I know what you're thinking: Either Henry is taking some well-deserved time off and I'm just helping to fill in during that vacation, or else he's currently tied up in my basement providing me occasional sound bites for food while I slowly take over the channel for good. To anyone worried about case #2, don't be silly. He's in the attic. Way too many escape routes in the basement.
I love how you could understand that with tenth grade math and eleventh grade physics, and also the satisfaction you get when it all clicks together. Grear job!
I am sure he wasn't even refering to this when saying that. He probably was refering to the crazyness of quantum theory and relativity, things so crazy that this seems like kids play.
John there is empty space at the other focus (in a real system there might be some dust or another planet passing near the focus though, but it can’t stay there)
“You don’t need calculus to understand this” *3 minutes later* “As you can see, if you keep adding infinitely small sections to this polygon, it trends toward a circle”
"What special curve satisfies the property that the tangency direction for a point theta radians off the horizontal is given by this vector from the special eccentric point from the circle to a point theta degrees around that circle from the vertical? Okay... Is the question clear?" Uhhhhhhhhhh... *infinite intelligence load error*
I am so sorry, but i just liked your comment, even though it had 69 likes. Thankfully, i have the infite intelligence required for this video and i managed to unlike it, not dislike, but unlike, so that it still has 69 likes. Sorry for the inconvenience
Basically you need to understand for any point along a curve, its velocity vector has a direction tangent to the path. The bit with constructing a circle by placing the velocity vector tail to tail stumps me tho. Rest of it is easily understood if you think about it.
Man, this 3b1b guy (grant sanderson) really deserves more recognition and some prestigious awards. He is one of the most influential math guy in present history, so many people like me are everyday getting inspiration to study mathematics from him.
Thank you for the effort that was put into this. Amazing people, teaching millions of anonymous people, you deserve more gratitude that can be offered in a comment!
Once I get into, and then through college, I'm definitely going to build a time machine and yank Feynman out of some class just to show him this video adaptation of his lecture. Beautifully conveyed!!
I admit I'll need to watch this many times before I might have a decent grasp of it. I'm in my 60's & was a high-school dropout. I went on to get a modest amount of formal education & training in a limited variety of subjects. I did okay with electronics algebra & basic trig, but then I hit a plateau. It took me a good decade to recover from that setback, and begin to realize that math can be awesome, beautiful, and even entertaining. I became a person who wished they could have been an astrophysicist. Part of that desire came from finding my way back to a youthful obsession with the nature of the universe, of which I'd all but forgotten. Later, I began to see how impressive were the skill sets of many of the world's physics giants. In the last several years, while I mainly do more-mundane, day-to-day achievements of a kind, I spend a lot of time examining everything I can find on the laws of nature & the stories of science. I can't seem to get enough of it. But I'm too often struggling with concepts that are way over my head, and I've wished to find an easy way to learn some of the fundamentals. Meanwhile, I've tried hard to acquaint myself with every existing variety of fields in which the highest math skills are put to work. I've gotten some great books from the library, and have devoured countless, thrilling stories of the history of science. I've been given or purchased several of my own, too, and have read all the magazines for the last 15 years.. I've learned about the important breakthroughs of Aristotle, Ptolemy, Newton, Brahe, Copernicus, and quite a few others, including Johannes Kepler. I have an awareness of a good number of modern-day achievements, along with today's heavy hitters. too. I can't entirely explain this fascination I've developed. It has a grip on me, and sometimes I think life would just be a lot easier, if I dropped the whole thing, but but just won't go away. Fortunately, like Ron Burgundy once said, that is in no way depressing. For all these reasons, I found a great deal of enjoyment in your fantastic video presentation. It's one of the most helpful demonstrations I've yet come across. You are to be commended, for providing the layman with such a near-intuitive overview of this sort of topic. I'm anxious to see what else you've posted. excellent job!
New MinutePhysics video notification: "oh neat, I'll add it to watch it later" Topic is "Feynman's Lost Lecture": "Maybe I'll listen to it in the background" Featuring 3Blue1Brown: **heavy breathing** Video duration is 21 minutes: **drop everything I'm doing and hit the fullscreen button**
this lecture is very relatable for me for puzzles that i picked up in povey's problems book and polygons with limits to circles, with even some physics i learnt in A-level. It was all just buried underneath layers of geometry and how the formation of triangles revolving around circles can be used in such a way. I like how you related a physics and mathematics interpretation of the problem not just for your viewers, but as a trace of what feynman truely believed and enjoyed life for. Thanks for releasing these videos 3B1B, and you minutephysics. Nicely done with physics and maths and i hope to see more collaborations in the future, if not already!
@@lorax121323 would agree, if you can't grasp why forming an elipse this way is not the definition of an elispe just worded a different way....you shouldn't be watching this channel
Rite! I especially like the anecdotal story of RF debating 2 post-grad guys in a cafeteria, about his alternative to cosmic expansion. And, despite the last scene of MIB 1, RF's shrinking universe hypothesis is un-disprovable!
On "watching Feynman 'splain things is just like watching Bobby Fisher play chess"... How true! In both cases, I feel I understand about 20% (to be generous) of what's happening. : ) (I think I'll come back to this video from time to time)
You know it think that's what we were born for. To gain infinite intelligence. Like you wil learn to take down walls if you run into them so often, and thus find yourself in always a bigger space, a bigger world, and have more freedom (guaranteed that you don't run into any titans).
Thank you for this! Several, "That is so cool!" moments in this video, and...as much as I love learning...I only went as far as Physics 101 in college. Thus, it's not just cool how all of this works out; it's cool that it can be broken down into individual pieces that are each relatively easy to digest. I'm suddenly reminded of Zen Archery. Don't think about the target; just get each individual step right, and your arrow will arrive at its target "on its own".
I think the visuals made it elementary to understand, but I loved the linguistic complexity needed to be able to effectively communicate the concept in the first place. Granted without the visuals I probably would not have understood, nor would I have wanted to understand. Great video!!!
I think this was actually somewhat easier to understand than some of his videos, although it might just be because I've has most of the past week off and am actually caught up on sleep.
Gives me hope that he'll cover my suggestions of RSA and knot theory someday. (Though the latter might be difficult to animate…) To anyone reading this, I highly suggest checking out Pulsar's write-up in the link given. It can help solidify any remaining confusions.
Thanks a lot for the video Grant...You really tried your best to keep it simple...even though I had to occasionally pause and ponder. I wish 3blue1brown makes a collection of all the lectures of Feyman !!!
10:48 *3B1B* : Well, specificly it says that this quantity times the mass of the object stays constant, but, I mean, the mass of the orbiting object isn't gonna be changing. *Michael* : Or is it?
@@Hexanitrobenzene Therefore the trajectory of a comet will involve a more difficult calculation.... Now imagine the rate of evaporation is inversely proportional to the distance to the sun as well as proportional to the surface area of the comet facing the sun, would that be a reasonably solvable situation(without getting into numerical analysis)?
Keep up the asking questions out loud stuff with a slight pause. It aids learning and facilitates the drawing together of seemingly unrelated threads within the consciousness of the viewer. Good work.
