Shaping a Universe (manifolds, and some conditions for embedding)

[@AndrewDotsonvideos]

I'm starting a super store that sells fans as it's sole product. I'm calling it only fans. I'd love for you to be part of it.

[@zachstar]

You got a customer right here

[@RezyGD]

@@zachstar lmao

[@PapaFlammy69]

Fkin sick

[@anshusingh1493]

Hey flammy you too watch his channel..you all are maths' birds.....hope all mathematician ever come together and project a nice discussion

[@pendragon7600]

I love how it starts as a serious math video and slowly devolves into 4 dimensional fever dream with metalhead grim reaper manipulating a manifold with the force.

[@Higgsinophysics]

I'm starting a Gofound me for mr yellow's upcoming psychologist bills after that diss 6:03

[@cycklist]

That was superb. The very best maths channel of them all.

[@SolidSiren]

better than 3b1b? I highly doubt that.

[@SpaghettiToaster]

@@SolidSiren Absolutely. 3b1b is great, but his memes are weak.

[@joshvenick2593]

1a. 2-torus b. Yes, it is closed and bounded, ie compact c. No it’s not nonorientable (it is orientable) d. It cannot be embedded in R^2 as it is compact. 2a. 2-cylinder b. No, it is not closed c. It is orientable d. Yes, it can. Let u and v be in R^2 minus the origin. Let x(u,v)=(u/sqrt(u^2+v^2), v/sqrt(u^2+v^2),ln(sqrt(u^2+v^2))) This takes each point of R^2 minus the origin and projects it onto the unit circle, where points further from the origin are mapped towards plus infinity in the z direction and points closer to the origin are mapped towards minus infinity. I believe this is in fact a diffeomorphism, but please correct me if I’m wrong.

[@carsonellaruddii5075]

Tool, math, universe talk, if this video could pour me a beer it would be perfect

[@ParthGChannel]

Dude, this is awesome :D

[@sleepheartcat]

Just some nitpicks on the animations in case anybody wonders: You say that Mr Blue lives on a sphere, but the animation suggests differently. When he exits the square at coordinates (x,y), he reemerges at (-x,-y). This exactly describes the projective plane (en.m.wikipedia.org/wiki/Real_projective_plane ). To describe a sphere, you could have exiting at (x,y) take him to (y,x). The flipping on the Möbius strip and Klein bottle are also a bit misleading: Mr Yellow and Mr Green ought to have been flipped vertically instead of horizontally. Otherwise, great video! These topics are really perfect examples of why topology is interesting :)

[@EpicMathTime]

Mr Blue is a bit misleading, if I was to preserve his direction, I needed to "distort" him as he approaches a boundary (as all boundary points are identified). Regarding the flipping, I had originally done that, but it was just too difficult to see the difference between a vertical flip and a rotation, but a horizontal flip looks more apparent. I'm alright with that, because it's really the same innate effect on the object/being (IE, they differ by a rotation within his space).

[@uv10100]

Having Tool in the background is very appropriate for a math channel

[@timberfinn]

Tool as background music was unexpected yet awesome, great video!

[@mychannelofawesome]

Yeah, I was like "is that Reflection?"... And then the bass kicked in, and I was like "yaaaas"

[@DannyVass]

For 1 it sounds like a 2-torus to me, which I think is closed and orientable. Since it's closed that means we can't embed it into R^2 based on what we learned in this video. For 2 we have the surface a cylinder that extends out infinitely in either direction. Since is extends infinitely it is not closed, but the cylinder is orientable. I believe it can be embedded into R^2, one possible way is to lie the cylinder along the y-axis and then project each point from the cylinder to the plane so that the line on the opposite side of the cylinder is at infinity. Hopefully this makes sense! I would attach a sketch if I could to help explain. I guess another way to think about it is to make an infinite cut along the length of the cylinder, then you uncurl and stretch it in such a way that it covers the whole plane.

[@No-uu7wm]

Would that projection of the cylinder not make it non-continuous? Or require overlapping at some point?

[@alxjones]

@@No-uu7wm Yes. In fact, the proper embedding would be like cutting the cylinder into a bunch of rings, then shrinking the rings as you go down the cylinder and growing them as you go up, so you can place them as concentric rings in the plane. Or in other words, deform the cylinder into a funnel shape and flatten it out onto the plane. This will leave the some point in the plane unused, but that's okay, an embedding doesn't need to be surjective.

