Unwrapping a tesseract (4d cube aka hypercube) 

well what you said is so accurate

Is it that difficult?

Lol I love it

Pretty accurate, but there will be a certain point of time when the blind person fully understands colours, and so I can kind of process what is going on. 4D is not that difficult to understand, it depends on the wildness of your brain.

yep buddy, it's annoying that we just can't visualize data that greater than 3D

Same, we can barely see 3d, since to us its just a 2d projection

You can't?

Yeah but at least you can understand 4d.

wait if we can project 3d things on a 2d screen, can we see 4d on a 3d screen?

😂

Looking that eighth cube below, at the bottom 1:00 I think that eighth cube below is unnecessary.

@@anarcocapitalista3700 no it is not

@@anarcocapitalista3700 There is supposed to be an eight cube.

4 sides, 6 planes, 8 cubes, 10 tesseracts, that how it goes?

As I said in the comment above, nobody can imagine an object with more than 3 spatial dimensions. What the animator did, is imagining of the projection of a normal cube on a wall, which is a smaller square in a bigger one and its vertices are connected with lines. At first you take the net of this thing an held it parallel to the wall. Of course you se the same thing on the wall, but eventually a little bigger due to the diffusion of the light. Then you fold the net up to a regular cube. As soon as you make it, the square in the center, the one which is surrounded by the for other squares, stays at its place. But the four squares around the centersquare are crooked up to trapezoids. And at last the sixth cube, which sits on one of the surroundingcubes, is streatched to a very wide thing, until it matches up to the bigger square, which is already shaped by the four crooked sourroundingcubes. Now take this, and exert it for the 3D-net of the 4D-Hypercube, the tesseract. It works simulatneously but at last with 8 threedimensional cubes instead of 6 twodimensional squares. I hope it helped a little bit! :)

Actually, the cubes aren't concentric. Since this is a 3D projection, we can't see 4D depth. The "smaller" cube is actually behind the "larger" cube in 4D space. Picture looking at a cube straight-on. For two-dimensional eyes it would look like a smaller square inside a larger square connected by lines. It's not impossible to imagine 4D space, it's just really hard and requires a lot of practice.

Bennimus Netzer That is exactly what it is about!

You seemed to be presenting the basics to me, so I tried to enlighten the situation.

Bennimus Netzer In some sense it's not quite that good either, since a 2D creature wouldn't see a square the same way we do. He would have to form the squares out of some translucent material in order to see through the front side of the outer square, the front side of the inner square, and the back side of the inner square in order to see the rest of the back side of the outer square. Thankfully, in 3D we don't have to use translucent material for our edges to make wireframe diagrams that are useful for visualization of higher dimensions - and we don't even have to put material on our faces because the edges themselves keep the figure connected. A 4D creature visualizing the 5th dimension could (but doesn't have to) form all the faces of that figure out of opaque material and still be able to use it as a visualization, but they couldn't make the 3D cells on the surface opaque. For these reasons, I believe that nD creatures are able to visualize (n+1)D slightly better than (n-1)D creatures are able to visualize nD, with the distinction being more important the lower n is. In the extreme case, we have a 1D creature trying to imagine 2D. He'd be so tremendously bad at understanding any concept of "length" that of course the 2D creature who knows what length is can imagine 3D better than the 1D creature can imagine 2D. Or if we really want to go extreme (and pretend these creatures are somehow biologically and neurologically feasible, even though that seems unlikely), a 0D creature would fail even harder at imagining 1D than the 1D creature does at imagining 2D, since at least the 1D creature understands what it means to see. His view may be only a point, but he can imagine that point changing color over time (if we pretend color is somehow viable). The 0D creature doesn't have any way of understanding what sight is. You probably didn't need to be told all of this, but I got carried away.

thanks for the hearty heehee

As you can see it looked like a cross after being unwrapped. Accept Jesus into your life. It is the only way.