Trying to visualize this is completely inversely proportional to the methods I was taught throughout all of my education. SAD. We should teach HOW to learn not just regurgitating "facts" and "laws" which, imho, are in "fact" just theories based upon the human's finite perception (real and imagined) ...nevermind...what was I saying? LOL
Very realistic, no joke, answer. An average human brain has ~1500 ccm of brain matter. Mathematicians like Gauss had ~1800 ccm of brain matter, that's 300 ccm or 1 coffee mug of brain matter more than regular people - there is just no way for a regular Joe to deeply understand advanced math, no matter how much effort he puts in, preiod. Your abilities are hard capped by the total number of axons and neurons, it's that simple. Parents, don't lie to your kids that they can be anything they want if they study hard enough, tell them the truth - they can only be what their genetics allow them to be - their abilities in life are predetermined from birth, nothing can change them. Blackpill 101
Unfortuentaly no, this is because at the beginning when the lines were drawn, they formed a perfect circle, so taking the perpendicular bisector of each one would still form a circle, just two smaller ones
Grant not only is a genius but he is also a fantastic teacher. Honestly, every time i didn't understand a specific part of the proof he addressed it right away, almost as if he could read my mind! That is, in essence, teaching, and he's brilliant at that!
David Goodstein is also the spiritual grandfather of 3B1b videos: he made the landmark “Mechanical Universe” series that aired on PBS. It featured a mix of animated equations and historical re-enactments that brought physics to life for a generation.
The Great Physicists' Road Trip by Ms. Rachel C. Millison Great physicists from the past decide to return to Earth for one last road-trip vacation to the coast together. They all appear on Earth on the appointed evening. Heisenberg pulls up behind the wheel of a gigantic 1930's car, a huge grin on his face. As they're getting in the car, Hubble looks up and says "What a wonderfully dark sky". "Shouldn't be" responds Olbers. "Always has been" says Hoyle. "No, it hasn't" says Lemaitre. "I knew that!" says an embarrassed Einstein. Once they're all in, Teller says "Hey guys, this trip is going to be The Bomb!". "Yeah, but why do I always have to organize?" asks Oppenheimer. "Where exactly will we end up?" asks Kepler. "That's impossible to predict" says Bohr. "I just can't believe that's true" says Einstein. Heisenberg punches the throttle and the old car roars off. "Say - this thing sure accelerates" says Newton. "I don't know, Isaac. It feels like gravity to me" smirks Einstein. Later that night, as they are speeding down a country road, a police car catches up to them and pulls them over.[1] "Do you know how fast you were going?" the cop asks. [1] "No, but I know exactly where I am" Heisenberg replies. [1] The cop says "You were doing 55 in a 35" [1] Heisenberg throws up his hands and shouts "Great! Now I'm lost!" [1] The cop thinks this is suspicious and orders him to pop open the trunk. He checks it out and says "Do you know you have a dead cat back here?" [1] "We do now, asshole!" shouts Schrodinger. [1] "I think it's time to split" says Everett. "Say, how did you manage to spot us on such a dark night?" asks Hubble. "I saw the light from your head lamps" says the cop. "How fast was *it* going?" asks Michelson. "That's simple addition" giggles Galileo. "Not exactly" says Lorentz. "Look here" says Heisenberg, "how do you know I was going that fast?" "I clocked you over a measured distance" says the cop. "How often?" asks Hertz. "I disagree with your measurement, officer" interjects Einstein. "Don't start tonight, Albert" says Bohr, shaking his head. "What Herr Einstein is trying to say" continues Heisenberg, "is that time was running at a different rate for you than for us". "WHAT!!!???" exclaims Newton. "It's true" says Maxwell. "We're all famous scientists and, believe us, Herr Einstein has proved it, though it came as no surprise to me". "Sounds complicated" responds the cop. "I'll draw you a simple diagram" says Feynman. Totally flummoxed, the cop lets them go with a warning. As he drives away, Doppler cocks his head and listens to the sound of the receding police car. "Gotta love that" he says. "Amen" responds Hubble. Returning to their car, Lord Kelvin remarks "Sure is warm tonight" "Yep - lots of disorder" replies Boltzmann. "In places you'd never expect" adds Hawking. "I was lucky to get away with that" says Heisenberg. "Most cops think they're better than everyone else". "Yes - I hate inequality" adds Bell. "Though you *were* speeding" says Faraday to Heisenberg. "I carefully observed the needle creep from 35 to 55". "Actually, it was jumping, Michael" replies Planck. As they pile back into the car, Bohr says "See here - you must fill the seats in order - no empty spaces allowed. And stop interfering with each other!" "Only one of you can sit next to me!" yells an agitated Pauli. "Say, Werner - it's stuffy in here. Be a good chap and crack the window a bit" says Hawking. "Sorry, Stephen. It can be all the way up or all the way down, but nowhere in between" replies Heisenberg. "Hey guys - Albert and I just figured out a great shortcut. Only one bridge" announces Rosen. "It will save us a lot of distance" says Einstein, "but it might get spooky". Arriving at the beach the next morning, they hurry from the car and stand looking out over the ocean. "Look at the wonderful waves" says Schrodinger. "They don't look like waves to me" says Bohr. Looking down at the fine sand, Dirac exclaims "Look at all the particles!" "Now *those* look like waves" says De Broglie. "This is great!" exclaims Feynman, rubbing his hands together. "Now, lets go meet some girls!" "Let's delay" says Wheeler. "We have to be discrete" warns Bohm. "Girls? NEVER!" exclaims Newton. 1 Based on, and including the original, attributed to Rich Granger, engineer, Battelle.
If TH-cam channels like minutephysics or 3Blue1Brown existed when I was in high school I probably would have become a physicist or mathematician instead of a biologist.
I was a math major for 1 year before I switched to mechanical engineering. I'm now retied and can indulge my first passion. I simply loved this video. I do believe, though that the constructs are merely consequences of natural laws without any useful knowledge.
BLUEGENE13 The joke is that mathemathicians sometimes write QED at the their proofs, which is an abreviation of the latin words "quod erat demonstrandum" which means "what had to be demonstrated".
I appreciate your through discussion of this. It really reminds me of my grandfathers explanation. I was looking forward to your method of explanation, and was quite entertained
*Yes, I'm going to pretend like my brain has enough computing power to fully comprehend every single word in this video and instantly apply it to every subject previous brought up, and watch the video a ×1 speed without pauses.*
Think of operating a cnc machine when carving out, the chips fly in those directions, if the tool breaks it also flys in that direction, just have the infinite intelligence to have the guards shut when it dose!
Wow!! I'm a mathematician, and as my colleagues will, I think, agree, this video gives a lot more intuition and insight than the standard analytical mechanics-differential equation proof which has hardly any geometry and only blind calculation. Thank you!!!
Somehow this seemed even denser than most of 3blue1brown's other material. I feel like I could probably get it all if I spent a couple hours working it out for myself, but right now my head just kinda hurts.
Physics is a different mindset from math, so yeah this did have a different feel. Orbits are really tough at first encounter but incredibly satisfying once you understand, keep at it!
