Gord Sellar wrote:
>
>Don't 4D objects, when represented in 3D, look sort of like items with a
>smaller version of the item inside itself?
>
This is the "projective" way of representing 4D things in 3D. The
idea is that you take a point external to the 4D object,
a hyperplane [a 3D space] at the other side of the 4D object,
and project the object in that hyperplane. Since this hyperplane
is 3D, we can see it.
>That's how this tesseract-cube
>like thing I've seen before looks.
>
The reason for that is that the tesseract is a "prism-like" thing, so
the bigger cube is the hyperface closest to the center of projection,
and the smaller cube is the hyperface farthest away from the center
of projection.
This model is good, because the 6 sideways faces seem like
distorted cubes joining the outside cube and the inside cube.
>I've heard that described as a 3D shadow
>of the 4D object in 3D? The problem is that you need an extra dimension
>that runs orthogonal (kinda like right angles) with the other 3, is it not?
>
You can do that with time. For example, the tesseract might be
represented by a cube [make each aresta 300,000 km long]
that suddenly appears, then it exists for 1 second, and then it
vanishes.
Or it might be a point that appears, then grows to become a
tetrahedron, then, while still growing, lets its vertices become
small triangles, that also grow, until they join and it becomes
an octrahedron, and the whole process is repeated [but
with a twist, so that the initial tetrahedron and the final
tetrahedron are in symmetric positions].
Or it might be an aresta that appears, grows into a triangular
prism, then each triangular face of the prism gets cut in
their aresta becoming hexagons, until it grows into a
(regular hexagon) prism, and then it repeats the whole thing
in reverse.
>Ow. The whole idea hurts my head, though. But I gotta ask, when did our
>universe become a 4-space? (ie. can you explain how this was deduced?
>Everywhere I look I see a 3-space.) Or are you using time as a
>"dimensional" axis?
>
Yep
Alberto Monteiro
