Off The Main Sequence

by Robert A. Heinlein

  Bailey studied the figure, then shook his head. “I still don’t see but two cubes, a big one and a little one. Those other six things, they look like pyramids this time instead of prisms, but they still aren’t cubes."

  “Certainly, certainly, you are seeing them in different perspective. Can’t you see that?"

  “Well, maybe. But that room on the inside, there. It’s completely surrounded by the thingamujigs. I thought you said it had windows on four sides."

  “It has — it just looks like it was surrounded. That’s the grand feature about a tesseract house, complete outside exposure for every room, yet every wall serves two rooms and an eight-room house requires only a one-room foundation. It’s revolutionary."

  “That’s putting it mildly. You’re crazy, bud; you can’t build a house like that. That inside room is on the inside, and there she stays."

  Teal looked at his friend in controlled exasperation. “It’s guys like you that keep architecture in its infancy. How many square sides has a cube?"

  “Six."

  “How many of them are inside?"

  “Why, none of 'em. They’re all on the outside."

  “All right. Now listen — a tesseract has eight cubical sides, all on the outside. Now watch me. I’m going to open up this tesseract like you can open up a cubical pasteboard box, until it’s flat. That way you’ll be able to see all eight of the cubes." Working very rapidly he constructed four cubes, piling one on top of the other in an unsteady tower. He then built out four more cubes from the four exposed faces of the second cube in the pile. The structure swayed a little under the loose coupling of the clay pellets, but it stood, eight cubes in an inverted cross, a double cross, as the four additional cubes stuck out in four directions. “Do you see it now? It rests on the ground floor room, the next six cubes are the living rooms, and there is your study, up at the top."

  Bailey regarded it with more approval than he had the other figures. “At least I can understand it. You say that is a tesseract, too?"

  “That is a tesseract unfolded in three dimensions. To put it back together you tuck the top cube onto the bottom cube, fold those side cubes in till they meet the top cube and there you are. You do all this folding through a fourth dimension of course; you don’t distort any of the cubes, or fold them into each other."

  Bailey studied the wobbly framework further. “Look here," he said at last, “why don’t you forget about folding this thing up through a fourth dimension — you can’t anyway — and build a house like this?"

  “What do you mean, I can’t? It’s a simple mathematical problem —"

  “Take it easy, son. It may be simple in mathematics, but you could never get your plans approved for construction. There isn’t any fourth dimension; forget it. But this kind of a house — it might have some advantages."

  Checked, Teal studied the model. “Hm-m-m — Maybe you got something. We could have the same number of rooms, and we’d save the same amount of ground space. Yes, and we would set that middle cross-shaped floor northeast, southwest, and so forth, so that every room would get sunlight all day long. That central axis lends itself nicely to central heating. We’ll put the dining room on the northeast and the kitchen on the southeast, with big view windows in every room. O.K., Homer, I’ll do it! Where do you want it built?"

  “Wait a minute! Wait a minute! I didn’t say you were going to build it for me —"

  “Of course I am. Who else? Your wife wants a new house; this is it."

  “But Mrs. Bailey wants a Georgian house —"

  “Just an idea she has. Women don’t know what they want —"

  “Mrs. Bailey does."

  “Just some idea an out-of-date architect has put in her head. She drives a new car, doesn’t she? She wears the very latest styles — why should she live in an eighteenth century house? This house will be even later than this year’s model; it’s years in the future. She’ll be the talk of the town."

  “Well — I’ll have to talk to her."

  “Nothing of the sort. We’ll surprise her with it. Have another drink."

  “Anyhow, we can’t do anything about it now. Mrs. Bailey and I are driving up to Bakersfield tomorrow. The company’s bringing in a couple of wells tomorrow."

  “Nonsense. That’s just the opportunity we want. It will be a surprise for her when you get back. You can just write me a check right now, and your worries are over."

  “I oughtn’t to do anything like this without consulting her. She won’t like it."

  “Say, who wears the pants in your family anyhow?"

  The check was signed about halfway down the second bottle.

