@@loop_mind But, the cube and the light source can't be rotated in four dimensions. If you were to somehow do that, and the cube wasn't a tesseract, then the cube would either partially or wholly vanish into the 4th dimension, right?
You can rotate a 2D square or a 1D line in 3D and see how its shadow distorts. This is what's going on here, just with a 4D cube and 10 other dimensions.
Then you are normal. People are freaking out because of a 3D animation and calling it a projection of multiverses or some other nonsense. But then they will deny that nature has been designed by God. Whatever.
There's something that really annoys me about knowing that we'll NEVER know what a 4D shape actually looks like, and that we physically can't even imagine it
Additional TL;DR for TL;DR: I think this has great potential for further visualization in an user-interactable setting. Sources at the Bottom. TL;DR: I go full nerd mode just to try and explain how a comprehensive visualization of much much higher dimensions would be cool to play with. When really all I wanted to explain was a separated visualization option of what was done in this video. Such as a graph charting each points movement through time. While playing with alternate timelines, multiverses, and higher/lower/adjacent dimensions would be fantastic to play with, I redundantly and needlessly explain things I don't understand. To my current understanding as a layman, supposedly, according to the current definition of Bosonic String Theory, there are 26 Dimensions. And with a very quick and self-admittedly not thorough enough google search, the research paper by Frank D. Smith Jr. titled "Physical Interpretation of the 26 Dimensions of Bosonic String Theory," the abstract of said paper reads "The 26 dimensions of Closed Unoriented Bosonic String Theory are interpreted as the 26 dimensions of the traceless Jordan algebra J3(O)o of 3x3 Octonionic matrices, with each of the 3 Octonionic dimensions of J3(O)o having the following physical interpretation: 4-dimensional physical spacetime plus 4-dimensional internal symmetry space; 8 first-generation fermion particles; 8 first-generation fermion anti-particles. This interpretation is consistent with interpreting the strings as World Lines of the Worlds of Many-Worlds Quantum Theory and the 26 dimensions as the degrees of freedom of the Worlds of the Many-Worlds." Traceless Jordan Algebra is just a type of algebra to represent the above concepts through pure mathematics. A full breakdown according to en.wikipedia.org/wiki/Jordan_algebra A single Octonion Dimension is defined as "Octonions have eight dimensions; twice the number of dimensions of the quaternions, of which they are an extension. They are noncommutative and nonassociative, but satisfy a weaker form of associativity; namely, they are alternative. They are also power associative." This concept is very abstract to me, but with some google searches, there seem to be visualizations of a single octonion dimension. Connecting multiple octonion dimensions would be difficult to visualize, but I assume it can be done with effort and time. A nice visualization of a single octonionic dimension comes from theoryofeverything.org/theToE/tags/octonion/ The concept of 3x3 Octonionic Matrices is very difficult for me to wrap my head around, but with some quick google searches, it seems as though as this would be 72-dimensional, so what happened to the 26-dimensional concept from earlier? Well, skimming through a description on valdostamuseum.com/hamsmith/3x3OctCnf.html it seems to explain this a lot better. 4-dimensional physical spacetime is, super-simplified, as "3 spatial dimensions with 1 dimension of time." This is easily visualizable, but of course with the condition that it needs to be projected to a 2D screen. This, I believe, doesn't need any visualization sources. So I won't put any. "There are four basic isometries of 4-dimensional point symmetry: reflection symmetry, rotational symmetry, rotoreflection, and double rotation." Reflection, Rotational, and Rotoflection (or Improper Rotation) are all easily done in 3-dimensions. However, double rotation is, from what I can understand, something a higher-dimensional object can perform. Which also seems visualizable. At least according to en.wikipedia.org/wiki/Rotations_in_4-dimensional_Euclidean_space first-generation fermion particles and the anti-particles are just types of particles, and (from what I understand) don't need visualization. I think the in-depth visualization work done by UA-camrs such as CodeParade, Zenorogue, [mtbdesignworks {Miegakure, 4D Toys}], and Tomfractals are very good non-Euclidean/ non-3D visualizations. Higher-Dimensional Space. I think the game "5d chess with multiverse time travel" is a good representation of Higher-Dimensional time. There was a much older game that I swear Nerd^3 played a while back that was very similar to the concept of alternate timeline travel gameplay, but I can't seem to find it. Sources: UA-camrs: CodeParade, Zenorogue, [mtbdesignworks {Miegakure, 4D Toys}], and Tomfractals Games: "5d chess with multiverse time travel" Websites: en.wikipedia.org/wiki/Rotations_in_4-dimensional_Euclidean_space valdostamuseum.com/hamsmith/3x3OctCnf.html theoryofeverything.org/theToE/tags/octonion/ Paper: ui.adsabs.harvard.edu/abs/2001physics...2042S/abstract#:~:text=The%2026%20dimensions%20of%20Closed,physical%20spacetime%20plus%204-dimensional
@@nosamgeography1249 Congrats! You had the option of not reading passed the first TL;DR, and yet you still decided to tell me how long the comment was.
This should have the freebird guitar solo like the rotating rat videos! Sometime this year I'm planning to learn blender, maybe I'll make something inspired by it, if I ever get around to it. Back when I was studying physics and had a wolfram mathematica license I once made some 4d-hypersphere visualizations, so maybe I'll make a version of the rat but it's spinning in 4D 😅
Same feelings when you playing a game and using glitches to pivote object you are not supposed to, they move the same way and get deformed as well just the same way. Little big planet ⚰️
That's because 3D rotations are made through a projection of quaternions which are 4D hyper spheres. It's really easier to compute 3D rotations using a 4D object than to go straight into 3D.
