sorry dude but above time there isnt dimension anymore. Dimension means: borders, boundaries, mathematical dependency and can be explained by formula (only from a higher dimension into a lower one) every try to explain higher dimension from a lower is a CONCEPT and isnt true but only approaches the truth eg klein bottle. Concept: a lower dimension thinking about a higher one Definition: a higher dimension observing a lower one. a mobius strip is the two dimensional infinity and can only exist by staying in a higher dimension! 6:15 - is what we see as a donut shape. The torus. The klein bottle is the three dimensional infinity existing in a higher dimension (=something like a proof there is at least one higher dimension above 3D, what i called CONCEPT above)

en.wikipedia.org/wiki/Curse_of_dimensionality more views means a better idea of the concept of the dimension that is above 3D (4D i think is the time dimensionality)

How do you make a cone this way?

Want a Mobius strip? I'll sell them for half price of the Kline bottle. Some assemble will be required because the Mobius strip is delivered as a post card to you and you have to tape the two ends of the postcard together yourself. The instructions are on the post card. In fact, the instructions appear on both sides of the post card after you have taped the ends together to form the Mobius strip.

Drink from that Klein bottle! ooeorr rueuvoo ruruv kvooki u dudue

You won't , ask them who are data scientist..😂

Me to

If we were 2D people . You would have said the same that you wouldn't need 3 Dimension 🤣🤣

same

Need? It's a prerequisite.

YEAH!!

Numberphile reference

Yeah boiii man that guy is great

Ah, yes

Lmao. Everyone Edit: Actually I thought more about Matt Parker of Stand-up Maths at first.

R u the author or

Bruh!

That 5 minutes might be your biggest contribution to humanity considering the reach. Unless you are a teacher of some sort.

​@@aqaridot en.m.wikipedia.org/wiki/File:TorusAsSquare.svg here it says "Drawn in en:Inkscape by Ilmari Karonen"

That's awesome.

Mathematically, this is a visual of the failure of a certain property of functions.. For an object to embed in n-dimensional space, there must be a function that brings the object into n-dimensional space that is, among other requirements, one-to-one. The object intersecting itself is a manifestation of the function's failure to be one-to-one. Points that were previously distinct on the object are brought to the same point.

This was the best explanation of the concept behind the Klein Bottle I've ever heard. The comparison was great and really helped me understand

Tgon Mwort you don’t need to see it. no one can imagine 4 dimensions, and a taurus is embedded in 4d. but you can imagine a cube, and you can imagine a drawing of a cube, and you can see how certain point have to intersect on the paper to represent it. despite these apparent intersections, you know that none of the vertices of a cube actually overlap, and you can compare that to a drawing of a klein bottle. remember, you don’t need to imagine it. just understand the comparison.

Tgon Mwort no one can. just the way the brain works.

@Tgon Mwort wait how can you see into the future

This was really well explained. Thank you.

Yeah, the video also had me think "what about spheres?" at several points. The thing about spheres is you can't topologically embed them in a plane, so it's hard to compare. If we use something like Mercator projection (how globe maps are usually drawn), yes if you go west you come out on the east end, but the same is not true for north-south. As you move towards a north-south edge of a map, once you're there, you come back down from the same edge but in opposite direction (on the map) at a different point that isn't even connected to the previous one. That's because essentially, if you embed a sphere in a plane, you have to turn the poles from points into edges (the north and south edge of the map). So basically, if such a 2D game were to have spherical-ish topology, if you go through the left border you'd come out on the right, but if you move through the bottom border (going down) you come out on the bottom border going up but exactly half a screen length displaced.

Interesting thoughts. I did think asteroids is a sphere. The issue I had with a torus was, I thought if your spaceship was on the inner ring, and pointing along the mid plane of the torus, if you press up then your spaceship would move in a circle on the screen (or perhaps run along a single vector line and back again without going off screen). Ultimately, the entire surface of a sphere cannot be laid flat in 2D to make a SQUARE, but with a torus it can... I think... The bend radius would have to be very small. Ok now I need some paper and scissors! It would have been good if this was mentioned in the video.

@@gmweb1304 I don't know if this is relevant, but the position of the observer is different in the two examples. When mapping a sphere we do so from a position above the flat surface to be mapped. With the game of Asteroids it appears as though the point of observation is from below what could be described as the flat surface of their environment.

The sphere can be pictured with a rectangle. Just look at a world map. If you travel to the top (or bottom) you still come out to the top (or bottom) just at a different point - left or right.

**SM64 file select music starts playing**

@@moversti92 Step 1: build up speed for 12 hours

circle

The asteroid shape is torus Or is it? *Music intensified

W H E R E A R E T H E T U R T L E S

I doubt it will ever be tangible to us, sadly. Unless, we give our brain a 4D update lol

@@angadsingh9314 Lmao xD

@@arunavaghatak8614 Nobody wants to see that shit.

Game Theory X Evolution is typing...

π=3 but π^2=10

@@bayekofsiwa7035 no, it's g but g is 10... ok nevermind

Really sad, but yeah thats the truth...lesser ppl are getting into true math by the time.

