Movement in its simplest form is a trip from A to B. There are two ways one can look at such a movement: (1) as the line segment from A to B, or (2) as the angle between the lines from A to a reference point and A to B. Each of these may be spatial or temporal. Let’s look at these in more detail.

Linear measures:

(1a) Spatially, a *line segment* from A to B is measured with a co-extensive unit of length by a calibrated rod. This linear distance is the basis of space, which has a Euclidean metric, in which the locus of points equidistant from a point forms a sphere.

(1b) Temporally, a *cycle period* from A to B is measured with a co-extensive unit of time by a stop watch. This cyclic duration is the basis of time, which has a Euclidean metric, in which the locus of point events equal in time from a point event forms a cycle (or *sphycle* since it is 3D).

Angular measures:

(2a) Spatially, the *angle* between the lines from A to a reference point and A to B is measured with a co-extensive unit of angle by two lines and a protractor or two line segments and trigonometry.

(2b) Temporally, the *turning angle* between the directions from A to a reference point and A to B is measured with a co-extensive unit of angular speed by a clock and a stop watch. The clock provides the unit of angular speed and the stop watch provides the unit of measure, though they may be combined into one device. The temporal angle might be called a *tangle*.

There are two kinds of length and two kinds of angle: spatial and temporal. Both the spatial and the temporal measures have three dimensions because they have three degrees of freedom. Temporal geometry is comparable to spatial geometry but all measures are temporal: linear and angular durations of movement.

Space-time is formed from a union of these measures and has a hyperbolic metric. The locus of space-time points equal in space-time from a space-time point forms a space-time hyperbola.