Let some particle P be characterized by a ordered  chain of events

that is repetitive so that may also be written as

where each orbital cycle is composed of sub-orbital events written as

The orbital radius of P is noted by and is its wavelength. A spatial orientation for P is specified by , and . We use these characteristics to define the following numbers for describing sub-orbital events

where is the phase angle of P. Then using the Cartesian unit vectors , and , a displacement vector for P is defined by

If we switch to implicitly using Cartesian basis vectors, we can express the displacement as an ordered set

EthnoPhysics uses a finite categorical scheme of binary distinctions to describe sensation. So the number of sub-orbital events may be large but not infinite. In principle is finite and accordingly displacements may be small, negligible or nil, but not infinitesimal. Later we may assume that is large enough to make an approximation to spatial continuity, then allowing the use of calculus.