You say, "Your world is a distorted transcript of the one in which I live."
"Prove it to me," says the spoon-man.
With a foot-rule you proceed to make measurements to show the rectangularity of the room in which you are standing. Simultaneously he makes measurements giving the same numerical results; for his foot-rule shrinks and curves in the exact proportion to give the true number of feet when he measures his shrunken and distorted rear wall. No measurement you can apply will prove you in the right, nor him in the wrong. Indeed he is likely to retort upon you that it is your room which is distorted, for he can show that in spite of all its nightmare aspects his world is governed by the same orderly geometry that governs yours.
The above illustration deals purely with space relations, for such relations are easily grasped; but certain distortions in time relations are no less absolutely imperceptible and unprovable. So far from having any advantage over the spoon-man, our plight is his. The Principle of Relativity discovers us in the predicament of the Mikado's "prisoner pent," condemned to play with crooked cues and elliptical billiard balls, and of the opium victim, for whom "space swells" and time moves sometimes swift and sometimes slow.
THE ORBITAL MOVEMENT OF TIME
Now if our space is curved in higher space, since such curvature is at present undetectable by us, we must assume, as Hinton chose to assume, that it curves in the minute, or, as some astronomers assume, that its curve is vast. These assumptions are not mutually exclusive: they are quite in analogy with the general curvature of the earth's surface which is in no wise interfered with by the lesser curvatures represented by mountains and valleys. It is easiest to think of our space as completely curved in higher space in analogy with the surface of a sphere.