[AntonioLao]

Georg Friedrich Bernhard Riemann (1826-66), within the short lifespan of 40 years, had achieved what 400 years of mathematicians cannot. Starting from his doctoral thesis at age 25, which is the foundation of complex analysis, he had written numerous foundational papers including what is to be the beginning of spacetime mathematics. The title of this particular paper is ‘On the Hypotheses which lie at the Bases of Geometry’. http://www.emis.de/classics/Riemann/WKCGeom.pdf He would have been the first to formulate the principle of general relativity but unfortunately his life was cut short by tuberculosis.

Roughly ten years after his death, the English mathematician William Kingdon Clifford, one of the few who realized the significance of Riemann’s opus, responded to the task of translating his papers into English. The rest of this story is history.

Although Riemann’s paper only talked about n-ply extended magnitude of space and manifold, his n-ply extended magnitude can easily and logically be applied to time. This is possible if and only if it is agreed that time, like space, can also be multidimensional. Furthermore that the multiple dimensions of time can only be found at the infinitesimal region of space, and this tiny region of space and time can truly be called a region of spacetime. The quantization of spacetime is a necessary outcome when both time and space are attributed with directional properties given by definitions of their respective unit vectors (and to satisfy the continuum hypothesis, these unit vectors become the null vectors when viewed globally). These spacetime quanta could never have been more lucidly described than by reading Max Jammer’s book ‘Concepts of Space: The History of Theories of Space in Physics’, 3rd and enlarged edition, pages 162-63, Dover, 1993.