Math disagrees with you. You can view a three dimensional object as projection onto a 2D canvas. I suppose I should add the stipulation of 'n>2', but I'm not wrong.
It's a 2D representation(because it's flat on your screen) of what a 4D cube would look like from a 3D inhabitant's perspective.
Just as a sphere passing through a plane would like like a circle that expands and contracts yet would also be viewed as a line that expands and contracts to 'inhabitants' of this 2D flatland.
This GIF shows the tesseract passing through itself because in those sections where it must reorient, it is not passing through itself, just passing by itself in a fourth dimension, but we cannot see that fourth dimension, so this is how the 4D cube would apear in our 3D world(theoretically).
TL;DR - it's still 4D, just what 4D looks like in a 3D world.
I have all three on my comp. I agree with doimas on the fact that #s 2 and 3 were pretty bad compared to #1, but I did enjoy the twist at the end of #3
I'll explain
It's like drawing a 3D cube on a paper, now you watch a 3D cube in 2D.
That is a 4D cube, and since we live in a 3D world, we can only watch the 4D cube from a 3D perspective.
This is a 3 dimensional representation of a 4 dimensional cube (tesseract). This is a 3 dimensional representation because we cannot comprehend 4 dimensional objects because we comprehend the universe in a 3 dimensional reality. The 4th dimension is generally considered time. with time being the 4th dimension, and this being a four dimensional object, the object seems as though it's moving because we can only see any instant of the fourth dimension - time. if we perceived a four dimensional world, than we would be able to see all 3 dimensional objects, and inside them, and the nature of the objects through time all at the same instant.
The interesting thing here is that it isn't actually moving. We actually live in a universe of many dimensions (11 observable, at least last I read). Aforementioned, we cannot perceive four dimensional objects, so to represent them on a 3 dimensional plane, it must be moving to show its existence on a linear timeline.
TL;DR: it isn't actually moving. it only looks like it is because it is 4 dimensional (the 4th dimension is time) and we can only see 3 dimensions
The fourth dimension isn't time, it's just another dimension of space. Time and space work on different planes, one is linear the other is not. Which is why we use the term "Time-space" for the awkward part between the two. As for it's movement, it has to be moving because it's the only way to comprehend a fourth dimension without "Trinoculars" which is a device that splits our vision into a third plane in which we can see four dimensional objects. Without this impossible device, all you can do is imagine it as a moving object along a linear plane. It's actually one of the more simple parts of the Theory of Quantum Entanglement, which has to do with how the dimensions are tied on a multi-infinite level
As I said, The 4th dimension is not i fact time. It is generally regarded by us as time. While it is a spatial dimension, we regard it as time because that is how we see it as 3-dimensional beings.
I'm also notoriously bad at explaining things, so that doesn't help
no. no. no. no. no. Take a point in 3D space. Pick a point. Any point. call it (a,b,c,d). Divide by d to get (a/d,b/d,c/d). Drop the third axis. (a/d,b/d). Draw that point on a graph. You just did a 4D projection, congrats!
The cool transformation comes from a rotation, but that requires a lil' bit of linear algebra to explain.
This is animated over time, so to talk about time as a dimension, this would be a 5D object.
I actually said that is a 3D representation (technically 2D since it's a picture) of a 4D object.
Also, no. you are overthinking the '5D object' aspect. if this picture were actually a 4D object, then yes, because it animation of what would be a 4D object. Unfortunately it's a 3D (yes it's a picture, so it's technically 2D, but we all know what I mean) animation, therefore a representation/simulation of a 4D object.
As I said below, I am notoriously bad at explaining things, so that is apparent here.
actually, a tessaract is in 4 spacial dimensions, what that animation is is what it's shadow would look like if it were rotating. you can see the concept by making a wire-frame cube and rotating it and looking at the shadow it creates. the cube makes a 2 dimensional shadow of several squares going into and out of eachother and connected at the corners, a tessaract makes a 3 dimensional shadow of several cubes going into and out of eachother.
so really, this .gif is a 2-dimensional representation of a 3-dimensional shadow of a 4-dimensional object slowly rotating.
Do people still believe that? I mean I guess it can be technically correct and a somewhat decent model to teach the concept by comparing apples to oranges by I didn't think it was still taught in that manner
Whether or not the fourth dimension is time is irrelvent hre. This is just a hypothetical mathematical concept in a fourth spacial dimension, it has nothing do with physics.
If you transform an object consisting of 8 cubes from a 4 dimensional vector space onto a 3 dimensional vector space, and then onto a 2 dimensional vector space, you get this.
The 4th dimension in physics might be time, but its not in mathematics
Probably a bit late to reply here (I haven't had Internet for a day or so), but here's a 2-dimensional representation of what you're saying.
Would you believe me if I told you that the shape outlined in red was a perfect square?
This is actually a 2D model of a cube, viewed from the front. All sides of the cube are perfect squares, and there are 6 sides (even though you can only see 5 of them from this angle, and only one of those appears to be a square).
Same thing with the tesseract. What you have is a 2D picture of a 3D model of a 4D object.
Just as a 1D line segment has two 0D "sides" that are points, a 2D square has 4 1D sides that are line segments, a 3D cube has 6 2D sides that are squares, and a 4D tesseract has 8 3D sides that are cubes. And so on.
Of course the 4th spatial dimension is a hypothetical mathematical concept. It could exist in theory, but if it does we cannot observe it.
After this entire conversation I did more research that I'd like to admit about the subject, mainly because I found it very interesting. I found out what a tesseract actually even is beyond my previous comprehension and basically found a textbook length explanation of what you condensed into a comment. I'll admit I did not know what I was talking about at the time and now am better educated for circumstances involving the subject in the future.
You obviously don't, since it's not a cube. Let me repeat that, the tesseract is the 2D representation of the 3D shadow of a 4D cube. The actual 3D shadow looks different, because humans cannot percieve 3D - and the 4D cube looks very different, because humans can't even imagine 4D since we live in 3D and our eyes watch in 2D.
Alright so then there must be an explanation for the distortion of the "cubes" since the tesseract is a standard, conceptual figure of our perception as a 4d figure.
I am tired of seeing this on the front page. As a 3d modeler, I know how to do this, it is just a cube going inside out over and over. I spend a half hour making a .Gif to show you what it is on simpler terms
In summary this "Tesseract" though it is called a Hyperplex cube is mainly the shadow of a forth dimension. It's inner working consist of 8 separate line diverging into a secondary cube. Somewhat paradoxically the inner lines in the forth dimension are at a 90 degree angle. The more you need to know
No, it's a 2 dimensional representation of a 4 dimensional object with 4^4^4 sides being represented in 3 dimensions, because your computer screen cannot display 3 dimensional objects.