[@DannyVass]

@@alxjones Interesting! I'm a 2nd year physics student and I don't know much topology yet, as such I was just trying to intuit my way to an answer. It's good to know there is a proper way of doing the embedding. Hopefully I'll learn more topology in the future.

[@MrRyanroberson1]

For the cylinder to be embedded you must maintain its essential property of being cyclic, so perhaps if you let the angle around its circumference be the polar angle and your height on the cylinder be the distance, you could convert a cylinder into polar coordinates and embed it that way, but then you would gain the property that the bottom circle forms a point, among other failures

[@matron9936]

Oh boy, you ain’t dead :) Edit: Loved the video! Was fully worth the time waiting!

[@colep9247]

Tool in the background

[@authentic56]

Can we all appreciate the beautiful editing and hardwork he has put in to make such a great video. This channel deserves a lot more :)

[@Assault_Butter_Knife]

Damn this has to be one of your best videos so far. I had no background in topology when I started this video, but understood everything perfectly. Can't wait for part 2 :D

[@natealbatros3848]

i really like all the effects lol make it feel like im in a movie through its math, keep up the great work

[@Tuffadandem]

Brooooo, I'm a Math major and literally just stumbled upon your channel. Your content is AMAZING! Keep up the fantastic work!

[@artunsaday6391]

You have quickly grown to be my second favorite math channel.

[@akshayakumar8706]

One of the best videos ever on KZbin

[@JoeySaves]

Dude your content is killing it!

[@EpicMathTime]

Thanks bro!

[@karanraina1431]

This man really deserves more viewers

[@1ec4]

Maybe people who have their insides flipped (situs inversus; about 1 in 10,000 have this) have that condition because some 4-dimensional being came along and flipped them through that 4th dimension 🤔

[@MrRyanroberson1]

Nah. Dopamine and its counterpart behave so wildly differently (among other chemicals) that such a person would have a horrible toxic reaction to most conventional foods

[@word6344]

What's situs ambiguus (both sides are mirror images)?

[@fritzheini9867]

very nice to see some geometry and topology

[@mychannelofawesome]

Awesome maths... And awesome music! Tool is epic

[@sanjaycosmos9679]

i like you explaining the difficult things in a simple way.

[@lorenzodeiaco8902]

Dude, this is your best video yet, sooo fucking good

[@SakisStrigas]

Excellent job my bro! 👍

[@abhilashsaha9931]

Oh God, I was gonna go to sleep. Not anymore, I guess.

[@nadiyayasmeen3928]

Amazing video

[@Jop_pop]

These animations are so key

[@gregoriousmaths266]

Ok this was absolutely epic.

[@cezarstroescu228]

Best video yet! Very nice editing

[@Akira-shakira]

I see how Stroke’s theorem can be related to this, thank you

[@salimn.1097]

Astonishingly good video.

[@DiegoMathemagician]

sick edition lol (trapcode shine?), thanks a lot for doing this video

[@EpicMathTime]

Yes, I'm Red Gianting like crazy. I'll eventually get tired of it, but for now, consider it a new toy.

[@DiegoMathemagician]

​@@EpicMathTime I love your style, play with it as long as you want :) yeah, Red Giant is awesome. Cheers

[@SolidSiren]

Awesome soundtrack!

[@pralay1762]

This channel is amazing it deserves much more love 🤩🤩

[@ElenaSemanova]

Fascinating

[@mikeyoung3870]

You make some really great animations and illustrations in your videos. I hope you get more sub!

[@drandrewsanchez]

jesus christ your channel is seriously AMAZING!!!

[@Technium]

Holy SHIT this video is amazing

[@mtripledot8910]

Amazing video!

[@AndresFirte]

I enjoyed this video so much! I had always wanted to know what a Manifold was but I didn’t understand anything from Wikipedia haha. I love your editing style btw

[@alkankondo89]

Wow! The production value of this video is SO INSANELY HIGH! It's almost too much! I'm referring primarily to the graphics, but this can also refer to the ease-of-understandability of the lesson, the humor, the comments, etc. Hell, even the correction at 3:10 was so expertly edited! Great production, Epic Math Time!

[@2false637]

3:10 LOL

[@nathangrinalds2536]

Why don't more people watch this guy? This channel is dope 🔥

[@EpicMathTime]

We are a super secret elite special club.

[@user-cj9fk8un3i]

Very epic video!

[@makessense7095]

This channel helps people like me with low verbal reasoning but decent math skills. Higher maths textbooks are a bish... Subbed!

[@johnchristian5027]

I'm sure our DMT overlords chuckled at the end of this video

[@2false637]

This video was awesome. Keep it up!

