14:07 "As your lovely illustrations will show..." One of the most awesome things you see here is just the mutual respect they have for each other, Terence and Grant. It really does show how important cooperation is in the sciences and mathematics
Terence Tao is really quite an inspiration. On the one hand, if he was simply a genius and only really worked by himself, the opposite would be true. But the fact that he is so collaborative, and works with so many people really gives young mathematicians like myself a drive to think that one day we might have the opportunity of working with alongside somebody like him. In a sense, he is inspirational not because of his raw genius, but because of his ability and humility to allow himself to work with so many other people. Incredible person.
I doubt it. He's so prolific, I would it strange to focus so hard on the image and do such vast amounts of good to great work. That would actually be impressive amount of effort imho. It's like 20-30 years of data, you'd expect to have at least some data points to contradict his image.
Watching this makes you really respect the sheer determination and ingenuity over centuries to estimate these first astronomical distances and guess the shape of the orbits. This rich history should be known to everyone from high-school students to graduate level researchers. Literal chills, can't wait for part 2 to blow my mind.
I have VERY rarely commented on a video in my decade+ on TH-cam but I had to for this one. This is one of the most inspiring, fascinating things I’ve ever watched. I just love how approachable it is and how it flows logically as we follow the steps that these astronomers took from one measurement to the next. 10/10
2 ชั่วโมงที่ผ่านมา +34
Tao is a gift to the world, what a genuine lovely dude, as well as a genius.
I wish this was the kind of stuff we learned at school. Not just what we know, but how we arrived at that knowledge, and the animations and graphs you're showing are incredible at explaining it in a simple manner, even though the mathematics behind it is incredibly complex!
I applaud you for doing a truly good astronomy explanation video, the best I have seen in the internet with the exception of the video done by Hindemburg Melao Jr on the case of Galileo. This video takes you from the basics and explain clearly what is happening, what the ancients knew and did not knew (some people make them look dumb, which is sad), and makes sure that everything is put in a conceptually correct framework and a solid ground, with the inferences that were made so we could know what we know today. This is true scientific communication. Teaching how science is made, not just throwing facts at the face of the audience and expecting they to believe dogmatically. Brilliant work Grant and Tao!!
Kepler's method is just so magnificent. I have never been so awestruck. Brilliant work, and that includes you and Tao for bringing Kepler's method alive and visually appealing!
this is so cool! I've heard this story at least 15 times before, different videos, different books... But I never had the opportunity to appreciate the geniality of how he figured the orbits!
Just why would he ever delete without any valid reasons? Its like would you destroy your painting which took lots of hard work to create. or would you ever delete your very beautiful picture which you took after travelling for 10000 km in aeroplane and hiking for 3 days without any reason?
Exactly, I intend to show this video to my kids. I am aware of a good chunk of the contents of the video. However, It logically clicks each piece step by step in an artistic way
Tao with grey hair - suddenly I realize I am now an old man. He was at the IMO 2008 ceremony and I was thinking man this guy is so young and so genious.
The story of Tycho Brahe is really fascinating and as someone who lives about an hour from the island of Ven i would highly recommend anyone to visit his mansion aswell as the island as a whole which is truly beautiful during the summer. Glad to hear him being brought up:)
Thank you so much. It goes without saying that the ideas here are interesting. However, the content combined with the presentation elevated this to something else. It moved me, the way that art does. I felt my heart and mind race. Again, thank you.
Fascinating, absolutely fascinating. All sorts of lightbulbs went off in my head. It was as if the swirl of numbers and bits of data I had learned from lifes experience over the years started aligning themselves, and suddenly, I could, by analogy, more easily conceptualize how other phenomena around me could be explained in a simpler way you'd never forget once told. When you hear the history of something like how some of the mathematical techniques came to be and how it all helped unlock the world around us, then IMHO, learning becomes a passion beyond the classroom for the curious.
For anyone interested there's another great two part video that digs on Kepler's investigation of mars orbit. It's called "How the Bizarre Path of Mars Reshaped Astronomy" by "Welch Labs". Excellent video, I love that you took the method/process approach to this insights. It's really inspiring and teaches us better ways to approach novel problems instead of repeating answers to already solved ones.
