tagIllustratedLife In The Tesseract

Life In The Tesseract


Author's note: This story is a continuation of Undiscovered Countries

…Matt and Kathy kissed, and then each placed a hand on the door's horizontal bar, pushed down together, and heard a resounding click!

Chapter 1.

The first thing they noticed, even before pushing the door open, was that the lights of the stairwell dimmed to half-power, and then toggled between normal brightness and half-power every second. During every transition, there was also a brief but distinct horn sound. Turning back to the last escalator flight, Kathy and Matt were amazed to see that the stairs had stopped moving…

"Don't even think about it, Matt. We could never climb 200 miles of stairs, even under the best of conditions. And these flashing lights and horns have the distinct urgency of an evacuation warning…"

"My gosh, Kathy! Look at the top of the stairs! Let's get out of here!"

Slowly cascading down the stairs was a deep black ink, reflecting no light at all, even in the flashing lights. Kathy and Matt quickly pushed open the door and went through, closing the door behind them. They found themselves in a hexagonal tube, about six feet per side, fortunately oriented with a flat floor. The flashing lights and horn sound were still present, and Matt and Kathy began to run down the tube. They exited after a minute of running, entering the corner of a large cubical room. Turning around, they watched the tube's hexagonal aperture smoothly shrink to nothing, leaving a smooth wall in its place. The horn sound and flashing lights were no longer present.

"Well" said Kathy, looking around. "After 12 days of gray, I guess it's nice to see a little color, and some open space. Get a load of the height of this ceiling! This whole room looks like a perfect cube!"

Kathy and Matt were standing in the corner of large cubical room, about 45 feet on each side, providing over 2000 sq ft of floor space. The room was moderately lit, with a cream color ceiling, floor, and three walls. The fourth wall opposite them was a light orange color. Halfway between each corner, along the center of each of the four walls, was a closed dark-brown door. In the center of the room was a gold spiral staircase, extending both up and down. Otherwise, the room was empty.

"Well, not quite what I was expecting, Kathy. Coming into an empty cube. Actually, I take that back, I don't know what I was expecting… The orange color is useful for orientation. Let's call that north. It seems we have a choice of going north, east, south, west, up, or down, assuming all these doors are unlocked. Any preference on which one you want to try first?"

"None at all. I'm standing closest to east. How about we try that? The spiral staircase is pretty, but I think I've had enough of stairs over the last 12 days."

Kathy and Matt walked over to the east door. There was a small sliding lever adjacent to it on the wall, and Matt found he could control the room lighting, from quite bright to pitch dark. "Wow. It feels nice to be able to control the environment again, at least a little bit…"

Kathy smiled and slid open the door, glanced at the next room, and shouted "Yes!" Before them was laid out a large kitchen area, with the same cubical proportions and color scheme as the empty room they were exiting. Walking in, they saw the kitchen also had a door in each of its four walls, plus another spiral staircase at its center. Ignoring the six exits for the moment, they both walked briskly to a large refrigerator…

"Excellent!" said Matt. "This thing is packed with food. I see eggs, green peppers, mushrooms, cheese, bacon… I can make a wicked Western omelet, care for one?"

"Sounds great!" I'll find some glasses for the milk and OJ. There's also a large plate of bagels here, and the bowl of spinach leaves looks delicious too." While Matt ate an apple and cooked the omelets, Kathy munched the spinach and set the table. She then began to explore the great number of kitchen cabinets.

"There's a huge amount of food in this kitchen, Matt. All these cabinets are packed! At least the ones I've opened are. It's so amazing to see them go right up to the ceiling. It must be 40 to 50 feet high. How would we ever get to the top ones? I don't see any ladders…"

Kathy and Matt had a great time enjoying their first real meal in 12 days. "All this food was terrific!" said Matt. "Super fresh. This kitchen is so amazing. It looks so much like home, except for its size. Any guesses, Kathy? Is this Earth, or not Earth?"

"Gravity feels like Earth. Actually, if we traveled down 200 miles, gravity should be 5% less. My guess is not Earth. How about you?"

"My gut says not Earth, too. Though this kitchen does feel a bit like home, despite its size… Look, it even has its own dishwasher."

Matt loaded the dishes into the dishwasher, and was then was puzzled by the lack of controls, just a single button near the top. Pressing it, he heard the soft ding of a bell, but nothing else. Kathy opened the unit, and they were both surprised to see the dishes spotlessly clean. "Wow" said Kathy, "I'd love to have this in my apartment in Chicago."

