Post by Judge Sam on Aug 10, 2009 2:39:30 GMT -5
Before the game I wrote up an Imprisonment story based on the concept of traveling through dimensions. I did some fun research and then tried to incorporate that research into a story. As always it got really long so I divided it up into three parts! Here's the whole thing from start to finish. Or you can read Imprisonments #3, #7, and #11.
“Wow, take a look at that huge stadium!” Cindy exclaimed as she pointed towards the baseball stadium they were approaching. “There’s something so classic, so prestigious about a big league baseball game. Something so American about it.”
“Cindy, I know you’re new to the whole baseball thing, but…” Darrell started.
“I can’t wait to eat a great American hotdog!” Cindy interrupted. “Speaking of vendor food, I wonder if some guy carrying a giant tray of peanuts will traipse through the stands yelling: ‘Get yerr ‘nuts, get ‘em while they’re hot!’ That’d be exciting!”
“After that we could go to the gift shop and buy all sorts of things. I want to buy a jersey, a foam baseball finger, autographed baseballs, and…”
“One of those ten dollar seat cushions for your butt would be nice.” Aaron stated. “Last time I was here, my friend bought two. One for his butt and one for his back. Those fold-up plastic seats aren’t very comfortable.”
“And I want a pretty little stuffed animal with the team’s mascot on it.” Cindy continued as the group got out of the car, closed the car doors, and walked towards the stadium. “Maybe a cute teddy bear, or a lion, or maybe some kind of cat. That reminds me, what is the mascot for this major league team anyway? I hope it’s adorable!”
Just then, as they were walking into the stadium, a man in a costume consisting of a giant yellow fuzzy ball came up to them. After waving hello, he started making a cartoonish zipp-ing sound as smaller yellow balls attached to circular wires rotated around him.
“Hey Orbit!” Darrell said as he gave the Albuquerque Isotope’s mascot, a life-sized electron, a high five. “Can’t wait to see a fantastic game!”
Cindy, Darrell, Melvin, and Aaron were sitting comfortably in their upper-deck seats, waiting for the minor league game to begin. As is common in many minor league baseball games, there was a variety of pre-game entertainment to get everyone pumped up. An Elvis impersonator had just finished his song. Rolled up t-shirts were currently being slingshot into the stands all around the stadium. The three were enjoying themselves and the entertainment when they spotted some friends four rows beneath them.
“Evan and Edith!”
Evan and Edith turned around in their seats. Seeing their friends, they stood up and decided to sit beside them.
“It’s good to see you guys! It’s been such a long time. Man, just what are the odds of us meeting at a place like this!” Evan said, incredulous. He paused, snorted to himself, and answered his own question: “Hmm… it’s probably the exact same odds of finding an electron from the 5d orbital inside the 4f shell.”
“Hehehehe.” Edith guffawed. “Orbital! Get it? Like the mascot?”
Melvin stared back blankly.
“Electrons… orbiting around the nucleus in specific shells Which aren’t actual shells but simply a designated level of probability as to the location of an uncertainly-located electron floating around in three dimensional space?”
“…”
“That reminds me! Continuing back to our earlier conversation,” Evan said to Edith, “Before we came over here, Edith and I were talking earnestly about the fourth dimension!”
“The fourth dimension? You mean time?” Aaron said smugly. “Yeah I knew that already.” Aaron looked down hopefully at his watch and at the giant screen above the field, wishing this educational conversation would be cut short by the beginning of the game. “Too bad we haven’t quite gained full control of that dimension yet.”
“Uh, that’s a negative, welcome to 1916 Mr. Woodrow Wilson.” Edith laughed snottily. “Time as the fourth dimension with regards to Einstein’s theory of general relativity is old news. I’m sure I could educate you on that topic other time. We’re talking about the fourth spatial dimension.”
“Do I even want to ask what that is?” Darrell looked at his two friends questioningly.
“It’s simple.” Edith responded. “You’ve got the second dimension, which is basically like a flat piece of paper. That’s all of your existence – everybody and everything lives on that flat paper. Then you’ve got the third dimension, which is well, what we’re living in right now.”