This kind of video is perfect to display the struggle and importance of science. Our scientific institutions need to better communicate and interact with the public. The fact Keplar's discoveries depended on such prerequisites should help us understand how fragile our progress into the future can be. Science history should be more emphasized. I remember having a similar feeling when I watched one of the Voyager documentaries.
Whoa, this might be one of best cross over in the universe, 3b1b with Terrence Tao in numberphile style. Terrence must one of nicest people out there. Out of plethora topics he picked something people can relate to. He also gives off this vibe in every video with him I've seen. Like 2nd Erdos. Nice, nice, nice.
Thank you for the animating these brilliant methods that expand human's mind! It's very illuminating. The moment of revalation that the planet's orbit is elliptical brought me to tears. Imagine you were Kepler dicovering the fact for the first time in human history, using heritage of obsevation data passing generation by generation over millenium. It's also amazing that ancient Greek more than 2000 year ago already device methods to measure shape, size, and distance of Moon and Sun, with geometry and reasoning which are far surpassing their technology.
Thank you for this. I've read explanations of these developments, and seen other videos. Due to the shorter video format and the static drawings in books, there were elements I couldn't get my brain around. You filled in those gaps for me. Eagerly awaiting part 2.
Just realizing the half moon is not half way a circular orbit, just now is mindblowing even if it's obvious if you think of it in math But visuals usually depict a large sun and parallel rays so it becomes close to just halfway around a moon orbit.
Terrance Tao is one of my heroes. I like him because he is so 'matter-of-fact' when talking about things, yet always leaves room for discussion and questions. He's a bit intense but honestly, that makes it much more fun.
When you learn a new word, do you know that feeling that you suddenly start hearing it everywhere? Well, this has to be like 10th thing I stumbled upon about astronomy since I started watching "on the movements of the earth".
He really loves to talk about this subject. I watched another video of him talking about this. It might be because most of the math he works with daily is completely incomprehensible to most people.
This comment is completely irrelevant to the subject of the video. But here I share a math problem that I stumbled upon years ago. Consider a unit circle of the equation x²+y²=1. Now, take a chord on the circle and its reflection along the Y axis. The chord has a special property that is, the distance between its and its reflection's feet is same as the chord's length. The word 'foot' means the point on the chord which has the least y coordinate value. In other words, the chord's length is double of the absolute value of the x coordinate of its foot. Now, 1. There are infinitely many chords on the circle with such property. 2. Every point on the circumference corresponds to only one unique chord with such property where that point is the foot of the chord. Now, if you draw all such chords on this circle, a part of the circle will be completely shaded by the chords and one part will remain unshaded. Find the area of the part which will remain unshaded. This problem is not meant to be a challenge to you guys, it's just a "fun with math" thing. Because the part that will remain unshaded here, will have a shape of the cartoon water drop (💧) we are all familiar with. Try it, it's fascinating. If many of you are curious, let me know in the replies and I will share the answer. (Of course not the whole solution, it's huge)
Learning the history of how we know the things we know is so fascinating. We were always taught the Kepler's 3 laws but never how he found this out. So this video really puts into perspective how difficult it was
Dunno if you'll read this grant, but ever since i watched your video on Quaternions during 2020, I have been HOOKED on math. After finishing my degree on mechanical engineering, I plan on formally studying math. All that thanks to you man.
There is also an Andalusian scholar named Ibn Mu'adh who lived in the 11 century. He was able to calculate the hight of the atmosphere just by using geometry. This geometrical calculations blow my mind every time I look at them, it's so beautifull😍.
Fabulous video. I love your content! Thank you for sharing your skills in such a thoughtful, impactful way. Your narration and animations are ridiculously easy to understand.
The platonic solids and orbits hypothesis bit makes a brief appearance in _Euler's Gem_ , if my memory serves me. By today's lens, people got (and still do get) caught up on (a lot of) wrongheaded ideas that hinge on an assumption of perfection (to the way things work) on their journey towards a better understanding of any number of topics. This realization, that the universe is whatever is, even if it doesn't make sense to you (or is imperfect or counterintuitive), is a huge insight that allows for one to reach the place that allows understanding _why_ P-Hacking is a danger (even by those that don't mean to do it). It also leads to one of the insightful logical underpinnings that inspired the famous Enrico Fermi quote: "Whatever Nature has in store for mankind, unpleasant as it may be, men must accept, for ignorance is never better than knowledge."
