Tesseract - 6 Rotations
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- Опубліковано 15 січ 2008
- All six rotations of a transparent tesseract. Each rotation that includes the w axis is a minute long, while the other three are each 20 seconds long. This way, you'll be able to zone out and better visualize the tesseract.
Note that the tesseract resides in four Euclidean spacial dimensions.
0:00 XW
1:00 YW
2:00 ZW
3:00 XZ
3:20 YZ
3:40 XY
4:00 All rotations in succession
Holy crap...
I think I get it now.
The smaller cube on the inside, it's not smaller, it's further away!
yup
yup))
I don't see any cube inside...
exactly, there's some other videos explaining it which are very good
After realizing what you said it looks different now wtf
I really like this representation. I especially like how all eight cubic cells are a different color so that we can see the relationship as it rotates. Well done!
how old r u
@@chemokinesis 43.
WOAH!!! For the first time, I can actually picture it rotating instead of just seeing it squeeze inside of itself!!!!
that just happened to me too. it's so freaking neat!
Same here, mate.
after a certain point you stop seeing bigger and smaller cubes, instead a rotation of each of its pieces
Михаил Гинков same, but it's still 4d
This is really amazing. The shape is widening and narrowing as if the rest of it's going to a different place we can't see. I can't say I understand it completely but I could stare at it for hours.
We are watching 3D shadow of 4D object in 2D :D
+Karel Valečka (Karamal) And if you believe the world is flat, you're doing so while living in 1D :D
@@josegomez6549 no
in a snarky voice * NEEEEERD!
being processed in your 1d brain in your 0d life
we always see in 2D. technically we can two slightly separated 2D images that we interpret as a 3 dimensional object. so if the analogy holds, which it might not, then a 4D being would see the full inside and outside of a 3D object and it would use multiple 3D images to interpret the 4th dimensionality of it.
I can see the rotation now holy shit that is amazing
onth3hous3 same
onth3hous3 lol don't get too exited, your still not at a 4d object.
Welcome to The Enlightened hahaha
the color coding actually makes it a lot easier to grasp. good job!
Visualizing this is like trying to come up with a completely new color, you can't.
Then how was the Second color found and named?
Except we literally are visualizing it. Developing an intuition and learning to interpret it correctly is challenging, but quite possible.
My extremely limited understanding of this concept is that this is something our brains simply cannot comprehend. Analogous to the members of Carl Sagan's Flatland, our brains are hard-wired to live in a three-dimensional universe. Our sensory equipment and our evolutionary history has been molded in order to represent and understand a 3D world. So attempting to visualize a fourth spatial dimension is something we just can't do, like trying to imagine an entirely new color.
Additionally, this is confounded by the fact that we're looking at a 3D shadow of this 4D object, similar to looking at a 2D doodle of a 3D cube.
Or am I wrong about this? Am I personally unable to visualize this fourth spatial dimension, but can others think about it and suddenly have it click for them? Does anybody have a mental image of what this tesseract would actually look like in four dimensions? Or are we forever doomed to frustratingly watch videos of it's 3D shadow while unsuccessfully trying to picture it?
Well here's the funny thing about the human imagination. Our imagination is limited to no colour nor spacial dimension. In theory, we could imagine anything. Some people have very powerful and trained minds that can imagine artificial colours that don't exist in any spectrum of light. Meditation can help achieve this level of mental imagery, as well as some practices such as lucid dreaming. Though even if someone thinks they imagined a tesseract, there would be no way they would be able to prove to themselves that an actual tesseract looks like that.
Do you mean Edwin Abbott's Flatland?
You are right, but adding a fourth dimension cannot be seen all the time, but it can be felt. For example when u go in a hot room, the conditions of that room are 4th dimensional, where there is the variables of x,y,z and temperature. We cannot see this but if u had infrared vision u could see a 4 dimension of space+heat speactrum. Dimensions are the variables our senses choose to conceive as dimensions, but the real world has many different variables connected to each other.
digerpaji You're mistaken when you classify "temperature" as a fourth dimension. Temperature is simply a description-a three-dimensional description-of the motion of particles.
