How can a dimension curve?

Question

The word "dimension" is a descriptive word. Isn't saying dimensions can curve like saying the number "3" can curve?

Answer 1

In mathematics, "dimension" and "curvature" have separate, precise meanings. Technically speaking (in the mathematical sense), a dimension cannot curve. But objects in two dimensions or more can curve.

Thus, in a two-dimensional (flat) world, a squiggly line or a circle would curve, and there are ways to calculate the degree to which it curves (its curvature) at each point.

In three dimensions, surfaces can curve, but because the curvature at a point may be different depending upon the direction in which we move from the point, we have to be more careful about which specific curvature we mean.

The notion of a three dimensional surface can be made more abstract, and extended to higher dimensions than three. A "manifold" is one such abstraction, and it can have a curvature as well, in many dimensions.

You may have heard about "the curvature of space-time", but in this context, space-time is like a surface, and it is this which is curving, not the four dimensions themselves.

Answer 2

I expect your name is an acronym. The answer lies is what it is that actually curves - like space surrounding a gravitational field. The curvature in this instance is not something static. It is a continual forming structure. It is not made up of a line as we would draw on paper, rather an energy source ever expanding outward in single formed lines. Were there actual perceived curvature to a field as this, the curvature would not exist within the field, rather with the relationship the observed had to it.

Answer 3

if a dimension can from from the same place where evrything else came from


the curved dimension helps to explain what else comes from where the dimension comes from

Answer 4

The same way that a trampoline curves when a fat person sits in it. This is one way to visualise the effect of gravity.