  Things are done fast in southern California. Ordinary houses there are usually built in a month’s time. Under Teal’s impassioned heckling the tesseract house climbed dizzily skyward in days rather than weeks, and its cross-shaped second story came jutting out at the four corners of the world. He had some trouble at first with the inspectors over those four projecting rooms but by using strong girders and folding money he had been able to convince them of the soundness of his engineering.

  By arrangement, Teal drove up in front of the Bailey residence the morning after their return to town. He improvised on his two-tone horn. Bailey stuck his head out the front door. “Why don’t you use the bell?"

  “Too slow," answered Teal cheerfully. “I’m a man of action. Is Mrs. Bailey ready? Ah, there you are, Mrs. Bailey! Welcome home, welcome home. Jump in, we’ve got a surprise for you!"

  “You know Teal, my dear," Bailey put in uncomfortably.

  Mrs. Bailey sniffed. “I know him. We’ll go in our own car, Homer."

  “Certainly, my dear."

  “Good idea," Teal agreed;" 'sgot more power than mine; we’ll get there faster. I’ll drive, I know the way." He took the keys from Bailey, slid into the driver’s seat, and had the engine started before Mrs. Bailey could rally her forces.

  “Never have to worry about my driving," he assured Mrs. Bailey, turning his head as he did so, while he shot the powerful car down the avenue and swung onto Sunset Boulevard, “it’s a matter of power and control, a dynamic process, just my meat — I’ve never had a serious accident."

  “You won’t have but one," she said bitingly. “Will you please keep your eyes on the traffic?"

  He attempted to explain to her that a traffic situation was a matter, not of eyesight, but intuitive integration of courses, speeds, and probabilities, but Bailey cut him short. “Where is the house, Quintus?"

  “House?" asked Mrs. Bailey suspiciously. “What’s this about a house, Homer? Have you been up to something without telling me?"

  Teal cut in with his best diplomatic manner. “It certainly is a house, Mrs. Bailey. And what a house! It’s a surprise for you from a devoted husband. Just wait till you see it —"

  “I shall," she agreed grimly. “What style is it?"

  “This house sets a new style. It’s later than television, newer than next week. It must be seen to be appreciated. By the way," he went on rapidly, heading off any retort, “did you folks feel the earthquake last night?"

  “Earthquake? What earthquake? Homer, was there an earthquake?"

  “Just a little one," Teal continued, “about two A.M. If I hadn’t been awake, I wouldn’t have noticed it."

  Mrs. Bailey shuddered. “Oh, this awful country! Do you hear that, Homer? We might have been killed in our beds and never have known it. Why did I ever let you persuade me to leave Iowa?"

  “But my dear," he protested hopelessly, “you wanted to come out to California; you didn’t like Des Moines."

  “We needn’t go into that," she said firmly. “You are a man; you should anticipate such things. Earthquakes!"

  “That’s one thing you needn’t fear in your new home, Mrs. Bailey," Teal told her. “It’s absolutely earthquake-proof; every part is in perfect dynamic balance with every other part."

  “Well, I hope so. Where is this house?"

  “Just around this bend. T
here’s the sign now." A large arrow sign of the sort favored by real estate promoters proclaimed in letters that were large and bright even for southern California:

  THE HOUSE OF THE FUTURE!!!

  COLOSSAL — AMAZING —

  REVOLUTIONARY

  See How Your Grandchildren

  Will Live!

  Q. Teal, Architect

  “Of course that will be taken down," he added hastily, noting her expression, “as soon as you take possession." He slued around the corner and brought the car to a squealing halt in front of the House of the Future. “Voila!" He watched their faces for response.

  Bailey stared unbelievingly, Mrs. Bailey in open dislike. They saw a simple cubical mass, possessing doors and windows, but no other architectural features, save that it was decorated in intricate mathematical designs. “Teal," Bailey asked slowly, “what have you been up to?"

  Teal turned from their faces to the house. Gone was the crazy tower with its jutting second-story rooms. No trace remained of the seven rooms above ground floor level. Nothing remained but the single room that rested on the foundations. “Great jumping cats!" he yelled, “I’ve been robbed!"

