"H-m-m," he said. "Might be just what I need to explain things to Dr. Pillbot."
"I shall take this matter before the Psychiatric Society," Pillbot was saying excitedly. "Undoubtedly you have some strange faculty—an instinctive perception of four dimensional laws ... what was that, Professor?"
"I said if you will step over to this desk I will explain to you in elementary terms—very elementary and easy to understand—why you will never be able to study four dimensional beings—if any exist!" Gault's voice was tinged with sarcasm.
Pillbot came over, followed by Harper, who was interested in any explanations about the fourth dimension—even elementary ones....
Gault, with a glint in his eye, pressed the paper figure flatly on the surface of Harper's desk.
"This paper man, we will say, represents a two dimensional creature. We lay him flatly against the desk, which represents his world—Flatland, we mathematicians call it. Mr. Flatlander can't see into our world. He can see only along the flat plane of his own world. To see us, for instance, he would have to look up, which is the third dimension, a direction inconceivable to him. Now, Doctor, are you beginning to understand why we can never see four dimensional beings?"
Pillbot frowned thoughtfully, then looked up. "And what about the viewpoint of the four dimensioners themselves—what would prevent them from seeing us?"
Harper hardly heard the Professor's snort of disgust. This two dimensional cutout in "Flatland" fascinated him. An idea occurred to him. Now, just supposing the....
As Gault and Pillbot argued, Harper grasped the paper cutout, and bent it, "jacknifed" it, creasing it firmly in the middle. Then he raised the upper half so that it rose vertically from the desk, while the lower half was still pressed flatly against the desk surface.