[@charlesrockafellor4200]

Oh! No cylinder or projective sphere? Oh well, still a beautiful presentation! :-)

[@PhysicsBro-xb8qx]

Bro your amazing!!

[@chemistro9440]

13:00 Ok... but Cliff Stoll has on multiple occasions said that the Klein bottle does not "divide the universe into an inside and an outside" due to nonorientability, so isn't that in conflict with the idea of the "solid Klein bottle"?

[@EpicMathTime]

The Klein bottle contains a 3-dimensional volume, but the ambient space is 4-dimensional, so Cliff Stoll's description isn't in conflict.

[@brunojambeiro6776]

Epic Math Time so it’s like a plane that has no 3D volume, but has a 2d volume(area)?

[@EpicMathTime]

@@brunojambeiro6776 Yes, we can say that a square "contains a two dimensional volume", but if it is embedded in R^3, it is not dividing R^3 into an inside and an outside.

[@williamwesner4268]

You are probably aware of this already, but the axis of reflection for the "reversed" yellow creature at 6:25 is incorrect. As animated, the creature would have also had to turn around 180° during its trip around the Möbius loop - basically, it starts "walking" forward but then appears from the other side walking backwards. The axis of reflection should be aligned in the same direction the yellow object is moving, so the x-axis, which would flip up/down instead if left/right.

[@EpicMathTime]

You are correct. The reason for that is that the effect becomes much less recognizable (it is not immediately apparent that the creature is not just "upside down" rather than reversed). I later realized that maybe keeping the horizontal reflection but moving up would have been best, but as you said, they are really the same innate effect on the creature (since they only differ by a rotation in his own space).

[@antonioILbig]

Topology is a Mobius trip

[@FF-qo6rm]

Beautiful 😍

[@diegorodriguesdesouza7389]

I agree with the idea that 4th dimension beings would not perceive us. We don't even know about anything that is truly 2D.

[@EpicMathTime]

My statement that we could not percieve a 2d being was inspired by a conversation I just previously had. There is this popular idea that a 4d being could observe us without knowing, just as we could observe a 2d being from outside of its space without it knowing. The thing is, it is not apparent to me at all why we would have the ability to perceive a 2 dimensional object of any kind, so I don't know why this is said so frequently.

[@TranquilSeaOfMath]

I thought it was a nice idea that Star Trek The Next Generation explored encountering a 2D creature in the episode "The Loss."

[@idrissmo418]

Very good video! Can you do a video on tensors?

[@NonTwinBrothers]

16:24 oh look he's oriented normal now! lol

[@IshaaqNewton]

This guy needs more attentions. Come on! What is going on?

[@jollyjokress3852]

This is making me nervous cuz it's going deep. This is a good thing.

[@hafizajiaziz8773]

I was wondering, can Mr. Blue distinguishes whether he live on a sphere or on a torus?

[@benjaminbrady7459]

Yes, he could. As long as he lives on a Riemannian manifold he could preform experiments such as parallel transport to determine the Riemann curvature tensor and differentiate which manifold he lives on up to homeomorphism. All of these terms are worth reading into if you're interested :)

[@MyAce8]

toward the beginning of the video you say mr blue is living on a sphere, but there are many surfaces where going in one direction will always bring you back to where you started (i.e. a torus)

[@MyAce8]

speaking of tori people are saying problem 1 is a 2-torus but to me it seems like a torus. If you glue the top and bottom you get a cylinder, and then you glue both ends of the cylinder and get a torus.

[@EpicMathTime]

People who write "2-torus" are just specifying the dimension, so it's not clear to me what your objection is here. A torus does not have the feature of all geodesics being closed. Moving vertically gives a closed geodesic, moving horizontally gives a closed geodesic, but almost any other direction is not a closed geodesic. It is true that Mr. Blue could live on other manifolds, though, but none of them have a straightforward representation as a surface in Euclidean geometry. In total, he could live on: (i)The 2-sphere, (ii) the complex projective plane, (iii) the quaternion projective plane (iv) the octonion projective plane. None of these embed in R^2, and they are rather exotic for this video. The sphere is the "obvious" answer, but generally speaking, the number of closed geodesics won't determine a single topology.

[@MyAce8]

@@EpicMathTime for some reason I thought a 2 torus was a genus, that's what I get for not having taken topology yet. also yeah I know realized my mistake with the torus example oops

Very nice and enjoyable video with a unique style! Just some hmm "meant to be funny" notice: Mr Red and Mr Blue cannot use their eyes, since from 2D perspective their eyes are embedded into their bodies :) also for the mouth, btw. OK, ok, silly point, I admit.

