e the model that we have is being used for last half of the century and the equations it gives agrees with observable phenomenon and has been put into good use and gets us actual results. So why would anyone Change it for something completely new, you know the phrase that "if it ain't broke then don't fix it". You may come up with a better/different model but at the end of the day it's gonna be just that man, a model. I don't believe we as humans can ever completely know the true objective nature of the universe as it's filtered through our own brain and there will come a point where our brain's resolution wouldn't be enough to capture some of the finer details. So yeah I can say the same thing about any theory you make and call it's just a model/conjecture and there will be more than one ways to look at it just like Newtonian mechanics in the video. I leave the making of better models to those who are smarter then me and want to completely sacrifice their life to science. That's why I became and engineer and not a scientist... And I wish you luck, tell me when you get the Nobel prize for your model. Also bro please understand what science is. Science is not a religion, there is no alter to worship in science. One day suddenly something may be found that shakes our theories to the ground. And you know what scientists are going to do then? They are going to admit being wrong and try develop a new model taking into account the new things that were observed. Smaller theories keep changing and made better everyday. In science we don't get fixed into one mindset that's why there are peer reviews in science. If you are really about disproving the general relativity then you know what the scientists would say? They'd say you are welcome to try. If you can give and actual mathematical proof it will be peer reviewed and accepted because a theory that disproves relativity is going to be ground shattering and very important milestone. I urge you to do that instead of acting superior by looking down on the work done by many. Also do read about the scientific process. Facts and theories are inherently related. It's very logical. First you observe a phenomena/facts actually happening then you create a hypothesis i.e you try to give an explanation of why the thing you saw happening, happened. Then You experiment/test your hypothesis by trying out different test cases to see if your hypothesis can account for all conditions, if it can it becomes a theory until someone finds something that breaks it. If it can't then you go back to step two to create a new hypothesis. So you see it's only after confirming with experimentation that a hypothesis becomes a theory. I.e facts have a lot to do with it.
Could we see it through model of Copenhagen interpretation model also that is, like a Quantum object it chooses all the possible paths but the one that become reality to us, is the only one which follows the laws of least action. Is it could also be the case? Please also share your precious view on it so that I could become more clear about it. Once again thanks for another enlightening video.😊😊keep it up.👍👍
I know something about Langrangian Mechanics and didn't think a short video could be of any value. But this was a great introduction.
While studying QED, I ran into a problem. My professor suggested that I write Dr. Feynman for his help. He wrote back and told me just to use the model and not to get caught up in any physical interpretation. It has been a guiding principle for me ever since. My copy of his lectures has a special place in my library.
What if things take all paths, and the shortest path, is the one realised by the particle, or the path of highest probability?
Edit: I think the principle of least action makes me wonder if life in the universe is inevitable as the fastest way for the universe to increase entropy with less action.
Especially intelligent life, we can process and waste a lot of usable energy and increase the universes total entropy.
In 1933, Paul Dirac discerned the quantum mechanical underpinning of the principle in the quantum interference of amplitudes (en.wikipedia.org/wiki/Principle_of_least_action)
What if all paths were taken, and the one taking the least time collapses the wave so it becomes reality?
This is essentially the Feynman path integral formulation or "sum over histories". Except it is not necessary to collapse the wave function as that is a feature of interaction with a larger system. What it does mean is that you add together the probability amplitudes of the all the possible paths, which interfere with each other to produce the amplitude of the most likely path. Amazingly, this probabilistic treatment works out the same as the principle of least action. (Although maybe not so amazing as quantum action is at the heart of the Schrodinger equation).
But if it doesn’t become reality until the wave function collapses, then the ones that didn’t collapse it weren’t real, were they? And how can something that’s not real take a path? The path isn’t even real. You’ve done something really important, here, which is to show that QM, to a much higher degree than NM, is just a model. It’s not a description of reality, but only a way of calculating outcome probabilities.
Then why does double slit experiment not always collapse and only cause two lines ?
@@matgggg55
That happens when they take the measurment BEFORE it moves through the slits.
@@dialecticalmonist3405 I don’t get ur point? If the original comment is right then that shouldn’t matter wether it was measured before or after which is why I said “always”
Can anyone explain new concepts better than Jade?
6:47
What are you stuck on mate?
Fineman was pretty good
Jade is great
I conclude that I have a problem with keeping attention for any more than a moment. I have always felt this for most part of my life, in school, around people, while reading, thinking, etc. Right now, I understood the idea Jade tried to explain us in this video, I understood the examples as well - but the thing is, I have watched this video at least 5 times and did not have any context what of what was going on, earlier. New dots have connected now.
Thank you.
Hi Jade, I have an arts background and find your physics presentations lively and interesting.
I am now in my 60s and choose to broaden my topics of learning to include science related presentations yours are refreshing, Thank you, Lewis
3:08 amazingly, ur husband looks pretty much alike pierre de fermat! ;)
We're in a simulation and the person who made it wants to minimize the power needed to calculate all this. Plain and simple, mistery solved, gimme my nobel.
Sorry, no Nobel for you... the person who made this simulation has no reason to minimize the power since they are also only a simulation.
@@Hank254 ah shite of course, the simulaception
or how about this: we dont actually exist
we are what it is to be 'nonexistent', and what all we think is existence is merely the ground state for nonexistence.
It is a bit over my head, but I listen and try to keep up. I have learned from watching your videos.
Wow ....spend my whole day trying to understand D’Alembert and lagrangian theory..... finally I did understand with this video .... thanks
I might have cried at the end...
I wish my professors had your same approach, this care for our understanding of the topic and concepts warmed my heart.
I hope you get to reach as many people as possible and show them how amazing physics is and how anyone can learn it
I'm picking "nits" on your pronunciation of "Leibniz" because it should end with "nits" ;p
Seems like your question about physics being a model is closely related to the question of why is math so good at describing reality. So, for me, the question boils down to: is math discovered (in this case physics would point to truths about the world) or invented (here, physics is just a model)? IMO, this is the most interesting question in the world... is math simply a language or is it THE language.
If information is a carrier of existence then we are unavoidably inventing models of it. If information is actually what existence is made out of, then we are discovering it. And this is of course not an answer to your most interesting question, but it is my personal most interesting question. I don't expect either of us getting an answer in our lifetimes, for better or for worse.
This was already the way I saw physics. Didn't know it was an actual principle
Exactly lol. The moment I learned electrons go back to their ground state, I was like these guys sure seem lazy. Of course optics and QM confirmed this further
Very, very interesting issue. Nowadays I tend to think that physics, chemistry and all forms of science are models. They are ways in which we make phenomena understandable to ourselves and we use them because they work for us to calculate and predict the behavior of matter and energy for instance. Of course, we are yet to discover many nuances, facts and phenomena that might have been unobserved so far but do have effects that appear to us as anomalies of flaws in current models. Dark matter for instance, is a concept which results from observing gravitational acceleration in universe at rates that do not match observable matter. The current model takes us to think that there is some matter that we cannot see by using the available technology. But that we might discover some other causes which lead to update or change the model is a possibility. Excellent video, Jade 😀👍
I have been studying physics for a long time and that is THE best explanation for the principal of least action I have ever seen!!! Wonderful!