P Sharma I think it's actually the math perspective that's throwing me here. I have a pretty good intuitive understanding of orbits from physics in terms of angular momentum and potential energy (and let's be honest, most of my intuition for orbital dynamics comes from playing Kerbal Space Program) so this sorta abstract mathematical approach is throwing me off. I often find that math is very dense though, so it's not too surprising. The people who came up with our mathematical language did a very good job of distilling complicated ideas into concise and precise language.
I suggest checking orbits out in a college level classical mechanics text, there's way more math involved but it may help you reconcile everything here. The actual derivation of elliptical orbits from Newton's second law is truly awesome and it was a lecture I don't think I'll forget, hopefully you'll enjoy that too.
pyropulse your comment made me laugh so much... If you think physics and math are the same thing then you're either just barely through your majors and trying to talk big or you've been taught rather poorly. This was a wonderful video but it was very noticeably done from a mathematician's perspective, he didn't hit on physical intuition very much because he used math proofs instead which (I'm guessing) is why OP felt like something was different, you with your double major should've recognized that.
Loved this collab. Thanks for this video! Knowledge just blasting off from this video, like water sprinkler.I don't think I managed to catch all the water.
Great video. It's a bit like the classic Cambridge natsci/physics interview question "describe how you might approach proving the following or what laws you would need to invoke'. Thankfully mine was simpler however. We had a first edition of Newton's Opticks in the college library and I was kind of thrilled to request it and read a chapter... in a long-gone innocent age where there was no door security on the college or the reading room.
Latin focō (as in the video) is the ablative of focus, which means at the fireplace. the form focus derives from the nominative which is focus not foco.
Can you imagine what sort of lectures and presentations Feynman would have produced if he had access to the same animation software used to make this video...? 😮
@@Ax_x1om You need to stop judging the quality of a lecture by the fame of the lecturer. This isn't tribalism. There are actual intellectual criteria at play here. Use them.
@@Ax_x1om He gave a series of lectures on quantum mechanics once that I actually used to like... until I thought about them a little more and then it became clear that what he was teaching gave people the wrong intuition about what is actually going on in quantum mechanics. I know that (and why) in his mind it all made perfect sense, but what he was communicating doesn't reduce to the correct physics in the mind of the audience because they lack his theoretical background.
12:41 shows a coordinate frame shift from position to velocity space. I was just looking at the Royal Institute Sean Carroll lecture on Relativity where the simple statement of 'speed of light is a constant' would be a very interesting mental frame to explore. I have been questioning why time is the proper dimension to differentiate on vs any other. What happens if we shift our entire mental frame from position being the default (requiring differentiating to get rates of change) to a mind model where velocity is default on a unit coordinate system? What happens to the other physical constants when c=1 what values would they be and how do they build into something like the fine structure constant?
"So the question is: What special curve satisfies the property that the tangency direction of the slope for any point theta-radians off the horizontal is given by /this vector/ from a special eccentric point on the circle to a point theta-degrees around that circle from the vertical? Okay, so is the question clear?" XD
With each new replay of the video, the question becomes clearer by 1 word. All in all, 41-43 concentrated plays of this video are required for the question to be clear. If you want proof... well, you have this line that shows it if you just turn it 90 degrees into your brain. Good luck & have fun!
This is EXACTLY what I have pondered for many years! Now it is time to take it to the next step: The algorithm is quite simple actually, all mathematics can be defined with only a couple of variables. My computer science professor would look at me cross-eyed every time is suggested that digital and analog were not meant to be separated and thus the constant battle for accuracy with "smaller and smaller slices" so to speak....
Goddammit grant. You couldn't just be a teaching god on one channel, you gotta invade minute physics too? Jk, love you both. Henry, you got me into physics when I was in middle school (going into uni in 2 months) and Grant, recently you made linear algebra make sense. Which was strange for me, because my teacher did an absolutely awful job. Thank you both, you've helped me and many others immensely.
Every bit of this statement is true...... Everytime I watch one of your videos, you take my breath away......just as talented as the honorable Christopher Nolan.
I had almost the exact same experience. Henry got me into physics, Sal Khan got me into calculus, I'm now going to second year math studies in uni with Grant inspiring me with every upload! These people are gifts to humanity!
pyropulse dude, everyone is different. I just took my differential equations course and my first nuclear physics course, maybe half an hour of studying a week per class. Aced it. Not all of us have inferiority complexes like you, and not everyone has to study like you.
Newton started off with a bet to prove this (the ellipse being a consequence of the inverse square law) and produced a series of publications, eventually compiling the principia mathematica out of this seed. However, although he never states this clearly, I'm sure he realized that the proof he gave was for the converse: that given an elliptic orbit, an inverse square force law follows. This was much easier at the time because so much was known about the geometric properties of the ellipse than was about F=m a. In fact, Newton couldn't really mathematically use velocities because they compare two quantities with unequal units (distance, time). Also of course algebraic notations and vectors weren't invented yet. But still Newton claimed to have won his bet, and the Principia avoids any clarity about proving the inverse square law vs. the converse (proving the elliptic shape). I'm sure Newton would have LOVED this type of proof, and this proof in particular! Although I'm sure he'd appreciate how much more powerful modern mathematical notation and ideas such as vector or Lagrangian calculus are. And that's where Feynman and 3blue1brown comes in: Elementary proofs just are the next level of understanding: being able to explain something seemingly complicated in simple terms. With intuitive concepts, but with methods not more complicated that what was available to Newton.
I am not a mathematician but I love it! I once took a physics class called Physics for Poets and this is exactly what it was like. You and of course Feynman deconstructed this concept so that even a guy like me could appreciate its beauty. Thanks!
I just wanna thank you I did not completely grasp it but I do have some insights on it Thank you very much to Grant Anderson and Richard Feynman And of course Newton
Wondered why there's just three likes for this awesome video, turns out I was just one of the first ones to watch it. Now, I should resume watching the vid.
I personally Love Feynman's work... His brilliance wasn't in just discovering new things, but being able to explain them at an elementary level. It is almost like watching Monet paint, or Bach compose music... if we could, that is. My only problem with the video is... how does one pronounce "Principia" correctly, but not "Foci?" They are both Latin words, in which the c is always pronounced hard, like a k. Everything else in the video made perfect sense, but it was like hearing nails across a chalkboard every single time he said it. On a side note, speaking of the relation of Kepler and Newton... Kepler spent over 30 years to develop his laws of planetary motion. There is a museum to him that actually still holds thousands of notes on his work. This is actually motivated Newton to try and find an easier way to solve the "Tangent Line Problem." But, don't be fooled... what Newton wrote about in The Principia was not The Calculus we regularly learn. He discusses it in the third part of the book, and it mostly deals with differential equations. Libenitz really was the one who developed most of The Calculus we learn in school. Newton took the claim solely because he was the head of the Royal Society at the time. The same position Stephen Hawking held until he passed away.
@@coolcat23 I've got degrees in Maths and Stats. We are all horrible spellers... And names. Do you know how annoying it is to have classes with people for 4 years, but everyone forgets each other's names? That is the real reason why we seem so quite, lol.
