Mrs. Resnick held out an arm in front of her kids as they began leaning forward for a closer look. “Not too close,” she warned.
Their dad’s team had learned that the cube was made of an unknown material and pulsed with an unknown energy—an energy they sensed was vast but that they had been unable to measure.
It also weighed 200,000 pounds! Slightly more than your average Rubik’s cube.
When the cube had been found, Ben Resnick insisted on proceeding with extreme caution. Before it was touched or anything that might be a control was tried, he intended to contain it within the strongest force-shield Earth technology could manage. Human equipment that was to be used to accomplish this feat had been gathered and stored against one wall.
They would soon be ready to begin experiments, but Mr. Resnick had recently changed his mind about the cube. He was now arguing that it shouldn’t be studied any further, no matter how great the precautions. The team had long talked about the danger of playing with advanced technology they didn’t understand. How even an innocent electrical outlet could be lethal to a caveman who decided to stick a finger inside to investigate. But in the case of the Enigma Cube, Mr. Resnick believed they were more like cavemen who had stumbled upon a nuclear warhead, and that it was best to leave it completely alone.
Ben Resnick worried they might accidentally trigger the Enigma Cube to unleash some horror upon the world. He was a scientist who had dedicated his life to the pursuit of knowledge, but he was also absolutely terrified of this alien artifact.
After seeing the cube for themselves, Ryan and Regan couldn’t blame him. The power throbbing away inside this unearthly object would scare any sane person.
CHAPTER 6
Entering Other Dimensions
Mrs. Resnick drove the electric cart to the silver, octagonal building that housed both her and her husband’s labs. Both kids were unusually quiet during the two-mile journey.
“We’re on a bit of a tight schedule,” said Mrs. Resnick as they arrived. “So why don’t you two grab an early lunch while I finish packing for the trip.”
“What kind of food are we bringing to Isis?” asked Ryan, trying to hide his concern but failing.
“Don’t worry, Ryan, since it’s only a weekend trip everyone is bringing their own food. I’ll make sure you don’t starve. I’m bringing enough peanut butter to last a week.”
“What about pizza?” said Ryan.
“Sorry. Unless you can figure out how to keep it cold or cook it over an open fire, frozen pizza is out. I’m pretty sure you can survive two days without it. I guess we’re going to find out,” she said in amusement.
Ryan and Regan were almost complete opposites when it came to food. Regan ate very little but made healthy choices and actively sought out new and unusual dishes to try. Ryan consumed more fuel than a blast furnace but was probably the pickiest kid on the planet. Aside from junk food, he lived almost entirely on pepperoni pizza, peanut butter, and hotdogs. If it weren’t for peanut butter, one of the world’s most nutritious foods, his parents were convinced he would now be only three feet tall.
A small kitchenette had been built in the corner of Mr. Resnick’s lab. While their mother packed, the kids entered the lab to find their father seated in front of his computer eating a submarine sandwich. He was short and what Regan termed cuddly-looking, with a few strands of white hair now at his temples where a uniform lawn of brown used to be. Unable to keep his hair from pointing in a dozen directions or his shirts tucked in and unwrinkled, he had finally given up. Now he kept his hair short and wore nothing but wrinkle-free polo shirts and black jeans.
“So what did you think of the Enigma Cube?” asked Mr. Resnick after greeting them.
“It’s the coolest thing I’ve ever seen,” replied Ryan.
“I’m glad you got to see it before we put a vault over it and locked it away forever.”
Ryan raised his eyebrows. “When are you going to do that?”
“Hopefully on Monday. That’s when the Managing Committee will take a vote. I think I’ve convinced a majority of members that it’s too risky to study any further.” He sighed. “At least I hope I have.”
“What about Dr. Harris?” asked Regan.
“Even though he’s the head of the project, he only gets one vote. That’s not to say his opinion doesn’t carry a lot of weight. The good news is that I think he’s leaning toward my point of view. He told me he was going to visit the Enigma building one last time today and make his final decision.”
Mr. Resnick held up his nearly finished sandwich. “Is Mom going to make you lunch?”
“No,” said Regan. “She said she needed to finish packing for the trip. We’re just gonna find something for ourselves.”
She and her brother headed off toward the kitchenette, but they were blocked from their destination by five large whiteboards that had been pulled together like train cars. The boards were covered with equations, strange symbols of every type, and indescribably strange geometric shapes. And four words—“stadium in a barrel”.
“Sorry about that,” said Mr. Resnick, rolling two of the boards apart so they could get through.