@@JesusProtects It’s the animation glitching out because we can’t see beyond 2D, it’s not reality for US because we are in 3D, 4D is already beyond our compression I’m very far to begin to imagine 10D
I’ll do you one better: Imagine 26 of these all put together into a 4d 3x3x3 Rubik’s cube that you not only need to rotate into a proper perspective, but also solve.
Yeah I though it was only X Y Z W but then When I saw V (fifth axis) I thought now it was ten dimensions Here are all the axis in order X Y Z W V U T S R Q
4D is used all of the time in game dev. Especially in the 90s camera movement has been calculated including the W dimension which leads to smoother and faster results compared to using only X Y and Z.
@@FredTheRed27 to describe that in a single yt comment would be probably very hard, but look up quaternions in the context of unreal engine or unity, there are some solid articles on the web
This is a bit misleading. In a purely mathematical sense a quaternion is a four-dimensional object, but in video games it's used to represent the orientation of a 3d object in 3d space (which is nothing like the brain bending stuff happening in this video). The quaternion's values of X, Y, Z form a vector and W is an angle of rotation around that vector. Usage of quaternions in video games is simply to save time and space in calculations. Alternatives such as rotation matrices are quite bulky and euler angles suffer from gimbal lock.
I always love thinking about dimensions and our perspectives on it, like how if we were suddenly made 2D, we'd be bisected, because of our digestive system. I can only imagine what would happen to a 4th Dimensional Being, if they suddenly became 3D. They'd probably become inverted into themselves and die. 🌵👽
I've had fever dreams where I could translate and rotate in as many dimensions as this probably more but still had a 3D perspective and understanding. It was what I think hell is like.
Mathematically, dealing with higher dimensions is as easy as just accommodating the current models and adding the extra spacial values on. Actually _showing_ the results of this however is a whole other story...
HEY thanks for example of rotation in multiple directions(I mean xyz is 3d and you give also w d v etc.). I see this for first time Btw, I have question. Is it possible to be able rotating with 3 coordinates simultaneously, of course in higher dimensions
Rotations work by locking every other plane of rotation other than 2 at a time, such as XZ with Y not changing. You can rotate XYZ simultaneously by simply doing every rotation after one another: First XZ, then XY and ZY (and higher-dimensional rotations). If it's possible to rotate 3 coordinates simultaneously, yes! Just rotate XZ, XY and XZ after one another.
Oh, very cool. I totally understand everything about this. Thanks for just making a visual of this thing I already definitely understood. I absolutely get it.
this reminds me of that game where you can change an object's size based on how far it is from your perspective, only here you can change its shape lol. someone should make a game like that
Kind of, but its projection would stay, just as it is shown in the video with tesseract i.e. its projection, being 3d, 2d or 1d Not a silly question at all, rather a great question to think about
Yes, I can come up with a mathematical proof of a result that contradicts the video, though I'm not sure if my way is the most elegant way to do it. (It was surprisingly hard to make the proof!) Theorem 1: For any 10D to 2D perspective projection and any half-plane of the 2D screen, the set of all possible points that project onto the half-plane on the 2D screen form a half-plane of the 10D space. The opposite half-plane in the 2D space corresponds to the opposite half-plane in the 10D space. Proof: I'm sure the video uses perspective projection. TL;DR the 10D half-plane is bounded by the face of a 10D pyramid whose tip is the camera location. This is similar to the faces of the 3D rectangular pyramid that bounds a 3D perspective projection to a rectangular 2D viewport. More rigorous proof at the end, it's not as relevant to my overall result but I add it for completeness. Theorem 2: The intersection of a hyperplane with a convex set is another convex set. Proof: This is an elementary theorem in convex analysis, since a hyperplane is convex. Theorem 3: Under any 10D to 2D perspective projection, any line in 10D space gets projected into either a line or a point on the 2D screen. If a line is formed, any line segment along the line in 10D space is projected into the line segment on the 2D screen between the projections of the two endpoints. Proof: Trivial by using the formula of a line, applying the perspective projection's transformation, and recovering the formula of a line or a point. Also trivial to demonstrate a one-to-one relation between the line segments. Theorem 4: The convex hull of the vertices of a polytope is the polytope itself. Proof: It's a well-known theorem about polytopes. Theorem 5: The 1D interior of the line segment between two vertices on a ND polytope is contained in the MD interior of one of its MD faces (M = 2 contains edges of the polytope. Proof: Edges are 1D faces and polytopes have finite size by definition. Given the half-planes bounding the MD face, it must be possible to possible to find M - 1 of them that intersect at a line, otherwise the polytope can be shown to be infinitely big. This intersection contains an edge by definition. Theorem 7 (the actual result we want): When using perspective projection to display a polytope like a 4D tesseract from 10D space onto a 2D screen, there does not exist a half-plane on the 2D screen that intersects only the projection of two vertices and no other points of the wireframe of the polytope. Proof: Suppose for contradiction that it is possible to do achieve this configuration. Call the two special vertices in 10D space A and B, which get projected into A' and B'. If we draw a line that intersects the wireframe at A' and B', there is a half-plane on the 2D screen containing only A' and B', and by theorem 1 there is a corresponding half-plane on the 10D space that contain A and B. Call the 2D half-plane H_2 and the 10D half-plane H_10. The half-plane opposite H_2 contains all the vertices of the projected view, so by theorem 1 the half-plane space opposite H_10 contains all the vertices of the polytope. By theorem 4 and definition of convex hull, the whole polytope lies within the half-plane opposite H_10. Therefore, there cannot be any pair of points in the polytope that lie strictly on opposite sides of H_10's boundary. Because a polytope is convex, by theorem 2 the intersection of H_10's boundary and the polytope is a convex set. The intersection must at least