@@englishmotherfucker1058 no i meant that in engineering they take π^2=10

@@bayekofsiwa7035 I hope you are saying this ironically

I think it was not a sphere because you can make a sphere using only one kind of circles that continues to go in one direction anywhere. That creates a sphere successfully. The answer was torus because you cant only do it with one sphere going one direction and you need two so that the hole of the torus can be made. And i know i explained that very terribly but im tired.

@@alexumitsuu3237 its cool, thanks! hope you get some rest

​@@randaljr.8581 ssssssssaaaaaaaaaaaaaaaaaaame on the oc lol

me too

Np

Papa flamy!

@@rainbow-cl4rk

A rare instance of a mathmatician complementing an engineer

>snecc

Don't tread on me.

N И

Ñ Й

@@rainbowbloom575 X X :P

@@MsSonali1980 q р

@Rainbow Bloom d b

When you do enough math, you'll see that you can have a product of a lot of different things, provided that you can define the product.

How was this made yesterday?

Obama i think it's that patreons can see the video earlier than anyone else

@@barni3045 wtfff. No way.

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@@angadsingh9314 way

Honestly, yeah, that is sorta what a torus is, a loop traced along another loop. Although I suppose the bead and necklace idea that I associate with that idea does make think of those oops as separate from each other I'd more readily picture them as dangling from each other, but I'm pretty sure that's just a "me" thing. It's probably why I'd try to describe the loops of a torus as embedded into each other, but I'm pretty sure I'm just being pedantic.

a klein-donut

You could do 2 of the connections in 3 dimensions, it's that last connection that gets you into trouble.

Me too!!!

sorry, but real envolve doesn't think of dimension as dimensions but realtime

sciencephile the AI references here

I was sitting here "It's a Klein Bottle it's a Klein Bottle, tell me that I'm correct" like I was sitting on hot coal. (Yes, I'm that person). Had never thought that topology was so exciting for me. I always had problems with geometry but was good in function analysis or probability.

A sphere is the same as RxR but you need to add an extra point at infinity.

You ask the same question as me😂 Are you in my head?😂😂

I thought the same thing about the sphere

1.) This results in what's called the real projective plane, or RP^2. It is a well-studied object, so just Googling that will give you plenty of information. 2.) There are no such factor spaces of the sphere. Showing this is true is a bit out of scope here (off hand I think we will need to invoke algebraic topology for a proof). Intuitively, one might think of spheres as more "fundamental" or "prime" topological spaces.

Epic Math Time Thanks for the explanation! I'd wondered if the sphere would be considered "prime". Might take awhile to wrap my head around RP^2 though...

Thats a really goo remark and i think its just because we are born and live in a 3d space. There is the 4th dimension - time, but we actually cannot feel or observe it. We measure it, we live in it, we count it, but how would you imagine it? You live in it and it became such a inseparable part of our existence that it become impossible for a normal human to "think outside of the box". I bet that if you got even a glimpse of 4th space dimension, you would no longer have problem imagining it further, but in this case its like trying to imagine a color that you have not seen. It just too different from what your brain has observed up till now...

It's a really interesting question. Would a physically 4D brain hooked up from birth to a simulated 3D world like ours nonetheless somehow be capable to imagine the 4th dimension, just by virtue of physically inhabiting it? Personally I don't think so, but I imagine to have a clear answer we would have to try en experiment with a 3D brain hooked up to a 2D simulator from birth. Problem is (ethical issues aside) I don't imagine a 2D simulation would be enough for a brain to evolve complex functions like language and spatial awareness, for us to be able to ask them to imagine another dimension. Still, I believe the answer lies in the psychology of the brain and not in the physical substrate it is made of.

Eyes see pictures of the worlds, basically we see in 2D, but because we have 2 of them and the brain is actually smart, it can deduce the 3 dimension from that. I believe we instantly a Cube as a Cube simply because of experience thus (can be demonstrated with optical illusions too, it's quite easy to trick the brain with fake or impossible perspective). A flatlander would only see a line, so it would see in 1D, but with its experience, it could understand what a square is like, however there would be too much missing information for a cube. now I'm really not sure, but maybe if we found a way to have eyes that can see in 3D, we could then see objects in 4D much better. A flatlander sees 1 or 2 line from a square, but we see the whole square at once, no matter what is its rotation. Our 2D eyes see only 3 faces of a cube at most, but a 3D eye could see the entire cube at once. If you had 2 3D-eyes, maybe that would be enough to fully see in 4D? In any case, I'm confident to say it's beyond human comprehension, simply because the brain is made to interpret and compare 2D pictures, not entire 3D spaces, so even if you somehow injected 3D eyes into the brain, it probably wouldn't be able to understand anything.

Tomáš Musil why 4th dimension of space? Space cannot be has only 3 dimension and 4the or 5th beside time , there might be other dimension but not space. Something we cannot understand

with yo 1D brain

E

Hey there! I saw the answer to this in a thread nearby, and someone said that it was called the Real Projective Plane (represented as RP^2). There's a few good Wikipedia articles on the topic, so here they are: REAL PROJECTIVE PLANE - en.wikipedia.org/wiki/Real_projective_plane REAL PROJECTIVE SPACE - en.wikipedia.org/wiki/Real_projective_space