Just as we can coordinatize one of the dimensions of space by means of real numbers without being committed to the anisotropy of that spatial dimension, so also we can coordinatize a topologically open time-continuum without prejudice to whether there exist irreversible processes which render that continuum anisotropic. For so long as the states of the world (as defined by some one simultaneity criterion) are ordered by a relation of temporal betweenness having the same formal properties as the spatial betweenness on a Euclidean straight line, there will be two senses which are opposite to each other. And we can then assign increasing real number coordinates in one of these senses and decreasing ones in the other by convention without assuming that these two senses are further distinguished by the structural property that some kinds of sequences of states encountered along one of them are never encountered along the other.