This video required infinite intelligence to understand. I'd say I understood about 60% of it. 60% of infinity is still infinity. Hence.... you get my point.
its beautiful. When i first learned about the focal length constancy in ellipses it drew all my attention. Maybe should have looked deeper. Maybe thats what makes a Feynmann
Just loved this video ! 3Blue1Brown : you are the best at explaining complex concepts step by step with very elaborated (and beautiful !) animations. thank you
this was a strange experience for me and i dont know what to make of it- but despite never seeing this idea before, almost as soon as i heard the introduction i knew almost every step we were going to use to get there (of course it wasnt a full proof in my head using theories and all, but like the vectors making a circle and the rotations and some of the perpendicular bisector stuff, really all the visual ideas). it just... came to me at the start. never had that happen before.
Newton was using some statements of theorems that he assumed readers of his time would know: that the two lines from the foci of an elipse to the circumference, form equal angles with the tangent to the ellipse.
Interesting to note, at the end of the book "Feynman's lost lecture" the authors reveal that the arguments were first found by Maxwell (From Maxwell's equations) in his book Motion and Matter. So I'd reason that Feynman, who was famously well read in physics books/papers, probably adapted the arguments there for his lecture. Not taking away from the brilliance of the argument and the presentation of course.
But it had a hard K sound before the "u", why not the "i"? Later in the talk he mentioned Newton's "Principia" and used a hard K for the "c" before "i". It's too early here to start drinking.
In (classical) latin Cs are always hard. Caesar is actually pronounced Kaesar which is where the word german Kaiser for emperor comes from. However 'i' should be pronounced like 'ee' rather than the english 'aye', and the 'o' should be a short 'o-' rather than the english 'owe' sound.
I know what you're thinking: Either Henry is taking some well-deserved time off and I'm just helping to fill in during that vacation, or else he's currently tied up in my basement providing me occasional sound bites for food while I slowly take over the channel for good. To anyone worried about case #2, don't be silly.
He's in the attic. Way too many escape routes in the basement.
I love how you could understand that with tenth grade math and eleventh grade physics, and also the satisfaction you get when it all clicks together. Grear job!
Lmao
3b1b: it is case #3 I'm interested in. Got an answer for the LAG of gravity given its known speed? (see separate question)
3Blue1Brown loooool🤣🤣🤣🤣
You think of everything.... until you find out he can break through the roof tiles
As Feynman once said "...it takes tremendous strain on the mind to understand certain concepts.." now I know he was right.
I am sure he wasn't even refering to this when saying that. He probably was refering to the crazyness of quantum theory and relativity, things so crazy that this seems like kids play.
Unfortunately Feynman never explained some of the simplest concepts, like the ellipse. What is at the other focus?
Unfortunately Feynman never explained some of the simplest concepts. What is at the other focus?
John there is empty space at the other focus (in a real system there might be some dust or another planet passing near the focus though, but it can’t stay there)
@@zephilandevol exactly, theres nothing there. so Feynman's analogy is false
“You don’t need calculus to understand this”
*3 minutes later*
“As you can see, if you keep adding infinitely small sections to this polygon, it trends toward a circle”
😂 ∆x v/s dx
Daniel Kunigan
Caculus
@@YaseenKhan-qf8mq The Calculus.
Lmao
i was tricked
"What special curve satisfies the property that the tangency direction for a point theta radians off the horizontal is given by this vector from the special eccentric point from the circle to a point theta degrees around that circle from the vertical?
Okay... Is the question clear?"
Uhhhhhhhhhh... *infinite intelligence load error*
That has stumped me for a minute :D
ngl, i repeated that single sentence at least 5-6 times before i didn't understand it and sucked it up and went on with it
I am so sorry, but i just liked your comment, even though it had 69 likes. Thankfully, i have the infite intelligence required for this video and i managed to unlike it, not dislike, but unlike, so that it still has 69 likes. Sorry for the inconvenience
Basically,... we're back to the (constructed) ellipse within the circle, made with the string and two focal points.
.
Basically you need to understand for any point along a curve, its velocity vector has a direction tangent to the path. The bit with constructing a circle by placing the velocity vector tail to tail stumps me tho. Rest of it is easily understood if you think about it.
Man, this 3b1b guy (grant sanderson) really deserves more recognition and some prestigious awards. He is one of the most influential math guy in present history, so many people like me are everyday getting inspiration to study mathematics from him.
Coming from Al Farabi, that surely means something :)
Why mean@@kamiel79
I find it fitting that a guest video was used to talk about a guest lecture
Serendipitous, to be honest...
@@mabell01 now rotate that by 90°
where can you find that "infinate intellegence" lecture can you please tell me?
G squared?
ooh this gonna be good
Tibees It seems like all my fav science/educational youtubers are on this video or in the comments, incredible, didnt expect to see you here
Yeah it's great!
can you explain what he said at 15:49 please
Heeeey... Good to see you here...
JEE girl.
Thank you for the effort that was put into this. Amazing people, teaching millions of anonymous people, you deserve more gratitude that can be offered in a comment!
I've seen this video 3 times already. I understand what he's saying everytime I watch it, and then forget how he did it the next time I come around.
Write it down
That probably means it's not explained well.
Once I get into, and then through college, I'm definitely going to build a time machine and yank Feynman out of some class just to show him this video adaptation of his lecture. Beautifully conveyed!!
Minutephysics + 3blue1brown + Feynman? Knowledge-gasm!
Sebastian Elytron agree
I consumed so much knowledge that I pooped out an introduction to physics book the next day.
Quantum tunneled.
Sebastian Elytron
Good one...
LOL
I admit I'll need to watch this many times before I might have a decent grasp of it. I'm in my 60's & was a high-school dropout. I went on to get a modest amount of formal education & training in a limited variety of subjects. I did okay with electronics algebra & basic trig, but then I hit a plateau. It took me a good decade to recover from that setback, and begin to realize that math can be awesome, beautiful, and even entertaining. I became a person who wished they could have been an astrophysicist. Part of that desire came from finding my way back to a youthful obsession with the nature of the universe, of which I'd all but forgotten. Later, I began to see how impressive were the skill sets of many of the world's physics giants. In the last several years, while I mainly do more-mundane, day-to-day achievements of a kind, I spend a lot of time examining everything I can find on the laws of nature & the stories of science. I can't seem to get enough of it. But I'm too often struggling with concepts that are way over my head, and I've wished to find an easy way to learn some of the fundamentals. Meanwhile, I've tried hard to acquaint myself with every existing variety of fields in which the highest math skills are put to work. I've gotten some great books from the library, and have devoured countless, thrilling stories of the history of science. I've been given or purchased several of my own, too, and have read all the magazines for the last 15 years.. I've learned about the important breakthroughs of Aristotle, Ptolemy, Newton, Brahe, Copernicus, and quite a few others, including Johannes Kepler. I have an awareness of a good number of modern-day achievements, along with today's heavy hitters. too. I can't entirely explain this fascination I've developed. It has a grip on me, and sometimes I think life would just be a lot easier, if I dropped the whole thing, but but just won't go away. Fortunately, like Ron Burgundy once said, that is in no way depressing. For all these reasons, I found a great deal of enjoyment in your fantastic video presentation. It's one of the most helpful demonstrations I've yet come across. You are to be commended, for providing the layman with such a near-intuitive overview of this sort of topic. I'm anxious to see what else you've posted. excellent job!
