Each point on a sphere is not considered a separate dimension; rather, a sphere is a two-dimensional surface within three-dimensional space. The discussion highlights the distinction between dimensions, noting that a plane is inherently two-dimensional. The concept of a "hyperplane" in linear algebra introduces objects of lower dimensions within higher-dimensional spaces. The original question also touches on the relevance of these concepts to Quantum Physics, although the connection remains unclear. Overall, the conversation clarifies the dimensional properties of geometric shapes without delving deeply into quantum implications.