where each event is characterized by its displacement. Then the position of event may be defined by
where is arbitrary. Please notice that this algebraic vector has been defined entirely through a systematic description of sensation. So our ideas about position are based on an empirical approach that is scientific and consistent with the premise of EthnoPhysics. If all events are assigned a position, then can be expressed as an ordered set of position vectors
Consider an ordered pair of events from noted by . The separation vector between these two occurrences is defined by
And the norm of the separation is defined as the distance between events
The foregoing definitions imply that position, separation and distance are all quantized. Their variation is discontinuous because EthnoPhysics is based on a finite categorical scheme of binary distinctions. Quantization comes from the logical structure of the descriptive method, even for a continuous sensorium. In principle, motion is always some sort of quantum leaping or jumping from event to event. Phenomena like this have certainly been observed in twentieth-century physics and can, for example, be used to understand Zener diodes and the Stern–Gerlach experiment. For EthnoPhysics, smoothly continuous motion is therefore presumed to be a macroscopic approximation. We are cautious about using calculus because the logical foundations of both differential and integral calculus are proven using assumptions about continuity. So EthnoPhysics does not require calculus. Instead calculations are designed to be implemented on digital computers, in a finite number of discrete steps.