Multidimensionality

200px-Flatland_coverMy study of the fourth dimension began with the book Flatland: A Romance of Many Dimensions. Although written as a satire of Victorian England, it also delves into the idea of multidimensionality. I was instantly attracted to the logical patterns and possibility of the fourth dimension. Mathematically speaking, there are an infinite number of dimensions. Physically speaking, the verdict’s still out.

My interest in the mathematical aspect of multidimensionality led me on a journey into religion, quantum physics, and string theory. Although a novice, I was fascinated by what I discovered and realized the fourth dimension is a wholly untapped area of exploration.

Below is Faedra’s second 4-D Basics class, which is not in “The Shifter”. It sheds light on some of the rudimentary aspects of the fourth dimension.

 

After a quick glance around the 4-D basics room, I walked to the most inconspicuous seat possible. Dr. Brown waddled into the room, wearing a shocking pink floral dress and matching lipstick. Given one of her legs was shorter than the other, her movement seemed labored. As the rest of the class walked in and settled themselves, Dr. Brown fiddled with her plasma paper.

Our watches announced the beginning of class.

Dr. Brown straightened as much as she could and plastered a large, goofy smile on her face. Gazing at the class, she tapped her finger on the desk and paused as if for effect. With a mere click of her pen, a transparent screen descended from the ceiling.

“Imagine an ellipse,” she said, waving the pen in midair. A large oval appeared on the glass screen as she did. The lines of the oval glowed incandescent blue, and the class was spellbound by the large, glimmering shape which seemingly hovered in the middle of the room. “Imagine this ellipse is a pictorial representation of time as we know it. Time begins on one end of the ellipse at the Big Bang. The universe expands outward for billions of years, following this path on top of the ellipse. At the other end of the ellipse, the expansion of our universe ceases—reaches its maximum width—and begins to fall back in on itself. We follow the path of our universe collapsing for billions of years on the bottom of our ellipse. The universe, and time, ends right back where it started at the Big Crunch. Notice that the Big Bang and the Big Crunch can be drawn at the same point.”

 

2014-09-11 09.26.11 pm

Dr. Brown paused to give us time to catch up to her words.

“Or maybe time is parabolic: it will continue to go on forever. Our universe will continue expanding but at a slower rate. Gravity is strong enough to slow the movement, but not strong enough to stop it. Of course, as it is understood now, our universe is not only expanding but it’s expanding at a faster rate. It will keeping spreading out, and will spread out faster with each passing century.”

“There are other theories as well. But any of these pictures can be used to illustrate my meaning, and so I will use the ellipse. Understand that the true picture of this ellipse, as it represents the entirety of time, would be enormous. And your life would be just a tiny speck on that gigantic ellipse. For all intents and purposes, your life would be a tiny line segment: perfectly straight. In fact, all recorded history is minute enough in comparison to seem like a mere line segment. Our experience of time is linear, or line-like.”

2014-09-11 09.30.01 pm

The room was silent as overstretched brains churned with the new information.

“Now, instead of this one-dimensional line, imagine that we have a two-dimensional surface,” Dr. Brown said. “If time were laid on the two-dimensional surface of our screen, then it’s conceivable that we could travel off our little line of time. But in order to understand this—to understand the fourth dimension—it’s necessary to understand the dimensions before it. I want you to form yourselves into pairs and discuss the first four dimensions with your partner. Draw pictures if you can.”

Immediately, I looked to where Lucy sat. Emma and Lucy were already chatting, clearly having paired themselves together. Even with my roommates I was odd girl out. Adam and Adrian eagerly began discussing the topic, and I looked around for someone else without a partner. There were several girls, and I hoped one of them would look my way. But all of their attention was on Dominic Archer. Unfortunately, all of his attention was on me.

“Why?” I asked after he turned his desk to face me.

“Why what?”

“There are at least … a dozen girls dying to be partners with you right now,” I said. “Why me?”

“Because none look quite as desperate as you,” he said, tapping his plasma paper. “Are you ready to discuss, or would you rather keep wasting our time?”