“Ooh, this is the good part.” Evan said. “Go on go on!”
“And the fourth dimension is well, it’s like a totally other direction outside the third dimension, see instead of moving up, left, or back you move kata, and… er… it looks like…”
Evan tapped his foot impatiently as Edith floundered trying to explain. “I know something that will help. Tell them about the usefulness of using stereographic projections to visualize a 24-cell from 4-space into three dimensions.”
upload.wikimedia.org/wikipedia/en/3/3d/Stereographic_polytope_24cell_faces.png
“Hmm… that might be a little complicated. Just talking about the fourth dimension out of nowhere is tough. You know, maybe we could start with something easier, something we could all grasp…”
As Edith was talking, the Albuquerque Isotopes game was about to begin. The conversation ended as everyone turned to watch the opening pitch thrown from the pitcher’s mound. As the ball neared home plate, a loud thwack reverberated through the stadium. But it wasn’t the sound of the baseball bat hitting the ball…
Time stopped, and when Cindy gathered her senses, she found herself looking straight ahead. In a line. A very thin, one-dimensional line.
Aaron, Evan, Edith, Cindy, Melvin, and Darrell inexplicably found themselves as super-tiny lines, living in a 1-dimensional world.
A 1-dimensional world looks like this to an outsider:
<------------------------------------------------->
It is simply a line that goes left and right and nowhere else.
But for Cindy, who was now living on this 1-dimensional world, there was a totally different perspective. As a dot facing forward her entire field of vision was seeing things in one way – looking completely straight forward as if her eyes were locked in place. And that one way forward vision was completely engulfed and blocked by another large black point known as Darrell.
“Darrell, move out of the way!” Cindy said as she moved forward trying to get past him. “MOVE!”
Cindy tried to take a sidestep to get around him, but she quickly found this was impossible, as there was no side to step to. She then tried to look around her new world, but also found this was impossible as there was only other one way to look: backwards. That was it – either you look forwards, or you look backwards along this line.
Suddenly she ‘turned’ her head and a whole new reality – the reality that was behind her – appeared. Darrel’s big black point was now nowhere to be seen. She continued along this new path until she ran into a big black point known as Evan. Likewise, she was unable to pass him.
“Oh fabulous. I’m stuck between Evan and Darrell and there is literally no one else I can talk to.” she thought. “And the worst thing is, even in this 1-dimensional world, I’m still forced to have to look at Darrell’s big fat ass.”
“So Evan,” she said gamely. “What the hell is this?”
Evan was giddy at his new surroundings, and about-faced to face Cindy. “This is so exciting!” He said. “We’re tiny points in 1-dimensional space. Just livin’ on a line like we’re at -1999!”
“And that means…”
“Well think of it this way,” Evan began. “Remember that baseball pitch the pitcher threw to home plate? Pretend he threw the ball in an exactly straight line. We’re now living entirely on just that line. The mound, the bleachers, and everywhere else is completely invisible to us, because we can’t even imagine those directions right now. Even though it’s all still there, just out of reach, it is completely outside our world.”
“That sucks. I wanted to see the game.” Cindy said.
It quickly became apparent that living in the first dimension was not nearly as exciting as Evan thought. There were only two ways to move – forward and backward. And only two people to talk to.
But soon the excitement was about to ramp up (or ramp left, I should say) as suddenly, with another baseball-bat-sound-thwack, 5 of them were transported into the second dimension.
“So now we’re in two dimensions, huh.” Aaron said as he surveyed his surroundings. He was now living on the flat plane of the ground of the baseball field. His world had gained an extra dimension – width in addition to length – and he could now move left and right as well as forward and backwards.
Aaron himself had changed shape as well. Just as people living in a 3-dimensional world are 3-dimensional shapes, people living in a 2-dimensional world are 2-dimensional shapes. Aaron himself was now a square. Edith had turned into a circle, Darrell was a triangle, Evan was a hexagon, and Cindy now looked like Pac-Man. Melvin was nowhere to be found.
From an outsider’s point of view, the five looked just like shapes drawn on a flat piece of paper. Their whole world was just that piece of paper – they could move left/right and up/down, but nowhere else. The stadium around them had turned from a normal stadium into a simple oval that was now the boundary of their world.
