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THE FOURTH DIMENSION SIMPLY EXPLAINED

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Figure 3

These objects may be moved in a straight line, but not out of it. In trying to make the pointsA'B'C'coincide withABC, he would find it impossible to do so by sliding along the line, but a

rotation about oin the second dimension would bring them together. By analogy he might thinkthat if he could turn his triangle over in the third dimension aboutAC, he could solve his

problem. But he has no conception of such a motion, though he might call his work with thetriangle made of flexible cord a revolution in the third dimension.

By a miracle one of these shadow beings becomes endowed with a knowledge of threedimensions. He does marvelous things in the eyes of his neighbors. He can disappear and

reappear at will. The strongest prison cannot hold him. If he moves out of the plane in which hehas lived he can look down into the houses, even into the insides of his neighbors. If, beforereturning to shadow land, he should turn himself over, he would be a sort of reflection of his

former self to his friends. His heart would be on the right side instead of the left. To his friendshe would be left-handed instead of right-handed.

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After amusing himself with his two-dimensional people, the student returned to his inquiry asto four dimensions. By analogy he supposed our space of three dimensions to lie in the midst of aspace of four dimensions, just as his shadow land lay in the midst of three-dimensional space. He

might speak of all people and objects as three-dimensional shadows of four-dimensional things.If now by supernatural means a person becomes endowed with four-dimensional knowledge, he

can perform the same kind of antics that his two-dimensional analogue did in shadow land. Noprison could hold him. He could take money from a sealed box without making an opening. Hecould disappear and reappear at will.

In three dimensions we have similar solids which cannot be made to occupy the same space;for example, the right and the left hand. By analogy with the schoolboy's triangle problem, the

student conceived of one of such a pair of objects being carried into the fourth dimension turnedover and brought back. The two objects can now be made to occupy the same place. Turning a

right-hand glove inside out to make it fit the left hand would have the same effect as turning itover in the fourth dimension.1

Since the inhabitants of shadow land have no sense of "up" or "down," they cannot perceive in

any way the plane upon which they move but which is present at every point. The imaginativestudent might then say that the ether which physicists claim to permeate our whole space is butthe three-dimensional analogue to the plane of shadow land. So he could go on indefinitely withhis analogies, but we must not forget that it is all the product of his imagination, and that there

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is no more probability of the existence of his four-dimensional beings than of his two-dimensional ones