3Blue1Brown - 2018-11-18
Solving a discrete math puzzle using topology. Home page: https://www.3blue1brown.com Brought to you by you: http://3b1b.co/borsuk-thanks Want more fair division math fun? Check out this Mathologer video https://youtu.be/7s-YM-kcKME (Seriously, Mathologer is great) These videos are supported by the community. https://www.patreon.com/3blue1brown The original 1986 by Alon and West with this proof https://m.tau.ac.il/~nogaa/PDFS/Publications/The%20Borsuk-Ulam%20Theorem%20and%20bisection%20of%20necklaces.pdf VSauce on fixed points https://youtu.be/csInNn6pfT4 EE Paper using ideas related to this puzzle https://dl.acm.org/citation.cfm?id=802179 I first came across this paper thanks to Alon Amit's answer on this Quora post https://www.quora.com/As-of-2016-what-do-mathematicians-on-Quora-think-of-the-3Blue1Brown-maths-videos If you want to contribute translated subtitles or to help review those that have already been made by others and need approval, you can click the gear icon in the video and go to subtitles/cc, then "add subtitles/cc". I really appreciate those who do this, as it helps make the lessons accessible to more people. Music by Vincent Rubinetti: https://vincerubinetti.bandcamp.com/album/the-music-of-3blue1brown ------------------ 3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted on new videos, subscribe: http://3b1b.co/subscribe Various social media stuffs: Website: https://www.3blue1brown.com Twitter: https://twitter.com/3blue1brown Reddit: https://www.reddit.com/r/3blue1brown Instagram: https://www.instagram.com/3blue1brown_animations/ Patreon: https://patreon.com/3blue1brown Facebook: https://www.facebook.com/3blue1brown
2 thiefs have stolen a 17 jewels-type necklace.
One to the other: "Yo, wanna count the jewels and split them evenly?"
The other one: "Nah, let's construct 18-dimensional hypersphere to help us out!"
xD
I charge with theft
No, this proof is not constructive. It means that the proof tells us the existence, but doesn't tell us what the object actually is.
I prefer to cut the necklace into separate individual jewels
The Bright Side Of Mathematics
Ha, I didn’t expect to see you here. I like your measure theory playlist!
@Niels Leest In reality you would simply use gradient descent to find the correct divisions. It's honestly not that hard. Probably doable on a laptop. Because we're only solving for the discrete case and not the continuous case, it's perfectly reasonable to get near-perfect accuracy within a few hundred cycles of Newton-Raphson at most. Every mathematician should know how powerful numerical methods are on modern hardware.
3:56 don't cut or tear the sphere
FLASHBACK TO HOW TO TURN A SPHERE INSIDE OUT
@DemonixTB Rewatching it won't make it go away, if you understand complex math it shouldn't be hard to understand this :D
“Y o u ‘ r e P u l l i n g I t I n f i n i t e l y T i g h t .”
Hydra'sLair
Sure, but that doesn’t prove that you cna actually do it.
Thanks I watched it again and I FINALLY GOT IT
@Facehunter2003 mustn't've'd
This is the first video where I tried to understand fully every single step along the way. It took me nearly an hour to finish the video, but I’m glad I did! Having had no formal math education since graduating high school four years ago, it was harder than it should have been. It gave me an important insight in understanding math I hope someone else will be helped by: to ask with every step why it needs to be the case. If you can’t answer that question, try to figure it out for yourself. This way you will play with the math yourself, which I’ve found to be the only way to truly grasp and enjoy anything.
Thank you so much 3Blue1Brown for making these videos and explaining everything so clearly!
Thanks for putting in the time!
3Blue1Brown i was lost in this video sensei :(
Your active engagement in math is what will take you the furthest, no matter where you started. I'm glad to see a comment with such courage inside the ocean of puns.
"nearly an hour"
I'm a math major and it would probably take me several DAYS to understand this video.
So it's time to learn to evaluate and steal necklaces
Grant, you should really do a ‘essance of topology’ series. It would be perfect for it’s a complicated topic, really hard to visualize
🙂🙂Like to make grant see this comment!
I would love this!
I'm an architect and I would sploosh so hard
please!
