The concept of spatial dimensions is related to the number of independent directions in which an object or system can move. In our everyday experience, we perceive and navigate the world in three spatial dimensions: length, width, and height. These dimensions are commonly referred to as three-dimensional space.
While the number of points on the surface of a sphere is indeed infinite, it does not necessarily imply that there must be an infinite number of spatial dimensions. The infinite number of points on the surface of a sphere simply reflects the continuous nature of the sphere's geometry.
The idea of additional spatial dimensions beyond the three we perceive is a topic that arises in certain areas of theoretical physics, such as string theory and some cosmological models. These theories propose that there could be extra dimensions "curled up" or compactified at extremely small scales, beyond our current ability to directly observe or experience them.
However, in our macroscopic everyday experience, the three dimensions of space are sufficient to describe the vast majority of physical phenomena. Our perception is limited to three dimensions, and the laws of physics as we currently understand them are formulated in terms of three dimensions. So, while mathematical constructs and theoretical frameworks may entertain the possibility of additional dimensions, our practical experience and scientific observations indicate that three dimensions are the primary ones relevant to our existence.