# Distance, duration and direction

A related post is here.

There are three measures of motion: distance, duration, and direction in three dimensions. Direction in three dimensions requires two angles. Distance and duration are non-negative scalars. All measures are relative to an observer.

From these base measures several others are derived:

Distance divided by duration is a rate called speed. Duration divided by distance is a rate called inverse speed or pace.

Distance and direction form a vector called displacement in a vector space called (confusingly) space. Duration and direction form a vector called dischronment in a vector space called time (which can also mean duration).

Distance, 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 distance for velocity. Direction is attached to duration for lenticity.

The kinematics of space with duration is 3+1, three dimensions of space and one dimension of time. The kinematics of time with distance is 1+3, one dimension of space and three dimensions of time.

In order to represent both the kinematics of space with duration and the kinematics of time with distance, a structure of three dimensional space and three dimensional time (3+3) is used. Because direction appears twice in this structure, 3+3 is an intermediate structure, which must be resolved into 3+1 or 1+3 before being applied.