Yes please
Yeeeeeasssss
"You're probably a mathematician at heart" Thanks for the vote of confidence but I have my doubts lol
What is a sphere? A miserable little pile of coordinates of equal metric. But enough talk!
HA
I smiled when he said "You and your friends want to split the booty evenly".
Great video btw
3:00 "trying to minimize sharting"
Generally a good idea
Math is deep
42
This, my friends, is the day when peak awakening was reached.
Math = 42... How am I just now hearing about this?!?
@aTallGuyNH No, MATHS is deep, and M+A+T+H+S = 61.
@Toby M Sucks that the UK, the origin of The Hitchhiker's Guide to the Galaxy and the mythos of 42, uses the word MATHS which is 61 instead of MATH which is 42... so clearly the UK should switch to the word MATH instead of MATHS. QED.
1. I was going to say that, but I didn't feel like it...
2. OMG AWAKENING IS ONE OF MY FAVORITE WORDS EVER...!!!!
The earth is flat
This video was first called:
"Who (else) cares about topology? Stolen Necklace Problem"
No wonder I got confused when looking for it again
Every day you post is like a surprise Christmas
Yeah. Bewarb of those fake math channels. They're no good.
ALON AMIT INSPIRED 3B1B!!!!
My life is hence complete
I shall now die in peace
Sounds like the biggest crossover in history
Wrong Alon, you're thinking of Noga Alon the one also responsible for combinatorial nullstellensatz. I know this comment is old, but had to include this.
@Tes Set umm I'm sorry but who??
After watching this, I legit ran to my parents screaming "IT'S ALL CONNECTED"
Everytime a new 3Blue1Brown video comes out I almost get a heart attack because I am so excited to be educated!😍😂 If only school was like this haha 😂
t. gobold Do you like 1+
If public schools were like this, the society must have become totally different. Just imagine smart and well educated people everywhere you look.
It is for me!
Just finished the new vid, this is definitely an improvement! Understanding this one felt effortless :)
To get a better understanding of just Borsuk Ulam Theorem watch Vsauce video on Fixed Points.
can we just take a minute to appreciate the beautiful music at the end though? this vincent rubinetti guy knows what's up
edit: just listened to some of the 3b1b album, it's really nice. kinda got a bit of classical meets steve reich meets old school runescape music vibe going on
0:26 Math is deep -> I would love a T-shirt with that!
1:10 Sapphires, emeralds, diamonds, and —what?!
rubys
"Lets color each segment of line instead of jewels".
me colorblind: wait what?
やっばああああーーーー！！！数学やっぱり好きだあああああああああ
9:54 Vsauce
So, this is the same video but different?!
The proof of the Borsak-Ulam theorem is entirely different. Most of the rest is similar, though.
...Is it weird that I remember what he did last time from memory?
@Conor O'Neill I remember as well! This new proof is more elegant, but there is the detail of making sure the wrapping number around the origin is not 0. That is very intuitive, but it's not immediately obvious how you would prove it. In the specific case of a symmetric path in 2D I can use the angle from the origin to finish the proof, but I'm not sure how to generalize this to higher dimensions.
In fact, the winding number can be any odd number (but, crucially, not zero).
Please make an “essence of algebraic geometry”!!! You are the hope of mathematics education!
The link to the EE Paper appears to be broken. Edit: He fixed it!
This channel is sooo wonderful, the “poetry and literature” made accessible to those of us who struggle with the “grammar”!
2:30 - you do not need 2nd cut (from the left), 1st sapphire could go down, 2nd and 3rd - up
Thief returned back the necklace after watching this.😢
12:30 That line is very thin and the colors are very similar.
Unbelievably great video, anyways!
I'm blown away by how beautiful that proof is! You've given me something to take to Thanksgiving to dazzle my family with! All credit will be given of course, but more people need to be aware of how incredible math is!
16:45 It's November and my brain is burning with other thoughts right now.
I think this is my favorite 3blue1brown video yet! It's such a beautiful proof! Who knew higher dimensional spheres could be practical?
after showing that "sections of a line segment of 1" I suddenly realized that was the way to solve the problem.
