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

where each event is characterized by its displacement vector where

Then the **abscissa** of event is defined by

where is arbitrary and often set to zero. The **ordinate** is defined as

And the -cooordinate or **applicate** of event is

Recall that the -component of the displacement is just a simple linear function of the wavelength. So if P is isolated then it moves in regular steps along the polar-axis, and can be described by

The three numbers , and are called the **Cartesian coordinates** of event after the work of RenΓ© Descartes . More exactly, they are the *rectangular* Cartesian coordinates in a descriptive system that is centered on P. We use them to express the position of an event as

EthnoPhysics uses a finite categorical scheme of binary distinctions to describe sensation. So , the total number of quarks in a description, may be large but not infinite. In principle is finite and accordingly displacements may be small, negligible or nil, but not infinitesimal. Later we assume that is large enough to make an approximation to spatial continuity. Then the use of calculus may be appropriate.