It'd be like saying if you walked into a room, there'd be the X, Y, and Z dimension, but if there were some bouncy balls being bounced around the room, they'd be a fourth dimension in the room.
I've been able to visualize 4 dimensional shapes, however it took a substance called Dimethyltryptamine (DMT) to allow me to see it. Furthermore, it wasn't with my eyes that I could see beyond 3D, but with my mind. I'm sure this sounds crazy, but if you've tried it, you would know where I'm coming from.
Thank you for posting this. I've seen a lot of attempts at depicting a tesseract (or the shadow therof) in 3-dimensional space, but this is the first one which (finally) allowed me to actually visualize its rotation on that 4th axis accurately. I think it was the color-coding which helped, as I could keep track of an individual "plane" (or surface-cube)'s rotation, whereas a singularly-colored tesseract is too distracting and easy to lose track of individual vertices within.
I can see... EVERYTHING
Gadget622 you're looking at a cube.
EVERYTHING XD
Ethan Salie 12 sided hypercube.
ciresi43 Well technically it's composed of 16 flat sides, and 6 cells (cubes)
Ethan Salie When taken apart. (See "unwrapping a tesseract.")
The added color actually makes it much easier to visualize the interaction and movement of the rotations of the cube. Good work.
Thank you.. this is exact what I needed to understand a tesseract
For anyone who doesn't see it, stare directly at one point (like the furthest corner of the wireframe cube, roughly at the center of the screen). For some reason when I follow any of the rotating cubes with my eyes I can only see it turning inside out. A few other things I noticed:
- Like another guy said, tilting your head really helps, especially with the one at 1:00
- We can't see the actual 4D space similar to how we can't see the 3D space inside a cube when looking at a 2D projection of the cube, only the edges and faces that border it, so it's impossible to see the actual 4D shape of a hypercube
- We also can't really understand how 8 cubes come together like that, since it's just not possible in 3D space
Great animation though, a lot of the ones I've seen have really bad perspective and draw lines on top of other lines in such a way that it forces you to see it as a cube turning inside out.
"We can't see the actual 4D space similar to how we can't see the 3D space inside a cube when looking at a 2D projection of the cube, only the edges and faces that border it, so it's impossible to see the actual 4D shape of a hypercube." This is true in the literal sense, we can see neither cubes nor hypercubes. But in the every day sense, we can "see" cubes by looking at their 2D projections from different angles. Why is a hypercube any different? We can see any 2D view of a hypercube we want to understand the object that way. What does it matter if we can't see hypercubes, or regular 3D cubes for that matter, the same way a 4D being could? Even a 4D being can't "truly" see a tesseract, as that requires 4D vision, so only a 5D being or above could.
"We also can't really understand how 8 cubes come together like that, since it's just not possible in 3D space." I completely disagree with you here. If you spend enough time manipulating virtual 4D models, you start to gain fluency in four-dimensional thinking. Eventually understanding how 8 cubes come together to form a hypercube becomes trivial. Just because it doesn't work in 3D space doesn't mean you can't learn to visualize it in 4D space.
There is a book called "A Wrinkle in Time" by Madeline L'Engle. She presented the tesseract as a vehicle to travel through time, space, and dimensions. I read that book over 50 years ago, it won some awards, even. Though after all these years, I may not remember all the details of the story, the tesseract surely made an impression on me. I hated geometry in school, even though I was in "advanced" math ... but I LOVE sacred geometry like this and the torus field, for example. It is truly fascinating, I highly recommend looking into this subject.
I understand what is happening, but what is happening is impossible.
Impossible in our dimension =]
Same
yes, you can't make 4 lines perpendicular to each other at the same time, so 4d is impossible
Only impossible if there are only 3 spatial dimensions.
its impossible like for a 2d organism to imagine a cube
A lot of people here say that it is impossible to visualize a 4th dimensional object... and they are right to an extent, however, we can understand all of it's parts and everything it's composed of. This isn't the entire thing. But it is really really close. Think of it like a cube being showed to a 2nd dimensional creature. now, this creature could never hope to see the entire thing at once, it just isn't possible, however it can see a slice of the object. Not only that, but it can see all the slices of the cube. now if it can see all the slices, Then it is seeing all of the object over a period of time. Now that isn't perfect, but it's close, really close, And the same thing is happening here. We are seeing all possible 3d manifestations of the 4d cube. Just as the 2d creature was seeing all 2d manifestations of a 3d square. Well, that's how I think of it. It's more informative than "We have a limited perspective" , at least.
