conceded grudgingly he “guessed , that was so.”
“Of course,” said Pierre. “So, in the eyes of X, V becomes a god. And not only can god Y climb over the object, he can lift the rocks into the air directly above the one-dimensional world. He can carry them over X’s head and replace them on the other side of him, much to X’s concern. He can turn the rocks upside down.”
“Very well,” said Hanling, “where’s all that get us?”
“It gets us,” continued Pierre, “to the two-dimensional world in which Y himself lives and where he is not a god at all. His world had length and height. He can rise straight up and he can dig straight down, besides traveling forward or backward. But he knows nothing of the world to the right or to the left. For him, that world has no existence.
“But one day he comes to an object that has three dimensions. It has the two qualities of his own world, length and height, but it also has breadth. He can still climb over as before, but he cannot go around. To do that he would have to step out of his own world. So, if you or I, living in a three-dimensional world, were to come along and pass around the object. Y himself would be confronted with ;t miracle.”
“All right,” said Hanling impatiently. “But J still don’t see—”
“Just this,” interrupted Pierre. “Why isn’t it possible for us, living in our three-dimensional world, to find ourselves facing the same problem . . . a miracle we might call the fourth dimension?”
“You mean—”
Pierre persisted. “I ask, what would be so incredible about this room we’re sitting in, sealed tight, windows locked, doors bolted, having that chair you're sitting in, Hanling, removed from it along the fourth dimension? Yes, and you along with it, too!”
THE train rolled to a stop at the Oak Lane station. There was a momentary pause for the discharge of passengers: then, smoothly, the train rolled out. Now Pierre’s face was sober. The left eyelid drooped a bit more. He stared out into the night, seeing nothing. Was there, he wondered, just a grain of truth in the argument he'd used to try to convince the others?
He'd never given much thought to things like that. The world, in which he’d always had a pretty good time, was quite an objective thing to him. And he'd never bothered his head a great deal about what might lie on the other side. He heard Hanling again:
“All supposition!”
He heard himself replying. “Certainly. Rut the three dimensions are only a human conception. Do you think they're necessarily the only combination?”
Now. why in the devil did he think of that?
Justin Hardt had coughed importantly and inclined his houndlike head and had finally spoken with that bombastic air of last-word authority for which, even more than his medical knowledge, he was celebrated, “Don't, sir,” he said, with a direct look at Hanling, “let the man befuddle you with such tish-tosh. I, who have made a study of the subject and believe nothing, can give you a much better argument. And,” turning to Pierre. “a much briefer one. I merely ask. what makes wood burn up into smoke and makes the smoke disappear?”
There was general laughter. Until Grillot broke in abruptly with dead seriousness:
“I don’t know. A man gets to thinking about things sometimes and he goes whacky. I get to thinking about figures. They’re simple little things. I’ve dealt with ’em all my life. There are only ten of them and after that there are just the same figures over and over again in combinations. But—well. I get to thinking sometimes that there's some mystery about ’em. Take a bond issue, just for example. One little abstract fraction of one per cent can make a whale of a lot of difference.
“I’ll worry stiff sometimes figuring what premium I ought to offer and what interest rate I’ll accept on an issue of upstate municipal debentures. The
“Of course,” said Pierre. “So, in the eyes of X, V becomes a god. And not only can god Y climb over the object, he can lift the rocks into the air directly above the one-dimensional world. He can carry them over X’s head and replace them on the other side of him, much to X’s concern. He can turn the rocks upside down.”
“Very well,” said Hanling, “where’s all that get us?”
“It gets us,” continued Pierre, “to the two-dimensional world in which Y himself lives and where he is not a god at all. His world had length and height. He can rise straight up and he can dig straight down, besides traveling forward or backward. But he knows nothing of the world to the right or to the left. For him, that world has no existence.
“But one day he comes to an object that has three dimensions. It has the two qualities of his own world, length and height, but it also has breadth. He can still climb over as before, but he cannot go around. To do that he would have to step out of his own world. So, if you or I, living in a three-dimensional world, were to come along and pass around the object. Y himself would be confronted with ;t miracle.”
“All right,” said Hanling impatiently. “But J still don’t see—”
“Just this,” interrupted Pierre. “Why isn’t it possible for us, living in our three-dimensional world, to find ourselves facing the same problem . . . a miracle we might call the fourth dimension?”
“You mean—”
Pierre persisted. “I ask, what would be so incredible about this room we’re sitting in, sealed tight, windows locked, doors bolted, having that chair you're sitting in, Hanling, removed from it along the fourth dimension? Yes, and you along with it, too!”
THE train rolled to a stop at the Oak Lane station. There was a momentary pause for the discharge of passengers: then, smoothly, the train rolled out. Now Pierre’s face was sober. The left eyelid drooped a bit more. He stared out into the night, seeing nothing. Was there, he wondered, just a grain of truth in the argument he'd used to try to convince the others?
He'd never given much thought to things like that. The world, in which he’d always had a pretty good time, was quite an objective thing to him. And he'd never bothered his head a great deal about what might lie on the other side. He heard Hanling again:
“All supposition!”
He heard himself replying. “Certainly. Rut the three dimensions are only a human conception. Do you think they're necessarily the only combination?”
Now. why in the devil did he think of that?
Justin Hardt had coughed importantly and inclined his houndlike head and had finally spoken with that bombastic air of last-word authority for which, even more than his medical knowledge, he was celebrated, “Don't, sir,” he said, with a direct look at Hanling, “let the man befuddle you with such tish-tosh. I, who have made a study of the subject and believe nothing, can give you a much better argument. And,” turning to Pierre. “a much briefer one. I merely ask. what makes wood burn up into smoke and makes the smoke disappear?”
There was general laughter. Until Grillot broke in abruptly with dead seriousness:
“I don’t know. A man gets to thinking about things sometimes and he goes whacky. I get to thinking about figures. They’re simple little things. I’ve dealt with ’em all my life. There are only ten of them and after that there are just the same figures over and over again in combinations. But—well. I get to thinking sometimes that there's some mystery about ’em. Take a bond issue, just for example. One little abstract fraction of one per cent can make a whale of a lot of difference.
“I’ll worry stiff sometimes figuring what premium I ought to offer and what interest rate I’ll accept on an issue of upstate municipal debentures. The
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