  He broke into a run.

  But it did him no good. Front or back, the story was the same: the other seven rooms had disappeared, vanished completely. Bailey caught up with him, and took his arm. “Explain yourself. What is this about being robbed? How come you built anything like this — it’s not according to agreement."

  “But I didn’t. I built just what we had planned to build, an eight-room house in the form of a developed tesseract. I’ve been sabotaged, that’s what it is! Jealousy! The other architects in town didn’t dare let me finish this job; they knew they’d be washed up if I did."

  “When were you last here?"

  “Yesterday afternoon."

  “Everything all right then?"

  “Yes. The gardeners were just finishing up."

  Bailey glanced around at the faultlessly manicured landscaping. “I don’t see how seven rooms could have been dismantled and carted away from here in a single night without wrecking this garden."

  Teal looked around, too. “It doesn’t look it. I don’t understand it."

  Mrs. Bailey joined them. “Well? Well? Am I to be left to amuse myself? We might as well look it over as long as we are here, though I’m warning you, Homer, I’m not going to like it."

  “We might as well," agreed Teal, and drew a key from his pocket with which he let them in the front door. “We may pick up some clues."

  The entrance hall was in perfect order, the sliding screens that separated it from the garage space were back, permitting them to see the entire compartment. “This looks all right," observed Bailey. “Let’s go up on the roof and try to figure out what happened. Where’s the staircase? Have they stolen that, too?"

  “Oh, no," Teal denied, “look —" He pressed a button below the light switch; a panel in the ceiling fell away and a light, graceful flight of stairs swung noiselessly down. Its strength members were the frosty silver of duralumin, its treads and risers transparent plastic. Teal wriggled like a boy who has successfully performed a card trick, while Mrs. Bailey thawed perceptibly.

  It was beautiful.

  “Pretty slick," Bailey admitted. “Howsomever it doesn’t seem to go any place —"

  “Oh, that —" Teal followed his gaze. “The cover lifts up as you approach the top. Open stair wells are anachronisms. Come on." As predicted, the lid of the staircase got out of their way as they climbed the flight and permitted them to debouch at the top, but not, as they had expected, on the roof of the single room. They found themselves standing in the middle one of the five rooms which constituted the second floor of the original structure.

  For the first time on record Teal had nothing to say. Bailey echoed him, chewing on his cigar. Everything was in perfect order. Before them, through open doorway and translucent partition lay the kitchen, a chefs dream of up-to-the-minute domestic engineering, monel metal, continuous counter space, concealed lighting, functional arrangement. On the left the formal, yet gracious and hospitable dining room awaited guests, its furniture in parade-ground alignment.

  Teal knew before he turned his head that the drawing room and lounge would be found in equally substantial and impossible existence.

  “Well, I must admit this is charming," Mrs. Bailey approved, “and the kitchen is just too quaint for words — though I would never have guessed from the exterior that this house had so much room upstairs. Of course some changes will have to be made. That secretary now — if we moved it over here and put the settle over there —"

  “Stow it, Matilda," Bailey cut in brusquely. “Wha’d’ yuh make of it, Teal?"

  “Why, Homer Bailey! The very id —"

  “Stow it, I said. Well, Teal?"

  The architect shuffled his rambling body. “I’m afraid to say. Let’s go on up."

  “How?"

  “Like this." He touched another button; a mate, in deeper colors, to the fairy bridge that had let them up from below offered them access to the next floor. They climbed it, Mrs. Bailey expostulating in the rear, and found themselves in the master bedroom. Its shades were drawn, as had been those on the level below, but the mellow lighting came on automatically. Teal at once activated the switch which controlled still another flight of stairs, and they hurried up into the top floor study.

  “Look, Teal," suggested Bailey when he had caught his breath, “can we get to the roof above this room? Then we could look around."

  “Sure, it’s an observatory platform." They climbed a fourth flight of stairs, but when the cover at the top lifted to let them reach the level above, they found themselves, not on the roof, but standing in the ground floor room where they had entered the house.