Regan pointed to the upper left corner of the board nearest her. “Stadium in a barrel, Dad? What does that mean?”
Mr. Resnick laughed. “It’s the result of a quick side calculation I did for fun. You know how Prometheus is far bigger than the hole it’s in. Well I calculated that when we enter this city, it’s the equivalent of stepping inside a barrel and finding a full-sized football stadium inside. A pretty neat trick.”
“Yeah, but we’ve known about that forever,” said Ryan.
“True. And I’ve always been pretty sure the key to pulling this off involves other dimensions. Well, I’m finally getting around to trying to understand this better mathematically.”
“Wait a minute, Dad,” said Ryan excitedly. “Back up for a second. Are you saying this city exists in another dimension?”
“Well, yes and no.”
“What does that mean?” said Ryan. He ran a hand through his hair. “And for that matter, what does another dimension even mean? You hear about traveling to other dimensions in science fiction all the time. But where exactly is that?”
Mr. Resnick looked at his watch. “Well, I suppose we have enough time before we need to head out. If you want, I’ll explain it to you. What do you say?”
“Are you kidding?” said Ryan. “I would love to hear this.”
Regan nodded in agreement.
“Okay,” said their father. “Why don’t you get something to eat while I erase a few of these white boards.”
“We’ll be right back,” said Ryan eagerly.
Once inside the kitchenette, Regan removed a bottle of water and a small container of low-fat yogurt from the refrigerator. She opened the yogurt, thrust a white plastic spoon inside, mixed in the strawberries on the bottom, and walked back to her father. Ryan eyed a frozen pepperoni pizza hungrily but knew he didn’t have the time to cook it. Instead he grabbed a bottle of water, an entire jar of peanut butter, and a plastic spoon before rushing to join his sister.
“Ready?” asked their father.
“Ready,” said Ryan for both of them, plunging his spoon into the jar and removing a brown, heaping mound of super-chunky peanut butter.
Regan shriveled up her nose as if a skunk were in the room. Ryan had eaten his favorite food straight out of the jar like this for years, but she wasn’t usually nearby when he did. What he was eating may have tasted great, but Regan thought it looked like something that should be coming out of his body rather than going in. “Ryan, why can’t you make a sandwich like everyone else?” she complained. “That is sooo disgusting.”
“Well I think yogurt is disgusting,” he replied, biting off the top portion of the brown lump loaded with countless bits of chopped up peanuts.
“Do you want to hear this or don’t you?” said Mr. Resnick pointedly. He waited for both kids to give him th
eir full attention and then began. “Okay, here we go. But I warn you. You’ll be pulling your hair out before I’m through and your brain will hurt. Don’t expect to understand everything I’m about to tell you. Believe me, I don’t fully understand everything I’m about to tell you.” He paused. “So what is a dimension in the first place?” he asked. “How would you even define the word?”
Both kids thought about this for a while. Finally Regan shrugged. “I don’t know. Something you can measure?” she said uncertainly.
“Okay,” said Mr. Resnick. “Something you can measure. That’s a reasonable definition, and as good a place to start as anywhere. So a line represents one dimension. Because you can only measure one thing about it: its length. That’s all. It doesn’t have any width or height. So then what figure would represent two dimensions?”
“A square,” said Ryan.
“Yes. Any flat shape would do, but a square works well. You can measure its length and width. But it still doesn’t have any height. So what figure would have three dimensions?”
Regan swallowed a spoonful of yogurt that the strawberries had turned pink. “A cube,” she replied. “You can measure three things. Its length, its width and its height.”
“Good,” said her father. “So these are the three dimensions we can perceive in our universe. And while you can think of a dimension as something you can measure, you can also think of dimensions as directions you can travel in. So let’s imagine for a moment that Brewster, Pennsylvania is the entire world.”
Ryan and Regan both groaned at the same time. “Are you trying to give us nightmares, Dad?” said Ryan with a grin.
Mr. Resnick laughed. “How about San Diego, California?”
“Now you’re talking,” said Regan.
“Okay,” said their father. “Suppose you were a conductor on a train going due north through San Diego. How many different directions could you go in?”
Regan tilted her head in thought. “Only one,” she said, wondering if this was a trick question. “You’d have to stay on the train track. So you could only go north.”
“Right. You can think of the train track as a line. A one-dimensional figure. And your options for travel in a one-dimensional world are extremely limited.” He paused. “Now let’s suppose you’re driving an off-road vehicle in the center of San Diego. What directions could you travel in?”