That was beautiful comment...I couldn't agree with you any more.
you are absolutely right
I remember I watched something of a scientist from around 40 years ago saying the same thing.
Dammit, brain! Y U NO LET ME THINK 4D
We need more good people like you:)
It's starting to make sense ... maybe a couple of more views! The best attempt to show this, that I've ever seen.Thanks!
Oh my God dude. The wierdest thing happened when I started watching this video. About 7 seconds into it, I was focusing on following the 'rotation' of it, and I comprehended the 4th dimension for a while. I'm seriously not lying. I understood it fully, but after about 2.5 seconds, I could not comprehend it, nor the concept, once again.
240p, we meet again!
lol
one of the best videos ever !!!!
Thanks to the fact that it's transparent we can get a sense of it. This is great, thanks.
If I only focus on one of the cubes, it totally looks like it’s just a rotating object! I never though I’d be able to intuitively picture a rotating tesseract, but here we are!
OMG I FINALLY SEE THE ROTATION THANK YOU
you know that thing called my mind, well you just blew it up
This is really hypnotic.
I love how this is making more sense. I see it rotating now, instead of it not making sense. yay!
When I keep looking at this, I feel as though I'm hitting the edge of my conceptual ability. I feel almost as if I can see the fourth dimension in my mind. Of course that's impossible. At least with today's technology. Perhaps we'll be able to modify the brain to see it.
Seeing this high I almost can imagine the fourth dimension
This is awesome I have just realized this is what I saw while on a dmt trip, I didn't know what it was at the time
It might have told you "Error, try again", but your earlier comment actually did post and I got to see the link. That is a great resource, thank you for showing it to me.
Hmmm, this requires acid.
you sir is indeed a good man
it's very colurful
am acid
Are we trying to see 4D on a 2D computer screen? That's so stupid... We should look at it on 3D projector or something...
Even though we have the ability to more intuitively understand three dimensions, we can only see in two dimensions. Even if you had this in a hologram, you'd only ever see a two-dimensional slice of the three-dimensional projection, but just from any three dimensional angle we choose.
This is extremely trippy. I must watch this when I am stoned.
Things like this amaze me.
Isn't it fascinating?
Nice. I like the way some people can actually visualize, and help others to do the same, tesseracts and other dimesions.
the colors are very cool, great works
Best tesseract simulation I've seen yet!
Basically, the best tesseract visualization I've ever watched.
1st level: seeing the cube rotate through the inside
2nd level: seeing the cube rotate behind it and realizing it's not smaller, just further away
3rd level: realizing all the cubes connect one to each other so that one side of a cube is also a side of another cube
4th level: changing perspective on it so much that you actually see the 4D rotation (5 perfect cubes at a time are possibly seen in the first 3 rotations other 3 cubes are distorted in any W rotation almost always)
This animation is really amazing and i can tell you from my experience that 4D really can be seen here, other animations of tesseract might be fakes.
Once you see the 4D in one of those rotations, you'll see it in all of them, but not at first, you have to have the 4D perspective 'activated' in your mind BEFORE you go onto the last 3 rotations, it's really hard to change the perspective on it once you've seen it do the 3D rotation, the more you look at it with your mere 3D perspective, the harder it is to see because when you activate the 4D perspective within your mind, the rotation is completely different, it's as if the same rotation is a completely different animation, as if when you change the perspective back to 3D it's as if you've entered a new reality and see something completely different even though it's still the same rotation, just mind blowing, i've been looking at this video for 4 days now nonstop every hour at least once lol :D i even see it when i close my eyes kinda now :D:D:D i even downloaded this video just in case it would be deleted one day because this is the only animated video in which i actually see the 4th dimension.
