Wednesday, July 18, 2012 3:24:33 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...
Saturday, July 7, 2012 7:47:53 AM
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.
Saturday, July 7, 2012 7:47:41 AM
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.
Saturday, July 7, 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 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.