thanks :-)
it's possible for an object to have two independent rotations at the same time. There is only one "kind" of rotation in the fourth dimension - everything rotates around a plane. I'm not sure what the SU(n) notation means - i could answer your question if you explained it.
I believe Charles H. Hinton coined them, and they are the greek prepositions meaning "up" and "down". Some people use the terms "upsilon" and "delta" (favored by Clifford A. Pickover). For directions relative to the orientation of an object (like left & right), i use the words "zant" and "wint"...
There are three camps:
1. small-higher-dimension camp: people who talk about string theory and related theories.
2. higher-dimensional geometry: higher dimensional polytopes, topology, etc
3. possibility of higher-dimensional life
I'm in camp number 3. It's a hobby to me, and i know that...
Now you're confusing "measurements" with "dimensions". In English, dimension can be used for the scientific sense, a linearly independent direction, or it can mean a measurement. These are completely different concepts. If you used dimensions this way, then the dimensions of a polygon would...
Also: between every two rationals there is a real number, and between every two reals there is a rational number.
Here is the big problem: Dimensions are linearly independent. The very word "diagonal" means you are using a linear combination of more than one dimension. Diagonally to the upper...
meekness is always desirable over arrogance...
I'm not quite clear on what you are claiming here. The only possibility that makes sense to me is the following:
You are describing vectors that are assigned to locations. Each location has two coordinates, and each vector has two coordinates...
maybe you're more advanced than me, i don't know what the Huyghen's principle is.
Back to my original question of how to create a force in the fourth dimension that diminishes with the square of distance. What if all particles had a 3-plane of gravity extending from them, and this 3-plane of...
i understand the radiation/energy wave diminishing principle, where in 3-space it diminishes with the square of the distance, but in 4-space it diminishes with the cube of the distance. I was just wondering if it was possible to have a force that didn't diminish like radiation, but diminished...
i just recently found this article on why we have three spatial dimensions and one time dimension:
http://www.hep.upenn.edu/~max/dimensions.pdf
basically, more that one time dimension destroys predictability so it isn't possible to have observers in such a universe.
is there any way to construct a fundamentally different physics system for the fourth dimension where gravity diminishes with an inverse square law instead of inverse cube law?
i did some brief scanning on the internet, and apparently it has something to do with the fact that there are no solutions to the two-body problem. Orbits below a particular threshold spiral to impact, and orbits above that threshold are sent into infinity. Also, the hydrogen atom in the fourth...
i think i just figured out what you meant by "energy packages would be cubes". In the third dimension, wave energy drops off using an inverse square law, so a portion of the wave front is a square. In the fourth dimension, wave energy drops off using an inverse cube law, so a portion of the wave...
i think the question was how the flatlander could perceive the shape as a circle, as opposed to them thinking it was a line, square, triangle, or any other shape. If they thought it was a line, then they would see a line grow & shrink instead of thinking it was a circle doing that.
Generalizing, a person of dimension n will see a hyperplane of dimension n-1 (flatlanders see a line, we see a plane, "tetronians" see a "realm"). Thus, a being in any dimension would only need 2 eyes, because the combination of the two images in the brain adds the last dimension and brings the...