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itzazoom Male, 1829, Europe 182 Posts

Wednesday, July 18, 2012 3:24:34 PM 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... 

MacGuffin Female, 3039, Europe 2597 Posts

Saturday, July 07, 2012 7:50:39 AM I can't wrap my head around this >_< Don't worry, that just means you're normal. ;) 

MacGuffin Female, 3039, Europe 2597 Posts

Saturday, July 07, 2012 7:47:54 AM
The real headspin comes when you appreciate how differently a 4dimensional 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. 

MacGuffin Female, 3039, Europe 2597 Posts

Saturday, July 07, 2012 7:47:41 AM
We see in 2D, because we can only ever see one twodimensional '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 consistentlypredictable features that we're seeing a single twodimensional aspect of each threedimensional object at a time as we move through the spacetime we and those 3D objects share. ...


MacGuffin Female, 3039, Europe 2597 Posts

Saturday, July 07, 2012 7:47:33 AM 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 twodimensional (it's projected onto a flat computer screen). It has 3dimensional 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* 2dimensional, even though we intuitively understand what we see around us to be 3dimensional space, and even though binocular eyes have certain amount of 'depth perception' out to about 30 feet. ...


kittilia Female, 1829, Western US 503 Posts

Friday, July 06, 2012 10:56:19 PM I can't wrap my head around this >_< 

comp_wizard Male, 1829, Eastern US 195 Posts

Friday, July 06, 2012 8:40:26 PM 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. 

MacGuffin Female, 3039, Europe 2597 Posts

Friday, July 06, 2012 4:59:20 AM
This video explains more about how considering how 2D relates to 3D, helps understand how 3D relates to 4D. 

MacGuffin Female, 3039, Europe 2597 Posts

Friday, July 06, 2012 4:59:15 AM >>>so.. every inside plane is also an outside plane?<<< Kind of. Not a plane, though, but a 3dimensional 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 sideon 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 3dimensional 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. ... 

junkaddy Female, 3039, Western US 261 Posts

Friday, July 06, 2012 2:59:42 AM Do...not...understand.... But it's pretty. 

miasmaat Female, 1829, Western US 299 Posts

Friday, July 06, 2012 12:58:55 AM so.. every inside plane is also an outside plane? 

Agent00Smith Male, 1829, Eastern US 2143 Posts

Thursday, July 05, 2012 10:48:47 PM It looks like it expands around itself then back in. 

Agent0024blo Male, 1829, Southern US 198 Posts

Thursday, July 05, 2012 10:16:13 PM I'm angry at things I don't understand! >:( 

keith2 Male, 1829, Midwest US 2550 Posts

Thursday, July 05, 2012 7:00:32 PM 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. 

BrimstoneOne Male, 3039, Canada 2239 Posts

Thursday, July 05, 2012 5:58:52 PM hypercube! 

TheGuySmiley Male, 1829, Canada 1222 Posts

Thursday, July 05, 2012 4:17:58 PM where do i get 4d glasses? 

bdowner60 Male, 4049, Midwest US 488 Posts

Thursday, July 05, 2012 2:26:50 PM Impossible to even imagine with our 3rd dimensional eyes and mind!!! 

gibb0 Male, 1317, Europe 187 Posts

Thursday, July 05, 2012 1:46:19 PM 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. 

MacGuffin Female, 3039, Europe 2597 Posts

Thursday, July 05, 2012 11:35:21 AM 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. 

DeadKittens Male, 3039, Canada 982 Posts

Thursday, July 05, 2012 11:20:28 AM 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 

earplay Male, 6069, Midwest US 121 Posts

Thursday, July 05, 2012 11:00:29 AM "Hyper cubes are fun to draw." and fun in my drink! 

bacon_pie Male, 3039, Southern US 2819 Posts

Thursday, July 05, 2012 10:49:24 AM I only like The 5th Dimension. 

MacGuffin Female, 3039, Europe 2597 Posts

Thursday, July 05, 2012 9:45:26 AM >>>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. 

MeGrendel Male, 4049, Southern US 4358 Posts

Thursday, July 05, 2012 9:40:46 AM Actually, a hypercube is ndimensional figure. It's not limited just to the fourth dimension. A fourdimensional 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. 

Justin9235 Male, 1829, Midwest US 1582 Posts

Thursday, July 05, 2012 8:47:05 AM Hyper cubes are fun to draw. 

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