But while it is helpful to imagine what these five looked like from up above, the perspective from their point of view down in 2-dimensions was a whole other story.
“Holy shit watch where you are going!” Aaron yelled as Darrell was walking toward him. Darrell, who was a triangle, was walking at Aaron pointy part first. His killer angle, a sharp wedge pointed straight at Aaron, could easily pierce the poor square in twain. That sharp angle would push into the side of the square and slice him in two. In a 2-dimensional world, having sharp angles was a liability.
“Sorry dude, still getting used to this whole flatland thing.”
Perhaps try and think about what it would be like to live on a piece of paper. Just like when in 3-d space you are unable to see someone’s back when you are talking to them, in 2-d space you can’t see the back of them either. When Aaron looks at Darrell in 2-d land it might look something like this:
Aaron(square) < Darrell ~ triangle
Aaron(square) ( Edith ~ circle
Basically everyone looks like line-shapes that change shape when they rotate or move. For a visual demonstration, you could watch this full-length movie about life in 2-dimensions.
Edith was having trouble moving around in her new 2-dimensional world. It was kind of like walking around a garden maze blind – you couldn’t really tell where you were going until you felt your way around the corner.
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When walking around one of those corners Edith bumped into Evan. (Thankfully the circle bumped into the hexagon side-first so everyone was safe.) The two started talking about their new world.
“You know the one thing that really makes me wonder,” Evan started. “Is how people in this 2-dimensional world eat. Take Cindy for instance. She looks like Pac-Man. If she were to actually eat one of those pac-man dots through her mouth, where would the dot go? Pretend she has a full set of intestines starting from her mouth and ending at her rectum. This hollow 2-dimensional tube that goes straight through her body would effectively cut her completely in half!”
“That’s true Evan, however, that leads us to a more important question,” Edith said. “How does she poop??”
Meanwhile, poopless Pac-Woman Cindy walked by a beautiful 2-d fountain (imagine what that looks like!) and spotted something strange out of the corner of her eye. It was Marvin. But he was still stuck in the 1st dimension!
Yep, there was Marvin, his tiny point-self, living on his impossibly thin line. He looked quite funny, pacing back and forth endlessly. Cindy waddled over to it to say hi. But then she remembered Marvin couldn’t see or hear her, just like she couldn’t see or hear the rest of the crowd in the baseball stadium when she was in the first dimension.
How could Cindy communicate with Marvin who was trapped in his one-dimensional world? Slowly, she put her ‘finger’ into the 1-dimensional line. To Marvin the finger showed up as a simple point. When Cindy pulled back her finger, the point disappeared.
Marvin stopped and stared at the disappearing point. No other point had done that in his world before. He didn’t have an explanation for it. There was no way he could deduce the entire existence of 2-dimensional life, with all its oddities and foibles. To Marvin, imagining the entire world of 2-dimensions simply from the appearance and disappearance of one point was unfathomable.
Meanwhile, Cindy decided to have a little fun. When Marvin moved backwards she popped her finger into the world right in front of him, stopping him in his path, causing Marvin to bump into it and figuratively fall flat on his face. Giggling, when he turned around to move the other way she popped another point right in front of him. Cindy was having way too much fun playing around with ant-Marvin when another baseball-bat-like thwack pierced all of the dimensions.
“Where could we possibly be now?!?” shrieked Aaron, his eyes closed, frightened of opening them to see what crazy world he would experience next.
“Guess, ya moron.”
Aaron opened his eyes and saw --- the regular ole baseball field. Plain old three dimensions. Everything back to normal.
“Oh.” Aaron said. He didn’t know how to feel.
“Well I for one am glad that’s over with!” exclaimed Darrell. “I have enough trouble making my way around in three dimensions without bumping into things, let alone the crazy worlds we just went through.”
“Yeah, I guess so.” Evan said, looking around him at the others. Darrell, Aaron, himself, Cindy… he knew Marvin was trapped in 1-dimensional land, but where was Edith?
“Edith is still trapped in flatland!”