New MinutePhysics video notification: "oh neat, I'll add it to watch it later"
Topic is "Feynman's Lost Lecture": "Maybe I'll listen to it in the background"
Featuring 3Blue1Brown: **heavy breathing**
Video duration is 21 minutes: **drop everything I'm doing and hit the fullscreen button**
Felipe Figueroa damn right
This is literally me!
damn true
That true. Just cancelled everything and went full screen.
Even though I couldn't follow everything exactly.
Ohhhhhh, it all makes sense now. Not to me but I'm sure to someone it does.
I'll just stick to god.
That's what I was going to say.
this lecture is very relatable for me for puzzles that i picked up in povey's problems book and polygons with limits to circles, with even some physics i learnt in A-level. It was all just buried underneath layers of geometry and how the formation of triangles revolving around circles can be used in such a way. I like how you related a physics and mathematics interpretation of the problem not just for your viewers, but as a trace of what feynman truely believed and enjoyed life for. Thanks for releasing these videos 3B1B, and you minutephysics. Nicely done with physics and maths and i hope to see more collaborations in the future, if not already!
Newton - "OMG they don't understand my physics!"
Feynman - "Hold my beer."
@@lorax121323 would agree, if you can't grasp why forming an elipse this way is not the definition of an elispe just worded a different way....you shouldn't be watching this channel
@@lorax121323 and that is why he wrote his own encryption ;-)
If anything, Feynman's gift was an ability to put the cookies on the bottom shelf
Hold my bonjos
Not only Newton. It should be all the other physicists vs. Feynman. Feynman was born too early. He should have appeared today on our planet.
"Surely you're joking, Mr Feymann !" is one of the best book I have ever read. Its deep, it's mind-boggling, and much more, it's fun !
My favorite work of nonfiction ever.
Rite! I especially like the anecdotal story of RF debating 2 post-grad guys in a cafeteria, about his alternative to cosmic expansion. And, despite the last scene of MIB 1, RF's shrinking universe hypothesis is un-disprovable!
My favorite book for sure
As my eyeballs glazed, I realized fully that I do not have 'infinite intelligence'.
I guess it's good for us to run into a wall now and then. Wow.
On "watching Feynman 'splain things is just like watching Bobby Fisher play chess"... How true! In both cases, I feel I understand about 20% (to be generous) of what's happening. : ) (I think I'll come back to this video from time to time)
You know it think that's what we were born for.
To gain infinite intelligence.
Like you wil learn to take down walls if you run into them so often, and thus find yourself in always a bigger space, a bigger world, and have more freedom (guaranteed that you don't run into any titans).
You know I'm amazed how aot connected here.
The linking of two masterpieces, so "mesmerizing?" yet so simple.
Thank you for this! Several, "That is so cool!" moments in this video, and...as much as I love learning...I only went as far as Physics 101 in college. Thus, it's not just cool how all of this works out; it's cool that it can be broken down into individual pieces that are each relatively easy to digest. I'm suddenly reminded of Zen Archery. Don't think about the target; just get each individual step right, and your arrow will arrive at its target "on its own".
I think the visuals made it elementary to understand, but I loved the linguistic complexity needed to be able to effectively communicate the concept in the first place. Granted without the visuals I probably would not have understood, nor would I have wanted to understand.
Great video!!!
My head hurts a little, but I think I understand most of it. Remembering it on the other hand.....
BlueKavet you can then always watch it again!
How I feel after every 3b1b video
I think this was actually somewhat easier to understand than some of his videos, although it might just be because I've has most of the past week off and am actually caught up on sleep.
There are three steps in understanding a proof:
1. You can understand the proof
2. You can reproduce the proof
3. You can find a better one
Vladimir Shitov true! I ALWAYS skip to number 3
Holy crap, I suggested this topic to Grant on his subreddit. I can't believe you guys are actually doing this! Awesome!
www.reddit.com/r/3Blue1Brown/comments/86e1jw/video_suggestion_a_geometric_proof_of_keplers/
Gives me hope that he'll cover my suggestions of RSA and knot theory someday. (Though the latter might be difficult to animate…)
To anyone reading this, I highly suggest checking out Pulsar's write-up in the link given. It can help solidify any remaining confusions.
O no you di'nt
Twenty One Minutes Physics
Isn't that the name of a band?
Twenty one savage
What an original joke that has never been used on this channel before.
Stephen Heirtzler What an original comment that has never been used on this channel before.
Zombie Salad What an original reply that has never been used on this channel before
Thanks a lot for the video Grant...You really tried your best to keep it simple...even though I had to occasionally pause and ponder.
I wish 3blue1brown makes a collection of all the lectures of Feyman !!!
Everything to know about physics relates to geometry. This was such a pleasure to watch
This is the most satisfying maths/physics video I've ever watched period.
LOLL'I579 Welcome to the 3blue1brown land.
I'm already a citizen of that place :D
go have a look on fractal geometry ;)
fierce competition? =p
urgh
10:48
*3B1B* : Well, specificly it says that this quantity times the mass of the object stays constant, but, I mean, the mass of the orbiting object isn't gonna be changing.
*Michael* : Or is it?
Well, if a comet goes near a Sun, significant part of it will evaporate. So, it does not hold always.
*Vsauce music intensifies*
*Michael* : Or is it?.. Change... This word is made up out of 6 roman letters..
*Me* : Wtf.....
@@Hexanitrobenzene Therefore the trajectory of a comet will involve a more difficult calculation.... Now imagine the rate of evaporation is inversely proportional to the distance to the sun as well as proportional to the surface area of the comet facing the sun, would that be a reasonably solvable situation(without getting into numerical analysis)?
Dun dun dunnnnnn
The video currently has 467,294 views including my 467,200 views to understand it
That too at 0.5X speed
LOL
LOL
LOL
LOL
LOL
3blue1brown: *explanations*, Right?
Me: Uhhh *brain.exe is not responding*
3Blue1Brown: *continues explaining*
Me: *brain.exe crashed*
David Timothy P yooo for true, I'm just ganna watch Feynman explain it
*_brain.exe_** has encountered a fatal error. Please try repairing the program before launching it again or contact your support team.*
Brain better off after the workout!
Keep up the asking questions out loud stuff with a slight pause. It aids learning and facilitates the drawing together of seemingly unrelated threads within the consciousness of the viewer. Good work.
A guest lecture about a guest lecture! Excellent! Hopefully this will never become known as "3Blue1Brown's Lost Lecture"
I'm afraid I only have a finite amount of intelligence.
otherwise you'd be the one reinterpreting newtons mechanics
Trying to visualize this is completely inversely proportional to the methods I was taught throughout all of my education. SAD. We should teach HOW to learn not just regurgitating "facts" and "laws" which, imho, are in "fact" just theories based upon the human's finite perception (real and imagined) ...nevermind...what was I saying? LOL
Sebastián that's what I'm saying
Very realistic, no joke, answer. An average human brain has ~1500 ccm of brain matter. Mathematicians like Gauss had ~1800 ccm of brain matter, that's 300 ccm or 1 coffee mug of brain matter more than regular people - there is just no way for a regular Joe to deeply understand advanced math, no matter how much effort he puts in, preiod. Your abilities are hard capped by the total number of axons and neurons, it's that simple. Parents, don't lie to your kids that they can be anything they want if they study hard enough, tell them the truth - they can only be what their genetics allow them to be - their abilities in life are predetermined from birth, nothing can change them. Blackpill 101
Sebastián
I feel soo sorry for you :/
I am definitely gonna have to rewatch this several times but I look forward to it
This is AWESOME ~ Thanks for sharing this!! Love 3Blue1Brown! You summed this up awesome!!