“Fine.”

“Okay, so the first dimension—“

“The zero dimension,” I said. “You need to start counting with zero. You can’t have something until you first have nothing.”

“I was saying that the first dimension we need to discuss is the zero dimension. But I guess you already know that.”

“It has neither width nor depth nor height.” I plunked the tip of my stylus on the screen to make a dot.

“Yes, and the first dimension is a line,” Nic said. He reached over to draw a line on my screen under the dot. I fought the urge to pull it away. “It has one dimension: width.”

“And the second dimension is a plane,” I said. “It has width and height but no depth.”

I drew a parallelogram to illustrate the concept and had barely finished when Nic grabbed the plasma paper from me.

“The third dimension has width, depth, and height, and can be represented by a cube,” he said as he drew. I held out my hand for him to return the device. “Those are the first four.”

2014-09-11 09.04.12 pm

He handed back my plasma paper, and we retreated as far as our seating arrangement would allow, arms crossed, pretending the other didn’t exist.

“Finished already?” Dr. Brown asked.

I hadn’t heard her approach, which was impressive given the volume of her limp.

“Yes,” Nic said.

“Really?” Dr. Brown rotated my plasma paper to view it better. “Well, very good.”

The plasma paper screeched softly as Dr. Brown twisted it back around, like two smooth stones sliding together. “But what does it mean? What does it mean for the people living in each of these dimensions?”

“Living in these dimensions?” I asked.

“Yes,” she said. “What kind of thing lives in a point, in a line, in a plane, in space?”

“We live in space,” I told her.

“Okay, now discuss the other dimensions.” Dr. Brown left to check on the other groups’ progress.

“What does that even mean?” I asked, not really intending Nic as the recipient of my inquiry.

“Like a point,” he said. “What lives in a point? You either have a point or you have nothing.”

“A point is nothing.”

“What’s your point?”

Given the stoic expression on his face, I couldn’t be certain if he meant to be funny. “So you’re saying everything that lives in the zero dimension is a point,” I said.

“That’s what I’m saying.”

“Then the first dimension could have points or—“

“Line segments.”

“I was going to say that,” I told him. “You don’t have to be better than me all the time.”

“I don’t have to be. It just sort of happens.”

I chose to ignore the slam. He was saying it just to annoy me.

“The second dimension, a plane, would have figures: a square or circle, any shape really,” I said.

“And the third dimension has solids.”

We crossed our arms again and stared in opposite directions. This time I heard Dr. Brown approach and was grateful for the interruption.

“Done already?” she asked.

“Yes.” Nic waved his hand in my direction. “Just ask her. She knows everything.”

Despite the sarcasm in his tone, Dr. Brown did as he suggested, and I was forced to regurgitate the conversation.

“You two are quite the team,” Dr. Brown said. “Nobody else has even finished describing the dimensions yet. They’re still stuck on the concept of time.” She looked between us as if she suspected some sort of outside help. “Well then, my next question is: what do the people of each dimension see when they look at each other? You’ll have to start with the first dimension since there can only be one point in any given zero dimension.”

She hobbled away again.

“What do people see when they look at each other?” I said. “Do you understand that?”

“Yeah,” he said. “Like what do you see when you look at me?”

Heat rushed to my face, and my eyes darted away in an effort to maintain a composed façade. I didn’t miss the amused smile that crept onto his face.

“I mean,” he said, “what do you, as a three-dimensional person, see when you look at other three-dimensional things?”

I swallowed. “That makes no sense; I see them. What else would I see?”

With an impatient sigh, he leaned forward to grab my plasma paper again. I recoiled. After deleting the previous contents, Nic drew a line on the screen and held it up for me.

2014-09-11 09.11.20 pm

“Here’s a line,” he said. “If line segments lived on this one-dimensional line, they’d look like this. What do they see when they look at each other?”

“Well, since they can’t see anything off the line, they’d see the part of the neighbor facing them: the endpoint. Person 2 would either see the endpoint of Person 1 or the endpoint of Person 3. Or both. Maybe Person 2 has two eyes.”