It was true, there was pac-woman Edith, still her two-dimensional self living on her flat piece of paper. But as the others looked down on her, something looked different from this perspective. Something strange.
“Oh my god, we can see her insides! Her brain! Her intestines!”
Yes, as I’m sure you know, when you draw a square on a piece of paper you are able to see both the inside of the square and of course the outside of the square. From their perspective in 2-d land, of course, all anyone could see was the outsides. But from this three dimensional vantage point they could see Cindy’s beating 2-d heart and throbbing 2-d lungs.
“Ew.”
Additionally, as three of the baseball fans were about to find out, a similar property exists in the fourth dimension. From the fourth dimension looking into our world, you can see the entirety of the inside of people’s bodies. Just as if it they were all laid out opened up on an autopsy table…
Thwack.
Evan, Aaron, and Cindy found themselves in the fourth dimension. Just one short simple sidestep away from the entire known 3-d universe.
Evan knew the first thing he wanted to do. He grabbed a bottle of wine and, without opening it in any way, drank all of it down.
After that, he skipped over to a UFO meeting of crackpots in Roswell, New Mexico. Tapping into 3-d space with his 4-d finger much like Cindy did to 1-dimensional Darnell, he sent the kooks screaming in all directions. All they saw an instantly-appearing and disappearing, constantly growing, shifting, and rotating, three dimensional figure that popped in and out of existence.
It’s hard to imagine the fourth dimension, and many people explain it better than I do. The simplest way is probably to imagine a square. Now put together a cube which has 6 square faces. A tesseract (a 4-d cube) has 8 cube ‘faces’ instead of squares surrounding it.
This video explains it very well. I’d skip chapter 1. Start on 2 if you want the 2-d to 3-d analogue, or start on 3 if you want to see a representation the 4-d stuff without a fuller explanation. Here is a table of contents which helps a lot. If you want something more entertaining, you could watch Flatland the Movie or read the 1884 novella it was based on.
But those three weren’t the only denizens of the fourth dimension.
A 600-cell figure appeared and began to chase down one of the villagers. This menacing figure, with 1,200 faces, undulated and rotated through the mysterious fourth dimension, chasing someone, until they became captured and taken to the zero-th dimension forever…
“Wow, take a look at that huge stadium!” Cindy exclaimed as she pointed towards the baseball stadium they were approaching. “There’s something so classic, so prestigious about a big league baseball game. Something so American about it.”
“Cindy, I know you’re new to the whole baseball thing, but…” Darrell started.
“I can’t wait to eat a great American hotdog!” Cindy interrupted. “Speaking of vendor food, I wonder if some guy carrying a giant tray of peanuts will traipse through the stands yelling: ‘Get yerr ‘nuts, get ‘em while they’re hot!’ That’d be exciting!”
“After that we could go to the gift shop and buy all sorts of things. I want to buy a jersey, a foam baseball finger, autographed baseballs, and…”
“One of those ten dollar seat cushions for your butt would be nice.” Aaron stated. “Last time I was here, my friend bought two. One for his butt and one for his back. Those fold-up plastic seats aren’t very comfortable.”
“And I want a pretty little stuffed animal with the team’s mascot on it.” Cindy continued as the group got out of the car, closed the car doors, and walked towards the stadium. “Maybe a cute teddy bear, or a lion, or maybe some kind of cat. That reminds me, what is the mascot for this major league team anyway? I hope it’s adorable!”
Just then, as they were walking into the stadium, a man in a costume consisting of a giant yellow fuzzy ball came up to them. After waving hello, he started making a cartoonish zipp-ing sound as smaller yellow balls attached to circular wires rotated around him.
“Hey Orbit!” Darrell said as he gave the Albuquerque Isotope’s mascot, a life-sized electron, a high five. “Can’t wait to see a fantastic game!”
Cindy, Darrell, Melvin, and Aaron were sitting comfortably in their upper-deck seats, waiting for the minor league game to begin. As is common in many minor league baseball games, there was a variety of pre-game entertainment to get everyone pumped up. An Elvis impersonator had just finished his song. Rolled up t-shirts were currently being slingshot into the stands all around the stadium. The three were enjoying themselves and the entertainment when they spotted some friends four rows beneath them.
