the Moving Point argument

the Moving Point argument



Suppose the location x of a particle on the real line R is given as a function of a time variable t, so x = x(t). The particle is moving in time.
The position of the particle can be plotted on a space-time diagram and it'll make some curve. This curve is a subset of the 2-dimensional manifold coordinitized by R and (T = all t). As such, it is unchanging/timeless/static in the sense all mathematical objects are. Therefore one can imagine the particle moving along the curve. This situation can be modeled as a curve in the manifold (RcrossT)crossT. But then the particle can be imagined to move on this curve, and etc.
At no stage have we incorporated the full behavior of time (or things in time), since each stage doesn't take into account the behavior leading to the stage after it.