“Right, they see points,” Nic said. “Which are—”

“Zero-dimensional. Okay, I get it. One-dimensional people would see zero-dimensionally, two-dimensional people see one-dimensionally, and three-dimensional people see two-dimensionally. You always see in the dimension below you.”

“Right.”

“Segments in a line see points. Surfaces in a plane see line segments. Solids in space see surfaces.”

I grabbed the plasma paper back from Nic, erased his drawing, and replaced it with one of my own.

2014-09-11 08.31.24 pm

“The triangle can only see the parts of the circle and square facing him,” I said. “It’s like looking at paper turned on its side.” Nic took a glance at my drawing. “That’s why I can’t see all of you at once. I can only see one surface of you at any given time. I can’t see your back side while looking at your front side.”

“What a disappointment for you,” he said offhandedly, returning my plasma paper.

I jerked the screen out of his hands. “What a disappointment for you. Only able to flaunt one side of your glorious appearance at any given time. That limitation must bother you to no end.”

At another standoff, we reclined again in our seats, arms folded. This time, however, we glared at each other, ready to pounce on the first syllable uttered by the other.

“I simply can’t keep up with you,” Dr. Brown said. “What have you discovered now?”

We both began talking at once, and Dr. Brown raised her hand. “I think I have the gist of it. But who’s to say the universe stops at only three dimensions. What about the fourth?”

“The fourth?” I said before Dr. Brown could waddle off again. “How can we describe the fourth? We can’t see it.”

“You’ve already described it,” Dr. Brown said. “Use the patterns.”

Once Dr. Brown had turned her attention to the next pair of students, I looked back down at the screen. “Another dimension,” I said to myself. “Which way would it go?”

“Some people believe time is the fourth dimension.”

I shook my head. “No, time may be unique to the physics of this universe, but it doesn’t encompass the fourth dimension.”

“How do you know?”

“I don’t,” I said. “It was just a reaction. Anyway, these patterns have nothing to do with time; they’re all spatial. Not that time couldn’t really be a spatial measurement.”

“We can’t label the direction of the fourth dimension like we did the others. There isn’t a word for it.”

“We don’t need to. Every person sees things in the dimension below them, so a four-dimensional person would see things three-dimensionally. A four-dimensional person would see all of you at once: top, bottom, back, front—all the way around.” I stopped and glanced at him, waiting for a sarcastic comment.

Dr. Brown returned, but before either of us could speak, she held up her hand to stop the imminent word vomit.

“Peter Justice, the founder of IDS, discovered a point at which a tangent three-dimensional universe could be entered,” she said. “It’s similar to two intersecting lines or two intersecting planes.” She grabbed my plasma paper and began sketching on the screen. “Although we still experience everything as three-dimensional beings, that doesn’t mean we’re in the same three-dimensional universe. However, in order to make this jump from one three-dimensional universe to another, a four-dimensional shift is necessary. In order to move from one line to another line, you need to move in a plane. In order to move from one plane to another plane, you need to move in space. In order to move from one three-dimensional universe to another, you need to move in the dimension above it—in the fourth.”

She drew the concept and handed the plasma paper back to me.

2014-09-11 09.19.18 pm

“Well, I think I’ve challenged your brains enough for today,” Dr. Brown said. “I’ve downloaded your assignment. Please, have the first ten pages read before class tomorrow. The name of this book is Flatland: A Romance of the Dimensions by Edwin A. Abbott. He was one of the first people to write about the fourth dimension, at least for the general public to read.”

Dr. Brown scanned the rest of the class, squinting periodically. “I’m impressed by how quickly you grasped the multidimensional concept. Would one of you be willing to share what you’ve discovered with the rest of the class?”

“Faedra loves sharing her knowledge,” Nic said before I could even process the question.

“Wonderful,” Dr. Brown said in her guttural voice.

So, there I was on the second day of school, teaching a group of premies about the fourth dimension. I was going to kill him.

 

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