There are three main arguments for duration to have three dimensions:
(1) The speed of light is a conversion factor between length space (distance) and duration (distime). Transportation conversion factors include the maximum, minimum, or typical speeds associated with different travel modes. Since length space is three dimensional, its conversion into duration space is also three-dimensional. The scale of maps may be in units either of length or of duration using a standard conversion speed.
(2) Observation follows the movement of light, which is three dimensional. In astronomy it is often said that observation of the sky is a way of looking into the past. Observation is a form of communication and any type of signal (sound, mail, etc.) will suffice though not as exact as light. As the observation of length space is three-dimensional, so the observation of duration space is also three-dimensional. Maps of duration space are similar to maps of length space: they show observations (signals) in different directions.
(3) Movement in orthogonal directions entails moving in three dimensions. Each dimension of movement has an average speed from the change in length divided by the change in duration . As movement is in three dimensions, so the duration aspect of movement is in three dimensions. Travel shows the same result. Maps of movement may show either stantial positions or temporal positions or both.
Each argument may be illustrated by a map. The conversion factor argument shows how any map may be scaled in units of length or duration. The observation argument shows that maps of observations have units or length or duration. The movement argument shows that maps of movement may show length space or duration space or both (as in a isochrone map).
Note that every argument has an analogue in ordinary travel and so is not unknown to nonspecialists. The arguments are however exact in the case of physics.