Numberphile - 2014-04-23
Main video at: http://youtu.be/hwOCqA9Xw6A More links & stuff in full description below ↓↓↓ Support us on Patreon: http://www.patreon.com/numberphile NUMBERPHILE Website: http://www.numberphile.com/ Numberphile on Facebook: http://www.facebook.com/numberphile Numberphile tweets: https://twitter.com/numberphile Subscribe: http://bit.ly/Numberphile_Sub Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): http://bit.ly/MSRINumberphile Videos by Brady Haran Brady's videos subreddit: http://www.reddit.com/r/BradyHaran/ Brady's latest videos across all channels: http://www.bradyharanblog.com/ Sign up for (occasional) emails: http://eepurl.com/YdjL9 Numberphile T-Shirts: https://teespring.com/stores/numberphile Other merchandise: https://store.dftba.com/collections/numberphile
Hi Brady!
I really enjoy extended interviews like this, but a lot from the interview usually already included in the final video. May be instead you could make something like hardcore versions of your videos?
Knowing about your busy schedule I am not insisting in any way, but in my editing workflow there is a stage of rough cut (just cut the bloopers and made some kind of order in clips). Thats pretty much my ideal hardcore numberfile video;)
It's true that programs for creating 3D animation tend employ extremely high level math at times, so I'm not surprised that Ricci Flow is one of them. As a 3D animator, I've found myself stumbling directly into these realms either due to strange bugs in a program or just because I was trying to better understand why certain things were happening in a scene (and then found myself way over my head :P). That said, even after watching all these videos, I couldn't tell you in the slightest where Maya, Blender, etc might be using Ricci Flow, like even vaguely.
Granted, I don't understand Quaternions either, but I know under what circumstances Maya uses them. So I think that's more a testament to the complexity of the subject than the quality of the explanation.
You can look in the source code
Of all the 3D programs I've used, only Blender is open source. But it wouldn't matter, I'm no programmer.
Don't forget, he also makes memes. His Facebookpage for his memes is 'Grigori Perelmeme'. He has a lot of high quality memes there. Most involving the Poincaré conjecture and the Fields medal
This is important information. Thank you from a fellow memer.
It's such a great processes...
This must be a really great job Brady, interviewing brilliant and interesting people all the time and learning new things.
What do you think the odds are that Poincare's Conjecture can also be proven by some of the other approaches?
{I hear that Mathematicians do sometimes indulge themselves Proving Theorems by Alternate Means...}
.....RVM45
Idk, but people are still trying really hard to formulate an algebraic proof of this conjecture.
mfw the extra footage is longer than the actual video
FIRST! for once =) Great videos Brady!
Interesting!
Brain demolished by 7:11, understood the first video though. Cheers for the vids.
Some say that Perelman's rejection of the major prize money was because of his objection to the politics that abound in the mathematics community, specifically about Shing-Tung Yau who apparently tried his best to steal the spotlight from Perelman. I would've liked to have heard James here give his opinion on that, seeing that he is part of this exclusive community. Overall still an awesome video!
there's a cool article from the new yorker that narrates all that story. There's a link to it in the references of Perelman's wikipedia article.
So basically, using Ricci flow describing the movement of the initial metric of the manifold to the metric of a sphere, and given that as long as all mutations in-between are known / computable (intermediate metrics?), it can be used to solve this conjecture?
That is totally neato! Subdivide until understandable. The universal way to solve all problems, even math conjectures. Elegant. I like it.
a random thought that came into my head after watching all these topology videos: is a sharp bend an extremely curved curve and a smooth circular curve just many compressed sharp bends?
and then if you were to draw a random 2D outline of a shape, which would exist first? The bends or the curves?
glad im in the small group that watched all the vids including the unlisted one on ricci flo. i remember i used to play with the idea of contoring when i was younger didnt know it was a uni topic i just thought i was messing with shapes.
Why did it take months to understand chapters of this book??
I think it's fair to say that most numberphile viewers do not know what a manifold is.
