iSoul In the beginning is reality

# Time and space as scalars or vectors

We need to distinguish between scalar (1D) and vector (3D) versions of both time and space. Motion in scalar (1D) time and scalar (1D) space is measured by clocks and linear references, respectively, and apply throughout the associated vector space or vector time (in Newtonian mechanics).

Scalar time is what a clock measures, which is the duration order of events. Scalar space is what an odometer measures, which is the length order of places. Each place in vector space is associated with a series of scalar time points, and each event in vector time is associated with a series of length points.

Motion in vector (3D) time and vector (3D) space is measured as points on a curve (trajectory), which may be decomposed into components. The position vector to each point is its distimement or displacement, respectively.

The travel time (or flight time) of a body between two points of vector time, A and B, may be measured with a stopwatch accompanying the body starting simultaneously with A and ending simultaneously with B. The travel distance of a body between two points in vector space, C and D, is measured with a measuring wheel (odometer) accompanying the body starting at location C and ending at location D.

The speed of a body is the travel distance per unit of travel time. The pace of a body is the travel time per unit of travel distance. The velocity and legerity include the vector travel direction of the body with the ratios given.

Since the travel time or travel distance may not be available to an observer not on the body, the velocity and legerity may make use of the scalar time or space in the denominator, respectively.

For the velocity one can substitute the vector travel distance per unit of scalar time. The speed uses the magnitude of the vector travel distance per unit of scalar time.

For the legerity one can substitute the vector of travel time per unit of scalar space. The pace uses the magnitude of the vector travel time per unit of scalar space.