What is single-value time?

Time is commonly expressed by a single value, a numerical expression of a point in time. A sequence of these points is also called time. Because of this, time is commonly considered one-dimensional.

Since time actually has three dimensions, what does this single value for time represent? It must be some function of the three-dimensional time. It could be, for example, their sum, their average, the magnitude of their resultant vector, or something else.

The answer is that a single value for time represents the (temporal) length of the path taken in time. If someone travels for 30 minutes east and 40 minutes north, the total duration is 70 minutes. That is what time it is relative to the starting point in time.

One could also say that effectively they’ve gone 50 minutes in the arctan(40/30) direction (about 53 degrees from the east). That is true but it is not what people mean by the time. How long it took to get to a point in time is all that a single value of time represents.

Once again space could be treated the same way. If someone travels for 30 kilometres east and 40 kilometres north, the total trip length is 70 kilometres. We could call that the “what space it is” relative to the starting point in space. But space is usually treated geometrically so the resultant distance and direction from the origin are often more significant than the path taken to get there.

To distinguish the two ways of looking at time (or space), let us call the single value perspective as the parametric and the three-dimensional perspective as the geometric. So time commonly refers to the parametric time and space commonly refers to geometric space.