Euclidean geometry can be easily visualized; this is the argument adduced for the unique position of Euclidean geometry in mathematics. It has been a… - Hans Reichenbach

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.

Common to the two geometries is only the general property of one-to-one correspondence, and the rule that this correspondence determines straight lines as shortest lines as well as their relations of intersection.

...the famous assertion by Einstein that the length of a rod depends on its velocity and on the chosen definition of simultaneity. ...is based on the fact that we do not measure the length of the rod, but its projection on a system at rest. How the length of the projection depends on the choice of simultaneity can be illustrated by reference to a photograph taken through a focal-plane shutter. Such a shutter... consists of a wide band with a horizontal slit, which slides down vertically. Different bands are photographed successively on the film. Moving objects are therefore strangely distorted; the wheels of a rapidly moving car for instance, appear to be slanted. The shape of the objects in the picture will evidently depend on the speed of the shutter. Similarly, the length of the moving segment depends on the definition of simultaneity. One definition of simultaneity differs from another because events that are simultaneous for one definition occur successively for another. What may be a simultaneity projection of a moving segment for one definition is a "focal-plane shutter photograph" for another.