I was reading a book "Hperspace-, Michio Kaku" and utterly dumbstruck,confused as to how he could suggests that there exists, in some remote part of our universe, so small that the energy required far surpasses all the collective energy output on the entire earth (plank energy constant), a FOURTH and even up to TEN spatial dimensions.....?

For instance
- take a plain 2D square of equal length
- place 5 additional 2D squares allof equal size making a cross or "t"
- folding those squares unto themselves producing a 3D Square or cube
- placing a further 7 cubes so that is similar to a cross but the additional 2 cubes are placed at the the same angle to the protruding cues whick gives your a TESSERACT

thus achieving 3 spatial dimensions

what really fucked me up was folding the tesseract unto itself and achieving 4 spatial dimensions........ :confused:

care to elaborate.......

Here's a link to a couple of animated hypercubes (another name for the tessaract)

http://www.maa.org/editorial/knot/tesseract.html

http://dogfeathers.com/java/hyprcube.html

The last one is stereoscopic, you need 3d glasses to see it right. If you ignore the duplicate hypercube, you should get the idea. The first link allows you to manipulate the hypercube.

I've seen hypercubes demonstrated, but I wonder what a hypersphere would look like. Maybe I'll do a search and see if anyone has come up with one.

I think we have to take this from the beginning. You start out correctly but this is the correct progression: Point 0-D, line segment 1-D, square 2-D, cube 3-D, tesseract=hypercube 4-D. A line segment is limited by 2 points, a square is limited by 4 line segments, a cube is limited by 6 squares, a tesseract is limited by eight cubes. The problem is that there is no way to make a tesseract in the world we inhabit. It is quite easy to handle mathematically but there is absolutely no evidence that it is even possible to construct a 4:th spatial dimension. It just seems logical that it should be possible but we really don't know. It is fun to try to see this for a while but unrewarding in the long run. I have heard of no one who claims to be able to visualize 4-spatial dimensions.

But, just as one can depict a 3-d cube on a 2-d surface, one should be able to render a 4-d cube on a 3-d surface. That's the problem of course, the links I posted above are trying to render 4-d on a 2-d surface. The stereoscopic version is just the illusion of 3-d.

There is also the problem that we can't really visualize how to render 4-d in 3-d. All that can be done is guess. No one knows what 4-d looks like. So, as you say, it's fun but unrewarding. The animation of the hypercube may not be real, but it does give the mind a new way of looking at things.

tama_x, have you read Flatland?