It takes me about 3 seconds now to change the perspective to 4D, right off the bat it took me more than a minute, it might also help if you tilt your head slightly to your left and perhaps try closing one of your eyes while tilting your head that might also help. Looking at the 3 white lines all the way back in what i understand to be the 4D space might also help.
It also helps if you look 'into it and behind it' you just have to, this is 4D.
(note that the cubes connect one to each other so that one side of the cube is also a side of another cube)
1:00 YW rotation is easiest to see in my experience. Remember level 3 at the beginning of my comment and get past it otherwise you'll never see the 4th dimension, you'll always just be stuck with your mind in 3rd and never get to 4th level to finally see it.
Consider yourself to be very lucky to have read this comment. I've discovered most of this in a day MYSELF no one told me anything i didn't research tesseract much or watched a lot of videos, only few before i got to this one, and skimmed through a tesseract wiki article but have seen the tesseract for the first time like 6 years ago, but didn't comprehend it back then of course and looked at it a few times since then and 4 days ago finally fully comprehended it and can see the 4D in this video.
Leave a reply if you can see it now, but i think even if i explain myself so much people will have hard time changing the perspective on reality as i can, perhaps it's a gift, i don't know, but i feel like the change of perspective to 4D is like magic, every time it shifts to it, it just looks so different.
English is my second language btw so sry if i made any mistakes.
Smithy, this is the only video that shows the rotation. Its not a gift, its a great video, or it was. I don't know why we still have only this video. Its really offsetting- many things have changed in the last 10 years and now the resolution is going to shit on our 1 video. This is the best Tesseract rotation video since 2008.
Great comment, when I tilt my head I can instantly see it. I'm very interested in this stuff as well and spent a lot of time trying to visualize 4D space lol.
Thanks for making the lines different colors. Before watching the video of the hyper cube with different colored sides I was under the impression that it was being distorted.
Thank you for all 5 minutes. Time is important when I need to look @ 4th dimension.
When you see the rotation, try to see the hyper volume of that thing. It's near impossible to make it tangible! This tesseract looks huge, like maybe three times the size of the screen, and yet every point where the cube-faces converge seem to cross each other in a way that makes it look like the tesseract has no volume inside. That's some crazy stuff!
Great work with the video.
I've been reviewing dimensions and getting some wonderful feedback. The first time I came across d being used to represent quantum natures was in 1990. I'm not an expert and I value all discussions on the topic. I notice a lot of issues for us because we tend to combine different approaches. Spatial representation seems effective but can be just as difficult as temporal, etc. I looked over recent comments and they all express valid possibilities and issues...
Thank you for that deep and insightful response. I'm not sure I'll ever be the same.
this is the most beautiful thing ive ever seen
Great advice. I get it now. It makes sense. So beautiful.
this is an OUTSTANDING representation of the 4th dimension. When I saw Sagan describe it and show a 4d cube shadow, I only partially imagined it.
This makes it much more understandable. This is what a 4d cube would look like to us while moving in 3d space. Awesome work!!
Wow, I was expecting this t be a TesseracT song. Good job.
The way to understand is to concentrate on a certain point and consider the direction of its rotation. Look at it stupidly and try to imagine each cube frozen. I can kind of see maybe 15-20% of what is going on and the hardest part to imagine is the part when it (kind of reshapes) and looks to be curved. Other than that most of the things look kind of okay. Yet it is just a projection
Very cool graphics. Thanks.
Hahaha, im loving the people who are being fooled by the "rotations". That's just the animator screwing with you :)The tesseract we can see in our 3D world is like the image in the middle of video when it stops "spinning" and rotates briefly. The spinning effect in merely a square expanding upwards then shrinking back, with another one expanding through the middle while the first shrinks, join the corners and taadaa! A clever animators way of screwing you over :) great animation btw!
This is one of the finest tesseract anmations I've seen. And I've seen lots. (something which I'm not exactly proud of, but will admit anyway)
YOU JUST MADE MY DAY LOL!!!!
Good, good work!!!
This may not truly be a tesseract, but it sure as hell helped me understand it.
