Space is measured from a specified point, which is called an origin or zero point in space. The spatial location of all other points in space are relative to this zero point. The zero point may represent “here” from which other locations near and far are measured. Or the zero point may be a beginning point from which there are trajectories toward ending points or destinations. If the same zero point is used by many people, it may be said to be the origin for a region or a chorography (a description or map of a region).
Time is measured from a specified event point (or point event), which is called an origin or a zero point in time. The temporal location of all other points in time are relative to this zero point. The zero point may be a now-point or present from which other times past and future are measured. Or the zero point may be a beginning point from which there is a trajectory toward an ending point or destination. If the same zero point is used by many people, it may be said to be the origin for an era or a chronography (a description or record of past time, a history).
isoline – a curve or polygon representing equal measures on a map or graphic.
isodistance – an isoline representing equal travel distance from a given spatial point.
isochron(e) – an isoline representing equal travel time from a given temporal point.
The Euclidean distance from the zero point of a point in space, symbolized by r, is the magnitude of the spatial location vector of the point. It is called the distance of the point from the zero point in space. This distance is the same for all points on its associated isodistance (or isomacron) curve.
The Euclidean distance from the zero point of a point in time, symbolized by t, is the magnitude of the temporal location vector of the point. It is called the duration of the point from the zero point in time. It is also called time, which may be confusing. This duration is the same for all points on its associated isochron curve.
The displacement is the vector representing a change in spatial location from one point to another. The relative distance of one point in space to another point is the magnitude of the displacement vector between them. The average spatial direction of a motion is the direction of its displacement.
The dischronment is the vector representing a change in temporal location from one point to another. The relative duration of one point in time to another point is the magnitude of the dischronment vector between them. The average temporal direction of motion is the direction of its dischronment.
With space-time the full 3D space is used plus 1D time from the travel time. Velocity is the displacement vector divided by the travel time.
with time-space the full 3D time is used plus 1D space from the travel length. 1D space is a stance line. Lenticity is the dischronment vector divided by the travel length.
A modal signal, if it exists, is the rate of a signal or reference motion that travels with maximum mobility through the mode. If a modal signal exists, then the space and time coordinates of a space-time (or time-space) vector may be converted into each other. This conversion is a formal relationship rather than a material one. It represents the motion of the modal signal for the same distance or duration.