Sphere Eversion with Transparency

[@lilak2136]

“That wasn’t easy to follow was it?”

[@vperez4796]

Cool. Symmetry was introduced long ago to categorize molecules in space groups. Nowaday, we have some books on the applications of topology (King's) that categorize dynamic chemical structures, i.e. inversion of :NH3. This inversion through its N atom has an energy consequence that is related to the distribution of electrons in it. It begins from a distorted pyramid, the hydrogens then go through a planar triangle with nitrogen at its center and continuing the inversion, the H atoms end up forming an homeomorphic distorted pyramid. The inversion barrier is of 24.7 KJoules/mole. The tricky thing is that a pair of electron sit on top of the pyramid (the NH3 molecule) I am supposing that the 2 electrons don't count for as a trigonal pyramid. The PH3 molecule is also a trigonal pyramid but with longer sides. The energy required to invert PH3 is 155 KJoules/mole. Is there a tool to relate size with energy in topology? Using Quantum Mechanics we can.

[@isavenewspapers8890]

@@vperez4796 What?

[@squiltzzquilts9997]

"actually yes, because of the visual representation."

[@tunajuice]

@@squiltzzquilts9997 use the fucking smiles

[@raffimolero64]

"I'll just poke a hole in it, and pull it right through!" Lo and behold, they made a hole without poking a hole.

[@endmysuffering7903]

remember, you mustn't crease it or tear it

[@iluv2troll619]

But if it passes trhough itself, then how is that not the same? If we tried to replicate that in reality it would create a hole.

[@arcaipekyun4232]

@@iluv2troll619 it is not a real object thats why

[@thegrassguy2871]

@@iluv2troll619 It's 4 dimensional. Same with the torus eversion.

[@zatzu]

Yes onii chan

[@NyscanRohid]

@@iluv2troll619 The rules are: The surface can pass through itself. The surface must remain smooth, as in, it cannot have discontinuities or limited differentiability.

[@marbleswan6664]

Is this it? Is this a sphere turning inside out?

[@mateuszszulecki5206]

You bet, that wasnt easy to follow wasnt it?

[@Vikasslytherine]

No this is our universe.

[@igorjosue8957]

someone explain why the headvoice changed?

[@patrickhodson8715]

I can turn a rubber band inside out

[@MarkeyJester]

I... am going to give you your 100th like sir, you.... you deserve this~

[@PizzaPieBros]

“This is great! Somebody should make a movie about this”

[@squitwart.tetanusbowls]

watch out for sharp creases!

[@honk5325]

bro there isnt stop copy pasting

[@squitwart.tetanusbowls]

@@honk5325 babes. chil. it’s a joke. also you can’t copy and paste yt comments 🙃

[@youngboo6578]

@@honk5325 na theirs an actualy vid that says that

[@saintsocramnymaia5511]

@@honk5325 dummy, we are referencing the original sphere turning video

[@mrcat1043]

Yk what? These comments are getting super annoying, on every single video about sphere eversions, the only comments are like “the sphere has a bowl, and the torus has a saddle!” Or something, it’s getting so annoying

[@wynneview]

This sphere has a three dimensional smile

[@Dexuz]

We also can't punch a hole through it.

[@Russia_Moscow_countryhuman]

You mustn’t tear or crease it.

[@robbay8610]

That's negative to the divorce papers

[@laurenpinschannels]

redesign your logo. we know what we're doing. we are here to help you. everything's connected.

[@WitherGaming69]

You did it, you turned a sphere inside out without tearing or creasing it.

[@CommonTater100]

we just won't talk about the surfaces passing through each other

[@Mystical-TEDDY_]

"That was a sharp Bend"

[@ripinpepperonies9754]

What about that ring around the equator

[@oshkiv4684]

@MyFatherWasGamer cringe

[@whocares8567]

@@oshkiv4684 sez u lul

[@EDoyl]

These ones are the best because they're the most likely to be misinterpreted as real comments about the actual video.

[@ncmariofan3605]

Remember! You mustn't tear or crease it!

