...the differential element of non-Euclidean spaces is Euclidean. This fact, however, is analogous to the relations between a straight line and a cur… - Hans Reichenbach

Some philosophers have believed that a philosophical clarification of space also provided a solution of the problem of time. Kant presented space and time as analogous forms of visualization and treated them in a common chapter in his major epistemological work. Time therefore seems to be much less problematic since it has none of the difficulties resulting from multidimensionality. Time does not have the problem of mirror-image congruence, i.e., the problem of equal and similarly shaped figures that cannot be superimposed, a problem that has played some role in Kant's philosophy. Furthermore, time has no problem analogous to non-Euclidean geometry. In a one-dimensional schema it is impossible to distinguish between straightness and curvature. ...A line may have external curvature but never an internal one, since this possibility exists only for a two-dimensional or higher continuum. Thus time lacks, because of its one-dimensionality, all those problems which have led to philosophical analysis of the problems of space.

...the relation of betweenness on the torus is undetermined for curves that cannot be contracted to a point [e.g., circles around a doughnut hole], i.e., for three of such curves it is not uniquely determined which of them lies between the other two. ..This indeterminateness... has the consequence that such a curve [alone] does not divide the surface of the torus into two separate domains; between points to the "right" and to the "left" of the line.

We are frequently faced with the necessity of looking for the picture required for the visualization of an object, not in the perception of this particular object, but in a different perceptual image. ...we can assert the discrepancy between the perceived picture and the objective state. This discrepancy... proves absolutely nothing against the fact that all visualizations are merely sense qualities of the perceptual space. ...If the parallelism is ...to be visualized, we must supplement our assertion by the description of certain qualities with which we are familiar from perceptual space.