“Evan and Edith!”
Evan and Edith turned around in their seats. Seeing their friends, they stood up and decided to sit beside them.
“It’s good to see you guys! It’s been such a long time. Man, just what are the odds of us meeting at a place like this!” Evan said, incredulous. He paused, snorted to himself, and answered his own question: “Hmm… it’s probably the exact same odds of finding an electron from the 5d orbital inside the 4f shell.”
“Hehehehe.” Edith guffawed. “Orbital! Get it? Like the mascot?”
Melvin stared back blankly.
“Electrons… orbiting around the nucleus in specific shells Which aren’t actual shells but simply a designated level of probability as to the location of an uncertainly-located electron floating around in three dimensional space?”
“…”
“That reminds me! Continuing back to our earlier conversation,” Evan said to Edith, “Before we came over here, Edith and I were talking earnestly about the fourth dimension!”
“The fourth dimension? You mean time?” Aaron said smugly. “Yeah I knew that already.” Aaron looked down hopefully at his watch and at the giant screen above the field, wishing this educational conversation would be cut short by the beginning of the game. “Too bad we haven’t quite gained full control of that dimension yet.”
“Uh, that’s a negative, welcome to 1916 Mr. Woodrow Wilson.” Edith laughed snottily. “Time as the fourth dimension with regards to Einstein’s theory of general relativity is old news. I’m sure I could educate you on that topic other time. We’re talking about the fourth spatial dimension.”
“Do I even want to ask what that is?” Darrell looked at his two friends questioningly.
“It’s simple.” Edith responded. “You’ve got the second dimension, which is basically like a flat piece of paper. That’s all of your existence – everybody and everything lives on that flat paper. Then you’ve got the third dimension, which is well, what we’re living in right now.”
“Ooh, this is the good part.” Evan said. “Go on go on!”
“And the fourth dimension is well, it’s like a totally other direction outside the third dimension, see instead of moving up, left, or back you move kata, and… er… it looks like…”
Evan tapped his foot impatiently as Edith floundered trying to explain. “I know something that will help. Tell them about the usefulness of using stereographic projections to visualize a 24-cell from 4-space into three dimensions.”
upload.wikimedia.org/wikipedia/en/3/3d/Stereographic_polytope_24cell_faces.png
“Hmm… that might be a little complicated. Just talking about the fourth dimension out of nowhere is tough. You know, maybe we could start with something easier, something we could all grasp…”
As Edith was talking, the Albuquerque Isotopes game was about to begin. The conversation ended as everyone turned to watch the opening pitch thrown from the pitcher’s mound. As the ball neared home plate, a loud thwack reverberated through the stadium. But it wasn’t the sound of the baseball bat hitting the ball…
Time stopped, and when Cindy gathered her senses, she found herself looking straight ahead. In a line. A very thin, one-dimensional line.
Aaron, Evan, Edith, Cindy, Melvin, and Darrell inexplicably found themselves as super-tiny lines, living in a 1-dimensional world.
A 1-dimensional world looks like this to an outsider:
<------------------------------------------------->
It is simply a line that goes left and right and nowhere else.
But for Cindy, who was now living on this 1-dimensional world, there was a totally different perspective. As a dot facing forward her entire field of vision was seeing things in one way – looking completely straight forward as if her eyes were locked in place. And that one way forward vision was completely engulfed and blocked by another large black point known as Darrell.
“Darrell, move out of the way!” Cindy said as she moved forward trying to get past him. “MOVE!”
Cindy tried to take a sidestep to get around him, but she quickly found this was impossible, as there was no side to step to. She then tried to look around her new world, but also found this was impossible as there was only other one way to look: backwards. That was it – either you look forwards, or you look backwards along this line.
Suddenly she ‘turned’ her head and a whole new reality – the reality that was behind her – appeared. Darrel’s big black point was now nowhere to be seen. She continued along this new path until she ran into a big black point known as Evan. Likewise, she was unable to pass him.