I love you! y'all, the Babylonians, the ancient Greeks, Copernicus, Kepler, my science teacher back in high school, 3B1B, Terence Tao, adn even TH-cam!
Excellent history. Of course what you had to leave out would fill a dozen or more videos. I have heard that Kepler was quite lucky in choosing Mars for his detailed analysis. The eccentricity of Mars' orbit is just enough that it forced him to throw away his circular-orbit/platonic-solid hypothesis. If the limits of precision of Tycho's data had been a tiny bit sloppier, or if Mars's orbit had been a tiny bit more nearly circular, he might have chased that rabbit down the hole for another generation or three.
Great video, looking forward to the next part. Hopefully you include a little discussion about how the distance to Betelgeuse was corrected by about a factor of 2 sometime in the last couple of years.
This is such a great video. A piece of art. The topic is so interesting ❤🎉😅 thanks 3Blue1Brown. I think this the best video on the series. It will take me multiple views to absorb.
As a physics graduate, I love the joke at 7:40. Also, I've always wondered how Kepler could deduce the orbit of planets from all the planetary data on periods and relative positions of each planets among background stars because it seems mind-boggling to me to find the answer from this mess. Thanks, 3b1b and Prof. Tao. Can't wait for the next part.
Very interesting!!! And great work on putting out these videos 3B1B, I salute your work in the domain; you are helping us globally. Please continue doing the good work.
![Civilization VII Editor Takeover! [Civilization VII]](http://i.ytimg.com/vi/DzGCyUSt2D4/mqdefault.jpg)
Using tau for Tao is genius
it's like omega for ohm
Nothing genius about this. 🤦🏻♂️ People are so cringe.
@johnnysilverhand1733 no johnny silverhand, it is not cringe, it is indeed genius to use tau for tao as pi said.
@johnnysilverhand1733you must be very fun at parties huh
@johnnysilverhand1733 u're cringe
This reminds me of oldschool Numberphile videos, with the wonderful touch of 3B1B style animation. Epic crossover of math.
Fun fact: Terence and Brady would have grown up only a few kilometres from each other, both being born in Adelaide in the mid-1970s.
Something something intersecting lines
14:07 "As your lovely illustrations will show..." One of the most awesome things you see here is just the mutual respect they have for each other, Terence and Grant. It really does show how important cooperation is in the sciences and mathematics
Terence Tao is really quite an inspiration. On the one hand, if he was simply a genius and only really worked by himself, the opposite would be true. But the fact that he is so collaborative, and works with so many people really gives young mathematicians like myself a drive to think that one day we might have the opportunity of working with alongside somebody like him.
In a sense, he is inspirational not because of his raw genius, but because of his ability and humility to allow himself to work with so many other people. Incredible person.
I feel it's just his impression management. something scary...
I doubt it. He's so prolific, I would it strange to focus so hard on the image and do such vast amounts of good to great work. That would actually be impressive amount of effort imho. It's like 20-30 years of data, you'd expect to have at least some data points to contradict his image.
@@IM-qq4tc are you serious bro..
Watching this makes you really respect the sheer determination and ingenuity over centuries to estimate these first astronomical distances and guess the shape of the orbits. This rich history should be known to everyone from high-school students to graduate level researchers. Literal chills, can't wait for part 2 to blow my mind.
0:36 the Tau creature lore drop was not one I was expecting today
I have VERY rarely commented on a video in my decade+ on TH-cam but I had to for this one. This is one of the most inspiring, fascinating things I’ve ever watched. I just love how approachable it is and how it flows logically as we follow the steps that these astronomers took from one measurement to the next. 10/10
Tao is a gift to the world, what a genuine lovely dude, as well as a genius.
Bro met the CEO of math
Lol
What an honour.
For Tao.
@@JMUDoc good one
Hopefully he doesn't meet Luigi...
John Math
I wish this was the kind of stuff we learned at school. Not just what we know, but how we arrived at that knowledge, and the animations and graphs you're showing are incredible at explaining it in a simple manner, even though the mathematics behind it is incredibly complex!
