02-08-2009, 06:25 PM
this is from wikipedia:
In mathematics, an n-dimensional space is a topological space whose dimension is n (where n is a fixed natural number). The archetypical example is n-dimensional Euclidean space, which describes Euclidean geometry in n dimensions.
Many familiar geometric objects can be generalized to any number of dimensions. For example, the two-dimensional triangle and the three-dimensional tetrahedron can be seen as specific instances of the n-dimensional simplex. Also, the circle and the sphere can be seen as specific instances of the n-dimensional hypersphere. More generally, an n-dimensional manifold is a space that locally looks like n-dimensional Euclidean space, but whose global structure may be non-Euclidean.
There are also notions of dimension (such as Hausdorff dimension in topology and Kodaira dimension in algebraic geometry) that apply to even more general spaces.
Sometimes it is convenient in science to describe an object with n degrees of freedom as if it were a point in some n-dimensional space. For example, classical mechanics describes the three-dimensional position and momentum of a point particle as a point in 6-dimensional phase space.
What this sounds to me like it's talking about is the kind of pure space in which we imagine pure euclidean geometrical shapes existing. What if that type of infinite space was the unity point, where there was one space for every one time, hence it's being even and infinite, and therefore euclidean and platonian shapes somehow resonate with this space? I'm totally pulling this out of my butt, but it's interesting to think about.
Another thing I was thinking is, what if instead of saying they don't come from zero, we just re-defined zero? I mean, what is Nothing, anyway? Seems like the only thing you could call Nothing is no-thing, or rather a lack of any thing-ness, or a formless infinite singularity. The equation I've made up to represent this is 0 = ∞ = 1. I just intuitively was drawn to such a concept, I don't know if I'm on the right track in relation to RST at all. Kinda sounds similar, though.
In mathematics, an n-dimensional space is a topological space whose dimension is n (where n is a fixed natural number). The archetypical example is n-dimensional Euclidean space, which describes Euclidean geometry in n dimensions.
Many familiar geometric objects can be generalized to any number of dimensions. For example, the two-dimensional triangle and the three-dimensional tetrahedron can be seen as specific instances of the n-dimensional simplex. Also, the circle and the sphere can be seen as specific instances of the n-dimensional hypersphere. More generally, an n-dimensional manifold is a space that locally looks like n-dimensional Euclidean space, but whose global structure may be non-Euclidean.
There are also notions of dimension (such as Hausdorff dimension in topology and Kodaira dimension in algebraic geometry) that apply to even more general spaces.
Sometimes it is convenient in science to describe an object with n degrees of freedom as if it were a point in some n-dimensional space. For example, classical mechanics describes the three-dimensional position and momentum of a point particle as a point in 6-dimensional phase space.
What this sounds to me like it's talking about is the kind of pure space in which we imagine pure euclidean geometrical shapes existing. What if that type of infinite space was the unity point, where there was one space for every one time, hence it's being even and infinite, and therefore euclidean and platonian shapes somehow resonate with this space? I'm totally pulling this out of my butt, but it's interesting to think about.
Another thing I was thinking is, what if instead of saying they don't come from zero, we just re-defined zero? I mean, what is Nothing, anyway? Seems like the only thing you could call Nothing is no-thing, or rather a lack of any thing-ness, or a formless infinite singularity. The equation I've made up to represent this is 0 = ∞ = 1. I just intuitively was drawn to such a concept, I don't know if I'm on the right track in relation to RST at all. Kinda sounds similar, though.