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Let particle P be described by a chain of events written as

\Psi^{\mathsf{P}} = \left( \mathsf{P}_{1}, \, \mathsf{P}_{2}, \, \mathsf{P}_{3} \, \ldots  \, \mathsf{P}_{k} \, \ldots \, \right)

where each event is characterized by   d \! \bar{r} its displacement. Then the position of event  \mathsf{P}_{k} may be defined by

\displaystyle \bar{r}_{k}  \equiv      \bar{r}_{\mathsf{o}} + \sum_{j=1}^{k} d \! \bar{r}_{j}

where  \bar{r}_{\mathsf{o}} 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  \Psi can be expressed as an ordered set of position vectors

\Psi \! \left(\bar{r}\right)^{\mathsf{P}} = \left( \bar{r}_{1}, \, \bar{r}_{2}, \, \bar{r}_{3} \, \ldots \,  \bar{r}_{k} \, \ldots \, \right)

Consider an ordered pair of events from  \Psi noted by  \left( \mathsf{P}_{i}, \, \mathsf{P}_{f} \right). The separation vector between these two occurrences is defined by

\Delta \bar{r} \equiv     \bar{r}_{f} - \bar{r}_{i}

And the norm of the separation is defined as the distance between events

\Delta r \equiv  \left\| \Delta \bar{r} \, \right\|

Spatial Quantization

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.

Position is defined by sums of displacements, somewhat like the pilih technique seen in this Maylasian textile.
Bidang 129, Iban people. Upper Rajang river, Kapit Division of Sarawak, 20th century, 118 x 46 cm. Pilih technique. From the Teo Family collection, Kuching. Photograph by D Dunlop.