@@melvincrossbred8750 Amen came for that cross and the unwrapping of the saturnien cube.

you have to draw your own. search up drawing a Tesseract. Two cubes first, almost touching, then attach the corners. Once you’ve drawn it, let your mind wander and try to find the eight different cubes inside. The cubes will overlap and appear to share 3 d space. When you see it, this is precisely the fourth dimension…… sadly nobody explains it this way. Some of the cubes will be distorted, but in reality they are not. The more you look at your Tesseract the more you will see this overlapping 3D space. Your brain will tell you that one cube HAS to de dominant, but that’s not the case in 4D. All of the cubes three dimensional overlap is correct and equally valid in the 4 dimensional volume. The key is to draw your own and let your mind be fluid. Edit: when you draw your own don’t put One cube inside the other like they show here although it’s probably technically correct it doesn’t help you understand. Start withdrawing one cube then draw another cube up and to the right on a 45° angle and almost touching. Just google images. Use a ruler and be clean and neat. For the lines attaching the cubes use dotted lines. this helps as well.

I think all of us are. That's kind of the point.

Jesusdragon737 This video is made to you too. All you need is try to do... Really. Good luck

Jesusdragon737 I can see how it folds into 4d from 3d, just as how a cube folds into 3d from 2d. But obviously humans cannot fully understand and see 4d space because we live in a 3d universe.

InfinityV0rtex Thats not sure, maybe we only think we life in a 3 dimensional Universe. Dark Matter for an example could exist in a higher dimensions of space, thats why it's there but we can't see it. It's only a theory of course.

Jesusdragon737 It's really not that difficult, if you think of it in this way: 1 dimension would simply be represented as the x-axis, where you can only go left and right. 2d is simply an expansion of space of that initial concept, in that by adding the y axis, you now have the ability to go up and down, because the second dimension, represented as y, is nothing more than an infinite stack of the x axis. Therefore, the 3rd dimension is nothing but an infinite stack of the 2nd dimension, represented by the z axis. Following this logic, it is then reasonable to assume that the 4th dimension is nothing more than an infinite stack of the 3rd dimension, which is hard to visualise, but can still be represented in 3d space, much the same way a cube can be represented on a flat sheet of paper.

Jesusdragon737 It's an 8 bit vortex ring when it moves on the YW axis. Watch a smoke vortex ring video and you will get a better grasp.

And trying to figure all of it out with a 1d brain

That contains 0D braincells

That are made of impossible -1 dimensional quantumly advanced atoms pulled together at 1.5x faster than light speed.

What if they are shadows of their 5D selves?

cross sections, not shadows

It's a projection, much like how you can draw a "3D" cube on paper a 2 medium

My opinion is that even we draw a 3d cube on a 2d paper (well not technically) we can still perceive that is a cube so same may apply for 4d too

The smaller cube inside is not really inside it per se, it's actually further away

But in a 4th dimension, all the cubes are the same size and not in angles like this

Ok then, assuming that it's just a 3d cube but you also see the inside A 3d cube has 6 faces. For each of those faces there exist an inside face Now, According to the assumption that you can see the inside side as well We see the 6 sides that exist in 3d Plus the other 6 sides that 6×2 = 12 So according to the assumption, the tesseract has 12 faces But actually, in theory we already know that a tesseract has 24 faces. Hence the assumption and your understanding is wrong. Your understanding of the “tesseract” is wrong but I can see where it comes from. Actually when you use the word tesseract in your understanding, it is not tesseract. It is a regular cube but from the perspective from 4th dimension. A man who exists in the 4th dimension can see the 6 sides we see and everything that is inside the cube (which are 6 more sides If the cube is hollow) all at once. But a tesseract is not just a cube in 4d but it is something Which can only exist in 4d. Similar to how a cube is not just a square in 3d but something that only exist in the 3d. A square in 3d is still a square. But in 3d we can look at all 4 sides of the square at once. In 2d we can only look at one side at a time. A tesseract is made by joining 8 cubes together. But we can't just do that by stacking 3d cubes together. all the cubes must be perpendicular to adjacent cubes. But doing so is physically impossible in 3d. We can only do this when we already have access to the 4th dimension For example A cube is formed by joining 6 squares (2d figures) So If we simply keep stacking the 2d figures together in 2d we would end up with a cross or a rectangle. The only way to form a cube is to stack the squares perpendicular to Thier adjacent squares and parallel to opposite squares. Again, we can't do this with access limited to the 2 dimensions and we would already need a 3rd dimension. An additional point to the tesseract is Out of the 6 sides of the cube used to form a tesseract. Only 3 of the sides are visible on the outside.

Us, as 3d beings, cannot comprehend dimensions beyond three dimensions. 4d beings can’t comprehend 5d and so on. Even if we were able to see 4d, we would only see a 2d representation of it.

