Three Dimensions Of Space And Two Of Time

Perpignan Square, Lancaster 

North side: the back of the Town Hall

East side: the front of the Magistrates' Court

South side: a terrace of offices

West side: one side of the Police Station

(Over the years, I have had business on all four sides of this square but for now let's just conduct a simple thought experiment.)

Thought Experiment

At 1:00 PM, I stand at the back of the Town Hall, facing south. I then walk south across the square until I am standing in front of an office in that terrace. The walk takes one minute so that I arrive at 1:01 PM. We can say that a spatial relationship, i.e., my position, has changed over the course of one minute. One part of the contents of a volume of three-dimensional space has changed over a short period of time. Another way to describe this is to divide that minute into a number of three-dimensional cross-sections. In the first cross-section, at 1:00 PM, I am outside the Town Hall. In the last cross-section, at 1:01 PM, I am outside an office. In every intermediate cross-section, I am at a different point on the square. That is how we describe motion in four dimensions.

Now let us add a second temporal dimension and let us consider just two four-dimensional cross-sections of this fifth dimension. In the first cross-section, I walk across the square as just described. In the second cross-section, I reach the midpoint of the square after thirty seconds, at 1:00:30 PM, as I had in the first cross-section, but, at that moment, a time criminal on a stolen Time Patrol timecycle appears in front of me, shoots me dead and immediately departs. The second cross-section differs from the first. To an observer in the first cross-section, someone looking out of the Police Station, I walk across the square without interruption. To the different version of that same observer in the second cross-section, I only reach the half-way point.

From his own perspective, the observer in the first cross-section - let's call him O1 - does not cease to exist. He can continue to observe me for the full minute. O2, in the second cross-section, might conceptualize the situation by saying either that O1 has never existed or that O1 has ceased to exist.

We need Temporal tenses instead of English tenses. O1 has never existed in the second four-dimensional cross-section but can be said to have ceased to exist in the second temporal dimension and, finally, continues to exist in his own cross-section. Using English tenses to describe all of this is what confuses us.