Which kind of distortion is NOT associated with cartesian (projected) coordinate systems?

In the context of Cartesian (projected) coordinate systems, the kind of distortion that is not associated with them is time. Cartesian coordinate systems, used in mapping and spatial analysis, are primarily concerned with accurately representing spatial relationships on a two-dimensional plane. These systems transform the Earth's three-dimensional surface onto a flat plane, which can lead to various types of distortions in area, shape, and direction depending on the type of projection used.

Area distortion refers to the incorrect representation of the relative size of features. For example, some map projections can make landmasses appear larger or smaller than they actually are.

Shape distortion occurs when the shape of geographical features is distorted. This is common in projections where one type of distortion is minimized at the expense of others, such as in conformal projections that maintain shape but not area.

Direction distortion involves the inaccuracies in angle and direction between features on the map. Some projections preserve direction locally but may misrepresent it globally.

In contrast, time does not fall under the category of distortions typically discussed with Cartesian coordinate systems. Time is a temporal dimension and is not directly involved in the spatial representation that these coordinate systems provide. Thus, the focus is on spatial accuracy rather than any consideration or representation of time-related metrics.