There are three different contexts for 3D time, depending on whether stance is continuously increasing and, if so, whether there is a conversion factor between space and time:

(A) Stance is not continuously increasing. This is the situation of a race or sport in which game time has a definite beginning and ending. For example, in many sports the game lasts a specific time. In a race, the length of the course is set and the time for each contestant ends when they cross the finish line. The average pace of a contestant is their race time divided by the course length.

(B) Stance is continuously increasing and there is a conversion factor between space and time. This is the situation of the theory of relativity and some transportation settings in which the minimum pace is the conversion pace (and maximum speed).

In this case, there is an increasing stance whether or not a positive time is measured. It is like a race that has no finish line. Without an increase in time the pace is at a minimum (or the speed is a maximum). As the amount of time measured increases, the pace increases (or the speed decreases). Remember that a small amount of time per unit stance interval is a fast motion, whereas a large amount of time per unit stance interval is a slow motion.

In this way, the pace increases indefinitely. A pace of infinity would be at rest. A pace of zero is the minimum pace, which in relativity is the speed of light. That is, the speed counts down from the speed of light. This has been misinterpreted as a transformation with superluminal speeds, but they are counting down, not up, and so are subluminal.

For the dual Lorentz transformation

The *cu* in *λ* is *u*/(1/c), which is the pace of the object divided by the pace of light. While *cu* is nominally equal to *c*/*v*, the denominator for pace is the stance, which is increasing at the conversion rate. As the time increases, the pace increases and the speed decreases from that of light toward zero. So, there is no square root of a negative number here.

(C) Stance is continuously increasing but there is no conversion factor between space and time. This is the situation of transportation in general. Space and time are not proportional, and the fastest route in space and time are in general different.