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.

Re:It is difficult, but...

[psych031337]

We have always lived in three dimensions, so visualizing 4 dimensions Per Se is almost impossible coz our nuerons have been hardwired for 3 dimensions.

Breaking up these limitations is not as hard as it might seem. The traditional length X width X depth is just an example of a 3d room. I understood multi-dimensionality with this simple analogy:

Imagine the "room of cookies"

1st dim: color (red, green, blue,...)
2nd dim: shape (round, square, triangular,...)
3rd dim: consistency (very hard, hard, soft,...)
4th dim: size (from very small to very large)

There you have it. A 4dim room that can be used to express any kind of cookie in a mathematical vector. For adding more dimensions all you have to make sure is that the new dimension os orthogonal, which means that the new component/unit has to be linear independent of all the other components/unit (which could for instance be the 5th dimension of texture (like smooth, rugged, etc.)

(Not an native english speaker, so please excuse me for using incorrect/half correct words.)