[@Juan_Garcia07]

Y: Hey, I read somewhere that mathematicians can turn a sphere inside out. X: Yes, that's true. Y: What's the big deal? Just poke a hole in it and pull it through. X: Sure, but the point is to do it without making a hole. Y: But then it seems impossible! X: You're right, you cannot do it with an ordinary sphere like a basketball. You have to understand the rules of the game: this sphere is made of an abstract elastic material that can stretch and bend and pass through itself. But you cannot rip or puncture this material without destroying it, and you cannot crease it or bend it sharply. Y: If the surface can pass through itself, what's the problem? X: Do you think allowing self-intersections makes it easy? Try it. Y: I'll push the two halves right through each other. X: Be careful. What about that ring around the equator? Remember, you mustn't tear or crease it. Y: Argh---let me try again. X: That's no good either---you're pinching it infinitely tight. Y: But then there's no way! It's impossible! You have to crease or pinch it to turn it inside out. X: It is surprising. But watch this: Y: ... Is this it? Is this a sphere turning inside out? X: You bet!

[@steffen5121]

Now I get it.

[@anatoliy333]

Amazing dialog.

[@ernestchan4557]

Hey is this the dialogue from that short clip that features the pink and purple sphere

[@priangsunath3951]

Just realized these omnisecnt voices were never given names

[@NicolaiWeitkemper]

@@ernestchan4557 Short clip? Guess you don't know the full version then. :)

[@wildin1170]

*[OI]* “This isn’t what a brother and sister are supposed to do!” “Why do you think our parents have the same last name?”

[@shane7778]

Because they’re married!

[@choco_jack7016]

this comment is a huggsbee reference but that video itself was a dub of the original with comedy added

[@Nirgranth]

Can I get a link

[@oyegorge7605]

@@Nirgranth search: turning a sphere outside in, the vídeo is a parody of the original

[@therealelement75]

​@@shane7778you've got a lot to learn

[@IshaaqNewton]

My blanket when I try to make it straight

[@kevinlee597]

like a basketball

[@LethalChicken77]

Actual footage of me committing tax eversion

[@leandrab.1741]

Well done! This is awesome!

[@joymoding]

Do you do this in your head, or do you figure this out while you're animating? I'm decently good at mental visualization, but I don't think I have the creativity or the concentration power to do this without a lot of practice.

[@ophello]

This is a mathematically-derived sphere eversion. The person who made this animation was just using that method to animate this video. They didn’t come up with the idea.

[@incription]

this guy can't invert a sphere in his mind

[@kbin7042]

@@nightero6873 there's an HD version now , had a great time watching it just right now at 2am , one would think i'd fall asleep but it was surprisingly interesting

[@raulalv33]

I dont know about it really, but it is probably a lot of shit hard maths hahahaha

[@Thejosiphas]

actually it was discovered theoretically first and took quite a while for mathematicians to come up with a visual interpretation like this since it makes use of higher dimensions

[@skiggywiggy8386]

Remember, you mustn’t tear nor crease it.

[@LevianDaWolforca]

idc

[@kordru]

based reference

[@Charlie_Or_So]

Mum!! Phineas and Ferb are turning a sphere inside out!!

[@NyscanRohid]

"Behold! My Tear-and-crease-inator! With this I'll publicly humiliate Roger by turning his three-piece suit into a human-sized potato sack."

[@Charlie_Or_So]

@@NyscanRohid Hahahah

[@CopperiiCitrate]

“Hey? I read somewhere that mathematicians can turn a sphere inside out, whats the big deal? Just poke a hole and pull it through.”

[@noyza2132]

"my god, where did you learn to use those fingers?" me:

[@Kerffus]

Realest shit

[@hatsukotaro]

Careful, you can't create sharp creases!

[@arithatariyanuchitkul4902]

And so do I

[@gauravchauhan554]

Say goodbye

[@NyscanRohid]

No! Someone removed the first reply!

[@AVSTMUSIC]

y o u m u s n t t e a r o r c r e a s e i t

[@invisyarcticfreak]

all of these comments are referencing outside in and i love it

[@PizzaPieBros]

This is great! Somebody should make a movie about this

[@ophello]

It’s also fucking annoying because this video isn’t the same method used in that documentary.

[@invisyarcticfreak]

@@ophello alright calm down

[@tridos2574]

@@ophello It's also fucking annoying 🤬🤬🤬

[@TunaBear64]

You could make a religion out of this!

[@bou7miid]

At 0:30 the sphere intersects itself! I don't know what the significance of this is (mathematically and geometrically). Good animation though!!!

[@Anorey]

it can intresect itself, but it cant bend sharply or rip

[@kevinlee597]

You have to know the rules of the game.

