iSoul In the beginning is reality

Linear, radial, and scalar space and time

In 3D space the distance between points is the magnitude of the displacement vector, which is a path length. In 3D time the duration between instants (time points) is the magnitude of the distimement vector, which is a path time.

Radial space is space with radial coordinates, 2D polar or 3D spherical, in which the distance from or to a point is the magnitude of the radial displacement. Radial time is time with radial coordinates, 2D polar or 3D spherical, in which the duration to an instant is the magnitude of the radial distimement. The radial space and time are “as the crow flies,” with the imaginary crow flying at a constant rate.

The distance between two points along a path (or curve) is the path length between them. The duration between two instants along a path in time is the path time between them. Each of these may be conceived of as one rectilinear dimension.

The result of a measuring wheel operated throughout a region or network is a (spatial) linear referencing system (LRS or SLRS), which produces a set of physical wayposts or conceptual waypoints. These are often used by highway departments with geographic information systems (GIS).

For more on linear referencing systems, see here and here.

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