Link: Visualizing The Fourth Spatial Dimension - This is a 4-dimensional analog of a 3-dimensional square--a tesseract--projected from the 4th to the 3rd dimension.

It`s also called a "hyper Cube". I`m glad we have reached a point where it can be created with computer graphics. When I first read about them, there was no moving example. It`s easier to understand when you see them moving. To really understand what you are seeing, you need to look up "Hypercube".

Actually, a hypercube is n-dimensional figure. It`s not limited just to the fourth dimension.

A four-dimensional representation of a cube (such as this is) is caleed a Tesseract. A tesseract is to the cube as the cube is to the square.

A tesseract is always a hypercube, but a hypercube is not always a tesseract. It could also be a penteract (5 dimensional) or a hexeract (6 dimensional) or on up to infinity.

Technically, a hypercube is a cube extended into any number of dimensions higher than three, such as this demonstration of extensions up to the sixth dimension shows. A Tesseract is specifically a 3D cube (or 2D square) extended into the fourth spatial dimension by extending every edge of the 3D cube out at 90 degrees to the up/down, left/right and forwards/backwards dimensions we`re familiar with. Just like when you project a cube onto a 2D surface like a piece of paper and you see two squares connected by lines:

So too can you project a 4D Tesseract onto 3 dimensional space. When you do, you see a series of cubes that appear to warp and turn inside out as the object rotates in 4D space. This is what the video shows.

Just pointing out that if it was just a cube not moving you would still be watching it in the 4th dimension, Duration/time. Y`know ..in theory lol

It`s the fourth *spatial* dimension that the Tesseract is rotating in, not a temporal (time) dimension. Although time is sometimes referred to as "the fourth dimension", that`s not what Mathematicians are referring to when they talk of higher spatial dimensions. There`s an excellent Arthur C Clarke short story entitled "Technical Error" that talks about the difference between the two concepts.

I disagree. Just from observation and imagination I`ve decided we stand at the extreme far side of the "4th spacial dimension." If I were to start moving towards the other side, you`d see me get smaller, as you`re still stuck moving in only 3. However, you`ll still see me in the room, tiny, probably looking as if I`m a sticker on your wall. When you move, you see me moving in parallax with yourself like the moon does for us on the ground. And you`ll see that no matter where you go, if I don`t move you`ll always see me in that position until I step back to the edge of 4d with you.

>>>so.. every inside plane is also an outside plane?<<<

Kind of. Not a plane, though, but a 3-dimensional object: every `surface` of a tesseract is a 3D cube.

A 3D cube is comprised of six 2D squares, all of which can be fitted into a single square in 2D space (look down on a cube directly from above, and you`ll see a square: four of the edges will be side-on to you in 3D, and two - the top and the bottom faces - will be one in front of the other). Similarly, a 4D tesseract is comprised of eight 3D cubes superimposed onto the same 3-dimensional space, taking up the same position in 3D, but shifted along a perpendicular axis into a fourth dimension we can`t observe directly. 3D objects can be turned "inside out" by shifting them through a fourth dimension, and pass through one another in 3D space.

Simulating a tesseract in 3D isn`t all that hard; as has been noted, it`s analogous to drawing a cube on paper. The problem is that making a video of it forces the image down to TWO dimensions, resulting in a figure that makes no sense whatsoever.

Simulating a tesseract in 3D isn`t all that hard; as has been noted, it`s analogous to drawing a cube on paper. The problem is that making a video of it forces the image down to TWO dimensions, resulting in a figure that makes no sense whatsoever.

You`re right of course. This video, as with everything seen by the human eye, is really two-dimensional (it`s projected onto a flat computer screen). It has 3-dimensional cues that help us to understand implied depth, but in reality it`s completely flat. However, the thing to realise is, the world as we perceive it is *always* 2-dimensional, even though we intuitively understand what we see around us to be 3-dimensional space, and even though binocular eyes have certain amount of `depth perception` out to about 30 feet.

We see in 2D, because we can only ever see one two-dimensional `window` of the 3D objects that surround us at any one time. We just extrapolate from the fact that we can see different sides of objects with consistently-predictable features that we`re seeing a single two-dimensional aspect of each three-dimensional object at a time as we move through the spacetime we and those 3D objects share.

