Chapter VI (part 7)

He would lack "necessary words." For instance, "section"—this would be for him a quite new and inconceivable word; then "angle"—again an inconceivable word; "centre"—still more inconceivable; the third perpendicular—something incomprehensible, lying outside of his geometry. The fallacy of his conception of time would be the most difficult thing for the plane being to understand. He could never understand that that which has passed and that which is to be are existing simultaneously on the lines perpendicular to his plane. And he could never conceive the idea that the past is identical with the future, because phenomena come from both sides and go in both directions. p. 69 But the most difficult thing for the plane being would be to conceive the idea that "time" includes in itself two ideas : the idea of space, and the idea of motion upon this space. We have shown that what the two-dimensional being living on the plane calls motion has for us a quite different aspect. In his book The Fourth Dimension , under the heading "The First Chapter in the History of Four-space," Hinton writes: Parmenides, and the Asiatic thinkers with whom he is in close affinity, propound a theory of existence which is in close accord with a conception of a possible relation between a higher and lower dimensional space. . . . It is one which in all ages has had a strong attraction for pure intellect, and is the natural mode of thought for those who refrain from projecting their own volition into nature under the guise of causality. According to Parmenides of the school of Elea the all is one, unmoving and unchanging. The permanent amid the transient—that foothold for thought, that solid ground for feeling, on the discovery of which depends all our life—is no phantom; it is the image amidst deception of true being, the eternal, the unmoved, the one. Thus says Parmenides. But how is it possible to explain the shifting scene, these mutations of things? "Illusion," answers Parmenides. Distinguishing between truth and error, he tells of the true doctrine of the one—the false opinion of a changing world. He is no less memorable for the manner of his advocacy than for the cause he advocates. Can the mind conceive a more delightful intellectual picture than that of Parmenides pointing to the one, the true, the unchanging, and yet on the other hand ready to discuss all manner of false opinion! . . . In support of the true opinion he proceeded by the negative way of showing the self-contradictions in the ideas of change and motion. . . . To express his doctrine in the ponderous modern way we must make the statement that motion is phenomenal, not real. Let us represent his doctrine. Imagine a sheet of still water into which a slanting stick is being lowered with a motion vertically downward. Let 1, 2, 3 ( Fig. 1 ) be three consecutive positions of the stick. A, B, C will be three connective positions of the meeting of the stick with the surface of the water. As the stick passes down, the meeting will move from A on to B and C. Suppose now all the water to be removed except a film. At the meeting of the film and the stick there will be an interruption of the film. If we suppose the film to have a property, like that of a soap bubble, of closing up round any penetrating object, then as the stick goes vertically down-ward the interruption in the film will move on. If we pass a spiral through the film the intersection will give a point moving in a circle (shown by the dotted lines in Fig. 2 ). p. 70 For the plane being such a point, moving in a circle in its plane, would probably constitute a cosmical phenomenon, something like the motion of a planet in its orbit.