George said, "Search me," but Myra went into a long explanation which George didn't understand at all.
When she finished, Arl shook his head. "Just what I thought. A lot of fuzzy thinking. Unfortunately, you're way off the beam. It's really simple. You have a world of two dimensions—length and breadth, and all you have to do to get a world of three dimensions is extend that world in a new direction—perpendicular to the first two. That direction is up or down, as the case may be. Either way, it's a direction at right angles to the first two, and the result is a world of three dimensions, this world."
George said he understood. "But that doesn't mean I'm going to send you back," he added.
Arl was all wrapped up in his explanation, and he ignored the remark. "Now, then. The same situation applies. The same relation exists between a world of three dimensions and one of four. You merely extend the three dimensions out in a direction at right angles to them—a direction which is perpendicular to length, breadth and thickness, and the result is a world of four dimensions. That's my world."
George was feeling chipper. "Well, a pat on the backside for you," he said. "Now I suppose you want me to send you back?"
Arl waved his hand. "No. I'm not finished. Let's go a step further. If a world of two dimensions existed—a whole world spread out perfectly flat on this table, with no dimension other than length or breadth, a flat world—if that world existed, do you realize all the power you, as a three-dimensional being, would have over it?"
George said that he didn't.
"Well, suppose something was enclosed in a square on that table. Just four lines, a square. That would be the equivalent of a cube in this world—say, of a safe. Say there was something in that square that the people of the flat world wanted to get out. But the square was locked. It was just four lines, forming an enclosed space, but because there was no such thing as up or down in that world, they couldn't get over, those lines and get out what they were looking for. It was utterly inaccessible.
"Now, then. You're a three-dimensional creature. All you'd have to do is reach down, pick the item up, transport it through the third dimension, and put it down again outside the square. You would have done the impossible. You would have taken something out of an utterly inaccessible place and put it elsewhere. Mysteriously.