[@hehebwoai3056]

I got the second question right but i'm a little bit confused for the first one. My intuition tells me it could be a sphere but as i scrolled past some comments, it is actually a torus (after some contemplation, it also makes sense). Topologically speaking, the sphere and torus are different in a sense that a sphere doesn't have a hole while a torus does. Can somebody explain me why the sphere is wrong? Feedback is much appreciated. As of now, i know nothing rigorous about topology (i am just a 1st year math major lol. I'll come back here once i fully understand all this madness and cool stuff). Cheers!

[@JPK314]

There's an invariant that has to do with the group structure of closed paths along the surface of the manifold in question. The torus can be considered as S^1×S^1 (there are two ways you can make a circle which are not "homotopy equivalent," i.e. there does not exist a continuous mapping from one to the other) which forms the free group with two generators, while the sphere can't be represented this way. In fact, any closed path on the sphere can be transformed continuously to a point (we say that these paths are "homotopy equivalent to a point"), which means that the sphere is what we call "simply connected." Intuitively, it seems like we can represent a sphere as a square with opposite sides "glued" together, as we know that going in one direction on the square should make us come out on the other side of the square facing the same direction. But if we simply identify opposite edges, we don't actually get this property in all directions - consider a slanted path: if we start somewhere near the bottom of the left edge of the square and move toward somewhere near the top of the right edge, we would not appear back where we started. Instead, we would appear somewhere near the top of the left edge. If the square represents the whole sphere, this cannot be what happens, as we can choose parameters such that this path will fill the whole space before reaching the starting point, and that's definitely not a possibility when moving in a straight line on a sphere. We can't even just identify all opposite points on the square, as this makes the surface non-orientable (this is a surface known as the real projective plane). Instead, the common approach is to identify ALL points on the edge of the square as the SAME point. This approach doesn't handle direction in an intuitive way, but being careful allows it to work

[@EpicMathTime]

@@JPK314 Right, the Mr. Blue animation is misleading in that regard. We can't consider the square the "whole" picture. I considered having him "distort" near the edges, but I just took the square visual as being a little "window" of his manifold.

[@AGuitarFreekOfficial]

Just finished differential topology last quarter. Turns out I have no idea what calculus is lol

[@diegorodriguesdesouza7389]

I have a question: If we live in a 3 dimensional non-orientable space, do we really need a higher dimensional being to change our orientation ? Isn't just a matter of passing trough the right place?

[@EpicMathTime]

Yes (it's a matter of just going through the orientation reversing loop), but that's not nearly as cool.

[@riennn2]

Hi, I may be wrong , but i think Mr Yellow is not in the good position after his move (6:26) i think he should be upsidedown... ?

[@EpicMathTime]

A vertical or horizontal reflection really results in the same intrinsic effect on the object in its space. They only differ by a rotation within the space (and this is true of reflection with respect to any line). The reason that I chose to flip horizontally instead is that it's much more visually apparent what happens. It's a lot harder to tell the difference between a vertical reflection and simply being rotated upside down. Imagine that you are reflected, as a (presumably) 3-dimensional being. No matter how you are reflected (horizontally, vertically, depthwise, etc) you will always be your mirror image afterwards, and you only have one mirror image. The only thing that differs is your orientation within your space after being reflected.

[@riennn2]

@@EpicMathTime thank you for your answer ! I saw it upsidedown doing a Mobius strip and drawing on it by my self :)

[@locallyringedspace3190]

great work, the music in some parts was too loud

[@EpicMathTime]

I agree, it was louder this time than usual, I'll tone it down.

[@absoluteexistence8279]

Came from Zach start

[@johannesh7610]

You missed that our universe IS a 4 dimensional manifold (General relativity). That manifold is not embedded in a higher Euclidean space. But maybe it could be in a 5 up to 8 dimensional Euclidean space. I just found out (you could also have mentioned that) that every differentiable nD manifold can be embedded into R^2n. Don't get me wrong, still a very cool video!

[@EpicMathTime]

Our spatial universe is a 3-dimensional manifold, and there is nothing "banned" about only considering spatial dimensions in some particular investigation or conversation. I don't know what you mean by "that manifold is not embedded in higher dimensional Euclidean space". Manifolds are not _innately_ embedded into anything.