Clicked on the video immediately when I saw Terence Tao on the thumbnail. He does not disappoint!
In my opinion, this is the best video in the entire platform
👍💯 agree
Yes.
I applaud you for doing a truly good astronomy explanation video, the best I have seen in the internet with the exception of the video done by Hindemburg Melao Jr on the case of Galileo. This video takes you from the basics and explain clearly what is happening, what the ancients knew and did not knew (some people make them look dumb, which is sad), and makes sure that everything is put in a conceptually correct framework and a solid ground, with the inferences that were made so we could know what we know today.
This is true scientific communication. Teaching how science is made, not just throwing facts at the face of the audience and expecting they to believe dogmatically. Brilliant work Grant and Tao!!
Kepler's method is just so magnificent. I have never been so awestruck. Brilliant work, and that includes you and Tao for bringing Kepler's method alive and visually appealing!
The cosmic ladder is truly insane. I remember when I first learned it and every single step is a leap of pure genius.
this is so cool!
I've heard this story at least 15 times before, different videos, different books... But I never had the opportunity to appreciate the geniality of how he figured the orbits!
One of the rarest video on cosmos. Please never ever delete this
Just why would he ever delete without any valid reasons? Its like would you destroy your painting which took lots of hard work to create. or would you ever delete your very beautiful picture which you took after travelling for 10000 km in aeroplane and hiking for 3 days without any reason?
@@gaurabdahal2cuz he can…
I don't understand what you mean by this. "One of the rarest video"? What does "rare" even mean in this context?
Exactly, I intend to show this video to my kids. I am aware of a good chunk of the contents of the video. However, It logically clicks each piece step by step in an artistic way
This might just be one of your best videos - which, considering how good they all are, is really saying somrthing.
Tao with grey hair - suddenly I realize I am now an old man. He was at the IMO 2008 ceremony and I was thinking man this guy is so young and so genious.
So nice to watch an interview being illustrated and animated in the 3b1b style!
Amazing video! Your visuals capture the magic and effort of those who came before us. I am hella hyped for the next part.
The story of Tycho Brahe is really fascinating and as someone who lives about an hour from the island of Ven i would highly recommend anyone to visit his mansion aswell as the island as a whole which is truly beautiful during the summer. Glad to hear him being brought up:)
Wild this is FREE! So good, i love how understandable each of the little steps are but how it builds into something SO GRAND
It does cost money to make though.
Tao is a genius to feed the viewers 3b1b style astronomy
numberphile style math story with 3b1b style visualisation is chef's kiss
my days, this was a work of art. Thank you for this Grant and Prof. Tao
Thank you so much. It goes without saying that the ideas here are interesting. However, the content combined with the presentation elevated this to something else. It moved me, the way that art does. I felt my heart and mind race. Again, thank you.
Fascinating, absolutely fascinating.
All sorts of lightbulbs went off in my head. It was as if the swirl of numbers and bits of data I had learned from lifes experience over the years started aligning themselves, and suddenly, I could, by analogy, more easily conceptualize how other phenomena around me could be explained in a simpler way you'd never forget once told.
When you hear the history of something like how some of the mathematical techniques came to be and how it all helped unlock the world around us, then IMHO, learning becomes a passion beyond the classroom for the curious.
For anyone interested there's another great two part video that digs on Kepler's investigation of mars orbit. It's called "How the Bizarre Path of Mars Reshaped Astronomy" by "Welch Labs".
Excellent video, I love that you took the method/process approach to this insights. It's really inspiring and teaches us better ways to approach novel problems instead of repeating answers to already solved ones.
This kind of video is perfect to display the struggle and importance of science. Our scientific institutions need to better communicate and interact with the public. The fact Keplar's discoveries depended on such prerequisites should help us understand how fragile our progress into the future can be. Science history should be more emphasized.
I remember having a similar feeling when I watched one of the Voyager documentaries.
Beautiful stuff! Cant wait for part two. Unlike most vids, think i actually understood almost everything you said!
Whoa, this might be one of best cross over in the universe, 3b1b with Terrence Tao in numberphile style.