After a brief discussion, they decided to continue heading east, keeping the kitchen's orange wall to their left as they exited. The next room was a large bedroom area, keeping the same color scheme, and with closets vaulting to the ceiling. Continuing eastward, they were delighted to find a super-sized bathroom, complete with his and her showers, plus an oversized Jacuzzi in the shape of a 20-foot radius quarter-circle, taking up nearly a quarter of the room. Both the new rooms also had the four side exit doors, plus their own spiral staircases in their centers.

"Matt, these showers look really tempting; as did that king-sized bed in the room we just left. My great curiosity is competing with my great fatigue. How about you?"

"You're right. We need rest, and the chance for a hot shower after 12 days of escalators is very appealing. Remember to be careful with the controls. If they are like the sinks, they'll give you the option of showering in boiling hot water. Let me satisfy just one last bit of my curiosity." Matt walked across the room to the east door and opened it. "Ah, this one is empty, just like the first room we entered. With all these doors and stairs, who knows how many rooms there are, thousand maybe… But you're right, a shower and bed would be delightful." Within a half hour, Kathy and Matt were sacked out for the night.

Chapter 2.

Matt was having the most delightful of dreams. Kathy was naked and smiling in delight as Matt mounted and entered her. They rolled coupled to each other in laughter and love, the sexuality so intense Matt could feel his orgasm building. His desire to orgasm became so overwhelming that it began to drive Matt from his sleep. He awoke lying on his back, opening his eyes to the beautiful sight of Kathy's labia right before him.

Kathy had reverse mounted him in his sleep, and Matt could feel his erect penis sliding against the far back of her throat. Her gentleness and sexuality were exquisite. Matt felt that his penis was buried in warm, wet feathers, and even in his sleep Matt's hips had started a rocking motion into Kathy's mouth. Sensing that Matt was awake, Kathy focused her attention on the head of his penis. Matt gasped as his hips thrust forward, and he started to ejaculate. Kathy switched her oral caress to a strong suckle.

After Matt finished his orgasm, Kathy rested the side of her head against his hip, sighing and relaxing. Matt gently began kissing the back of her legs, just where the thighs merged with her buttocks. Sensing Kathy's complete relaxation, Matt separated her buttocks and playfully began to lick her anus. Kathy tensed for a moment, but held her position, accepting the stimulation and the probing of Matt's tongue. In the following minutes, Kathy began to shiver and breathe in soft gasps, as her anus became slick and dilated with the continued probing. Matt felt driven by feelings of tenderness, realizing Kathy was actively supporting his access into her rectum. He thought he should ask about her desire before taking this any further…

"A dollar for your thoughts?"

"Oh, the loose change is all over! Ninety cents wants me to get on all fours, present my rump to you, and eagerly accept you to anal mount me. Nine cents is wondering how much it would hurt…"

"Katherine, I would never want pain to be part of our sexuality. I trust you for complete and honest feedback, to make sure it never happens…"

"I know. Dearest Matthew, I know..."

"…And the last penny?"

"…is me as a small child, ringing a school bell with my arm, and calling out: Where are you!?"

Matt glanced at the cavernous ceiling over 40 feet above his head. Suddenly he felt a little embarrassed for focusing on sexuality when so much of their situation was still unknown. "You've quite right, we should be paying attention to where we are…"

"Yes… Don't be embarrassed, Matt. I'm the one who started this. And this is the first time we've coupled sexually as husband and wife. I'll remember this moment forever!"

Kathy and Matt began exploring their giant bedroom and soon found numerous wardrobes in the closets and dressers. After selecting comfortable travel clothes, they headed west to the kitchen for breakfast, both commenting how restful it had been to get a solid 10 hours sleep in such a great bed, much more comfortable than metal floors! Finishing breakfast, they decided to continue traveling westward to begin their exploration.

"It's interesting how each room is so cubical; it provides a certain symmetry…" Matt commented, as he and Kathy walked across the empty room after leaving west from the kitchen. Opening the empty room's west door, they both stood quietly as they looked at the large bathroom, identical to the one they were in the previous night.

"Matt, you mentioned last night there was an empty room east of the other bathroom. This would make two duplicate rooms in a row. Do you think we'll find a duplicate bedroom if we continue west?"

"I'm trying to remember something my roommate Harold once told me about cubes, in my first year at Harvard. He was a math major. It might not be a duplicate… Let's take a look." Matt and Kathy walked west across the room and went through the door."

