In perception when we see things moving in an approximation to an instantaneous space, the future lines of motion as immediately perceived are rects which are never traversed.

These approximate rects are composed of small events, namely approximate routes and event-particles, which are passed away before the moving objects reach them.

Assuming that our forecasts of rectilinear motion are correct, these rects occupy the straight lines in timeless space which are traversed.

Thus the rects are symbols in immediate sense-awareness of a future which can only be expressed in terms of timeless space.
We are now in a position to explore the fundamental character of perpendicularity.

Consider the two time-systems {alpha} and {beta}, each with its own timeless space and its own family of instantaneous moments with their instantaneous spaces.