It's Wednesday night
January 27, 2016 9:32 PM   Subscribe

 
I LOVE THESE

When I get stoned this is like my The Wall.

also this
posted by special agent conrad uno at 9:48 PM on January 27, 2016 [1 favorite]


Oh god. Flashbacks to the first few homeworks of undergraduate topology. I told my mom I'd just bought a clothesline and some scissors so I could try manipulating knots because I couldn't visualize them well enough to do my knot theory homework and she thought I was joking. She was like, "Wait...you're serious? You survive long enough in your math major and you end up buying craft supplies to get through your problem sets?"

People tell you it's all toruses and coffee cups but it's a LIE. I am not a person who is great at visualizing objects in 3-space and I was just a travesty of a topology student.
posted by town of cats at 9:56 PM on January 27, 2016 [8 favorites]


Top comment on the 'and turn some spheres' video: "I couldn't find anything good on Pornhub so I turned to this"
posted by zippy at 10:22 PM on January 27, 2016 [8 favorites]


1994? I wonder how much time it took to render all of those images.
posted by benito.strauss at 10:28 PM on January 27, 2016 [3 favorites]


My tortelloni and I love this.
posted by yesster at 10:47 PM on January 27, 2016


Oooo, I remember someone showing me this in the early 2000's -- I didn't understand it then, and I still don't now, but pretty geometry will suck me in pretty much every time.
posted by not_on_display at 11:01 PM on January 27, 2016


Christ, this is like listening to my high school friends make fun of me for wanting to be a halfling fighter.

"Halflings are better at DEXTERITY actions, LOSER. Fighters are STRENGTH based. Lol."

Except instead of what I would say in return, the other voice is like, "of course. How stupid of me. Please tell me why these arbitrary restrictions work the way you insist, but DON'T tell me why we're placing these arbitrary restrictions in the first place. Clearly I am a placeholder for an idiot who acknowledges his idiocy but is subservient to a narrative he neither created nor understands."
posted by shmegegge at 12:49 AM on January 28, 2016


I loved it, but don't ask me to explain it.
posted by ActingTheGoat at 1:04 AM on January 28, 2016


they're not arbitrary restrictions. imagine taking a loop of film, like the circle with walls in the video, and turning it inside out while keeping the "wall" of the film upright. you can't do it. and the "you can't do it" is the restriction. it's a real, physical thing, not something pulled out of nowhere for shits and giggles.
posted by andrewcooke at 2:41 AM on January 28, 2016 [1 favorite]


Yes. Springy ball material that can pass through itself without actually puncturing is perfectly reasonable. Is this where I say just joshing?
posted by Splunge at 3:23 AM on January 28, 2016 [2 favorites]


You can't pass a material through itself in the real world. That's a real, physical thing, but the video just says "Okay, never mind that part of reality. Go ahead and do that." But then when it comes to sharp corners, reality is suddenly a binding factor again. That seems really arbitrary.

My guess, as a total nontopologist, is that it actually has nothing to do with the real world and the use of real world examples is just creating confusion. It reminds me of when my physics teacher explained gravity wells with the example of putting a bowling ball on a rubber sheet, and some students couldn't understand how you could explain gravity with an example like that because it required gravity in the first place to pull down on the bowling balls.

My guess (big guess) is that the issue is that it's a single requirement that has nothing to do with the real world: for any given point on the shape, one must be able to determine the orientation of the sides. If you think of the purple wall/yellow wall example, for any point, even an infinitely small point, you have to be able to say "purple is this direction, and yellow is that direction". But when you have a crease, it is no longer possible to determine which direction purple is and which direction yellow is. Therefore walls passing through other walls is fine. Super stretchiness is fine. But creases and points have no orientation, and therefore they aren't fine.

Anyone who understands this better, am I on the right track?
posted by Bugbread at 5:54 AM on January 28, 2016 [5 favorites]


I am not a person who is great at visualizing objects in 3-space and I was just a travesty of a topology student.

I'm so bad at 3-dimensional visualization that I can't translate the picture on the credit card swiper into the physical action of swiping the card in the right orientation, and I write research papers in algebraic topology!
posted by escabeche at 6:04 AM on January 28, 2016 [7 favorites]


toruses and coffee cups but it's a LIE

I see what you did there

(pronounced "lee" :-)
posted by sammyo at 6:18 AM on January 28, 2016 [7 favorites]


Am I the only one that flashed onto "Firesign Theater" while I listened to this???
posted by HuronBob at 6:51 AM on January 28, 2016


This is Thurston's eversion. There is also the minimax eversion by Kusner

You can also watch mathematicians explain it... dubbed in German and with groovy music.
posted by ennui.bz at 7:14 AM on January 28, 2016


I ordered a video of the first link for a library I worked for years ago, and enjoyed it so much, I brought it to a movie night with some non-mathematically inclined friends. I don't think they learned much topology, but they were deeply mesmerized. Glad to see it on the web where it can continue blowing minds.
posted by GenjiandProust at 7:16 AM on January 28, 2016


It reminds me of when my physics teacher explained gravity wells with the example of putting a bowling ball on a rubber sheet, and some students couldn't understand how you could explain gravity with an example like that because it required gravity in the first place to pull down on the bowling balls.

Relevant xkcd
posted by officer_fred at 7:42 AM on January 28, 2016 [3 favorites]


Another relevant xkcd
posted by Johnny Assay at 9:00 AM on January 28, 2016


The rules seem arbitrary out of context, but they make sense in the context of the study of smooth surfaces (technically, immersions of differentiable manifolds). We want our surfaces to be smooth because we want to be able to do calculus on them, they way we can do multivariable calculus on the plane. Each little piece of the surface must look like a (slightly bent) plane, so that we can define tangents and normals and all that nice stuff. Those are the rules.

Now suppose I start with a sphere and deform it in some weird way, ignoring the rules and passing through all sorts of pinches and creases, but eventually arriving at another smooth surface in the end -- a new immersion of the sphere. Can you always deform it back into the original sphere only by playing within the rules -- that is, without ever making the surface non-smooth at an intermediate step? Is the space of all immersions of a sphere connected, or is it composed of multiple "islands" that cannot be reached from one another without passing through a non-smooth configuration?

Stephen Smale answered this question for any k-dimensional sphere living in n-dimensional space. The surprising answer for the usual sphere in 3D is that there are no disconnected islands -- any immersion of the sphere can be deformed into any other one through a continuous series of smooth surfaces. Sphere eversion is just a special case, where you take the two immersions to be the original sphere and its inside-out version.
posted by a car full of lions at 2:55 PM on January 28, 2016 [4 favorites]


Whoo-hoo, that means my guess was right! Yay me!

(But, yeah, the video really could have explained that, even in passing, to make it seem less arbitrary-seeming)
posted by Bugbread at 3:31 PM on January 28, 2016


There are two things that I love but can never get too far into without brain vapor lock. One is topology. The other is fluid dynamics.
posted by Splunge at 4:22 PM on January 28, 2016


One is topology. The other is fluid dynamics.

And sometimes those are the same thing.
posted by escabeche at 5:16 PM on January 28, 2016 [1 favorite]


One is topology. The other is fluid dynamics.

And sometimes those are the same thing.

See also: knotted vortex rings.
posted by a car full of lions at 7:29 PM on January 28, 2016


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