contain the line segment AB. By theorem 3, this line segment projects into the line segment A'B'. By theorem 5, the line segment AB is also contained in the MD interior of one of the MD faces of the polytope. Take any point P on the interior of AB and consider all line segments that contain that point in the interior, and lie inside the MD face. Suppose for contradiction that at least one line segment CD containing P in the interior is projected into another line segment C'D' on the 2D screen that isn't entirely on the boundary of H_2. CD contains P on the interior, and since P is within AB it is projected to a point within A'B', and so C' and D' are on opposite sides of H_2. This means C and D are on opposite sides of H_10. But CD is part of the polytope, and the polytope does not contain points on opposite sides of H_10. Therefore, all the line segments containing P get projected into either P itself or line segments on the boundary of H_2. If we extend all those line segments into lines and take the union, the resulting set covers the whole MD subspace that contains the MD face, because P was in the interior of the MD face. So the whole MD space is projected onto the boundary of H_2. This includes the MD face itself. By theorem 6, the MD face contains an edge of the polytope, so there will be an edge that projects onto the boundary of H_2. But we finally reach a contradiction, because the wireframe must contain this edge, yet we don't see this edge on the boundary of H_2. H_2 by construction only contains A' and B', not some other edge. At many points in the video, such as 0:32, we see wireframes where it's possible to draw the half-plane containing only two vertices. By by my theorem, there should be at least one edge on the half-plane's boundary, but we don't see them. So the video is definitely not correctly showing a perspective projection. More rigorous proof of theorem 1: A 10D to 2D perspective projection is defined by the camera location, the camera's orientation unit vector, the 9D to 2D orthographic projection to the screen, and a characteristic distance 'w'. Draw the line containing the camera location along the camera's orientation vector; this is projected to a single point on the 2D screen. At a distance of w, points on the hyperplane normal to the orientation vector are projected according to the 9D to 2D orthographic projection - that's how we can define w. Now measure the distance on the screen from that point to the boundary of the 2D half-plane, call this x. Take the unit normal vector of the 2D half-plane's boundary, multiply by the transpose of the 9D to 2D projection vector, and add 1 / w times the orientation vector. This is the normal vector of the hyperplane in 10D space, and the definition is complete by having the hyperplane intersect the camera location. All points on one side of the hyperplane can be shown to project onto a half-plane of the 2D projection, and the points on the opposite side project onto the opposite half-plane of the 2D projection.
Theoretically you could compress some object that exists in some d dimensions all the way down to a point in a cross-section of it in the same d-dimensional space by having the freedom to rotate it in a 2d-dimensional space or greater d is not the abbreviation for dimension in this scenario, but a variable How? Take the good ol' cube, but this time, the cube is in a 6-dimensional world. Rotate it 90 degrees into the 4th dimension, so that when you take a cross section of the cube , it would appear 2-dimensional, like a square! Do the same thing, but with the 5th dimension, so that when you take a cross section of the cube, it would appear 1-dimensional, like a line! And finally, do it once again, but with the 6th dimension, and what was once a cube has now "turned into" a singular 0-dimensional point in space!
Sorry, but how do you know that? I don't quite understand or visualize what you mean with the theory, I guess I can't process that with my brain. What I got out of it is that a figure in a given dimension appears to be constantly being warped to an observer in a lower dimensional world. In other words, if I, as a 3D observer, have a cube in 4D and I rotate it about an axis that I do not have in 3D space, I will call it W, the cube will "change" shape. Also when rotating it on the axes XW, YW, ZW XYW, it will change since the expression of these axes depends on this new axis W. I, as an observer in a 3D world, will see how it deforms and changes constantly when rotating around axes that depend on W since I do not have the W axis to know the true shape of the 4D cube but if I were an observer in 4D its shape will always be the same.
@@ademarmontoto8736 A good way to see if what you said about 4D makes sense is to go through what you said and replace “4D” with “3D”. For example, if you say “In 4D, a cube would appear to change shape if you look at it from different angles.”, you may not be able to see if it makes sense intuitively, but if you look at the corresponding sentence, “In 3D, a square would appear to change shape if you look at it from different angles.”, then you can intuitively evaluate it. In this case, yes, it would appear to change shape, but in 3D, you understand that when you look at the square close up and it looks like a rhombus, then it’s just how the light goes into your eyes(also called projection) which makes the square look like that. In the same way, in 4D, when you look at the cube close up and it looks like a cuboid, then it’s just the projection which makes the cube look like that.(Notice how I copied almost word for word from the previous sentence-this is how similar 3D and 4D really are.) This can also help to combat misconceptions such as “The fourth dimension is time.”(corresponding statement: “The third dimension is time.” No it’s not, there are three directions you can move in, and things like rooms have a height, length and width. But you can see how a 2D being who experiences length and width might call time their “third dimension”, as time is the third number that you need to specify an event. In this way, time is not the third dimension.) or “In the fourth dimension, people can see each other’s insides”(corresponding statement: “In the third dimension, people can see each others’ insides.” No they can’t, it’s not like we’re sheets of paper! But we can see what’s within the edges of a piece of paper, so we can indeed see the insides of 2D things, just not 3D things.) Anyway, the reason I mentioned this is so that you now have another way to check if whatever you’re saying about the fourth dimension makes any sense
This is not the 4th dimension, it is impossible to draw the fourth dimension. Unless one of the old ones takes over your mind and makes you draw it. Relatable moment.
