Some views of the construction of a hypercube for your viewing pleasure today. If you start with a point (one dimension) and extend it in one direction you get a line. Now, perpendicular to the last extension, extend the line and you get a plane. Extend the plane (again, perpendicular to the last movement) and you fill in a cube. And then comes the hard part to visualize: extend the cube (somehow perpendicular to the last movement) and you get a hypercube. Strange. Hard to imagine. Different viewing angles give very different views of this shape. Dali used the unfolded version of the hypercube
 
In many science fiction tales (I remember those Madeline L'engel children's books) the hypercube (tesseract) is used as a teleportation device. Much like a maze drawn in 2 dimension (like on paper) is trivial if you can pick up your pen (into the higher, 3rd dimension) and put it back down at the exit, a 3 dimensional being could appear to transport to a different (non contiguous) part of space by having access to the higher dimensional hypercube.
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In many science fiction tales (I remember those Madeline L'engel children's books) the hypercube (tesseract) is used as a teleportation device. Much like a maze drawn in 2 dimension (like on paper) is trivial if you can pick up your pen (into the higher, 3rd dimension) and put it back down at the exit, a 3 dimensional being could appear to transport to a different (non contiguous) part of space by having access to the higher dimensional hypercube.
- jim 5-20-2000 3:33 pm