I offer for consideration a very interesting dialogue from the opening of H.G. Wells’ The Time Machine (Pocket Books, 2004, page 5). The protagonist begins:
“You know of course that a mathematical line, a line of thickness nil, has no real existence. They taught you that? Neither has a mathematical plane. These things are mere abstractions.”
“That’s all right,” said the Psychologist.
“Nor having only length, breadth, and thickness, can a cube have a real existence.”
“There I object,” said Filby. “Of course a solid body may exist. All real things —”
“So most people think. But wait a moment. Can an instantaneous cube exist?”
“Don’t follow,” said Filby.
Can a cube that does not last for any time at all, have a real existence?”
Filby became pensive.
“Clearly,” the Time Traveller proceeded, “any real body must have extension in four directions, it must have Length, Breadth, Thickness, and —Duration.”
The dialogue points to what is, in my experience, a much overlooked idea: that there is an interesting constraint applied to time by the first three spatial dimensions. When we look around, we don’t see triangles, we see things that look like triangles. This is the sort of thinking that led Plato to the idea of universal forms and the allegory of the Cave. The dialogue points out an interesting question: Supposing that one can obtain, say, a platonic solid, what if it exists only for an instant —that is, no duration at all? I don’t see this question come up often in the more academic forums; maybe it does and I am just missing it. Continue reading