It seems like the higher dimensions act like a computer of sorts that can pass through time and space to inspect all the facets and caveats of reality without issue
At first I thought i could handle it. “It’s a pair of squares clipping through each other” i thought to myself. “oh now it’s a cube inside a big cube, seems simple enough”… *i was a mere fool back then…*
![ОРБАН приехал к ПУТИНУ и "отчитался" о поездке в Киев 😁 [Пародия]](http://i.ytimg.com/vi/_0ukDovOWq8/mqdefault.jpg)
Me: trying to find the long side of the blanket
The blanket:
Lol
Factsss
Thish8tma little toanhrd
LOL nice one
hahahah
Remember, these are all 3D projections of a 4D tesseract on a 2D screen!
and i'm trying to understand this mess with my 1d brain
Spinning in 10D
...made out of 1D lines
Processed by your 1 dimensional brain. OOOOHHHHHHHHHH
understood with my 0d brain
I can't imagine what the cameraman is thinking
"haha funni cube"
@@pluckyscuds the cameraman comes from Ohio and is therefore something normal to him
@@Mr._Dooter so Ohio has 10 d beings?
@@cyanisnicelol yea, even up to 7046 d
@@Mr._Dooter that's scary cause if you are 4d and you see 3d you can touch inside the 3d and that scary
I expected it to somehow rotate back to its perceived normal shape, but I'm left dissatisfied and my world is falling apart.
I nearly screamed - bitch, turn it back
And he never did
Play it in reverse 😎
Just like the tesseract eh?
The WU rotation makes my brain turn into KFC.
same.
I want to think that he tried though, but just gave up after a minute
as soon as it got there, my initial understanding was
WV = wavy
WU = wuuUuUUUuUUUUUUUuuUU
That is, of course, the technical term for it.
ʷᵘᵘᵁᵘᵁᵁᵁᵘᵁᵁᵁᵁᵁᵁᵁᵘᵘᵁᵁ
wobble wobble wobble
When you mess with Mario’s face in the Mario 64 loading screen
Exactly what I was thinking 😂
I thought exactly that!
I'm sitting here wondering how its possible to rotate a 4D object in 10D without it disappearing into the 5th dimension
@@loop_mind But, the cube and the light source can't be rotated in four dimensions. If you were to somehow do that, and the cube wasn't a tesseract, then the cube would either partially or wholly vanish into the 4th dimension, right?
@@loop_mind this sort of makes sense, thanks
@@nef36 well, you can rotate a 2 dimensional square in 3 dimensions, so.. i guess it also applies to higher dimensions
You can rotate a 2D square or a 1D line in 3D and see how its shadow distorts. This is what's going on here, just with a 4D cube and 10 other dimensions.
my brain disappeared trying to understand u smart mthrfkrs
needs an increasingly distorted Freebird solo that stops when it doesn't rotate
no, that getting distorted shit is overrated :D
@@AjarSensation sus jokes are definitely overrated and yet i see them too often so shut up
I'm waiting until someone does that
ua-cam.com/video/YEE1GJnzi_g/v-deo.html
Someone did it
This needs some Funkytown music, and it should be 1 hour long
Tu tu tu tu tu tutu tu tu tu
Why does everything have to be a brain dead meme these days
@@herr_crustovsky GOTTA MAKE A MOVE TO A TOWN THATS RIGHT FOR MEEEEEE!
0:37 goofy ahh fish spinning
free bird
I cannot comprehend this video but 10/10
Then you are normal. People are freaking out because of a 3D animation and calling it a projection of multiverses or some other nonsense.
But then they will deny that nature has been designed by God. Whatever.
No, its inaccurate, 3.5/11
@@JesusProtects it's a projection of a mathematic concept
Bro same
@ArminMeiwes Your comment sounds like the situation of a cat trying to understand why animals need air to live.
Cue that a Jackie Chan
Lmao
There's something that really annoys me about knowing that we'll NEVER know what a 4D shape actually looks like, and that we physically can't even imagine it
With future technology, who knows? Maybe something smarter can process it more effectively, even without perceiving it. I hope so, anyway.
@@joanofsharc Maybe, but how would it display it in a way that we could properly see?
@@joanofsharc the universe is 3D. It's impossible to perceive 4D.
I think that if someone was ever to successfully imagine a complete 4D cube, that someone would disappear in the 4th dimension
This could be the most difficult rubicks cube ive ever seen
just need to look at it from the wrong side and the cube is already ahead from your understanding
Watching this while eating breakfast at 6 am is an experience
Lmao 😂
This dude's trying to make me understand a 4D object projected in 3D on a 2D screen to my 1D brain.
Edit- this comment is 98% of my notifications
The cube is actually 4 dimensions ahead of you💀
Line brain
@Asengamer-terry and primo they’re 2D lines though?
A line is one dimension
@@Dertava02 a horizontal or vertical one is. If it’s diagonal that’s two dimensions. X and Y
My brain when I am trying to sleep without any thoughts, just a blank mind...
well said
Pro tip: Sleeping is easier when you don't try to control your thoughts at all. Just watch whatever your brain makes like a movie.
Imagine how hard doing 10D shapes in maths in a 10D universe would be. So many multiplications
I feel bad for 10D students
*@Doggo's Science*
Can you do this video again, but color-code the lines, so they are easier to track through the rotations?
Now you need to redo this with a cross-view stereo version.
It'd break our brains
I can't believe I watched this, when I could be learning about how to turn a sphere inside out
0:35 doing the cha cha slide
Additional TL;DR for TL;DR: I think this has great potential for further visualization in an user-interactable setting.
