In the context of physics and mathematics, spacial dimensions are typically considered as positive integers because it aligns with our observations and mathematical models of the universe. The three spatial dimensions we commonly experience in our everyday lives are referred to as length, width, and height, and they are described using the positive integers 1, 2, and 3, respectively.
The choice of positive integers for spatial dimensions is rooted in the mathematical framework that underlies our understanding of physics. For example, in classical mechanics, the three-dimensional Euclidean space provides a suitable framework to describe the motion of objects. Similarly, in theories like general relativity, which describes the gravitational interactions on a larger scale, the universe is modeled with four dimensions, including three spatial dimensions and one time dimension.
While it's theoretically possible to consider other mathematical frameworks or geometries with fractional or non-integer dimensions, such as fractal geometries, these are typically abstract concepts used in specific contexts rather than describing the physical dimensions of our universe.
Regarding your question about the possibility of dimensions being bent or fractionated by gravity, it's important to note that the current understanding of gravity, as described by general relativity, does not imply the loss or bending of entire dimensions. General relativity describes gravity as the curvature of spacetime caused by massive objects. However, these curvatures still exist within the four-dimensional spacetime framework, and the dimensions themselves are not fundamentally lost or altered.
Speculations about additional dimensions beyond the three spatial dimensions we experience are explored in theoretical physics, particularly in areas like string theory and brane cosmology. These theories propose the existence of extra dimensions, which may be compactified or hidden from our everyday observations. However, these additional dimensions, if they exist, are still considered as part of the mathematical framework of the theory rather than being fractional or bent versions of the familiar three dimensions.