Visualizing The Fourth Spatial Dimension

Submitted by: MacGuffin 4 years ago Science

This is a 4-dimensional analog of a 3-dimensional square--a tesseract--projected from the 4th to the 3rd dimension.
There are 31 comments:
Male 182
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...
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Female 2,602
[quote]I can`t wrap my head around this >_< [/quote]

Don`t worry, that just means you`re normal. ;)
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Female 2,602

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.
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Female 2,602

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.

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Female 2,602
[quote]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.[/quote]

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.

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Female 500
I can`t wrap my head around this >_<
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Male 194
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.
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Female 2,602

This video explains more about how considering how 2D relates to 3D, helps understand how 3D relates to 4D.
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Female 2,602
>>>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.

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Female 261
Do...not...understand.... But it`s pretty.
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Female 298
so.. every inside plane is also an outside plane?
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Male 2,579
It looks like it expands around itself then back in.
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Male 197
I`m angry at things I don`t understand! >:(
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Male 2,592
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.
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Male 2,229
hyper-cube!
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Male 1,243
where do i get 4d glasses?
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Male 593
Impossible to even imagine with our 3rd dimensional eyes and mind!!!
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Male 192
It`s a 4D shape being viewed from different 3D perspectives. Just like a picture of a cube is a 3D shape being viewed at a particular 2D perspective.

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.
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Female 2,602
[quote]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[/quote]

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.
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Male 1,252
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
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Male 121
"Hyper cubes are fun to draw."

and fun in my drink!
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Male 3,061
I only like The 5th Dimension.
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Female 2,602
>>>It`s also called a "hyper Cube".<<<


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.
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Male 7,350
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.
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Male 1,582
Hyper cubes are fun to draw.
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Male 4,746
Keyh, that does a nice job of explaining higher dimensions (it`s actually a great video), but does not explain a hypercube.

Before the 80`s, all I had was some words on paper, describing a hypercube. It was hard to imagine it.
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Male 37,889

I don`t like looking at it.
It makes me feel like one of the apes from `2001:A Space Odyssey` encountering an obelisk
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Male 3,578
"hyper Cube" was okay not as good as the frist movie
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Male 226
I always thought this explained it pretty well:

http://youtu.be/XjsgoXvnStY

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Male 4,746
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".
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Female 2,602
Link: Visualizing The Fourth Spatial Dimension [Rate Link] - This is a 4-dimensional analog of a 3-dimensional square--a tesseract--projected from the 4th to the 3rd dimension.
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