Note: as the research develops this post will be updated.

Introduction

Experience shows motion takes place in three dimensions. There are two measures of the extent of motion: *length* and *duration*. The length of motion in three dimensions comprises three-dimensional *space*. The duration of motion in three dimensions comprises three-dimensional *time*. Length and duration are symmetric concepts, as will be shown below.

Introduction

An independent variable is specified prior to measuring any dependent variable, so an independent variable is the domain of a functionally-related dependent variable. The independent variable is commonly an interval of time. Distance is the independent variable of an inverse square law. In Hooke’s law the independent variable is mass.

A date-time or time-stamp is a combined time-of-day and date on the calendar, which is of interest in history and astronomy. A time interval or elapsed time is the difference between two date-times, which is of interest in science.

A linear reference is of interest in geography and transportation. The stance interval or distance is the difference between two linear references, which is of interest in science.

Distance is an equivalence relation between pairs of points in space. Distime is an equivalence relation between pairs of instants in time.

An elapsed time or *distime* is the date-time that changes during an event or motion. A travel stance or distance is the change in linear reference during an event or motion.

Variables of time periods and distances are fixed. Variables of elapsed values are increasing from a starting point. Intervals are deltas of elapsed values. E.g., time periods are deltas of time. Distances are deltas of *stances*, that is, stations or points along a line or curve. Elapsed time and elapsed distance, or *stance*, are increasing variables.

Given that there are three dimensions of motion, and that every motion is measured by its length and duration, then motion requires three dimensions of length and three dimensions of duration. Three dimensions of length are called three-dimensional *space*. Three dimensions of duration are called three-dimensional *time*.

For example, motion on a two-dimensional surface can be presented as a two-dimensional map scaled in units of length or as a two-dimensional map scaled in units of duration. [The latter *time maps* are …]

Read more →