0:54 - Notice that the endpoints of all those many line segments form two other circles. Is there a significance to that?
Unfortuentaly no, this is because at the beginning when the lines were drawn, they formed a perfect circle, so taking the perpendicular bisector of each one would still form a circle, just two smaller ones
This channel is amazing. Minute physics, your channel is one of the best out there. Keep it up!
This video came from 3blue1brown. See the video description for more videos like this.
20 minute Physics
Even better!
Grant not only is a genius but he is also a fantastic teacher. Honestly, every time i didn't understand a specific part of the proof he addressed it right away, almost as if he could read my mind! That is, in essence, teaching, and he's brilliant at that!
Thanks for the easy and simple explanation. Every thing is clear now.
David Goodstein is also the spiritual grandfather of 3B1b videos: he made the landmark “Mechanical Universe” series that aired on PBS. It featured a mix of animated equations and historical re-enactments that brought physics to life for a generation.
And the animation of Kepler’s second law is so close to the one from the Mechanical Universe that I think it might even be an homage.
True
2000 years later:
The physics/maths behind creating level II universes.
Animated and taught by 3b1b the 500th.
So each 3b1b lived for just under 4 years?
The Great Physicists' Road Trip by Ms. Rachel C. Millison
Great physicists from the past decide to return to Earth for one last road-trip vacation to the coast together. They all appear on Earth on the appointed evening. Heisenberg pulls up behind the wheel of a gigantic 1930's car, a huge grin on his face.
As they're getting in the car, Hubble looks up and says "What a wonderfully dark sky".
"Shouldn't be" responds Olbers.
"Always has been" says Hoyle.
"No, it hasn't" says Lemaitre.
"I knew that!" says an embarrassed Einstein.
Once they're all in, Teller says "Hey guys, this trip is going to be The Bomb!".
"Yeah, but why do I always have to organize?" asks Oppenheimer.
"Where exactly will we end up?" asks Kepler.
"That's impossible to predict" says Bohr.
"I just can't believe that's true" says Einstein.
Heisenberg punches the throttle and the old car roars off.
"Say - this thing sure accelerates" says Newton.
"I don't know, Isaac. It feels like gravity to me" smirks Einstein.
Later that night, as they are speeding down a country road, a police car catches up to them and pulls them over.[1]
"Do you know how fast you were going?" the cop asks. [1]
"No, but I know exactly where I am" Heisenberg replies. [1]
The cop says "You were doing 55 in a 35" [1]
Heisenberg throws up his hands and shouts "Great! Now I'm lost!" [1]
The cop thinks this is suspicious and orders him to pop open the trunk. He checks it out and says "Do you know you have a dead cat back here?" [1]
"We do now, asshole!" shouts Schrodinger. [1]
"I think it's time to split" says Everett.
"Say, how did you manage to spot us on such a dark night?" asks Hubble.
"I saw the light from your head lamps" says the cop.
"How fast was *it* going?" asks Michelson.
"That's simple addition" giggles Galileo.
"Not exactly" says Lorentz.
"Look here" says Heisenberg, "how do you know I was going that fast?"
"I clocked you over a measured distance" says the cop.
"How often?" asks Hertz.
"I disagree with your measurement, officer" interjects Einstein.
"Don't start tonight, Albert" says Bohr, shaking his head.
"What Herr Einstein is trying to say" continues Heisenberg, "is that time was running at a different rate for you than for us".
"WHAT!!!???" exclaims Newton.
"It's true" says Maxwell. "We're all famous scientists and, believe us, Herr Einstein has proved it, though it came as no surprise to me".
"Sounds complicated" responds the cop.
"I'll draw you a simple diagram" says Feynman.
Totally flummoxed, the cop lets them go with a warning. As he drives away, Doppler cocks his head and listens to the sound of the receding police car. "Gotta love that" he says.
"Amen" responds Hubble.
Returning to their car, Lord Kelvin remarks "Sure is warm tonight"
"Yep - lots of disorder" replies Boltzmann.
"In places you'd never expect" adds Hawking.
"I was lucky to get away with that" says Heisenberg. "Most cops think they're better than everyone else".
"Yes - I hate inequality" adds Bell.
"Though you *were* speeding" says Faraday to Heisenberg. "I carefully observed the needle creep from 35 to 55".
"Actually, it was jumping, Michael" replies Planck.
As they pile back into the car, Bohr says "See here - you must fill the seats in order - no empty spaces allowed. And stop interfering with each other!"
"Only one of you can sit next to me!" yells an agitated Pauli.
"Say, Werner - it's stuffy in here. Be a good chap and crack the window a bit" says Hawking.
"Sorry, Stephen. It can be all the way up or all the way down, but nowhere in between" replies Heisenberg.
"Hey guys - Albert and I just figured out a great shortcut. Only one bridge" announces Rosen.
"It will save us a lot of distance" says Einstein, "but it might get spooky".
Arriving at the beach the next morning, they hurry from the car and stand looking out over the ocean.
"Look at the wonderful waves" says Schrodinger.
"They don't look like waves to me" says Bohr.
Looking down at the fine sand, Dirac exclaims "Look at all the particles!"
"Now *those* look like waves" says De Broglie.
"This is great!" exclaims Feynman, rubbing his hands together. "Now, lets go meet some girls!"
"Let's delay" says Wheeler.
"We have to be discrete" warns Bohm.
"Girls? NEVER!" exclaims Newton.
1 Based on, and including the original, attributed to Rich Granger, engineer, Battelle.
thanks for putting this thing up, its awesome
Really enjoyed this one.
Most well crafted comment on youtube.
Thanks for sharing😉
I read one small excerpt from this and it was amazing. I didn't realize it was a full story!
I LOVE ANYTHING AND EVERYTHING FEYNMAN!!! This was a great video, and I love seeing the cooperation between math/physics/science channels.
Everything except the accent...
If TH-cam channels like minutephysics or 3Blue1Brown existed when I was in high school I probably would have become a physicist or mathematician instead of a biologist.
I was a math major for 1 year before I switched to mechanical engineering. I'm now retied and can indulge my first passion. I simply loved this video. I do believe, though that the constructs are merely consequences of natural laws without any useful knowledge.
That's a pretty *_normal_* way of constructing an ellipse!
I see what you did there
minute physics+3b1b+Feynman what could i want more, best day of this month
I am fully convinced that the term 'Quantum Electrodynamics' was coined solely to make the 'QED' joke
I think Feynman was trolling mathematicians. ;-)
Having heard Susskind's comments about Feynman's massive ego, it would be his kind way of saying, 'Take that, mathematicians; I win!'.
whats the joke
@@BLUEGENE13 r/whoosh
BLUEGENE13 The joke is that mathemathicians sometimes write QED at the their proofs, which is an abreviation of the latin words "quod erat demonstrandum" which means "what had to be demonstrated".