[@johannesh7610]

@@EpicMathTime As I understand it, we cannot separate time from space in GR. The curvature and anything is always considering all 4 dimensions. Outside of GR it still is interesting to describe our universe as potentially being homeomorphic to a 3-sphere or such as you did in your video. I meant that the first manifold one normal y learns about are submanifolds in R^n (M= f^-1({0}) for some f where at any point the df/dx^i are linearly independent), and the universe in GR is one we would not normally think of as embedded (in this sense) in R^n. Of course the Klein bottle and Möbius strip are as such also just general manifolds, but I, at least, first thought of them as submanifolds in R^3/ R^4. However, as any d-dimensional (smooth) manifold can be embedded into R^2d (I wasn't sure about that), there is not really a difference between general (smooth) manifolds and submanifolds.

[@EpicMathTime]

@@johannesh7610 Yes, every n-manifold embeds in R^2n, that's always true, but it is a rather "blanket statement" of an upper bound. That is, even without restrictions of properties of the manifold, the bound may be lower for a given dimension. Every 3-manifold embeds in R^5, for example. As for GR's model, I don't think looking at the spatial dimensions alone separates space from time, it is more analogous to a cross-section of the spacetime geometry, we don't have to destroy the association between those four dimensions in order to consider a smaller number of them.

[@karanraina1431]

Who's here to watch video just for graphics?

[@contaantiga5397]

Imagine having your eyes inside your body

[@crawfordrhoderick2942]

Not to be to stupid but what is a little a with arrow on top , help, . What about a black holes.

[@lany3570]

I only understood Mr. Green’s universe because I was just listening to Eric Weinstein’s explanation of the hand-cup analogy :)

[@bernardodocruzeiro2496]

Where can i find that explanation?

[@djvalentedochp]

Savage

[@contaantiga5397]

Mr. Pink can go in any direction in a straight line and get back to where he was, but he gets reverse in all of them, what is the shape of his universe?

[@pleaseenteraname4824]

Pedro Leao Is it a projective plane? Don't really know how to justify the answers, I just remember it exists and that can be obtained as a quotient space from a square lol

[@contaantiga5397]

@@pleaseenteraname4824 I also don't know, it was a genuine question

[@EpicMathTime]

I do think _a space_ homeomorphic to the real projective plane does this. (Namely, I am picturing a half-sphere which glues antipodal points of the cut side together). One thing that I glossed over (regrettably), is that these closed paths' connection to the topology is very tenuous at best ("straight paths" aren't preserved under a homeomorphism, for one). Even if the topology can be determined, it may only hold for a specific _geometry_ as well. I heavily implied that these paths determine the topology, but that is not always true. I think it's better to think of these results as answers of the form "given this number of straight paths doing this, what is a possible topology that is _compatible_ with this?" And yes, I think the real projective plane is _compatible_ with that.

[@Assault_Butter_Knife]

Imagine if we live on a 3d-equivalent of the 2d mobius strip manifold, meaning that if you go far enough in one axis you return to where you started, but rotated along a 4th dimensional axis, meaning you are rotated inside-out, with all your skin on the inside of you and all your organs on the outside Is that what hell is like?

[@marcovillalobos5177]

Correct me if I'm wrong, but there is an insight that the whole 3D universe we live in could have some kind of spherical '' intrinsic'' curvature. How can this be coherent with 2:43?

[@EpicMathTime]

Similarly, if our 3d universe is spherical, then it does not embed in 3-dimensional Euclidean space, it embeds in 4-dimensional Euclidean space. EDIT: when I said that we couldn't put that "2d manifold into three dimensions," I really meant two dimensions. I'm amazed that I never noticed that I said that. We can certainly embed a 2-sphere into three dimensions, we do it all the time. 😂

[@marcovillalobos5177]

@@EpicMathTime The thing is that I heard somewhere that there was a possibility to have a closed '' spherical '' universe without an extra dimension. I may just misunderstood. Thanks for the patience. I'm not a native speaker hahaha

[@marcovillalobos5177]

Keep going with the content, I really enjoy it

[@EpicMathTime]

@@marcovillalobos5177 Whether or not there "is" another dimension is a bit nebulous, what we can say is that it cannot fit into three dimensional _Euclidean_ space, but can fit into four dimensional _Euclidean_ space. This doesn't mean that there is any ambient Euclidean space that contains our universe in some physical, concrete way.

[@marcovillalobos5177]

@@EpicMathTime I get it, so is possible to have the blue creature closure effect if the 2D space is not strictly Euclidean??