“Oh fabulous. I’m stuck between Evan and Darrell and there is literally no one else I can talk to.” she thought. “And the worst thing is, even in this 1-dimensional world, I’m still forced to have to look at Darrell’s big fat ass.”
“So Evan,” she said gamely. “What the hell is this?”
Evan was giddy at his new surroundings, and about-faced to face Cindy. “This is so exciting!” He said. “We’re tiny points in 1-dimensional space. Just livin’ on a line like we’re at -1999!”
“And that means…”
“Well think of it this way,” Evan began. “Remember that baseball pitch the pitcher threw to home plate? Pretend he threw the ball in an exactly straight line. We’re now living entirely on just that line. The mound, the bleachers, and everywhere else is completely invisible to us, because we can’t even imagine those directions right now. Even though it’s all still there, just out of reach, it is completely outside our world.”
“That sucks. I wanted to see the game.” Cindy said.
It quickly became apparent that living in the first dimension was not nearly as exciting as Evan thought. There were only two ways to move – forward and backward. And only two people to talk to.
But soon the excitement was about to ramp up (or ramp left, I should say) as suddenly, with another baseball-bat-sound-thwack, 5 of them were transported into the second dimension.
“So now we’re in two dimensions, huh.” Aaron said as he surveyed his surroundings. He was now living on the flat plane of the ground of the baseball field. His world had gained an extra dimension – width in addition to length – and he could now move left and right as well as forward and backwards.
Aaron himself had changed shape as well. Just as people living in a 3-dimensional world are 3-dimensional shapes, people living in a 2-dimensional world are 2-dimensional shapes. Aaron himself was now a square. Edith had turned into a circle, Darrell was a triangle, Evan was a hexagon, and Cindy now looked like Pac-Man. Melvin was nowhere to be found.
From an outsider’s point of view, the five looked just like shapes drawn on a flat piece of paper. Their whole world was just that piece of paper – they could move left/right and up/down, but nowhere else. The stadium around them had turned from a normal stadium into a simple oval that was now the boundary of their world.
But while it is helpful to imagine what these five looked like from up above, the perspective from their point of view down in 2-dimensions was a whole other story.
“Holy shit watch where you are going!” Aaron yelled as Darrell was walking toward him. Darrell, who was a triangle, was walking at Aaron pointy part first. His killer angle, a sharp wedge pointed straight at Aaron, could easily pierce the poor square in twain. That sharp angle would push into the side of the square and slice him in two. In a 2-dimensional world, having sharp angles was a liability.
“Sorry dude, still getting used to this whole flatland thing.”
Perhaps try and think about what it would be like to live on a piece of paper. Just like when in 3-d space you are unable to see someone’s back when you are talking to them, in 2-d space you can’t see the back of them either. When Aaron looks at Darrell in 2-d land it might look something like this:
Aaron(square) < Darrell ~ triangle
Aaron(square) ( Edith ~ circle
Basically everyone looks like line-shapes that change shape when they rotate or move. For a visual demonstration, you could watch this full-length movie about life in 2-dimensions.
Edith was having trouble moving around in her new 2-dimensional world. It was kind of like walking around a garden maze blind – you couldn’t really tell where you were going until you felt your way around the corner.
When walking around one of those corners Edith bumped into Evan. (Thankfully the circle bumped into the hexagon side-first so everyone was safe.) The two started talking about their new world.
“You know the one thing that really makes me wonder,” Evan started. “Is how people in this 2-dimensional world eat. Take Cindy for instance. She looks like Pac-Man. If she were to actually eat one of those pac-man dots through her mouth, where would the dot go? Pretend she has a full set of intestines starting from her mouth and ending at her rectum. This hollow 2-dimensional tube that goes straight through her body would effectively cut her completely in half!”
“That’s true Evan, however, that leads us to a more important question,” Edith said. “How does she poop??”
Meanwhile, poopless Pac-Woman Cindy walked by a beautiful 2-d fountain (imagine what that looks like!) and spotted something strange out of the corner of her eye. It was Marvin. But he was still stuck in the 1st dimension!