Feynman was an artist who had shown us some ultimate beauties of universe through the colours of physics....
This is a gem.... 💎💎
I appreciate your through discussion of this. It really reminds me of my grandfathers explanation. I was looking forward to your method of explanation, and was quite entertained
That black dot on the screen from 1:43 to 1:48 got me! I was pawing at my screen trying to remove the 'spec'. How dare you! :3
*Yes, I'm going to pretend like my brain has enough computing power to fully comprehend every single word in this video and instantly apply it to every subject previous brought up, and watch the video a ×1 speed without pauses.*
I too, shall do this.
@@fanimeproductionst.v.3735 Wonderful, truly wonderful!
An energizing idea!
Think of operating a cnc machine when carving out, the chips fly in those directions, if the tool breaks it also flys in that direction, just have the infinite intelligence to have the guards shut when it dose!
Ok
Wow!! I'm a mathematician, and as my colleagues will, I think, agree, this video gives a lot more intuition and insight than the standard analytical mechanics-differential equation proof which has hardly any geometry and only blind calculation. Thank you!!!
I don't think a Mathematician would ever say "blind calculation".
I'm impressed with the accuracy Grant can predict each moment my is brain is about to melt
Somehow this seemed even denser than most of 3blue1brown's other material. I feel like I could probably get it all if I spent a couple hours working it out for myself, but right now my head just kinda hurts.
Physics is a different mindset from math, so yeah this did have a different feel. Orbits are really tough at first encounter but incredibly satisfying once you understand, keep at it!
P Sharma I think it's actually the math perspective that's throwing me here. I have a pretty good intuitive understanding of orbits from physics in terms of angular momentum and potential energy (and let's be honest, most of my intuition for orbital dynamics comes from playing Kerbal Space Program) so this sorta abstract mathematical approach is throwing me off.
I often find that math is very dense though, so it's not too surprising. The people who came up with our mathematical language did a very good job of distilling complicated ideas into concise and precise language.
I suggest checking orbits out in a college level classical mechanics text, there's way more math involved but it may help you reconcile everything here. The actual derivation of elliptical orbits from Newton's second law is truly awesome and it was a lecture I don't think I'll forget, hopefully you'll enjoy that too.
pyropulse your comment made me laugh so much... If you think physics and math are the same thing then you're either just barely through your majors and trying to talk big or you've been taught rather poorly. This was a wonderful video but it was very noticeably done from a mathematician's perspective, he didn't hit on physical intuition very much because he used math proofs instead which (I'm guessing) is why OP felt like something was different, you with your double major should've recognized that.
That escalated quickly
“So I’m gonna draw it nice and thiccc”
*12 year olds have entered the chat
Alex Matsumura “so you can see all the parts” 😂
NANI
timestamps??
10:00
Loved this collab. Thanks for this video!
Knowledge just blasting off from this video, like water sprinkler.I don't think I managed to catch all the water.
Fantastic video. Grant does a good job of graphically summarizing Feynam’s lost lecture.
Great video. It's a bit like the classic Cambridge natsci/physics interview question "describe how you might approach proving the following or what laws you would need to invoke'. Thankfully mine was simpler however. We had a first edition of Newton's Opticks in the college library and I was kind of thrilled to request it and read a chapter... in a long-gone innocent age where there was no door security on the college or the reading room.
Didn't think it was serious until he said Go full screen.
It's the only way to watch a 3blue1brown video imo!
Latin focō (as in the video) is the ablative of focus, which means at the fireplace. the form focus derives from the nominative which is focus not foco.
Woah 3blue1brown! :)
Fingernail Clipper I believe it was supposed to say, G's up ho's down
Thanks
Can you imagine what sort of lectures and presentations Feynman would have produced if he had access to the same animation software used to make this video...? 😮
Even worse ones. ;-)
@@schmetterling4477 Ok
@@Ax_x1om You need to stop judging the quality of a lecture by the fame of the lecturer. This isn't tribalism. There are actual intellectual criteria at play here. Use them.
@@schmetterling4477 Ok, may you explain why Feynman was a bad lecturer then?
@@Ax_x1om He gave a series of lectures on quantum mechanics once that I actually used to like... until I thought about them a little more and then it became clear that what he was teaching gave people the wrong intuition about what is actually going on in quantum mechanics. I know that (and why) in his mind it all made perfect sense, but what he was communicating doesn't reduce to the correct physics in the mind of the audience because they lack his theoretical background.
Was I the only one that forgot this was a minute physics video?
No
'No,' sarcastically or literally? It can _go either way!_
Literally, it’s just like a 3b1b video: long and interesting af.
kindlin I had just taken it literally but now I'm curious
Nah
I thought it was 3blue1brown who uploaded video
Chandravijay Agrawal I did too lol
Chandravijay Agrawal me too
Same
tru
me too
The PCA explanation by 3blue1brown got me a job ❤️
Rohan Damodar could you link to the video?
Not exactly a video on PCA. But understanding the eigen values and eigen vectors helped me a lot.
@@ROHAN0APK to q,2
I accidentally replied
thank you for making this !!! love you !!!
12:41 shows a coordinate frame shift from position to velocity space. I was just looking at the Royal Institute Sean Carroll lecture on Relativity where the simple statement of 'speed of light is a constant' would be a very interesting mental frame to explore. I have been questioning why time is the proper dimension to differentiate on vs any other. What happens if we shift our entire mental frame from position being the default (requiring differentiating to get rates of change) to a mind model where velocity is default on a unit coordinate system? What happens to the other physical constants when c=1 what values would they be and how do they build into something like the fine structure constant?
"So the question is: What special curve satisfies the property that the tangency direction of the slope for any point theta-radians off the horizontal is given by /this vector/ from a special eccentric point on the circle to a point theta-degrees around that circle from the vertical? Okay, so is the question clear?" XD
With each new replay of the video, the question becomes clearer by 1 word. All in all, 41-43 concentrated plays of this video are required for the question to be clear.
If you want proof... well, you have this line that shows it if you just turn it 90 degrees into your brain. Good luck & have fun!
+Amar Are you telling me the answer is 42?
the answer is an ellipse. which is a curve that satisfies the above property
@@yashpandey5416 that's an elliptical way to say 42
This is EXACTLY what I have pondered for many years! Now it is time to take it to the next step: The algorithm is quite simple actually, all mathematics can be defined with only a couple of variables. My computer science professor would look at me cross-eyed every time is suggested that digital and analog were not meant to be separated and thus the constant battle for accuracy with "smaller and smaller slices" so to speak....
Goddammit grant. You couldn't just be a teaching god on one channel, you gotta invade minute physics too? Jk, love you both. Henry, you got me into physics when I was in middle school (going into uni in 2 months) and Grant, recently you made linear algebra make sense. Which was strange for me, because my teacher did an absolutely awful job. Thank you both, you've helped me and many others immensely.
Every bit of this statement is true...... Everytime I watch one of your videos, you take my breath away......just as talented as the honorable Christopher Nolan.
