See 4-D Space With 3-D Glasses

purpleant writes: "A hyperplane is a 3-dimensional space that slices through the 4-dimensional space, the same way a 2-dimensional plane can slice through our 3-dimensional space. The bounding hyperplanes can be extended infinitely so that they criss-cross through each other, chopping up hyperspace into many 4-dimensional 'chunks.' Again the inner chunks are finite, and they are distributed in shells around the core polytope. The HyperStar applet displays those finite chunks, one shell at a time. The inner shells are complete -- each shell completely encases the previous shell. The outermost shells have holes in them."

Comments

This was an old college argument...

[Thalia]

We used to argue this in the computer science lab at college. Can the human mind gain visualization skills in four dimensional geometry? We came up with the following interesting answers:

1. It's hard. We never see four diminsions. The brain would keep wanting to make one dimension some known continuim such as time, a color sequence, tone, or intensity. Only after this intermediate step would you get a true four dimensional geometry in your head.

2. You would need to have a true 3D display. Current rendering of three dimensional pictures flattened onto simple two dimensional screens would never work. Imagine using a laser pointer as a point source, and imagine that you had never seen a three dimensional object; now draw a three dimensional picture of a pick-up truck using the laser pointer. At the time, we were trying to get a simple three dimensional output, like <a href="http://www.stereographics.com/frames/frame-p rod.html">Crystal Eyes</a>. Now there are liquid crystal on silicon solutions that are much cleaner, if not cheaper.

We were students once, and poor.