This video and this image show a tesseract, which is a 4d cube:
In what sense is this cube 4 dimensional? Where is time? (commonly called the 4th dimension, although I realize here its probably some sort of direction).
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9$\begingroup$ You are "seeing" a two dimensional model of a three dimensional model of a 4-dimensional figure. In four dimensions, any two edges meet at right angles; it's of course impossible to picture such an object in 3-dimensions, just like it is impossible to draw a cube in 2 dimensions in such a way that any two edges meet at right angles. You are seeing a projection of a projction. $\endgroup$– Arturo MagidinAug 3, 2011 at 21:19
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1$\begingroup$ Cube? Just looks like a bunch of 2D squares to me... ;) $\endgroup$– anonAug 3, 2011 at 21:20
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4$\begingroup$ In addition: mathematically, "time" is not "the fourth dimension"; "space time" is a particular physical model, but in mathematics, 4-dimensional Euclidean space is simply the set of all ordered 4-tuples $(a,b,c,d)$ with $a,b,c,d$ real numbers, satisfying certain axioms. Time doesn't enter into it. $\endgroup$– Arturo MagidinAug 3, 2011 at 21:20
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2$\begingroup$ If you looked at a still holographic projection of a 1x1x1 in^3 cube for 1 second, and identified 1 in = 1 sec, then you'd be seeing a tesseract using time as a "dimension." Although only one 3D cross-section of it at any given moment... $\endgroup$– anonAug 3, 2011 at 21:30
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$\begingroup$ Nice animation! Who made it? $\endgroup$– TonyKAug 3, 2011 at 21:30
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3 Answers
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The tesseract is the four dimensional analog of the cube. It lives in $\mathbb{R}^4$, four dimensional euclidean space. This four dimensional space has all dimensions equivalent, with none of them being special like time. The space is the set of points $(x,y,z,w)$ where the coordinates range over the reals. One of the tesseracts has $16$ vertices, with all combinations of $\pm 1$.
answered Aug 3, 2011 at 21:21
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You picture displays a 3-D model of a 4-D object. Time is not one of the dimensions in this case.
Wikipedia has a nice description:
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13$\begingroup$ Or rather, a 2-D picture of a 3-D model of a 4-D object.... $\endgroup$ Aug 3, 2011 at 21:21
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I think I understand this better now. The 4th dimension is shown ALONG THE AXIS OF THE CUBES EDGES (an axis "overlapping" the 3d space that the cube volume is shown in).
There is a continuum of 3d Volumes that extends across a 4th dimension. An image is shown here.