Terrence must one of nicest people out there. Out of plethora topics he picked something people can relate to. He also gives off this vibe in every video with him I've seen. Like 2nd Erdos. Nice, nice, nice.
Thank you for the animating these brilliant methods that expand human's mind! It's very illuminating.
The moment of revalation that the planet's orbit is elliptical brought me to tears. Imagine you were Kepler dicovering the fact for the first time in human history, using heritage of obsevation data passing generation by generation over millenium.
It's also amazing that ancient Greek more than 2000 year ago already device methods to measure shape, size, and distance of Moon and Sun, with geometry and reasoning which are far surpassing their technology.
Thank you for this. I've read explanations of these developments, and seen other videos. Due to the shorter video format and the static drawings in books, there were elements I couldn't get my brain around. You filled in those gaps for me. Eagerly awaiting part 2.
Just realizing the half moon is not half way a circular orbit, just now is mindblowing even if it's obvious if you think of it in math
But visuals usually depict a large sun and parallel rays so it becomes close to just halfway around a moon orbit.
Well, a quarter of the way around, but yeah..
Terrance Tao is one of my heroes. I like him because he is so 'matter-of-fact' when talking about things, yet always leaves room for discussion and questions. He's a bit intense but honestly, that makes it much more fun.
When you learn a new word, do you know that feeling that you suddenly start hearing it everywhere?
Well, this has to be like 10th thing I stumbled upon about astronomy since I started watching "on the movements of the earth".
red car theory
algorithm
He really loves to talk about this subject. I watched another video of him talking about this. It might be because most of the math he works with daily is completely incomprehensible to most people.
This guy loves to talk about many topics. pure genius
This comment is completely irrelevant to the subject of the video. But here I share a math problem that I stumbled upon years ago.
Consider a unit circle of the equation x²+y²=1.
Now, take a chord on the circle and its reflection along the Y axis. The chord has a special property that is, the distance between its and its reflection's feet is same as the chord's length. The word 'foot' means the point on the chord which has the least y coordinate value. In other words, the chord's length is double of the absolute value of the x coordinate of its foot.
Now,
1. There are infinitely many chords on the circle with such property.
2. Every point on the circumference corresponds to only one unique chord with such property where that point is the foot of the chord.
Now, if you draw all such chords on this circle, a part of the circle will be completely shaded by the chords and one part will remain unshaded.
Find the area of the part which will remain unshaded.
This problem is not meant to be a challenge to you guys, it's just a "fun with math" thing. Because the part that will remain unshaded here, will have a shape of the cartoon water drop (💧) we are all familiar with. Try it, it's fascinating.
If many of you are curious, let me know in the replies and I will share the answer. (Of course not the whole solution, it's huge)
Terence puts a smile on my face whenever I see or hear him.
Learning the history of how we know the things we know is so fascinating. We were always taught the Kepler's 3 laws but never how he found this out. So this video really puts into perspective how difficult it was
Absolutely stellar content! Sending you all love from Greece!
Haven't expected Tao here! Superb!
Only a minute in and im already loving this new style of video! please continue making videos such as these.
Very well timed with the "Orb: On the movements of the earth" anime.
07:49 the nerd laughter is a mathematical proof that Terence Tao is a genius.
Dunno if you'll read this grant, but ever since i watched your video on Quaternions during 2020, I have been HOOKED on math. After finishing my degree on mechanical engineering, I plan on formally studying math. All that thanks to you man.
Amazing video, super thank you for your contributions to the spread of science, both 3Blue and Terence ❤
Cosmic thanks to both of you! ❤️
There is also an Andalusian scholar named Ibn Mu'adh who lived in the 11 century. He was able to calculate the hight of the atmosphere just by using geometry. This geometrical calculations blow my mind every time I look at them, it's so beautifull😍.
Fabulous video. I love your content! Thank you for sharing your skills in such a thoughtful, impactful way. Your narration and animations are ridiculously easy to understand.
Human ingenuity never ceases to amaze!
Your videos are amazing, congrats on the quality of all of them
Your work is amazing but this is a completely different level. What an extraordinary piece of work. Bravo 👏👏👏
This was incredible! Thank you 3B1B!