I had almost the exact same experience. Henry got me into physics, Sal Khan got me into calculus, I'm now going to second year math studies in uni with Grant inspiring me with every upload! These people are gifts to humanity!
There's always that one guy.
pyropulse dude, everyone is different. I just took my differential equations course and my first nuclear physics course, maybe half an hour of studying a week per class. Aced it. Not all of us have inferiority complexes like you, and not everyone has to study like you.
Ok
Newton started off with a bet to prove this (the ellipse being a consequence of the inverse square law) and produced a series of publications, eventually compiling the principia mathematica out of this seed. However, although he never states this clearly, I'm sure he realized that the proof he gave was for the converse: that given an elliptic orbit, an inverse square force law follows. This was much easier at the time because so much was known about the geometric properties of the ellipse than was about F=m a. In fact, Newton couldn't really mathematically use velocities because they compare two quantities with unequal units (distance, time). Also of course algebraic notations and vectors weren't invented yet. But still Newton claimed to have won his bet, and the Principia avoids any clarity about proving the inverse square law vs. the converse (proving the elliptic shape).
I'm sure Newton would have LOVED this type of proof, and this proof in particular! Although I'm sure he'd appreciate how much more powerful modern mathematical notation and ideas such as vector or Lagrangian calculus are. And that's where Feynman and 3blue1brown comes in: Elementary proofs just are the next level of understanding: being able to explain something seemingly complicated in simple terms. With intuitive concepts, but with methods not more complicated that what was available to Newton.
Wow! What a trickster!!!
God not again
Beat Toedtli I didn’t even read the comment because I knew I wouldn’t understand it but I’m acting like I do understand it so I seem smart.
wait Newton didnt have vector????
I think he proved it both ways.
"Stay focused"
I see what you probably weren't intending to do there.
The incredible nature of the rubber band. Think like Feynman. He amazed me when I found his lectures on you tube. I love this man
When 3B1B hosts this channel:
*Bravo Six, going dark.*
Wow...loved this one...
1:00 top row 2nd square
*GRID-CEPTION*
Grant: "Ok? is the question clear?"
Me: Nods in liar liar pants on fire
I find it simply amazing we can know so much and yet understand so little.
Thanks for sharing!
"...approaches a Perfect Circle. Isn't that neat?" - "indeed it is!" (Walks away and puts Lateralus by Tool on play)
How did I not knew about 3blue1brown till now? I'm now subscribed to him. Thank you.
I am not a mathematician but I love it! I once took a physics class called Physics for Poets and this is exactly what it was like. You and of course Feynman deconstructed this concept so that even a guy like me could appreciate its beauty. Thanks!
I just wanna thank you I did not completely grasp it but I do have some insights on it
Thank you very much to Grant Anderson and Richard Feynman And of course Newton
The video that introduced me to 3Blue1Brown last year.
I was so obsessed with Feynman and his works and I landed here.
Wondered why there's just three likes for this awesome video, turns out I was just one of the first ones to watch it.
Now, I should resume watching the vid.
Faramond Stgandr so hirotaka has other interests than video games too! ^_^
Was watching it while playing a video game.
quit slacking off, focus on the kills!
Fine, fine~
You might have been one of the first to *load* the video, but since you paused, you almost definitely weren't one of the first to watch it.
I personally Love Feynman's work... His brilliance wasn't in just discovering new things, but being able to explain them at an elementary level. It is almost like watching Monet paint, or Bach compose music... if we could, that is.
My only problem with the video is... how does one pronounce "Principia" correctly, but not "Foci?" They are both Latin words, in which the c is always pronounced hard, like a k. Everything else in the video made perfect sense, but it was like hearing nails across a chalkboard every single time he said it.
On a side note, speaking of the relation of Kepler and Newton... Kepler spent over 30 years to develop his laws of planetary motion. There is a museum to him that actually still holds thousands of notes on his work. This is actually motivated Newton to try and find an easier way to solve the "Tangent Line Problem." But, don't be fooled... what Newton wrote about in The Principia was not The Calculus we regularly learn. He discusses it in the third part of the book, and it mostly deals with differential equations. Libenitz really was the one who developed most of The Calculus we learn in school. Newton took the claim solely because he was the head of the Royal Society at the time. The same position Stephen Hawking held until he passed away.
"Leibniz" not "Libenitz"
@@coolcat23 I've got degrees in Maths and Stats. We are all horrible spellers...
And names. Do you know how annoying it is to have classes with people for 4 years, but everyone forgets each other's names? That is the real reason why we seem so quite, lol.
This video required infinite intelligence to understand. I'd say I understood about 60% of it. 60% of infinity is still infinity. Hence.... you get my point.
Damn right
Your comment itself is the proof - you are indeed a genius!
How sophomoric of you.
its beautiful. When i first learned about the focal length constancy in ellipses it drew all my attention. Maybe should have looked deeper. Maybe thats what makes a Feynmann
Just loved this video ! 3Blue1Brown : you are the best at explaining complex concepts step by step with very elaborated (and beautiful !) animations. thank you
It’s a very effective lullaby for me I almost fall asleep watching half the video
yeah 3blue1brown you are my daily dose of intelligence
Infinite intelligence? :P
honestly it kind of does the opposite and reminds me that i still have much to learn.
Beautiful graphics! :)
This is probably my favorite video on youtube.
this was a strange experience for me and i dont know what to make of it- but despite never seeing this idea before, almost as soon as i heard the introduction i knew almost every step we were going to use to get there (of course it wasnt a full proof in my head using theories and all, but like the vectors making a circle and the rotations and some of the perpendicular bisector stuff, really all the visual ideas). it just... came to me at the start. never had that happen before.
Wonderful presentation and explanation...now, I want to know what was Newton's working which Fenyman couldn't follow, if that is what Grant said.
Newton was using some statements of theorems that he assumed readers of his time would know: that the two lines from the foci of an elipse to the circumference, form equal angles with the tangent to the ellipse.
3 colossus in one video, ooh may godness
Shout out to Tommy Tellarico for being the first person to prove the Law of Ellipses!!!!!!!!!!!
Interesting to note, at the end of the book "Feynman's lost lecture" the authors reveal that the arguments were first found by Maxwell (From Maxwell's equations) in his book Motion and Matter. So I'd reason that Feynman, who was famously well read in physics books/papers, probably adapted the arguments there for his lecture. Not taking away from the brilliance of the argument and the presentation of course.
At 6:13, I love the animation of the focus acting like a sprinkler! I played it 10 times.
wait... isn't foci pronounced with a k-sound? o.0
no, thank god latin does not have english pronunciation
But it had a hard K sound before the "u", why not the "i"?
Later in the talk he mentioned Newton's "Principia" and used a hard K for the "c" before "i".
It's too early here to start drinking.
In (classical) latin Cs are always hard. Caesar is actually pronounced Kaesar which is where the word german Kaiser for emperor comes from. However 'i' should be pronounced like 'ee' rather than the english 'aye', and the 'o' should be a short 'o-' rather than the english 'owe' sound.
But it is clearly not pronounced as it would be in latin
he also pronounces φ as "phee"