"It is a duplicate bedroom!"

"Not quite, Kathy. Look! The bed is ruffled exactly as we left it. And here's the dress you wore in the escalators. This isn't a duplicate bedroom, it's the same room!"

"How is that possible? We didn't make any turns. Are you saying we traveled in a circle?"

"Yes, sort of. Did you ever hear of a tesseract?"

"Vaguely. Is it like a dodecahedron, or something?"

"Ha! A bit, I guess. It's a cube with four spatial dimensions."


"Think of a line as a set of points between 0 and 1. Think of a square as a set of points between (0,0) and (1,1). Think of a cube as a set of points between (0,0,0) and (1,1,1). Think of a tesseract as a set of points between (0,0,0,0) and (1,1,1,1). See?"

"I guess. But Matt, that's pure math. This is physical. There are only three physical spatial dimensions…"

"Not here. These rooms, the escalator well, that hexagonal access tube we ran through yesterday, perhaps they all exist in extra spatial dimensions. It all hangs together with the joining of the escalator well with the Morningstar tower. You don't have to tear the whole building apart. You just have to push the top tip of the escalator well to the 3-D coordinates of the top of the tower, to make the connection."

"So we're still only 200 miles from Earth?"

"Sort of. 200 miles distant from Earth, 200 miles from our entire universe... Or maybe not, I don't know... The technology to do this seems like complete magic to me…"

"Matt, what's a tesseract like?"

"Think first of a square and a cube. A square has four one-dimensional surfaces, lines, at its boundaries. If you move along the four lines, you get back to where you started. A cube has six two-dimensional surfaces, squares, at its boundaries. If you move along the squares, in either north-south or east-west directions, you can navigate the surface of the cube. After four jumps in the same direction, you're always back to the same square. The tesseract is the next level, with four spatial dimensions. It has eight three-dimensional cubes as its boundaries. If you move along the cubes, in either north-south, east-west, or up-down directions, you can navigate the surface of the tesseract. After four jumps in the same direction, you're always back in the same cube."

"But Matt, how do we ever leave the tesseract?"

"We don't, if we just keep moving in three dimensions. We'll always be on the 3-D surface of the tesseract. We'll need something like that hexagonal access tube to leave. The entity who brought us here will have to provide it…"

"So we're prisoners?"

"Yeah. It's a prison without walls, but a bounded 3-D space. We'll need help to leave. I remember reading a story by Heinlein called "And He Built A Crooked House" when I was a boy, about living in a tesseract. Heinlein wasn't quite right in his story, he had windows looking out on some walls. In a real tesseract, each wall of each cube joins with the wall of another cube…. There's something else about tesseracts I'm trying to remember, something about them being very unfriendly to lifeforms, but I can't remember quite what it was. We'll just have to trust the entity to keep us safe. With the nice rooms we've found so far, I feel it is trying to be kind to us."

"I'm beginning to get a feel for how this works, Matt. We'll find the other four rooms by going north-south and up-down, right?"

"Yeah. Either north-south or up-down will reveal the rest of the rooms. Going north and east will be the same as going up or down, you'll see… There's still something about this I'm forgetting, Kathy…"

"Well, keep thinking! Meanwhile, how about we head north? Will you take my diary? I think you have a better spatial picture of what's going on here, compared to me. Thanks. Please try to draw a map of how these rooms are connected to each other…"

Matt and Kathy exited their bedroom through the room's northern orange wall. They entered a large living area; filled with couches, play tables, reclining chairs, a huge multimedia center, and a library whose books, games, CDs, and DVDs stretched to the ceiling. "Wow, what a great place to relax. You're right, Matt, the entity is trying to be very kind to us…"

Kathy and Matt continued north from the living room, and entered the south side of the empty cube. "Of course!" said Matt. "The empty cube is the cube that's on the opposite side of the tesseract, relative to the bedroom. Each cube joins to six other cubes, with the north, south, east, west, up, and down exits. For each cube, there's one cube that it doesn't directly touch, but can be reached by traveling two cubes in any direction. For example, from the bedroom, we can travel down two cubes to enter the top of the empty room, south two cubes to enter the north of the empty room, etc. This means the kitchen is the opposite room of the bathroom, and this living room is the opposite room to whatever is south of the bedroom…" Matt started taking notes in the diary.

