Dimensionality extends far beyond the familiar three spatial dimensions, forming the silent scaffold underpinning physical laws, statistical behavior, and computational intelligence. In molecular systems, the number of active degrees of freedom—energy modes—defines a system’s thermodynamic geometry, where entropy emerges as a measure of accessible dimensional volume in phase space. This geometric perspective reveals how temperature scales not merely as a heat intensity but as a dimensional scaling factor governing microstate accessibility. Similarly, in algorithm design, dimensionality dictates energy landscapes, data complexity, and learning stability, forming a bridge between physical intuition and machine learning dynamics. Read more