13???????????

Wut?

Exactly. It's a perfect example of how three dimensional cubes are comprised of two dimensional places with each side running parallel or perpendicular to each other. So a fourth dimensional cube would be compressed of three dimensional sides each running parallel or perpendicular to each other. Obviously thats not what we see in the video because a fourth dimensional object cannot be represented accurately in three dimensional space. Drawing a cube on paper gives a similar distortion. The sides are no longer all parallel or perpendicular. We lost a dimension and therefore the image is not accurate.

4d hypercubes*

And a pentaract has 10 tesseracts

@@DaddyJoks_ THAT'S what a 5d square is called??

@@scrunkliestscrimbo9981 yeah and 6d is a hexaract

​@@DaddyJoks_Please continue with more dimensional cubes names

​@@IluminousOne-9.7.2another name for a hexaract is sexaract btw

@Charles Bruins i mean . . . a 4d being could draw in 3 dimensions, on a 3d "sheet" of paper . . . i imagine it wouldn't be terribly difficult for them XD

This is actually a great analogy and it helped me understand the transition between a 3d cube and a 4d hypercube a bit more. Thanks a lot!

He came back to heart this comment after 11 years, what a legend

@@Dylank001 I feel honored 🤭

@@Dylank001 i'm still watching for you ))))

Thanks, he's all right.

​@@vvpanfilovno way...

Tho when you unfold a 4D object, it turns in a 3d object, just like unfolding a cube makes squares, and unfolding squares makes lines.

You got it, congrats! )

So basically you have to train your mind to understand and imagine 4d. I think with your eyes closed you can achieve this after some time.

in the order of: 2 points, 4 lines, 6 squares, and 8 cubes. so, a 5th dimension object can be represented by a volume bound by 16 tesseracts

@@luvustelewis there can be no 4th dimension if time is not explained. 3-d+time. so first, the time has to be thoroughly explained and defined before progression can be made to the supposed 4th dimension. and time is a paradox, if explained right it self-resolves into oneness. After 3-d empiricism breaks down and collapses. To solve the collapse is to solve the paradox into a self-resolving paradox and the end of mechanical thinking. --> CTMU

Width then Length then Height and Time/Trength and ????

Lewis Luvuste It doesn’t double each dimension, it increases by 2. A 5d hypercube is bound by 10 tesseracts.

My brain is made out of a potato

Wrong video idiot

@@alreadynestedhumanwine no need for toxicity idiot

Math example: Corners/vertices always double. Example: The shift from 12 to 32 edges goes like this: e(2)+c = new number of edges. (Note: e = edges and c = corners.) Same formula applies to the other units, like squares: s(2)+e = new number of squares.

Fun fact: My personal mathematics professor brought me a vintage homemade wood model of a mind-boggling 4-dimensional hypercube.

What happened?

@@ylanberri1464 read the description

That’s basically what it is just like you said, with 4d and 3D instead of 3D and 2d.

Chikane same here! it's such an intriguing concept, and i had it for a second. it made so much sense but then it disappeared

Tá tudo em inglês

I disagree. You may not be able to figure out where to place the axis, but you can totally see it's affects from visualization. it would work just like any other axis. Get closer on that axis, and the object appears larger. Rotate around the object on that particular axis, and it changes shape and size. It would be no different with 4 dimensions. Put 2 3D cubes on the same X,Y, and Z but with a bit of space between them on W. From the right angle they look like they're in the same spot. Move along W and you see the space between them.

you just broke my mind, thanks

@@sofiel.1931 lol your welcome, hopefully one day we will be able to somehow visualize 4d in a more intuitive way

well well said man this is so nice way of explaining it

@@iamnode2088 thanks bro

Like going through an interdimensional portal. Going in and out.

It’s not really changing properties of what they can do, but it’s the right idea. Like how it would be confusing for a creature in 2-D space to perceive an object moving through 3-D space when it’s just being moved along another dimension. Objects can’t move THROUGH themselves in 4-D, but it seems like it does from our spacial perception. It’s just a different frame of mind when there’s an extra dimension to explore. :)

@@josephsmith3961 soon it will be possible to visualize 4 dimensions. all we need is to wait for the available technology to insert 700 billion more neurons in our brains, connect these new neurons to the "dimensionality perceptor engine" and voila, you can see 4 dimensions now. It is just the question of neuronal resources.