[@pablopereyra7126]

@@kevinlee597 YOU MUSN'T TEAR OR CREASE IT

[@patrickhodson8715]

I can turn a rubber band inside out

[@pablopereyra7126]

@@patrickhodson8715 But only using the third dimension. There is no way to turn a circle inside out without making it intersect itself

[@marstrooper8043]

Any video where a shape turns inside out: *exists* Everyone: OMG!!! OUTSIDE IN REFERENCE??!

[@WitherGaming69]

let us have our fun

[@LadyJuse]

It's like _the_ video for sphere eversion - of course we are gonna quote it.

[@Raflemakt]

A life saver ! Now I will evert all my spheres in no time .

[@bluemym1nd]

This is what my dog sees when it sees any mechanism

[@imranhq13]

eversion means?

[@KnakuanaRka]

This might be easier to follow if the two sides were more different colors (like red and blue) so you can easily tell what's on top; here they're really similar, so it's hard to see what's happening, especially with how it's colored meshing instead of a transparent film.

[@zanepeterson777]

At this point my brain cannot continue to comprehend 0:35

[@That_One_Guy...]

The sphere is transformed into Klein Bottle, KB is basically 4D version of Mobius Strip, and Mobius Strip is basically 3D version of Infinity symbol ♾️ (MS basically doesn't have intersection, unlike Infinity symbol)

[@That_One_Guy...]

That's why it's hard to grasp, because the klein bottle in this video is just the 3D slice of it's 4D version

[@MichaelDarrow-tr1mn]

​@@That_One_Guy... a klein bottle is a different shape than a sphere topologically. also a 3d slice of a klein bottle in 4d would have 1d lines because klein bottle is internally 2d

[@mrnogot4251]

0:17 is where I get lost. I feel like I’m watching a visual representation of what my brain is doing while I am trying to understand this lol.

[@someoneunknown6553]

So this is how baskets are made

[@georgerendell7292]

I don’t understand what’s happening at 0:22 when the blue appears to just expand past the green?

[@That_One_Guy...]

It's just some balloon pump that exist in 4D world expanding the blue balloon, but in exchange for shrinking green balloon.

[@cheeseburgermonkey7104]

This sphere is made of an abstract elastic material that can stretch, and bend, and pass through itself. -The female voice from Outside In, probably

[@FireyDeath4]

Oh, you know what might make it more understandable? Have two views, with one being opaque, and one hiding the outermost material layer like those one-way textures you can see sometimes in modelling programs

[@xavierlu5849]

"Smiles are like bowls, curving up. *booooooooop* " "Frowns are like domes, curving down. *bopppppppp* " *But there are other points that are neither bowls or domes, they are saddles. *Beeeeeeeeeeeeow* "

[@Garrett_Thompson]

A loop is a corner is disguise

[@kboltiz]

I was totally on track till the dark blue lines phased through the green ones

[@JayzzzTV]

am i supposed to belive you can turn a sphere inside out but not a circle?

[@ophello]

Yes.

[@elinope4745]

I don't understand the fold at 0:26 where the blue part is being pulled over, I don't see where it is being pulled from.

[@That_One_Guy...]

From 4D world, I'm serious because this is not possible in real life

[@CatkinsonGD]

Wholesome 😊

[@peterschroder8919]

Very nice!

[@Ukraine-is-Corrupt]

No matter how many times I try, I can't get my head around any of this

[@氣Pluh]

“Argh; let me try again”

[@kondrax5452]

"watch out for that sharp bend!"

[@jackvortack3782]

Do you mean inversion?

[@celeolou4167]

Okay, so in topology, a surface can pass through itself without invalidating the transformation ? As seen at 0:23. So my dream to "evert" a ballon should still wait ?

[@PC-wi1tk]

This is amazing. Wonderful video.

[@infogitaarles4007]

Is it based on Steve Smale’s theory?

[@isavenewspapers8890]

But took seven years until Arnold Shapiro found a practical way to do it.

[@SomeRandomDuude]

Nice!

[@luzherrera4463]

THIS IS NOT WHAT A BROTHER AND SISTER ARE SUPPOSED TO DO

[@magusperde365]

"Onee-san-

[@gargipatil6261]

I wonder why anyone hasn't made a twenty minute video on this?

[@bogdanostaficiuc6385]

Me when i try to make an sphere inside-out:

[@erawanpencil]

Why @0:26 can you suddenly push the blue lines up through the green? Not intuitive. Why couldn't you have just done that at the start without all the twisting?

