# Length, duration and direction

A related post is here.

There are three measures of motion: length, duration, and direction in three dimensions. Direction in three dimensions requires two angles or three rectilinear coordinates. Length and duration are non-negative scalars. All measures are relative to an oriented observer.

From these base measures several others are derived:

Length divided by time is a rate called speed. Duration divided by distance is a rate called inverse speed or pace.

Length and direction form a vector called displacement in a vector space called length space. Duration and direction form a vector called dischronment in a vector space called duration space.

Length, duration and direction can be combined in two ways. Speed merged with displacement is velocity in a kinematics of space with duration. Inverse speed merged with dischronment is lenticity in a kinematics of time with distance. Direction is attached to length for velocity. Direction is attached to duration for lenticity.

The kinematics of space with duration is 3+1, three dimensions of length and time, which is one-dimensional. The kinematics of duration with distance is 1+3, distance, which is one-dimensional, and three dimensions of duration.

In order to represent both the kinematics of length space with time and the kinematics of duration space with distance, a structure of three dimensional length space and three dimensional duration space (3+3) is used. The study of causality requires ordered events, so either length is limited to one dimension called distance or duration is limited to one dimension called time.