you than any other of the systems which the brain of the mathematician has invented. But we must remember that its subject matter involves the behaviour of material scales—the properties of matter. Its laws are just as much laws of physics as, for example, the laws of electromagnetism.
Phys. Do you mean to compare space to a kind of magnetic field? I scarcely understand.
Rel. You say that you cannot explore the world without some kind of apparatus. If you explore with a scale, you find out the natural geometry; if you explore with a magnetic needle, you find out the magnetic field. What we may call the field of extension, or space-field, is just as much a physical quality as the magnetic field. You can think of them both existing together in the aether, if you like. The laws of both must be determined by experiment. Of course, certain approximate laws of the space-field (Euclidean geometry) have been familiar to us from childhood; but we must get rid of the idea that there is anything inevitable about these laws, and that it would be impossible to find in other parts of the universe space-fields where these laws do not apply. As to how far space really resembles a magnetic field, I do not wish to dogmatise; my point is that they present themselves to experimental investigation in very much the same way.
Let us proceed to examine the laws of natural geometry. I have a tape-measure, and here is the triangle. in., in., in. Why, your proposition does not hold!
Phys. You know very well what is wrong. You gave the tape-measure a big stretch when you measured .
Rel. Why shouldn't I?
Phys. Of course, a length must be measured with a rigid scale.
Rel. That is an important addition to our definition of length. But what is a rigid scale?
Phys. A scale which always keeps the same length.
Rel. But we have just defined length as the quantity arrived at by measures with a rigid scale; so you will want another rigid scale to test whether the first one changes length; and a third to test the second; and so ad infinitum. You remind me of the incident of the clock and time-gun in Egypt. The man in charge