Sources at the Bottom.
TL;DR: I go full nerd mode just to try and explain how a comprehensive visualization of much much higher dimensions would be cool to play with. When really all I wanted to explain was a separated visualization option of what was done in this video. Such as a graph charting each points movement through time. While playing with alternate timelines, multiverses, and higher/lower/adjacent dimensions would be fantastic to play with, I redundantly and needlessly explain things I don't understand.
To my current understanding as a layman, supposedly, according to the current definition of Bosonic String Theory, there are 26 Dimensions. And with a very quick and self-admittedly not thorough enough google search, the research paper by Frank D. Smith Jr. titled "Physical Interpretation of the 26 Dimensions of Bosonic String Theory," the abstract of said paper reads "The 26 dimensions of Closed Unoriented Bosonic String Theory are interpreted as the 26 dimensions of the traceless Jordan algebra J3(O)o of 3x3 Octonionic matrices, with each of the 3 Octonionic dimensions of J3(O)o having the following physical interpretation: 4-dimensional physical spacetime plus 4-dimensional internal symmetry space; 8 first-generation fermion particles; 8 first-generation fermion anti-particles. This interpretation is consistent with interpreting the strings as World Lines of the Worlds of Many-Worlds Quantum Theory and the 26 dimensions as the degrees of freedom of the Worlds of the Many-Worlds."
Traceless Jordan Algebra is just a type of algebra to represent the above concepts through pure mathematics. A full breakdown according to en.wikipedia.org/wiki/Jordan_algebra
A single Octonion Dimension is defined as "Octonions have eight dimensions; twice the number of dimensions of the quaternions, of which they are an extension. They are noncommutative and nonassociative, but satisfy a weaker form of associativity; namely, they are alternative. They are also power associative." This concept is very abstract to me, but with some google searches, there seem to be visualizations of a single octonion dimension. Connecting multiple octonion dimensions would be difficult to visualize, but I assume it can be done with effort and time. A nice visualization of a single octonionic dimension comes from theoryofeverything.org/theToE/tags/octonion/
The concept of 3x3 Octonionic Matrices is very difficult for me to wrap my head around, but with some quick google searches, it seems as though as this would be 72-dimensional, so what happened to the 26-dimensional concept from earlier? Well, skimming through a description on valdostamuseum.com/hamsmith/3x3OctCnf.html it seems to explain this a lot better.
4-dimensional physical spacetime is, super-simplified, as "3 spatial dimensions with 1 dimension of time." This is easily visualizable, but of course with the condition that it needs to be projected to a 2D screen. This, I believe, doesn't need any visualization sources. So I won't put any.
"There are four basic isometries of 4-dimensional point symmetry: reflection symmetry, rotational symmetry, rotoreflection, and double rotation."
Reflection, Rotational, and Rotoflection (or Improper Rotation) are all easily done in 3-dimensions. However, double rotation is, from what I can understand, something a higher-dimensional object can perform. Which also seems visualizable. At least according to en.wikipedia.org/wiki/Rotations_in_4-dimensional_Euclidean_space
first-generation fermion particles and the anti-particles are just types of particles, and (from what I understand) don't need visualization.
I think the in-depth visualization work done by UA-camrs such as CodeParade, Zenorogue, [mtbdesignworks {Miegakure, 4D Toys}], and Tomfractals are very good non-Euclidean/ non-3D visualizations. Higher-Dimensional Space.
I think the game "5d chess with multiverse time travel" is a good representation of Higher-Dimensional time. There was a much older game that I swear Nerd^3 played a while back that was very similar to the concept of alternate timeline travel gameplay, but I can't seem to find it.
Sources:
UA-camrs: CodeParade, Zenorogue, [mtbdesignworks {Miegakure, 4D Toys}], and Tomfractals
Games: "5d chess with multiverse time travel"
Websites:
en.wikipedia.org/wiki/Rotations_in_4-dimensional_Euclidean_space
valdostamuseum.com/hamsmith/3x3OctCnf.html
theoryofeverything.org/theToE/tags/octonion/
Paper:
ui.adsabs.harvard.edu/abs/2001physics...2042S/abstract#:~:text=The%2026%20dimensions%20of%20Closed,physical%20spacetime%20plus%204-dimensional
@malteese267 Well, you ARE in luck, my friend. You have the option of simply NOT reading it at all if you so wish.
This is an yt comment not an essay document but props on the work
@@nosamgeography1249 Congrats! You had the option of not reading passed the first TL;DR, and yet you still decided to tell me how long the comment was.
Holy
Moly
This should have the freebird guitar solo like the rotating rat videos!
Sometime this year I'm planning to learn blender, maybe I'll make something inspired by it, if I ever get around to it.
Back when I was studying physics and had a wolfram mathematica license I once made some 4d-hypersphere visualizations, so maybe I'll make a version of the rat but it's spinning in 4D 😅
I see too many of those dumb spinning memes, but I would LOVE to see a change in the spinning style. Let's try spinning a rat on the W Axis.
Me: *rolls over*
Every object in my bed:
When the cube move in W , I felt heaven
Same feelings when you playing a game and using glitches to pivote object you are not supposed to, they move the same way and get deformed as well just the same way.
Little big planet ⚰️
That's because 3D rotations are made through a projection of quaternions which are 4D hyper spheres. It's really easier to compute 3D rotations using a 4D object than to go straight into 3D.
Is just a 3D animation of some lines. Is... Nonsense. Not reality.