Fun fact: Everything you see here is just the *surface* (not the inside) of the tesseract. The 8 cubes you see - the "outer" one, the "inner" one (which each represent opposite ends of the 4D axis), and the 6 in between them (which look skewed just as most of the squares in the 2D shadow of a 3D cube are skewed) - only make up the surface of the tesseract, *not* its interior. Just as a 1D line has 2 0D sides (points), a 2D square has 4 1D sides (lines), and a cube has 6 2D sides (squares), a tesseract has 8 3D sides (cubes). See the pattern? So the inside of the tesseract isn't represented in this video at all. How could it be? It's 4D!
This if very helpful, thank you endlessly
I'm very glad you remembered all eight cubes, some people forget to represent that one properly during a rotation.
brilliant animation, i see it differently each time :D
Oh, that actually makes sense. Thanks for clarifying that for me.
I perceived it, LIKE A BOSS!
That is freaking Amazing....I feel like I just stepped into another world.
You create your own universe as you go along ! - that's the right one, I believe.
Taking a closer look at natures/behaviors of shadows can really help a lot. I think it makes sense to say a 3d cube is like a 4d shadow.
When we place a solid cube in front of us, we can't naturally see all sides. Simply put, spatially a 4d being would see all sides of a 3d cube.
More relevant: if you moved in a 4th dimensional direction, then you would be at an angle to see all sides of the cube.
The 8th cube is on the "outside" or front face of the tesseract. It's difficult to see, but you can see cubes rotating to that position. It might be easier to visualize if the cubes were shrunk slightly, but that might take away from the certain aspects of the visualization.
I'm sure POV-Ray can be used to draw tesseracts, in fact I've considered it to perhaps render four dimensional videos with more than one object, such as mazes, but I haven't quite figured it out yet.
the tesseract... even in three dimensions, such a beautiful object. i bet the fourth dimension is a beautiful place, unlike anything the human mind can imagine.
wow, I think the colors help, can finally kind of see this as something rotating and not transforming
this is awesome
holy shit i see what you're talking about, it starts to boggle my brain before it finishes rotating..
Alright, so I watched this while I was high... REALLY amazing. Instead of seeing the cube within the tesseract moving and expanding/overflowing (I don't know, that's usually how I think of it), I saw the whole thing as, well, a whole. Like.. as if it was a solid object that could be 3-D being rotated, instead of actually moving. It awed me. Haha. :)
Bravo. Excellent post.
Yes, we may exist in three dimensions, but we can only see in two dimensions. Light reflects off of two-dimensional surfaces and onto the two-dimensional surface of our retina.
We can never truly see depth, only infer it.
MINDABLOWN!
this is fantastic. i still dont understand it completely. the mind is so powerful. simply fanstastic
wow i actually see it for what it really is! With the color coding, it makes it much easier
just smoked dmt. best postcard i can send is this video.
life is infinite. understanding > knowledge
its beautiful
Thanks!
I haven't heard of them, but I'll look them up. I've considered using an anaglyphed video, but that would take away from the color of the video. Depth perception would be quite beneficial.
I used Blender, a free raytracer, as a 3d environment that I could easily render and project the tesseract on to. I used python code and some trigonometry to project the rotating tesseract onto the space provided by Blender. I used basically the same technique used to project 3d onto 2d.
@FreakyKing2 You can move an object with x dimensions two ways along each of the x axises perpendicular to each other. Meaning, you can move said object in 2x directions. So yes, a 4D object can move in 2*4=8 directions and a 5D object in 2*5=10. The directions of which an object can move increases linearly with the amount of dimentions the object has.
@theforbiddenplanet
I think the mention of time is only relevant if you consider time one of the dimensions we're discussing, but unless we're divulging onto movement within the dimension of time, instead of the euclidean dimensions, I'm not entirely convinced (or perhaps knowledgeable enough to understand) that it's a factor.
as far as I know, the temporal dimension is tied to the spatial dimension by the theory of relativity, space and time are related to speed at which space is traversed.
Yes, the colors help a lot. I can finally see it :)
WOOOO IT S WONDERFUL
Ah, yes! I see it!
This one is so much better than that annoying gif I see everwhere. Making it out of shaded, 3D cylinders just stops you from seeing it from a 4D perspective. Wireframes like in this vid are so much better for this stuff.