[@mustafaa3370]

Why do I feel like this was inspired by the book flatland (could be forgetting the exact name)

[@kaceyclark7756]

The explanation of the Klein bottle is reversed. There are infinitely many directions which lead to reflections and only one that doesn’t.

[@EpicMathTime]

That's right, thank you for the correction.

[@mikhailmikhailov8781]

Is that hooded mathematical God an amalgamation of Misha Gromov, Henri Poincare, Grothendieck and Bill Thurston?

[@ivanjorromedina4010]

No hassler whitney?? 😢

[@mikhailmikhailov8781]

@@ivanjorromedina4010 Sorry ;(

[@ivanjorromedina4010]

@@mikhailmikhailov8781 no place for him in the olympus of differential topology??

[@mikhailmikhailov8781]

@@ivanjorromedina4010 Well, many many people are there. Might as well bring up Milnor, Pontrjagin, Chern, Smale, Thom, etc. The Olympus of differential topology is a well populated pantheon to say the least.

[@EpicMathTime]

I thought it was clear from the context, but it's Ronnie James Dio.

[@sashabell9997]

1a torus 1b yes 1c no 1d no 2a infinitely long cylinder 2b no 2c no 2d no

[@chemistro9440]

why is a cylinder closed?

[@pleaseenteraname4824]

I think a non-compact cylinder would better describe the second case, so it wouldn't be closed. Also both the compact and non-compact cylinders are homeomorphic to a circular crown (is that how it's called in English?), so they can be embedded in the plane

[@chemistro9440]

@@pleaseenteraname4824 I think you mean an annulus or washer, I thought about it as a "punctured plane" since the map is supposed to go forever but I guess that doesn't really matter.

[@sashabell9997]

@@chemistro9440 it's an infinite cylinder

[@chemistro9440]

@@sashabell9997 Doesn't that mean that it _isn't_ closed?

[@2funky4u88]

Can you do more videos on intro topology, like some actual proofs and theorems, because your videos are really interesting but getting into the actual definitions and so on is very much non motivated. As far as I know a toplogy on a set is just a sort of structure defining property, but the axioms still seem unmotivated. Anyway, I think all of your videos are great.

[@EpicMathTime]

Sure, I can do that!

[@leokovacic707]

Never seen a video on math with exercises at the end😵🤯🤦

[@charlesrockafellor4200]

Check out "PBS Space Time" then, and I think that "Mathologer" does them too.

[@icanfast]

After diving(hehe) into deep learning for a while, "embedding" triggers me in a wrong way.

[@zeroTorsion]

This is for Reals

[@andrasfogarasi5014]

Except the universe isn't actually 3 dimensional as of Einstein inventing general relativity. Spacetime is 4D. Homework: Visualise an enclosed non-orientable 4-manifold. Ponder the implications of being flipped in spacetime. Prove the Poincaré conjecture.

[@EpicMathTime]

The universe has three spatial dimensions.

[@rajibsarmah6744]

Did space is a manifold

[@fritzheini9867]

A bit flat at the beginning

[@CMDRunematti]

would Mr yellow notice anything strange inside himself when flipping? and where is the point of flip...? 😖

[@EpicMathTime]

He would never notice anything has happened to him, to him, the rest of his space has flipped, not him.

[@CMDRunematti]

@@EpicMathTime but how does it look like when its partially flipped? kind of sounds like stuff far from him have their parts compressed, even farther from him they would look like multiple things are at the same place. im just trying to visualize it and failing miserably

[@EpicMathTime]

If we gave Mr. Yellow unlimited vision, when he looks down this path, he will see infinitely many copies of his universe. In his vision, he will see his universe continously shrink in size to a point, and then grow back in the reverse orientation at the next copy. When he moves down this path, he never feels that he is shrinking or flipping, he always sees shrinking and flipping in the distance, it is a relative perception of that space from where he is.

[@CMDRunematti]

@@EpicMathTime wait so...theres a place in the distance where he sees everything shrinking into a singular point, and then, everything after that is getting bigger... but will it look bigger than life or just big as in we know its far, but it grew back to original size..?

[@EpicMathTime]

Just back to its original size.

[@mikhailmikhailov8781]

Also, I am pretty sure non orientability fucks with physics somehow, conservation laws and all sorts of shite will be fucked full time and I have no fucking clue about orientability of einstenian manifolds.

[@raresneagu6928]

3D Omnipotent Gods😂😂😂

[@LitLightskin]

hey bro can you really me out the way other larger yters helped you out !!!!

[@muskyoxes]

Of course the characters are male, just like in any form of fiction.

[@SolidSiren]

We are not special