@@JesusProtects
It’s the animation glitching out because we can’t see beyond 2D, it’s not reality for US because we are in 3D, 4D is already beyond our compression I’m very far to begin to imagine 10D
it would be cool to be able to play with this as a game, mess up it’s rotation and then solve it, like a rubik’s cube
I’ll do you one better: Imagine 26 of these all put together into a 4d 3x3x3 Rubik’s cube that you not only need to rotate into a proper perspective, but also solve.
Teacher: the test isn't that confusing
The test:
I was like wait what are the other letters 💀 then it didn't made sense anymore
Yeah I though it was only X Y Z W but then When I saw V (fifth axis) I thought now it was ten dimensions
Here are all the axis in order
X Y Z W V U T S R Q
Grandpa: “All dreams have a meaning, so talk about them to your family!”
My dreams:
That's not what scientists say.
fr
No scientists have said that, that sounds something my aunt would say lmao
hehe it looks like a softbody simulation that got messed up
Me in beamng messing around with the node grabber:
"It's like looking into the face of an angel, Andy. It's too much for humans"
This looks like something that you would expect to be played with freebird playing in the background
4D is used all of the time in game dev. Especially in the 90s camera movement has been calculated including the W dimension which leads to smoother and faster results compared to using only X Y and Z.
Wait what? Can you elaborate on how that works because that’s fascinating
@@FredTheRed27 to describe that in a single yt comment would be probably very hard, but look up quaternions in the context of unreal engine or unity, there are some solid articles on the web
This is a bit misleading. In a purely mathematical sense a quaternion is a four-dimensional object, but in video games it's used to represent the orientation of a 3d object in 3d space (which is nothing like the brain bending stuff happening in this video). The quaternion's values of X, Y, Z form a vector and W is an angle of rotation around that vector. Usage of quaternions in video games is simply to save time and space in calculations. Alternatives such as rotation matrices are quite bulky and euler angles suffer from gimbal lock.
When you gotta pay little Timmy down the street 5 bucks to fix your Rubik's cube again.
I always love thinking about dimensions and our perspectives on it, like how if we were suddenly made 2D, we'd be bisected, because of our digestive system. I can only imagine what would happen to a 4th Dimensional Being, if they suddenly became 3D. They'd probably become inverted into themselves and die. 🌵👽
we need volumetric screens so we can project a 4d tesseract onto a 3d screen
Imagine if we grow a brain in a lab and just feed it 4d animations
you'd need to grow a brain properly in the first place
That's when neural network comes in
We always love a video of a dancing 4d cube!
I've had fever dreams where I could translate and rotate in as many dimensions as this probably more but still had a 3D perspective and understanding. It was what I think hell is like.
Mathematically, dealing with higher dimensions is as easy as just accommodating the current models and adding the extra spacial values on.
Actually _showing_ the results of this however is a whole other story...
HEY thanks for example of rotation in multiple directions(I mean xyz is 3d and you give also w d v etc.). I see this for first time
Btw, I have question. Is it possible to be able rotating with 3 coordinates simultaneously, of course in higher dimensions
why would I know
@@victorvillegas911 maybe it wasn't for you
@@victorvillegas911 arent you the one supposed to know?
Rotations work by locking every other plane of rotation other than 2 at a time, such as XZ with Y not changing. You can rotate XYZ simultaneously by simply doing every rotation after one another: First XZ, then XY and ZY (and higher-dimensional rotations).
If it's possible to rotate 3 coordinates simultaneously, yes! Just rotate XZ, XY and XZ after one another.
@@linuskinn9106 thx for answer.
Oh, very cool. I totally understand everything about this. Thanks for just making a visual of this thing I already definitely understood. I absolutely get it.
This is by far the smoothest animation on higher dimensions rotating I have ever seen.
POV: *blanket at 3 am*
This is what’s gonna play in my mind when I’m trying to be serious
🤣🤣🤣
I didn't know this existed. I cant even begin to comprehend this. I am amazed
Barely 20 seconds in and this is already starting to melt my brain
For some reason I laughed so hard at this
this reminds me of that game where you can change an object's size based on how far it is from your perspective, only here you can change its shape lol. someone should make a game like that
Superliminal?
this comment is literally superliminal....
Me when my comment is literally superliminal
Me fucking around with the Yoshi drawing on the SM64DS title screen by simultaneously stretching and rotating it
i dont know why i watch this, but i would watch this again in the future
i just checked the script
what have you actually done i could not comprehend even the first line of code also how did you manage to do it on scratch 😭
This was made on Scratch???
I've got a question, maybe a silly one: if you rotate a sphere in a 4th d plane, would it disappear from the pov of a viewer in the 3d plane?
Kind of, but its projection would stay, just as it is shown in the video with tesseract i.e. its projection, being 3d, 2d or 1d
Not a silly question at all, rather a great question to think about
This is what your body feels like when you stand up to fast
This is literally mind boggling, totally insane!
A tesseract is a convex polytope, you've definitely got something wrong because your wireframe turned nonconvex somewhere in the video
does the convexity still apply when projected to screen
Yes, I can come up with a mathematical proof of a result that contradicts the video, though I'm not sure if my way is the most elegant way to do it. (It was surprisingly hard to make the proof!)
Theorem 1: For any 10D to 2D perspective projection and any half-plane of the 2D screen, the set of all possible points that project onto the half-plane on the 2D screen form a half-plane of the 10D space. The opposite half-plane in the 2D space corresponds to the opposite half-plane in the 10D space.
Proof: I'm sure the video uses perspective projection. TL;DR the 10D half-plane is bounded by the face of a 10D pyramid whose tip is the camera location. This is similar to the faces of the 3D rectangular pyramid that bounds a 3D perspective projection to a rectangular 2D viewport. More rigorous proof at the end, it's not as relevant to my overall result but I add it for completeness.
