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…And He Built A Crooked House — Robert A. Heinlein

Bailey reached up and shook his arm. “Snap out of it. What the hell are you talking about, four dimensions? Time is the fourth dimension; you can’t drive nails into that.”

Teal shrugged him off. “Sure. Sure. Time is a fourth dimension, but I’m thinking about a fourth spatial dimension, like length, breadth and thickness. For economy of materials and convenience of arrangement you couldn’t beat it. To say nothing of the saving of ground space — you could put an eight-room house on the land now occupied by a one-room house. Like a tesseract — ”

“What’s a tesseract?”

“Didn’t you go to school? A tesseract is a hypercube, a square figure with four dimensions to it, like a cube has three, and a square has two. Here, I’ll show you.” Teal dashed out into the kitchen of his apartment and returned with a box of toothpicks which he spilled on the table between them, brushing glasses and a nearly empty Holland gin bottle carelessly aside. “I’ll need some plasticine. I had some around here last week.” He burrowed into a drawer of the littered desk which crowded one corner of his dining room and emerged with a lump of oily sculptor’s clay. “Here’s some.”

“What are you going to do?”

“I’ll show you.” Teal rapidly pinched off small masses of the clay and rolled them into pea-sized balls. He stuck toothpicks into four of these and hooked them together into a square. “There! That’s a square.”

“Obviously.”

“Another one like it, four more toothpicks, and we make a cube.” The toothpicks were now arranged in the framework of a square box, a cube, with the pellets of clay holding the corners together. “Now we make another cube just like the first one, and the two of them will be two sides of the tesseract.”

Bailey started to help him roll the little balls of clay for the second cube, but became diverted by the sensuous feel of the docile clay and started working and shaping it with his fingers.

“Look,” he said, holding up his effort, a tiny figurine, “Gypsy Rose Lee.”

“Looks more like Gargantua; she ought to sue you. Now pay attention. You open up one corner of the first cube, interlock the second cube at the corner, and then close the corner. Then take eight more toothpicks and join the bottom of the first cube to the bottom of the second, on a slant, and the top of the first to the top of the second, the same way.” This he did rapidly, while he talked.

“What’s that supposed to be?” Bailey demanded suspiciously.

“That’s a tesseract, eight cubes forming the sides of a hypercube in four dimensions.”

“It looks more like a cat’s cradle to me. You’ve only got two cubes there anyhow. Where are the other six?”

“Use your imagination, man. Consider the top of the first cube in relation to the top of the second; that’s cube number three. Then the two bottom squares, then the front faces of each cube, the back faces, the right hand, the left hand — eight cubes.” He pointed them out.

“Yeah, I see ’em. But they still aren’t cubes; they’re whatchamucallems — prisms. They are not square, they slant.”

“That’s just the way you look at it, in perspective. If you drew a picture of a cube on a piece of paper, the side squares would be slaunchwise, wouldn’t they? That’s perspective. When you look at a four-dimensional figure in three dimensions, naturally it looks crooked. But those are all cubes just the same.”

“Maybe they are to you, brother, but they still look crooked to me.”

Teal ignored the objections and went on. “Now consider this as the framework of an eight-room house; there’s one room on the ground floor — that’s for service, utilities, and garage. There are six rooms opening off it on the next floor, living room, dining room, bath, bedrooms, and so forth. And up at the top, completely enclosed and with windows on four sides, is your study. There! How do you like it?”

“Seems to me you have the bathtub hanging out of the living room ceiling. Those rooms are interlaced like an octopus.”

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Categories: Heinlein, Robert
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