Algebraic Geometry: a Tool for Resolving the Enigma of Time?

Abstract

Although time is a concept that attracted and occupied the thoughts of a countless number of thinkers and scholars over centuries, its true nature still remains wrapped in a shroud of mystery. Perhaps the main reason why this is so is that there are too many aspects this notion entails. Out of these, there are two that deserve particular attention for, in our opinion, they characterize best the nature of time’s enigma. The first is the notion of physical or objective time. Time, from the physicist’s viewpoint, is one of the dimensions of a differentiable, Riemannian manifold. It is a linear variable, structureless and undifferentiated. It is very much like a spatial dimension, the only difference between the two being embodied in the Lorentz signature of the metric tensor. The second is psychological or subjective time; time as we perceive it, experience it. This time dimension exhibits a non-trivial internal structure, consisting of the past (events that have happened) and the future (events that will happen), the two domains being separated from each other by a unique moment of the present, the event that is happening. This is the time that seems to “flow”, to proceed at a steady pace from the past into the future - the time with an arrow pointing in one direction.