Theorem 2: The intersection of a hyperplane with a convex set is another convex set.
Proof: This is an elementary theorem in convex analysis, since a hyperplane is convex.
Theorem 3: Under any 10D to 2D perspective projection, any line in 10D space gets projected into either a line or a point on the 2D screen. If a line is formed, any line segment along the line in 10D space is projected into the line segment on the 2D screen between the projections of the two endpoints.
Proof: Trivial by using the formula of a line, applying the perspective projection's transformation, and recovering the formula of a line or a point. Also trivial to demonstrate a one-to-one relation between the line segments.
Theorem 4: The convex hull of the vertices of a polytope is the polytope itself.
Proof: It's a well-known theorem about polytopes.
Theorem 5: The 1D interior of the line segment between two vertices on a ND polytope is contained in the MD interior of one of its MD faces (M = 2 contains edges of the polytope.
Proof: Edges are 1D faces and polytopes have finite size by definition. Given the half-planes bounding the MD face, it must be possible to possible to find M - 1 of them that intersect at a line, otherwise the polytope can be shown to be infinitely big. This intersection contains an edge by definition.
Theorem 7 (the actual result we want): When using perspective projection to display a polytope like a 4D tesseract from 10D space onto a 2D screen, there does not exist a half-plane on the 2D screen that intersects only the projection of two vertices and no other points of the wireframe of the polytope.
Proof: Suppose for contradiction that it is possible to do achieve this configuration. Call the two special vertices in 10D space A and B, which get projected into A' and B'. If we draw a line that intersects the wireframe at A' and B', there is a half-plane on the 2D screen containing only A' and B', and by theorem 1 there is a corresponding half-plane on the 10D space that contain A and B. Call the 2D half-plane H_2 and the 10D half-plane H_10.
The half-plane opposite H_2 contains all the vertices of the projected view, so by theorem 1 the half-plane space opposite H_10 contains all the vertices of the polytope. By theorem 4 and definition of convex hull, the whole polytope lies within the half-plane opposite H_10. Therefore, there cannot be any pair of points in the polytope that lie strictly on opposite sides of H_10's boundary.
Because a polytope is convex, by theorem 2 the intersection of H_10's boundary and the polytope is a convex set. The intersection must at least contain the line segment AB. By theorem 3, this line segment projects into the line segment A'B'. By theorem 5, the line segment AB is also contained in the MD interior of one of the MD faces of the polytope. Take any point P on the interior of AB and consider all line segments that contain that point in the interior, and lie inside the MD face. Suppose for contradiction that at least one line segment CD containing P in the interior is projected into another line segment C'D' on the 2D screen that isn't entirely on the boundary of H_2. CD contains P on the interior, and since P is within AB it is projected to a point within A'B', and so C' and D' are on opposite sides of H_2. This means C and D are on opposite sides of H_10. But CD is part of the polytope, and the polytope does not contain points on opposite sides of H_10. Therefore, all the line segments containing P get projected into either P itself or line segments on the boundary of H_2.
If we extend all those line segments into lines and take the union, the resulting set covers the whole MD subspace that contains the MD face, because P was in the interior of the MD face. So the whole MD space is projected onto the boundary of H_2. This includes the MD face itself. By theorem 6, the MD face contains an edge of the polytope, so there will be an edge that projects onto the boundary of H_2. But we finally reach a contradiction, because the wireframe must contain this edge, yet we don't see this edge on the boundary of H_2. H_2 by construction only contains A' and B', not some other edge.
At many points in the video, such as 0:32, we see wireframes where it's possible to draw the half-plane containing only two vertices. By by my theorem, there should be at least one edge on the half-plane's boundary, but we don't see them. So the video is definitely not correctly showing a perspective projection.
More rigorous proof of theorem 1:
A 10D to 2D perspective projection is defined by the camera location, the camera's orientation unit vector, the 9D to 2D orthographic projection to the screen, and a characteristic distance 'w'. Draw the line containing the camera location along the camera's orientation vector; this is projected to a single point on the 2D screen. At a distance of w, points on the hyperplane normal to the orientation vector are projected according to the 9D to 2D orthographic projection - that's how we can define w. Now measure the distance on the screen from that point to the boundary of the 2D half-plane, call this x. Take the unit normal vector of the 2D half-plane's boundary, multiply by the transpose of the 9D to 2D projection vector, and add 1 / w times the orientation vector. This is the normal vector of the hyperplane in 10D space, and the definition is complete by having the hyperplane intersect the camera location. All points on one side of the hyperplane can be shown to project onto a half-plane of the 2D projection, and the points on the opposite side project onto the opposite half-plane of the 2D projection.
@@JubilantJerry ok god I'm sorry please I don't deserve this eye torture I agree with you
@@user-pr6ed3ri2k lmao 😂
@@JubilantJerry please write this on a paper and publish it. It really sucks to read it here and i kinda want to give it a read more calmly
Theoretically you could compress some object that exists in some d dimensions all the way down to a point in a cross-section of it in the same d-dimensional space by having the freedom to rotate it in a 2d-dimensional space or greater
d is not the abbreviation for dimension in this scenario, but a variable
How? Take the good ol' cube, but this time, the cube is in a 6-dimensional world.
Rotate it 90 degrees into the 4th dimension, so that when you take a cross section of the cube , it would appear 2-dimensional, like a square!
Do the same thing, but with the 5th dimension, so that when you take a cross section of the cube, it would appear 1-dimensional, like a line!
