"I find," said the prince with deliberation, "that in America you are familiar with the argument that, if your people understood only length and breadth and did not understand the Third Dimension--thickness--you could not then conceive of lifting, say, a square or a triangle and laying it down upon another square or triangle. In other words, you would not know anything of up and down."
St. George nodded. This was the familiar talk of college class-rooms.
"As it is," pursued the prince, "your people do perfectly understand lifting a square and placing it upon a square, or a triangle upon a triangle. But you do not know anything about placing a cube upon a cube, or a pyramid upon a pyramid so that both occupy the same space at the same time. We of Yaque have mastered that principle also," the prince tranquilly concluded, "and all that of which this is the alphabet. That is why we are able to keep our island unknown to the world--not to say 'invisible.'"
For a moment St. George looked at him speechlessly; then, in spite of himself, a slow smile overspread his face.
"But," he said, "your Highness, there is not a mathematician in the civilized world who has not considered that problem and cast it aside, with the word that if fourth-dimensional space does exist it can not possibly be inhabited."
"Quite so," said the prince, "and yet here we are."
And, if you come to think of it--as St. George did--that is the only answer to a world of impossibilities already proved possible. But the vista which all this opened smote him with irresistible humour.
"Ah well now, I suppose, your Highness," he said, "that our ocean liners sail clean through the island of Yaque, then, and never even have their smoke pushed sidewise?"
The prince laughed pleasantly.
"Have you ever," he asked, "had occasion to explain the principles of hydraulics, or chess, or philosophical idealism to a three-year-old child, or a charwoman? You must forgive me, but really I can think of no better comparison. I am quite as powerless now as you have been if you have ever attempted it. I can only assure you that such things are. Without Jarvo or Akko or some one who understood, you might have sailed the high seas all your life and never have come any nearer to Yaque."
St. George reflected.
"Is Yaque the only example of this kind of thing," he asked, "that the Fourth Dimension would reveal?"
"By no means," said the prince in surprise, "the world is literally teeming with like revelations, once the key is in your hands. The Fourth Dimension is only the beginning. We utilize that to isolate our island. But the higher dimensions are gradually being conquered, too. Nearly all of us can pass into the Fifth at will, 'disappearing,' as you have the word, from the lower dimensions. It is well-known to you that in a land whose people knew length and breadth, but no up and down, an object might be pushed, but never lifted up or put down. If it were to be lifted, such a people would believe it to have 'disappeared.' So, from you who know only three dimensions, Yaque has 'disappeared,' until one of us guides you here. Also we pass at will into the Fifth Dimension and even higher, and seem to 'disappear'; the only difference is that, there, we should not be able yet to guide one who did not himself understand how to pass there. Just as one who understands how to die and to come to life, as you have the phrase, would not be able to take with him any one who did not understand how to take himself there..."