Less fair to say than to calculate!
Do you mean as in something that has many possiblities which is what I originally thought of, I also thought of the pipe cover with multiple ingress and egress points commonly used on vehicles. However, I decided to go to Webster's to see what else a maifold could be and found this gem:
d : a topological space in which every point has a neighborhood that is homeomorphic to the interior of a sphere in Euclidean space of the same number of dimensions
I have decided that this is most likely what professor Isenberg meant when he speaks of a manifold. The possible meanings of "manifold" are in fact manifold.
I can't resist - FIRST!!! :D
Sir, with all due respect. You can put $ 1 million in the aZZ, along with jobs around the world and the Fields medal. But the title and the ability to solve a millennial problem,for example, such as Riemann Hypothesis .. not even for a billion I would trade this for my name in story as the guy who solved it! I would move to Siberia and live with my mother-in-law.
Why is the Ricci flow sometimes referred to as a program? Is there some analogy to a computer programs -- an algorithm of some kind?
Ricci flow is basically a PDE related to curvature. So, you're slowly evolving curvature to some target from your original manifold. You can discretize it (similar to SDEs like epidemic spread models or heat flow) and apply within a program to a given discrete version of a manifold. This is a nice property of many common PDEs.
I think it refers to the school Hamilton set up when he discovered/created ricci flow.
Thank you so much for putty this on youtube ! Such a cool story + problem.
After this video i'm imagining this as a math to describe the motion of fluid things over time into a sphere. How we could effectively describe in numbers the motion of a three dimensional splash of rainwater recollecting into a sphere overtime as gravity and surface tension take hold on some leaf. And maybe also being able to describe the physics and movement of the different components that make up the solution of rainwater as it is splashing and collecting.
Jyoshua Sanders Have you heard of the Navier-Stokes Equation?
This is a smoothing algorithm approach, probably very similar to the minimisation of surface area due to surface tension that you're referencing, but they won't be exactly the same I'm guessing. We already have maths and models for the kind of thing you're talking about though!
Does anyone know what archive he is talking about? Is it publicly accessable?
He's talking about THE archive located at arxiv.org. It's the place where basically all scientists post their articles before publication. The problem is it's basically impenetrable unless you know exactly what you're looking for. Total data overload and its not peer-reviewed.
It is called ArXiv. It is a place for people to publish there papers in areas of science and math. It is essentially a giant database of scientific and mathematical papers. The website is www.arxiv.org.
@Paul Dirac
You're number 20 writing me this. xD Seems like Youtube didn't want to tell you, that i have been helped 19 times before...
Messages didn't appear x)
why is this unlisted
Wait a second. Wave-like and heat-like? So hyperbolic and parabolic? Is there an elliptical counterpart?
If I understand what professor Isenberg is saying, I think it would be closer to say change the painting into a pair of movies, where the first one ends with things ending up in the form of the painting. The second and possibly more important one can then show you what happens next.
For instance, a brick that is in the air over someone's head isn't necessarily going to fall and hit him. It could be moving in a given direction and the painting shows the precise moment it was over the person's head. Likewise, your image of the object depends upon the positive or negative momentum, you need to figure that out to know what will happen next
its really hard to maintain concentration on the topic, such long flow of one idea make my brain so confused
I imagine that's why it was so difficult to prove.
"long flow" no pun intended
What are some practical applications for the Ricci Flow? I feel I'd have less trouble getting my head around the idea if I knew where it was commonly used.
Ricci flow is basically a PDE related to curvature. So, you're slowly evolving curvature to some target from your original manifold. You can discretize it (similar to SDEs like epidemic spread models or heat flow) and apply within a program to a given discrete version of a manifold. This is a nice property of many common PDEs.
The professor seamed kind of jealous/resentful when it comes to Grigori.
Cyrus - 2014-04-23
Brady must have been feeling really confused... He barely asked any of his usual questions.
Hermy - 2018-07-14
Cyrus, I don’t blame him.