And finally, do it once again, but with the 6th dimension, and what was once a cube has now "turned into" a singular 0-dimensional point in space!
Sorry, but how do you know that? I don't quite understand or visualize what you mean with the theory, I guess I can't process that with my brain.
What I got out of it is that a figure in a given dimension appears to be constantly being warped to an observer in a lower dimensional world.
In other words, if I, as a 3D observer, have a cube in 4D and I rotate it about an axis that I do not have in 3D space, I will call it W, the cube will "change" shape. Also when rotating it on the axes XW, YW, ZW XYW, it will change since the expression of these axes depends on this new axis W. I, as an observer in a 3D world, will see how it deforms and changes constantly when rotating around axes that depend on W since I do not have the W axis to know the true shape of the 4D cube but if I were an observer in 4D its shape will always be the same.
and with the 7th dimension?
@@ademarmontoto8736 A good way to see if what you said about 4D makes sense is to go through what you said and replace “4D” with “3D”. For example, if you say “In 4D, a cube would appear to change shape if you look at it from different angles.”, you may not be able to see if it makes sense intuitively, but if you look at the corresponding sentence, “In 3D, a square would appear to change shape if you look at it from different angles.”, then you can intuitively evaluate it. In this case, yes, it would appear to change shape, but in 3D, you understand that when you look at the square close up and it looks like a rhombus, then it’s just how the light goes into your eyes(also called projection) which makes the square look like that. In the same way, in 4D, when you look at the cube close up and it looks like a cuboid, then it’s just the projection which makes the cube look like that.(Notice how I copied almost word for word from the previous sentence-this is how similar 3D and 4D really are.)
This can also help to combat misconceptions such as “The fourth dimension is time.”(corresponding statement: “The third dimension is time.” No it’s not, there are three directions you can move in, and things like rooms have a height, length and width. But you can see how a 2D being who experiences length and width might call time their “third dimension”, as time is the third number that you need to specify an event. In this way, time is not the third dimension.) or “In the fourth dimension, people can see each other’s insides”(corresponding statement: “In the third dimension, people can see each others’ insides.” No they can’t, it’s not like we’re sheets of paper! But we can see what’s within the edges of a piece of paper, so we can indeed see the insides of 2D things, just not 3D things.)
Anyway, the reason I mentioned this is so that you now have another way to check if whatever you’re saying about the fourth dimension makes any sense
this is straight up mind bending
This created more questions than answers
just so you know, in 10-d space you will be spinning around a 8-d volume, not a 2d plane
also, what projection method are you using?
These are 10D rotations of a 4D object represented in a 3D plane which is projected on a 2D screen that you're trying to understand with your 1D brain
Hard to imagine that it's not truly changing shape, but only perspective.
Things like this makes my brain fold in on itself
*_Whoah!_* That’s trippy, man. 😵💫
Understanding dimensions is definitely harder than proving the multiverse theory
This is not the 4th dimension, it is impossible to draw the fourth dimension. Unless one of the old ones takes over your mind and makes you draw it. Relatable moment.
It is a projection
🗿 + 🤡 + fatherless + not а 🤓 + not relatable + not an old one + L + ratio
no shit 🤯🤯🤯
a 2d representation of a 3d shadow of a 4d object rotating in 10d
It seems like the higher dimensions act like a computer of sorts that can pass through time and space to inspect all the facets and caveats of reality without issue
missing link between platonic philosophy and modern physics
What?
@@Adi2561 p
@@Adi2561 you can watch a movie and fast forward and rewind it but you can’t interact or inspect the movie the same way you can with a computer.
The Waffle House has found its new host.
You're a real villain for not putting it back to normal
The Writer's brain who created the second Trilogy of Star Wars
My corpse being used as a chew toy by the hound of tindalos that just brutally killed me for having access to forbidden knowledge:
I've never been this confused in my whole life
My brain is breaking every second this plays
At first: "Oh okay that kinda makes sense I can kinda see whats goin on hear"
2 seconds later: incomprehensible
I like the UZ rotation cuz it looks like the Tessaract is cutting actual fucking shapes
nah ur not foolin me man you totally crumpled that thing up 8/10
Now simply fold the paper like this.
The origami teacher said calmly.
i have no idea why i’m here but i’m glad i am
My brain stopped working beyond XYZ
Kurła... Właśnie tak mi się w głowie kręci po bimbrze dziadka z Łomży.
Greeting from Mońki!
I think my brain just melted out of my ears
Fascinating
Me when I'm tryna find the long side of the blanket
My brain during the most intense, nerve racking, anxious, fear inducing moment that i have ever felt and will ever feel:
The planes that look like just a little wobble are the ones I was least prepared for.
All the 4D things in the 3D world on my 2D screen and understanding in my 1D brain, sigh.
I like how it just crumbles up
Thank you for this presentation. Now If I ever encounter tesseract, I know how to spin it so it fits in my pocket.
my favorite carnival ride
plane WS looked like me messing around with a board, nails, and a long piece of yarn
This just looks like snapshots of separate angles then being rotated upon themselves creating the illusion of there being another dimension
If that was the case though, snapshots would only be two dimensional, so the theoretical snapshot is maintaining its dimensional structure
im so confused but this is fascinating
good for her, good for her.
My blanket also is a 4D Tesseract spinning in 10 dimensions whenever I try to sleep
Everybodys headphones in a pocket
I didnt know it was possible to be this confused
At first I thought i could handle it. “It’s a pair of squares clipping through each other” i thought to myself. “oh now it’s a cube inside a big cube, seems simple enough”… *i was a mere fool back then…*
a small tesseract would be the best fidget toy
These are all Wavy