Now, the use of words corresponds to the storing up of our experience in a definite brain structure. A child, in the endless tactual, visual, mental manipulations it makes for itself, is best left to itself, but in the course of instruction the introduction of space names would make the teachers work more cumulative, and the child’s knowledge more social. Their full use can only be appreciated, if they are introduced early in the course of education; but in a minor degree any one can convince himself of their utility, especially in our immediate subject of handling four-dimensional shapes. The sum total of the results obtained in the preceding pages can be compendiously and accurately expressed in nine words of the Space Language. In one of Plato’s dialogues Socrates makes an experiment on a slave boy standing by. He makes certain perceptions of space awake in the mind of Meno’s slave by directing his close attention on some simple facts of geometry. By means of a few words and some simple forms we can repeat Plato’s experiment on new ground. Do we by directing our close attention on the facts of four dimensions awaken a latent faculty in ourselves? The old experiment of Plato’s, it seems to me, has come down to us as novel as on the day he incepted it, and its significance not better understood through all the discussion of which it has been the subject. Imagine a voiceless people living in a region where everything had a velvety surface, and who were thus deprived of all opportunity of experiencing what sound is. They could observe the slow pulsations of the air caused by their movements, and arguing from analogy, they would no doubt infer that more rapid vibrations were possible. From the theoretical side they could determine all about these more rapid vibrations. They merely differ, they would say, from slower ones, by the number that occur in a given time; there is a merely formal difference. But suppose they were to take the trouble, go to the pains of producing these more rapid vibrations, then a totally new sensation would fall on their rudimentary ears. Probably at first they would only be dimly conscious of Sound, but even from the first they would become aware that a merely formal difference, a mere difference in point of number in this particular respect, made a great difference practically, as related to them. And to us the difference between three and four dimensions is merely formal, numerical. We can tell formally all about four dimensions, calculate the relations that would exist. But that the difference is merely formal does not prove that it is a futile and empty task, to present to ourselves as closely as we can the phenomena of four dimensions. In our formal knowledge of it, the whole question of its actual relation to us, as we are, is left in abeyance.