  Mr. Bailey turned a sickly gray. “Angels in heaven," he cried, “this place is haunted. We’re getting out of here." Grabbing his wife he threw open the front door and plunged out.

  Teal was too much preoccupied to bother with their departure. There was an answer to all this, an answer that he did not believe. But he was forced to break off considering it because of hoarse shouts from somewhere above him. He lowered the staircase and rushed upstairs. Bailey was in the central room leaning over Mrs. Bailey, who had fainted. Teal took in the situation, went to the bar built into the lounge, and poured three fingers of brandy, which he returned with and handed to Bailey. “Here — this’ll fix her up."

  Bailey drank it.

  “That was for Mrs. Bailey," said Teal.

  “Don’t quibble," snapped Bailey. “Get her another." Teal took the precaution of taking one himself before returning with a dose earmarked for his client’s wife. He found her just opening her eyes.

  “Here, Mrs. Bailey," he soothed, “this will make you feel better."

  “I never touch spirits," she protested, and gulped it.

  “Now tell me what happened," suggested Teal. “I thought you two had left."

  “But we did — we walked out the front door and found ourselves up here, in the lounge."

  “The hell you say! Hm-m-m — wait a minute." Teal went into the lounge. There he found that the big view window at the end of the room was open. He peered cautiously through it. He stared, not out at the California countryside, but into the ground floor room — or a reasonable facsimile thereof. He said nothing, but went back to the stair well which he had left open and looked down it. The ground floor room was still in place. Somehow, it managed to be in two different places at once, on different levels.

  He came back into the central room and seated himself opposite Bailey in a deep, low chair, and sighted him past his upthrust bony knees. “Homer," he said impressively, “do you know what has happened?"

  “No, I don’t — but if I don’t find out pretty soon, something is going to happen and pretty drastic, too!"

  “Homer, this is a vindication of my theories. This house is a real tesseract."

  “What’s he talking about,
Homer?"

  “Wait, Matilda — now Teal, that’s ridiculous. You’ve pulled some hanky-panky here and I won’t have it — scaring Mrs. Bailey half to death, and making me nervous. All I want is to get out of here, with no more of your trapdoors and silly practical jokes."

  “Speak for yourself, Homer," Mrs. Bailey interrupted, “I was not frightened; I was just took all over queer for a moment. It’s my heart; all of my people are delicate and high-strung. Now about this tessy thing — explain yourself, Mr. Teal. Speak up."

  He told her as well as he could in the face of numerous interruptions the theory back of the house. “Now as I see it, Mrs. Bailey," he concluded, “this house, while perfectly stable in three dimensions, was not stable in four dimensions. I had built a house in the shape of an unfolded tesseract; something happened to it, some jar or side thrust, and it collapsed into its normal shape — it folded up." He snapped his fingers suddenly. “I’ve got it! The earthquake!"

  “Earthquake?"

  “Yes, yes, the little shake we had last night. From a four-dimensional standpoint this house was like a plane balanced on edge. One little push and it fell over, collapsed along its natural joints into a stable four-dimensional figure."

  “I thought you boasted about how safe this house was."

  “It is safe — three-dimensionally."

  “I don’t call a house safe," commented Bailey edgily, “that collapses at the first little temblor."

  “But look around you, man!" Teal protested. “Nothing has been disturbed, not a piece of glassware cracked. Rotation through a fourth dimension can’t affect a three-dimensional figure any more than you can shake letters off a printed page. If you had been sleeping in here last night, you would never have awakened."

  “That’s just what I’m afraid of. Incidentally, has your great genius figured out any way for us to get out of this booby trap?"

  “Huh? Oh, yes, you and Mrs. Bailey started to leave and landed back up here, didn’t you? But I’m sure there is no real difficulty — we came in, we can go out. I’ll try it." He was up and hurrying downstairs before he had finished talking. He flung open the front door, stepped through, and found himself staring at his companions, down the length of the second floor lounge. “Well, there does seem to be some slight problem," he admitted blandly. “A mere technicality, though — we can always go out a window." He jerked aside the long drapes that covered the deep French windows set in one side wall of the lounge. He stopped suddenly.