breadth and thickness. But space without time is as incomplete as a surface without thickness.
Math. Do you argue that the real world behind the phenomena is four-dimensional?
Rel. I think that in the real world there must be a set of entities related to one another in a four-dimensional order, and that these are the basis of the perceptual world so far as it is yet explored by physics. But it is possible to pick out a four-dimensional set of entities from a basal world of five dimensions, or even of three dimensions. The straight lines in three-dimensional space form a four-dimensional set of entities, i.e. they have a fourfold order. So one cannot predict the ultimate number of dimensions in the world—if indeed the expression dimensions is applicable.
Phys. What would a philosopher think of these conceptions? Or is he solely concerned with a metaphysical space and time which is not within reach of measurement.
Rel. In so far as he is a psychologist our results must concern him. Perception is a kind of crude physical measurement; and perceptual space and time is the same as the measured space and time, which is the subject-matter of natural geometry. In other respects he may not be so immediately concerned. Physicists and philosophers have long agreed that motion through absolute space can have no meaning; but in physics the question is whether motion through aether has any meaning. I consider that it has no meaning; but that answer, though it brings philosophy and physics into closer relation, has no bearing on the philosophic question of absolute motion. I think, however, we are entitled to expect a benevolent interest from philosophers, in that we are giving to their ideas a perhaps unexpected practical application.
Let me now try to sum up my conclusions from this conversation. We have been trying to give a precise meaning to the term space, so that we may be able to determine exactly the properties of the space we live in. There is no means of determining the properties of our space by a priori reasoning, because there are many possible kinds of space to choose from, no one of which can be considered more likely than any other. For