"Let's pick names for each room, Matt. Each one starting with a different letter. So far we have the Living Room, Kitchen, Bedroom… Let's call the bathroom the Jacuzzi room… The letter E is okay, but I don't like empty as a name, let's call this room the Entrance hall."

"Sounds good."

"You know, Matt, the spiral staircase in this Entrance hall room is a bit different from the others. See the storage box along its base? The other stairwells don't have it. I wonder what's inside?"

Kathy opened the box and was surprised to see two sets of wings, one set to fit her arms and another to fit Matt. There were even two sets of shoes with controllable web fans in the front and back. "There's also a level in here" Kathy commented, as she flipped the switch inside the box. Immediately her stomach gave a lurch, she had turned off the room's gravity. "This is so amazing, Matt!"

Matt reached into his pocket and held out a penny, gently releasing it at eye level. The penny gently hit the floor 10 seconds later. "Not quite zero gravity, but I think it's down over 99%. I've always wanted to fly! Want to try the wings?"

Matt and Kathy had a wonderful time in the next several hours, practicing how to fly. They would perch along the spiral staircase and launch themselves, laughing with the fun of learning to fly and steering with their arm-wings and foot-rudders. They only stopped when they decided to break for lunch, heading east to the kitchen.

"Tesseracts are really nice places to live, in a way," said Kathy, as she munched her sandwich and salad, "everything is so close to everything else. Very convenient! I love these spinach leaves, they're so fresh, even after being in the fridge overnight… Matt, I have an idea. Can I borrow your watch?"

Kathy placed the watch in the fridge, watched it run normally for a moment, then closed the door and looked at her own watch. After a minute, she opened the fridge and looked closely at Matt's watch. She then repeated the experiment with two of the kitchen cabinets. Matt had no idea what she was doing.

"Amazing, Matt! When the doors to the fridge or these cabinets are closed, your watch stops completely. There's no passing of time at all. Be careful never to get completely inside a cabinet. If the door closes behind you, you might wait for eternity to be let out."

"Heading north from the kitchen, Kathy and Matt were quite surprised about what they found next. "Look at this beautiful pool table, Matt! It's magnificent! My parents used to have one, rather than having a dining room, but nothing this grand. Let's call this the Poolroom. I used to love shooting pool with my mom and dad when I was a girl. Poison was one of my favorite games… But what's this?"

The room was divided into four quadrants. One quadrant held the pool table, the next two held tables of similar size, but one with a huge cube floating above it, and the other with a much more complicated geometric shape. The fourth quadrant held three sets of tables and chairs with various chessboards on them.

"Wow!" said Matt. This table is three-dimensional pool! I don't think there's any gravity at all inside the cube. Look! The cue-stick passes through without resistance, but the ball bounce off the inside surface of the cube. Here are the controls to rotate the cube in each of the three axes. This will be an incredible game to play. And this…" Matt stared at the next table "… is a four-dimensional pool table. This is so incredible. Look, here are the controls for rotating the tesseract along each of the four axes. Do you see the eight cubes, Kathy?"

"They look like prisms, not cubes."

"Exactly! The perspective frame of a simple cube will have prisms too. See? As I rotate the shape, you can see the underlying cubical structure along each of the four dimensions…"

"I see it, Matt! I'm a little surprised that I can. I was never that great with spatial issues. But I can see it clearly! Somehow my mind is learning how to see it…."

"These last three tables contain an 8 x 8 standard chess board, with 32 pieces, a cubic chessboard of 5 x 5 x 5, with 40 pieces, and a 4-D chess board, four towers of 4 x 4 x 4, with 64 pieces. This is really a good way to visualize the fourth dimension. Take the rook in the cubic chessboard. I once read a book on 3-D chess as a boy. This rook can go in one dimension, straight forward or back, straight left of right, or straight up and down. It passes through the six surfaces of the cells of the cubic board. The 2-D bishop passes through the edges of the cells, making XY, XZ, or YZ movements. This piece here is called a unicorn. It's a 3-D bishop. It passes through the eight corners of the cells, not the twelve edges. It makes XYZ movements only. The queen has the power of the rook, bishop, and unicorn. For tesseract chess, there's has to be an extra piece. Yes, here it is. Call it, well, how about a zebra? It's a fourth dimensional bishop. For very XYZ step, it also has to make one step to the next tower, making a WXYZ step. See how each tower is 3-D, and stepping to the next tower is moving in the fourth spatial dimension?"

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