This is a 4-dimensional analog of a 3-dimensional square--a tesseract--projected from the 4th to the 3rd dimension.

Log in with a social network:

This is a 4-dimensional analog of a 3-dimensional square--a tesseract--projected from the 4th to the 3rd dimension.

The Trending 10

- WEEK
- MONTH
- YEAR

12

11

257,869

483

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...

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

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.

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.

...

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.

...

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

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.

...

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.

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.

and fun in my drink!

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.

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.

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

I don`t like looking at it.

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

http://youtu.be/XjsgoXvnStY

- This is a 4-dimensional analog of a 3-dimensional square--a tesseract--projected from the 4th to the 3rd dimension.