clear by an illustration first suggested by Helmholtz, of which the following is in the nature of a paraphrase:
If you look at your own image in the shining surface of a teapot or the back of a silver spoon, all things therein appear grotesquely distorted, and all distances strangely exaggerated. But if you choose to make the bizarre supposition that this spoon-world is real, and your image—the spoon-man—a thinking and speaking being, certain interesting facts can be developed by a discussion between you and him.
You say, "Your world is a distorted reproduction 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 yielding 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, or him in the wrong. Indeed, he is likely to retort upon you that it is your room that 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 only with space relations, for such are easily grasped, but certain distortions in time relations are no less 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.
Another question—and perhaps the most important—raised by the Theory of Relativity is in regard to what may be called the spatiality of time. In other words, is time the fourth dimension of space?
This idea, startling as it may appear, stands the pragmatic test, that is to say, it "works." Mathematical physicists have found that experimental contradictions disappear, and the mathematical framework of physics is greatly simplified, if, instead of referring phenomena to a set of three space axes (corresponding to the three