The real headspin comes when you appreciate how differently a 4-dimensional being would be able to see those same 3D objects that surround us, as well as a 4D object like the tesseract in this video. They`d see in true 3D, and would consequently be able to see all six sides of the 3D cubes that make up each `surface` of the tesseract simultaneously. They`d also be able to see inside each constituent cube at the same time. This is analogous to how we can easily see all four sides of a 2D square and its interior too, because we`re looking at that 2D object in its entirety from the enhanced perspective of a third dimension. A 2D being would by contrast be able to see at most two sides of a square at a single time, with the interior of it hidden from them completely.

visualize a video of a normal rotating cube. We "know" that we are seeing a the projection of a rotation cube, but consider it from a purely 2d standpoint and conencting edges are stretching and twisting inexplicably. this is the same thing a dimension higher. if you knew 4d as normal, those edges would all be fixed length and its just a rotating shape. but its interesting because of the two "cubes" with connected edges and the whole multiple axees of rotation thing...

- This is a 4-dimensional analog of a 3-dimensional square--a tesseract--projected from the 4th to the 3rd dimension.
http://youtu.be/XjsgoXvnStY

I don`t like looking at it.

It makes me feel like one of the apes from `2001:A Space Odyssey` encountering an obelisk

Before the 80`s, all I had was some words on paper, describing a hypercube. It was hard to imagine it.

A four-dimensional representation of a cube (such as this is) is caleed a Tesseract. A tesseract is to the cube as the cube is to the square.

A tesseract is always a hypercube, but a hypercube is not always a tesseract. It could also be a penteract (5 dimensional) or a hexeract (6 dimensional) or on up to infinity.

Technically, a hypercube is a cube extended into any number of dimensions higher than three, such as this demonstration of extensions up to the sixth dimension shows. A Tesseract is specifically a 3D cube (or 2D square) extended into the fourth spatial dimension by extending every edge of the 3D cube out at 90 degrees to the up/down, left/right and forwards/backwards dimensions we`re familiar with. Just like when you project a cube onto a 2D surface like a piece of paper and you see two squares connected by lines:

So too can you project a 4D Tesseract onto 3 dimensional space. When you do, you see a series of cubes that appear to warp and turn inside out as the object rotates in 4D space. This is what the video shows.

and fun in my drink!

It`s the fourth *spatial* dimension that the Tesseract is rotating in, not a temporal (time) dimension. Although time is sometimes referred to as "the fourth dimension", that`s not what Mathematicians are referring to when they talk of higher spatial dimensions. There`s an excellent Arthur C Clarke short story entitled "Technical Error" that talks about the difference between the two concepts.

If you rotate the cube in the picture, the 2D projection changes, if you rotate the tesseract, the 3D projection changes.

It`s nice to be able to relate lower dimensions to higher ones.

Kind of. Not a plane, though, but a 3-dimensional object: every `surface` of a tesseract is a 3D cube.

A 3D cube is comprised of six 2D squares, all of which can be fitted into a single square in 2D space (look down on a cube directly from above, and you`ll see a square: four of the edges will be side-on to you in 3D, and two - the top and the bottom faces - will be one in front of the other). Similarly, a 4D tesseract is comprised of eight 3D cubes superimposed onto the same 3-dimensional space, taking up the same position in 3D, but shifted along a perpendicular axis into a fourth dimension we can`t observe directly. 3D objects can be turned "inside out" by shifting them through a fourth dimension, and pass through one another in 3D space.

...

This video explains more about how considering how 2D relates to 3D, helps understand how 3D relates to 4D.

You`re right of course. This video, as with everything seen by the human eye, is really two-dimensional (it`s projected onto a flat computer screen). It has 3-dimensional cues that help us to understand implied depth, but in reality it`s completely flat. However, the thing to realise is, the world as we perceive it is *always* 2-dimensional, even though we intuitively understand what we see around us to be 3-dimensional space, and even though binocular eyes have certain amount of `depth perception` out to about 30 feet.

...

We see in 2D, because we can only ever see one two-dimensional `window` of the 3D objects that surround us at any one time. We just extrapolate from the fact that we can see different sides of objects with consistently-predictable features that we`re seeing a single two-dimensional aspect of each three-dimensional object at a time as we move through the spacetime we and those 3D objects share.

...

The real headspin comes when you appreciate how differently a 4-dimensional being would be able to see those same 3D objects that surround us, as well as a 4D object like the tesseract in this video. They`d see in true 3D, and would consequently be able to see all six sides of the 3D cubes that make up each `surface` of the tesseract simultaneously. They`d also be able to see inside each constituent cube at the same time. This is analogous to how we can easily see all four sides of a 2D square and its interior too, because we`re looking at that 2D object in its entirety from the enhanced perspective of a third dimension. A 2D being would by contrast be able to see at most two sides of a square at a single time, with the interior of it hidden from them completely.

Don`t worry, that just means you`re normal. ;)

this is the same thing a dimension higher. if you knew 4d as normal, those edges would all be fixed length and its just a rotating shape.

but its interesting because of the two "cubes" with connected edges and the whole multiple axees of rotation thing...