[@want-diversecontent3887]

If you try to do it the simple way, pushing the hemispheres together, it creates a sharp bend, and for mathematical reasons it's more favorable to avoid those. There is a method whose first step is pushing the hemispheres together but stopping before the sharp bend, which you can find a visualization of with the title "Sphere Eversion: de Neve/Hills" (having comments with links is almost now due to spambots, but it has a distinct title so it can be easily searched for).

[@erawanpencil]

@@want-diversecontent3887 Thank you, I'll look for that. But it's correct that at some point or another one has to push the topological surfaces through each other right, that's one of the main freedom one has in this type of topology? thanks

[@paulfoss5385]

Are there smooth mappings between sphere eversions?

[@Shawn_TCW]

So I guess we all have saw the video, yes?

[@asura8495]

0:24 so they just go through each other like the outside is made out of air now?

[@asura8495]

@SArpnt yeah, help a small brain dude out, whats happening there, the blue colour is suddenly outside, why?

[@That_One_Guy...]

@@asura8495 Blue balloon is expanding because it's pumped by air pump that exist in 4D world, but in exchange Green Balloon is shrinking

[@williammurray6201]

Is this it? Is this a line of dialogue referencing an old video about a sphere turning inside out?

[@mikewasinger9029]

This helps a lot! Thank you! From 0:32-0:39 let me understand this better!

[@mollybdenum42]

This is not what siblings are supposed to do

[@aputsasana343]

Man fuck science

[@alostyen]

"Honey, it's 3am, time to watch whatever the fuck this is"

[@priyocoutinho]

But the inner surface is passing through the outer surface...is this step allowed

[@netric9084]

the sphere is made of an imaginary material that can stretch and bend and phase through itself, but is destroyed if you puncture it or crease it. the goal is to turn it inside out.

[@priyocoutinho]

@@netric9084 thankyou for the reply..

[@humha7613]

Ok, but what's the application irl?

[@theAmazingJunkman]

“That’s an interesting idea, so it’s against the rules!”

[@magnusphilosophus506]

Someone please make vr version of these

[@alexcwagner]

Spottswoode: Have you ever seen a man eat his own head?

[@thecooIdude87]

I should call her 😔

[@W4t3rf1r3]

I can actually visualize this :D

[@gigaprofisi]

Same, but no need to tell many people that

[@W4t3rf1r3]

@@gigaprofisi spoilsport

[@Gretanit]

why did it have to be proved?

[@ivanjefferson6344]

Are you telling me that you can turn a sphere inside out but not a circle

[@jackblack5082]

at 0:30 its a bit sus ... those seem to overlap

[@lionberryofskyclan]

you have to know the rules of the game. it can pass through itself, but you musn't tear or crease it.

[@That_One_Guy...]

@@lionberryofskyclan yes but this isn't what brother and sister supposed to do

[@中井誠二]

Still can't understand. Imaging 3D is too difficult for me.

[@951000jerome]

“like a basketball”

[@CY3ER]

If the shape can just go through itself why not just save a couple of steps and have the inside slide through the outside until it becomes the outside? What are the rules here?

[@Quilltergeist]

The rules are (from my knowledge) is that you cant create a crease as in you cant make a sharp corner. And you also cant cut through the material. Basically you have to turn it inside out without making a fold so you cant simply just pull one side to the other. At least thats what i got from another video explaining it.

[@EDoyl]

Do you think allowing self-intersections makes it easy? Try it.

[@CY3ER]

@@EDoyl No I don't understand what the restrictions are. Why can't the inside expand and the outside shrink so it's inside out? There's no context other than a ball doing yoga.

[@CY3ER]

@@Quilltergeist That makes a lot more sense now

[@EDoyl]

@@CY3ER (sorry, my comment was another line from the video all the other comments are quoting as a joke, I shouldn't have posted the meme in the replies of a serious comment that was asking a real question)

[@ilt255]

noooooo is this cause i watched eversion videos or that sphere video by huggbees

[@gunsparce]

“You’re pinching it infinitely tight”

[@HungryTacoBoy]

*Foreskin* Eversion with Transparency _Remember, don't tear it_

[@pawe2834]

What da ball doin?

[@therandomshow1265]

Is this it?

[@mlggyarados3240]

Reckon a certain edit of this video will bolster the views here

[@columbus8myhw]

Love it!