[Mathematics] is security. Certainty. Truth. Beauty. Insight. Structure. Architecture. I see mathematics, the part of human knowledge that I call mathematics, as one thing—one great, glorious thing. Whether it is differential topology, or functional analysis, or homological algebra, it is all one thing. ... They are intimately interconnected, they are all facets of the same thing. That interconnection, that architecture, is secure truth and is beauty. That's what mathematics is to me.”
― Paul R. Halmos
interlinked.
Shame that it has to be inconsistent. https://en.wikipedia.org/wiki/Gödel%27s_incompleteness_theorems
+totaltotalmonkey
That's not what it's saying...
totaltotalmonkey Gödel‘s incompleteness Theorem cleary does not state that maths is inconsistent, but rather that (quoting from your article) no consistent system of axioms whose Theorems can be listed by an effective procedure is capable of proving all truths about the arithmetic of the natural numbers. So it is rather incomplete.
Grant, this is seriously one of my favorite videos ever. The feeling I get when I see the connection... Wow.
I remember how I stop watching when you said about the temp and pressure on the globe, thinking how impossible that could be
Now I watch the video a year later and finally understood it. Thank you!
Love that intro! It's so satisfying to watch. 0:27 for instant replay
9:50 love that Hamilton reference. (Though it possibly was a coincidence).
You'll never stop to surprise me. This is wonderful. Your amazing work is like fuel for the flame of my curiosity. Your videos make me love math even more. It's amazing what math modelling can do. More beautiful than a piece of art.
I think he could have also used a two dimensional analogue of mapping a circumference to a line for a simpler visualization of the theorem. It is a lot easier to intuitively understand the mapping of two circumference points to a single point in a line, than to understand the mapping of points of a sphere to a plane.
You could only be sharing one type of jewel then.
@totaltotalmonkey what do you mean?
In the case of mapping a 3d sphere to a 2d plane there are two cuts, that allows two types of jewel to be shared equally, see 15:15. In the case of mapping a 2d circle to a line there is only one cut - only one type of jewel can be shared equally. To share three types of jewel you need to map a 4d sphere into a 3d space.
You need an extra dimension for each additional jewel type, as n jewel types require a minimum of n cuts, see 2:23.
I love how you took advantage of the symmetry between the two recipients of the jewels and related it to that between the positive and negative square roots. Absolutely fascinating!
omg never been this early
Please upload the EE paper link again. The present MIT link is broken. Amazing explanations as always :)
Honestly, the last five minutes of this vidio required me Lim(focus and concentration )-->oo{infinity}
😵😵😵
The first time I watched this, I struggled to keep up. Rewatching this now, at 1.5x speed, with no memory of the previous time, I was basically able to understand everything. Your changes were probably part of why.
9:52 "just you wait" is that a reference from Alexander Hamilton??
When Grant said " You are a mathematician at heart"💙
That wasn't the proof of that I was expecting.
Much shorter than the one I've seen before, however.
(vsauce also proved this theorem, but mostly through extensive use of the IVT)
The way he said MATH IS DEEP and bought out 42 ❤🔥
3Blue1Brown - 2018-11-18
By the way, Brady Haran recently started a numberphile podcast. I had the honor of being its first guest, and I'm looking forward to listening to some of the mathematicians he has lined up here. Go take a look!
http://www.bradyharanblog.com/blog/the-numberphile-podcast
Metal Monkey failed English - 2019-03-20
Hey make a illustration of flat earth
Flavio Rabelo - 2019-07-25
@3Blue1Brown Awesome video. Thanks for the wonderful content you give us.
For this video in particular I still have one question though: you proved that there is N cuts equals to N types of jewels, but it's not proved that N is the minimum. Am I wrong in this observation?
Ian Grant - 2019-10-09
The hypersphere should have some connection with the quaternion condition i^2 + j^2 + k^2 = ijk = -1. Another related note is that the reflection of a point p(a) to its antipodal point in 3-space is equivalent to a rotation, if you are only considering one point, but if you consider three points then there is no rotation that will do this, because the operation is an inversion through the origin: it has left and right-handed coordinate systems on opposite sides.
Aditya Marodia - 2019-10-14
@Aashish Singlawhat did you thought? GRAMMAR-2000
Hakan Kösebaş - 2020-03-12
How about topology optimization????