Yep, there was Marvin, his tiny point-self, living on his impossibly thin line. He looked quite funny, pacing back and forth endlessly. Cindy waddled over to it to say hi. But then she remembered Marvin couldn’t see or hear her, just like she couldn’t see or hear the rest of the crowd in the baseball stadium when she was in the first dimension.
How could Cindy communicate with Marvin who was trapped in his one-dimensional world? Slowly, she put her ‘finger’ into the 1-dimensional line. To Marvin the finger showed up as a simple point. When Cindy pulled back her finger, the point disappeared.
Marvin stopped and stared at the disappearing point. No other point had done that in his world before. He didn’t have an explanation for it. There was no way he could deduce the entire existence of 2-dimensional life, with all its oddities and foibles. To Marvin, imagining the entire world of 2-dimensions simply from the appearance and disappearance of one point was unfathomable.
Meanwhile, Cindy decided to have a little fun. When Marvin moved backwards she popped her finger into the world right in front of him, stopping him in his path, causing Marvin to bump into it and figuratively fall flat on his face. Giggling, when he turned around to move the other way she popped another point right in front of him. Cindy was having way too much fun playing around with ant-Marvin when another baseball-bat-like thwack pierced all of the dimensions.
“Where could we possibly be now?!?” shrieked Aaron, his eyes closed, frightened of opening them to see what crazy world he would experience next.
“Guess, ya moron.”
Aaron opened his eyes and saw --- the regular ole baseball field. Plain old three dimensions. Everything back to normal.
“Oh.” Aaron said. He didn’t know how to feel.
“Well I for one am glad that’s over with!” exclaimed Darrell. “I have enough trouble making my way around in three dimensions without bumping into things, let alone the crazy worlds we just went through.”
“Yeah, I guess so.” Evan said, looking around him at the others. Darrell, Aaron, himself, Cindy… he knew Marvin was trapped in 1-dimensional land, but where was Edith?
“Edith is still trapped in flatland!”
It was true, there was pac-woman Edith, still her two-dimensional self living on her flat piece of paper. But as the others looked down on her, something looked different from this perspective. Something strange.
“Oh my god, we can see her insides! Her brain! Her intestines!”
Yes, as I’m sure you know, when you draw a square on a piece of paper you are able to see both the inside of the square and of course the outside of the square. From their perspective in 2-d land, of course, all anyone could see was the outsides. But from this three dimensional vantage point they could see Cindy’s beating 2-d heart and throbbing 2-d lungs.
“Ew.”
Additionally, as three of the baseball fans were about to find out, a similar property exists in the fourth dimension. From the fourth dimension looking into our world, you can see the entirety of the inside of people’s bodies. Just as if it they were all laid out opened up on an autopsy table…
Thwack.
Evan, Aaron, and Cindy found themselves in the fourth dimension. Just one short simple sidestep away from the entire known 3-d universe.
Evan knew the first thing he wanted to do. He grabbed a bottle of wine and, without opening it in any way, drank all of it down.
After that, he skipped over to a UFO meeting of crackpots in Roswell, New Mexico. Tapping into 3-d space with his 4-d finger much like Cindy did to 1-dimensional Darnell, he sent the kooks screaming in all directions. All they saw an instantly-appearing and disappearing, constantly growing, shifting, and rotating, three dimensional figure that popped in and out of existence.
It’s hard to imagine the fourth dimension, and many people explain it better than I do. The simplest way is probably to imagine a square. Now put together a cube which has 6 square faces. A tesseract (a 4-d cube) has 8 cube ‘faces’ instead of squares surrounding it.
This video explains it very well. I’d skip chapter 1. Start on 2 if you want the 2-d to 3-d analogue, or start on 3 if you want to see a representation the 4-d stuff without a fuller explanation. Here is a table of contents which helps a lot. If you want something more entertaining, you could watch Flatland the Movie or read the 1884 novella it was based on.
But those three weren’t the only denizens of the fourth dimension.
A 600-cell figure appeared and began to chase down one of the villagers. This menacing figure, with 1,200 faces, undulated and rotated through the mysterious fourth dimension, chasing someone, until they became captured and taken to the zero-th dimension forever…