[@rjbond007]

0:23 - 0:30 isn't it intersecting with other surface? In 4D it isn't a issue, but in 3D it is impossible.

[@garlicicecream9087]

You must first know the rules of the game. The geometric surfaces of the circles can intersect and bend at will. The only thing they are strictly not allowed to do is tear or crease. Here is the video that made the whole thing a meme, it explains it really well. kzbin.info/www/bejne/rYCZYndvrZufhLs&ab_channel=ssgelm In the physical world, you are right, it would be impossible. But that's not what the problem is asking, so it's okay.

[@orlandomoreno6168]

This isn't about physical objects, but about space and shapes themselves

[@NyscanRohid]

So to recap: In 2 dimensions, turning a spheroid (circle) inside out is impossible without tearing or creasing. In 3 dimensions, turning a spheroid (sphere) inside out is impossible without it passing through itself. In 4 dimensions, turning a spheroid (hypersphere) inside out is possible (except for some weird rule for hyperdimensional objects that I don't know about).

[@WitherGaming69]

You have to understand the rules of the game. This sphere is made of an abstract elastic material that can stretch, and bend, and pass through itself. But you cannot rip or puncture this material without destroying it. And you cannot crease it, or bend it sharply.

[@surajchess3114]

What software are you using?

[@Cera_01]

Mathematics

[@surajchess3114]

@@Cera_01 did you mean Mathematica?

[@liox2597]

Is there any significance to a sphere turning inside out requiring a temporary Mobius, and a Torus eversion. Obviously there is a Mobius eversion because the sphere has to hit the milestone in order to successfully evert. So what would happen if you applied a Torus eversion to a Mobius strip. Breaks the game surely, but this has piqued my curiosity. Edit: it’s actually an umbilical torus, and there aren’t really any videos like this on them.

[@NHOrus]

Thats more understandable

[@Raggeon]

How do I finished here? Anyway. Sometimes we should be like that sphere, and reverse our skin just for fun

[@kyo4156]

I tried to understand, but this just doesn't make sense to me👁️👄👁️

[@Pienotto]

0:30 this is illegal, you know?

[@Scrimitch]

Whyd I read the title as sphere with tax evasion

[@cheeseburgermonkey7104]

[insert random line from _Outside In_ (1994) here]

[@preranajoshi2661]

"you musn't crease it"

[@Freedom-of-Thought]

4 dimension? 🧐🧐🧐

[@MostDopeLastYear]

the math takes a bunch of "sets" of numbers and basically says that the endpoints or boundaries can be nonexisttent, which means that if we use these sets of numbers to map a sphere, the end points can pass through eachother and we can flip a sphere inside out. Its completely abstract - taking general geometry concepts and making up new rules for them so the solution comes out the way you want it to.

[@denzali]

No pinching!

[@xylopiano3]

Like a basketball.

[@biggreenblob]

I still can't understand why there must be no creases or sharp bends. It seems like such an arbitrary rule, no less absurd than imagining a material that can pass through itself and stretch infinitely. Why not just imagine that the imaginary material can be creased???

[@dsgowo]

The rules make sense when you think of the sphere less as an actual material and more as a differentiable function that takes in latitude and longitude coordinates and maps them into 3D space. The simplest such function would be a sphere, but any shape is valid as long as the function remains differentiable. If there is a rip in the sphere, then the function is discontinuous and cannot be differentiable, and if there is a crease or sharp bend, then that would also be non-differentiable. On the other hand, if the material passes through itself, that's the same as the function taking two different inputs (taking two different points on the original sphere) and mapping them to the same output (pushing them into each other), and there's nothing wrong with that.

[@dsgowo]

Mathematically, this is a proof that the sphere and the inverted sphere are regular homotopic, meaning that there exists a continuous path between the two mappings such that all the intermediate states are also valid mappings.

[@omoliemi]

Is this yuri

[@thatnike2604]

How does one even think of this?

[@MiguelMartinez-wj9jv]

I feel like I just saw how gravity works

[@christiansmakingmusic777]

Yes, but making it overlap itself is not a possible in the real world. This exists in an abstract space where sometimes single points in the space are actually two points on the object.

[@NonTwinBrothers]

Tbh I like all the comments quoting the video, lol

[@ramosportillo2830]

It doesnt work guys i tried with a soccer ball and didnt work