The platonic solids and orbits hypothesis bit makes a brief appearance in _Euler's Gem_ , if my memory serves me. By today's lens, people got (and still do get) caught up on (a lot of) wrongheaded ideas that hinge on an assumption of perfection (to the way things work) on their journey towards a better understanding of any number of topics. This realization, that the universe is whatever is, even if it doesn't make sense to you (or is imperfect or counterintuitive), is a huge insight that allows for one to reach the place that allows understanding _why_ P-Hacking is a danger (even by those that don't mean to do it). It also leads to one of the insightful logical underpinnings that inspired the famous Enrico Fermi quote:
"Whatever Nature has in store for mankind, unpleasant as it may be, men must accept, for ignorance is never better than knowledge."
This video is a work of art.
LOVE how Tao is Tau in your video , Pi and Tau having a chat 😂 True mathematician's humour.
0:32 Welcome, τ
I love you! y'all, the Babylonians, the ancient Greeks, Copernicus, Kepler, my science teacher back in high school, 3B1B, Terence Tao, adn even TH-cam!
Excellent history. Of course what you had to leave out would fill a dozen or more videos. I have heard that Kepler was quite lucky in choosing Mars for his detailed analysis. The eccentricity of Mars' orbit is just enough that it forced him to throw away his circular-orbit/platonic-solid hypothesis. If the limits of precision of Tycho's data had been a tiny bit sloppier, or if Mars's orbit had been a tiny bit more nearly circular, he might have chased that rabbit down the hole for another generation or three.
@11:15 I would say time keeping, mathematics, logic, language, and recordkeeping are all "technology".
incredible to be able to watch this. Thank you for making this❤
Terence Tao interacting with the τ/2 creatures
Can't wait for part 2!
that you for a great video! Both wonderfully explained and visualized as always.
My favorite things in one video, complicated math, 3Blue1Brown video, astronomy, and part two being able to Jump-scare me later. 10/10.
Such an epic crossover!
Great video, looking forward to the next part. Hopefully you include a little discussion about how the distance to Betelgeuse was corrected by about a factor of 2 sometime in the last couple of years.
definetly giving this a listen later!
can't wait to see the next episode
This is such a great video. A piece of art. The topic is so interesting ❤🎉😅 thanks 3Blue1Brown. I think this the best video on the series. It will take me multiple views to absorb.
If Grant's having sitdown talks with Terence Tao then I'm clearing my diary, getting a pot of coffee on and giving my undivided attention.
I hope Sir Brian Cox can watch these series, too! Thank you so much. Lovely work, as always!
As a physics graduate, I love the joke at 7:40. Also, I've always wondered how Kepler could deduce the orbit of planets from all the planetary data on periods and relative positions of each planets among background stars because it seems mind-boggling to me to find the answer from this mess. Thanks, 3b1b and Prof. Tao. Can't wait for the next part.
We should learn this in school.
This might be the most important video you've ever done, when it comes to drawing people to math.
18:20 I love how this fact seems to so genuinely amuse him
best collab possible
Thanks for this work, i really enjoyed watching it
This really is pure genius. What a discovery!
7:41 I love his laugh
Great video and great animations! Thanks a lot for your quality videos!
Shear brilliance. I'm in awe.
Cant wait for the next video
This also depends on the assumption that the moon, the earth and the sun are co-planar.
What a fantastically presented video! Thoroughly enjoyed this :-)
Wow super cool and very watchable
Thanks! Great video, as usual.
Oh yes, my weekend has just been saved!
this video is going to do insane numbers 😭🙏
3b1b debunking the flat earthers with Prof. Tao, and I love it :D
This is beautiful.
Can't wait for part 2... What the inquisitive genius mind can do with the data is the process of creating science
this was such an awesome video than you so much grant and terence!!!
This video made me want to subscribe twice over when I saw the subscribe prompt. Amazing and beautiful
3b1b AND Astronomy? Oh happy days!
Very interesting!!! And great work on putting out these videos 3B1B, I salute your work in the domain; you are helping us globally. Please continue doing the good work.
This video is a gift to humanity 🎉
This video has one of the best ratios of length to times I said to myself "that's so cool!"
I love how Tao is represented with the Tau symbol