iSoul In the beginning is reality.

# Basic definitions

Independent variable is a quantity that is not dependent on another quantity, which is either (a) a quantity chosen before an experiment or race, or (b) an ever-increasing quantity. Dependent variable is a quantity that whose value is a function of another variable.

Length is measured by a rigid rod. 3D length space is length measured in three directions of motion.

Duration is measured by a stopwatch, timer, or clock. 3D duration is duration measured in three directions of motion.

Length space is (1) 3D differentiable manifold of length; (2) the order of events on a stanceline; (3) the stance, the reading on an metreloge.

Duration space is (1) a 3D differentiable manifold of duration; (2) the order of events on a time line; (3) the time, the reading on a clock.

Length-duration is the 6D manifold formed from 3D length space and 3D duration space. Worldline is the path in length-duration traced out by an object in motion.

Displacement is the vector between two points (events) on a worldline. Distance is the magnitude of a displacement.

Dischronment is the vector between two points (events) on a worldline. Distime is the magnitude of a dischronment.

Reference frame (or frame) is an abstract coordinate system and set of reference points in 3D length space that uniquely fix the coordinate system and standardize measurements. Rest frame of a body is the reference frame in which the body is moving at zero speed, which is the time conversion pace.

Reference timeframe (or timeframe) is an abstract coordinate system and set of reference points in 3D duration space that uniquely fix the coordinate system and standardize measurements. Freeflow frame of a body is the reference timeframe in which the body is moving at zero pace, which is the stance conversion speed.

Proper length is the length of a body measured by a rigid rod moving with it. Proper time is the time of a body measured by a clock moving with it.

Lorentz transformation is a set of equations that relate length space and duration space coordinates of reference frames moving at a constant velocity relative to each other.

Dual Lorentz transformation is a set of equations that relate length space and duration space coordinates of reference timeframes moving at a constant legerity relative to each other.