@@absolute___zero very intresting

no, it doesn't self intersect the reason it changes shape is because this a projection into 3D space, this doesn't really transfer over to the 4th dimension at all just as how when you unfold a cube into a cross, where all of the square faces don't change shape, the same way a 4D cube unfolds into some sort of tree without any of its cube faces deforming, its just that because you can't emulate the 4th axis without deformations in 3D space is why the cubes appear to pass through each other and change shape also its not necessarily harder to visualize the 4th dimension, if you've played any 4D games or gotten used to the math its actually fairly easy

They're not interjecting or phasing through. It's all due to perspective and the limitations of our 3D Universe. Try drawing a cube on a piece of paper (which is a 2D plain). Notice, how your squares of that cube look out of proportion, and seemingly intersecting with each other. Now, we know, it's because they're "behind" the other squares, but try to explain that concept to a 2D being, that doesn't know what "depth" is and see how far you can get. It's the same with 4D objects. The smaller cube inside the tesseract is the side that is the furthest away in the 4D space, and the cube that is "all-encompasing" is actually the front side of the tesseract, the closest to us in 4D space. Our brains developed their sense of direction within our 3D space, so exposing ourselves to this expanded 4D geometry, introducing a new axis of movement, leaves us with severe headache - it's normal though. We fail to visualize the 4D in our head, as we simply have no concept of this 4th direction, except for our familiar x y and z.

Don't kid your self lol

@@hydrogamer471 LMAO it makes a *bit* more sense now

How the hell did you get thosevwords?

Buddy, those new directions have been named "Ana" and "Kata". We cannot imagine those directions.

@@IluminousOne-9.7.2 yes, i know.

I lost you at "connected to two squares" I can count four squares. You may want to edit your comment and I'll be happy to follow your explanation.

@@LucasDanielSantoro You're right. Each square is connected to 4 squares, and each cube is connected to 6 cubes, one on each side.

and our consciousness is just a 3d shadow of 4d (aka REAL) consciousness of 4d beings. That explains why we don't understand wtf we're doing. We are just a 3d passengers LOL

@@samuraiesthetics I agree, some people's near death experience have exact details as 4d beings seeing a 3d space

mY bRaiN

*Oh sh*t.*

A brane has 10 tesseracts

@@butterscottowo In yours' the i(-th)'s missing

@@TT-ii9cm i meant like brane from membrane

Nice joke copied from that guy explaining the 11th dimension

@@bhavplayzz1739 what guy?

@Eye Sees You that's the mindblowing part. It's something that you can literally only try to imagine and even then it's not even close to what the reality is. It's just an insane concept to wrap your head around that you, me, and everything in this plane of dimension exist in a higher plane of dimension that isn't even tangible to the minds we exist with. It's like trying to draw a picture of nothing lol

We exist in a higher plane of existence? So the universe we exist in isn’t just 3 dimensional? Care to explain?

@@RC-hv1yx Nah

Well, a square has 4 sides, a cube has 6 faces, so it makes sense the tesseract would have 8 cubical “faces”.

a tesseract has 8... volumes

@@callyral a square doesn’t have “lengths”, and a cube doesn’t have “areas”, so why would a tesseract have “volumes”? I think “bodies” would be a better term but that’s just me

I know

for sure likeif smeone sees in 2d, then just show him your front face and then tel him to close his eyes and then turn around and show him your back.. boomhe thinks you sapeshifted! imagine samething but to us 3d people and someone just making a simple turn in 4d

Dank Beef It does. it'd be like looking at a piece of paper to us.

Dank Beef Maybe humans should hire a 4D being to perform surgery.

Exactly, it kinda finally clicked in my head how it works, didn't know that until now

Mine OW, too OW

I absolutely understand nothing but I like your theory

Same thing :D

Nooow I get it! There aren't actually smaller and bigger cubes. They are just getting further away on the extra axis and the extra axis is represented by the scaling of the cubes.

There's two faces for each axis - one front and one back. Each face is one-less dimensional. So in 1D we have 2 faces, each is a point, in 2D we have 4 faces, and each is a line, in 3D there are 6 faces, each is a surface and in 4D there are 8, each is a volume. The extra two are the front and back of the 4th axis, the smallest and largest cubes. So intuitive and cool! My mind is expanded.