# Moving bodies with space and time

Let us compare the motions of two bodies. Let the motion of one body be the reference motion. Let the motion of the other body be the target motion. Let the two bodies begin together at one place.

Definitions:

A place is the general term for an answer to Where? A point-place, or simply a point, is the smallest place. A translation is a vector from one point-place to another. Travel distance is the arc length of the trajectory of a motion, which includes any retracing of the trajectory.

Space and time refer to different perspectives of the universe of motion.

Space is the locus of all potential places for the observer’s rest motion. Displacement is a translation vector from one point to another point. The travel distance from the beginning point to the ending point, is the travel length for a motion.

Time is the locus of all potential places for the reference motion. Dischronment is a translation vector from one point to another point of the reference motion. The travel distime from the beginning instant to the ending instant of the reference motion, is the travel time for a motion.

There are two ways of proceeding:

(1) As the reference motion ends (physically or by marking), then stop or mark the end of the target motion. Measure each travel distance from beginning to end. This is the travel time.

(2) Or as the target motion ends (physically or by marking), then stop or mark the end of the reference motion. Measure each travel distance from beginning to end. This is the travel length.

Note: The reference motion could be a clock, in which case the travel distance would be the extent of angular motion.

In a ratio the independent variable is in the denominator and the dependent variable is in the numerator. That means there are two ways of forming a ratio of the target motion and the reference motion:

(A) The independent variable is the travel time of the reference motion. The dependent variable is the travel length or the displacement of the corresponding target motion. The mean speed is the travel time of the reference motion divided into the travel length of the corresponding target motion. The mean velocity is the travel time of the reference motion divided into the displacement of the corresponding target motion.

(B) The independent variable is the travel length of the target motion. The dependent variable is the travel time or the dischronment of the corresponding reference motion. The mean pace is the travel length of the target motion divided into the travel time of the corresponding reference motion. The mean lenticity is the travel length of the target motion divided into the dischronment of the corresponding reference motion.

An example of (A) is setting the course of the reference motion to go a certain time, as in a time period, then measuring the travel length of the target motion. An example of (B) is setting the course of the target motion to go a certain length, as in a race, then measuring the travel time of the reference motion.

Space and time are completely exchangeable because they are the same concept (i.e., distances or vectors) except that one arises from the target motion (space) and the other arises from the reference motion (time).