@yanchesanchez those "colors" are either the glare on your eyelids from outside lights *your eyelids are the thinnest skin on your body* OR visuals of colors you're imaging which are always colors you actually can see. OR the little specks of light you see are your rods and cones slowly losing the light they have just recently absored.
This makes more sense then other explanations
The 3rd D (Z) manages to be perpendicular/Independent from both the previous ones (X,Y) as Y and X are independent/perpendicular to each other. If you put a pt midway between two points on a line then lift it transcendentally 'out' a ways then you get 3 equidistant points. Put a point in the centre of a equilateral triangle a lift it a ways - get a tetrahedron (4 equidistant pts) 4 Triangle sides. Put a Pt in the center of a Tetrahedron, lift it, and get 5 sided 4D object with Tetrahedron sides.
@anatomiphile
yes, as I said, our brains can interpret the various 2D stimulus we have access to (touch & sight) as a 3D environment, plus predominately staying in contact with the ground is always a good indication of which way gravity is pulling you, and which way you have to push to stand up.
Hey, neat. I really do see it now. It's like a row of cubes when you rotate it like this.
@mitrospecto It is a three dimensional object rotating around an additional axis (which we don't have in our 3d (spatial) world)
@TheShadowThug One way to draw a cube is to draw a small square inside a bigger square and connect the vertices {This helps demonstrate the dimension-progression (IE translate a line segment a unit of distance and it sweeps out a square; move a square and it sweeps out a cube)}. We can dress up our depiction by making all the lines slightly curved for the one-eye-open perspective. Either way it depicts all the angles 90 degrees, because that is what they are and our drawing depicts what it is.
Ура! я смог увидеть вращение 4х мерного куба, а не его деформацию!! Cheers! I could see the rotating 4 dimensional cube, but not its deformation!!
This would be a great opportunity to mention some current "issues" physics is dealing with.
Imagine every side of the tesseract is our universe (or even different universes), we can measure to the edge (perimeters of our side) but we can't get past it.
What makes this really interesting is that such an edge may only be like a horizon effect (obviously at massive distances), and we think it may not even be an edge or that if there is an edge then it may actually be even further.
@mattxtraweek Yes. More so - Their square sides are connected. Move sqar away from itself and it's 2; begin and end square. While its four sides sweep out, replace themselves with, 4 sqars If the first sq was turning then the end sq is turning and all the in-between cross section squares too, the six sided Cube is turning. Looking from the side it looks like 4 squares chasing each other. Move Cube in 4D DIRECTION it becomes 2, while the 6 Sq sides sweep into six new connecting 3D sides. 8 sided
My mind is so freaking blown right now. I'm like, freaking out.
Square - spin it and look at it from the side (you are in flatland) the 4 sides (line segments) follow each other around, clockwise or counter clockwise.
Cube - you can make a cube out of that spinning square - put another one above it (and all the squares between - a stack)
So now the original spinning has one watching 4 Square-sides following each other. But there happen to be two new versions of this four in a row. (Thus 3 rotations.)
4D Cube - while the original cube spins on any axis
Thank you!!!
@LilShaggy82 Shadow is the term Carl uses in the video "Cosmos - Carl Sagan - 4th Dimension." Instead of on our screens these Ought be shown in Actual 3D. We're supposed to consider it 3D (that we happen to be seeing on our screen). This is a Projection "One-point projection" {The scene is a set of points, and these points are projected to a plane in front of the view point (the viewer's eye).} Because its 4D the flat-window is replaced by one with volumn. The '4D person' sees the same images.
This would make such an awesome screensaver.
This is technically the 3d shadow cast by a 4d tesseract. If you rotated a cube you wouldn't see the shadow come off the wall when it was rotated but you could see the lines moving. It is the same thing here. If the video was 3d it might be a little bit easier to grasp. But since we are stuck in 3dimensions we could never truly comprehend it's 4 dimensional beauty.
@Nickelskov Nickel, this is not modeling time as a 4th dimension. In the formulation of spacetime, time and the three dimensions for space have different metrics.
This is a 4 dimensional euclidean space (all dimensions are measured in the same metric.