70 Replies to “4D Hypercube Animation”

  1. maybe I’m missing something…(yes I did see the animated version), but couldn’t this object be made in RL with some sort of stretchy/gummy material?

  2. It is not possible to visualize a 4D object with 3D imaging no matter how fancy the animation. The visual concepts are beyond the abilities of the human brain. All we can visualize is the shadow of a hypercube presented as a 3D object just as a square is a 2D representation of a cube.

    it is however a very pretty animation

  3. If you’re interested in the fourth dimension, might I recommend “And He Built a Crooked House” by Robert A. Heinlein. Very cool short story if you’re geeky like me

  4. what does this cube represent? 4D. BUT can it be applied to anything? this doesnt explain 4D because it’s only a cube. but my question is: can anything be in 4D? or does it only have to be a cube? and isnt 4D time?

  5. Each edge of the cube is the same length, you cant reallly tell but if you think about it they would have to be, the cube inside is smaller because the cube could not only move up, down, left, right, in and out it can also move to seem smaller or bigger (shrink or expand). And to answer your question no it doesnt have to be a cube, yes 4D is time and this is basicly an example of 4D it is not what 4D IS but just an animation made to aid you in understanding it.

    Thats my opinion, pretty good stuff.

  6. i used to have this mind toy that was put together exactly like that. using tubes and elastic string. or something similar O.o fuuuuun

  7. Makes a lot of sense after taking it and watching it frame-by-frame in my cheap photoshop program…Still, excellent illusion

  8. That is not an illusion!! I can make that out of magnetix!!!!!!!!!!
    All the people that think this is an illusion are dumbasses! The rest of’em are on my side=^^=

  9. Ok, Anyone who thinks this is NOT a illusion is WRONG.

  10. i dont know about anyone else, but all i see is just a stupid picture of a shape that anyone can make out of magnetix sticks!!

  11. The picture did nothing. I clicked on “animation” and found an advertise window. Is this why we were asked to click on -animation- link? Please find other ways to advertise.

  12. Yes, this cube IS really called a tessaract, and yes, it IS really four dimensional. Look it UP!
    And don’t click on the picture, click on the link. Pay attention!

  13. Why can’t people read The Time Machine by H.G. Wells? The fourth dimension is time, all objects are in the fourth dimension. Time, duration, call it what you will, have you ever seen a cube in only 3d? An instantaneous cube?

  14. Nigel – You’re not really getting dimensions. Yes, the fourth dimension we, the common public, experience is time, but for mathematicians, who know there’s more, it would be bad practise to label time as the “4th” dimension when there are more spacial dimensions after the 3rd.

    1. those rnt dementions stupid all the dimentions are of a phyical mesurement length width highth time isnt a dimention and neither is light or else the original mario would be 4d which its not

  15. Mathematically four-dimensional space is simply a space with four spatial dimensions, that is a space that needs four parameters to specify a point in it. For example a general point might have position vector a, equal to

    \mathbf{a} = \begin{pmatrix} a_1 \\ a_2 \\ a_3 \\ a_4 \end{pmatrix}.

    This can be written in terms of the four standard basis vectors (e1, e2, e3, e4), given by

    \mathbf{e}_1 = \begin{pmatrix} 1 \\ 0 \\ 0 \\ 0 \end{pmatrix}; \mathbf{e}_2 = \begin{pmatrix} 0 \\ 1 \\ 0 \\ 0 \end{pmatrix}; \mathbf{e}_3 = \begin{pmatrix} 0 \\ 0 \\ 1 \\ 0 \end{pmatrix}; \mathbf{e}_4 = \begin{pmatrix} 0 \\ 0 \\ 0 \\ 1 \end{pmatrix},

    so the general vector a is

    \mathbf{a} = a_1\mathbf{e}_1 + a_2\mathbf{e}_2 + a_3\mathbf{e}_3 + a_4\mathbf{e}_4.

    Vectors add, subtract and scale as in three dimensions. The dot product also generalizes to four dimensions, like so:

    \mathbf{a} \cdot \mathbf{b} = a_1 b_1 + a_2 b_2 + a_3 b_3 + a_4 b_4.

    It can be used to calculate the norm or length of a vector,

    \left| \mathbf{a} \right| = \sqrt{\mathbf{a} \cdot \mathbf{a} } = \sqrt{{a_1}^2 + {a_2}^2 + {a_3}^2 + {a_4}^2},

    and calculate or define the angle between two vectors as

    \theta = \arccos{\frac{\mathbf{a} \cdot \mathbf{b}}{\left|\mathbf{a}\right| \left|\mathbf{b}\right|}}.

    The cross product is not defined in four dimensions. Instead the exterior product is used for some applications, and is defined as follows

    \mathbf{a} \wedge \mathbf{b} = (a_1b_2 – a_2b_1)\mathbf{e}_{12} + (a_1b_3 – a_3b_1)\mathbf{e}_{13} + (a_1b_4 – a_4b_1)\mathbf{e}_{14} + (a_2b_3 – a_3b_2)\mathbf{e}_{23} + (a_2b_4 – a_4b_2)\mathbf{e}_{24} + (a_3b_4 – a_4b_3)\mathbf{e}_{34}.

    This is bivector valued, with bivectors in four dimensions forming a six-dimensional linear space with basis (e12, e13, e14, e23, e24, e34). They can be used to generate rotations in four dimensions.

    thats the math behind it! =]

  16. MATH 4D is real, when it comes to “math” concepts only. Animating it is stupid as the real world is 3D, you only need to specify x, y, z, to get the point you want.

    any nD space is OK in math, but not in reality, the above image is silly, it’s just a 3D object anyway.

  17. Imagine looking at a video of a normal 3D cube rotating. Because of perspective the side away from you looks smaller. As the cube rotates it appears that different sides are getting smaller or larger.

    The animation above shows the same effect for a 4D cube. The perspective projection of the 4 dimensional cube onto a 2D surface means different edges will appear shorter or longer. The hypercube is not stretching. In four dimensions all of its edges are the same length and all the angles are 90 degrees. But as it rotates, the perspective projection makes it appear that parts are shrinking and that one cube is moving inside the other.

Leave a Reply

Your email address will not be published. Required fields are marked *