“Any direction you wanted to,” said Ryan. “North, south, east or west. Or anything in between.”
“That’s right. So the flat city of San Diego is like a two-dimensional figure. And you have lots of options for traveling in this two-dimensional world. Just adding a single dimension gives you a lot more freedom to move, doesn’t it?” He paused once again to give the kids time to digest this idea. “Now suppose you’re piloting a helicopter in the center of the city. What directions could you travel in now?”
“Well, you could travel north, south, east and west,” said Regan. “And up and down. And anywhere in between.”
“You’ve got it,” said Mr. Resnick. “So obviously, San Diego and the airspace above it represent a 3D figure. And once again, you have far more directions you can travel in.”
Mr. Resnick paused. “Okay,” he said. “So far this has been fairly simple. But it gets impossibly hard very quickly. Don’t worry if you don’t understand the rest of this. No one really does. Not completely. But I’m hoping you understand enough of it to at least get a sense of the possibilities.” He raised his eyebrows. “So what is the fourth dimension? And while ‘time’ can be considered a dimension, that’s not what I mean. I mean the fourth dimension of space.”
Both kids just stared at him blankly. Ryan even lowered his second mountainous spoonful of peanut butter to his side, and away from his mouth, for this first time.
“Well,” said their father. “Maybe we should review. To go from the first-dimension to the second, you have to move in a side to side direction. And to go from the second to the third, you have to move in an up and down direction. So what direction would you have to move in to get to the fourth dimension?”
They thought about this for about thirty seconds before giving up in total frustration.
“I think you’ve lost your mind, Dad,” said Ryan.
“Ryan’s right,” said Regan, taking a sip from the plastic water bottle in her hand. “There isn’t a fourth dimension. It’s a trick question. The universe ran out of dimensions after three.”
“You may be right,” said her father. “But then again, one of the most popular theories in modern physics suggests there are as many as 10 or 11 dimensions.” He smiled. “So I’ll tell you the answer. You would have to move in a direction that no human has ever been able to visualize. A direction that no human has ever moved in. A direction that isn’t north, south, east or west. Or up and down. Or anything in between.”
Ryan frowned. “There is no such direction,” he said in annoyance. “It’s ridiculous.”
“Just because we can’t imagine such a direction doesn’t necessarily mean it doesn’t exist. But even if we can’t visualize the fourth dimension, there are still ways we can understand some of its properties. Understand how beings living there would interact with us—with poor humans that can only sense three dimensions.”
Ryan shook his head. “I’m still going with the ‘you lost your mind’ thing,” he said.
Their father looked amused. “The best way to grasp some of the possibilities,” he said, “is to try a thought experiment.”
“A thought experiment?” repeated Ryan questioningly.
“Yes. An experiment you do in your mind only. Using nothing but your imagination. It’s an enormously powerful tool in physics. Some of Einstein’s greatest breakthroughs were the result of using this technique. The thought experiments we’ll be doing first appeared in a book written by an English schoolmaster, Edwin Abbott, in 1884. A book called Flatland.
“Abbott figured the best way to understand how we would appear to fourth dimensional beings,” continued Mr. Resnick, “is to think about how beings living in lower dimensions would appear to us. So he imagined a kingdom that existed in a universe with only one dimension. He called this Lineland. And he imagined a kingdom that existed in a universe with only two dimensions. He called this Flatland.”
Mr. Resnick raised his eyebrows. “So if there were a kingdom of people that existed in a universe with only one dimension, what would that kingdom be like?”
The siblings looked at each other perplexed. “I have no idea,” said Ryan for them both.
“Well, in Lineland, all the inhabitants would be line segments. And they could never change their order. Here, I’ll show you what I mean.”
He picked up a black marker and pulled off its cap with a loud pop. He went to the whiteboard and began writing squeakily.
Ben Resnick gave his kids a few seconds to digest his drawing and then, pointing to the line segment labeled, “The Queen,” he continued. “For example, if you were the Queen, you’d be stuck between the Court Jester and the King. Forever. Without any width dimension you couldn’t pass anyone—if you tried you would just slam into them. Like two trains trying to pass each other on the same track. Now if you could make use of the second dimension—move side to side—you could just move to a different track, so to speak, and easily get by. But a Linelander can’t. Their entire universe exists on a single line and they have no awareness of anything outside of this line.”
Mr. Resnick capped the marker and slid it onto the tray at the bottom of the whiteboard. He motioned to his desk. “I’m not a very good artist, so let’s move to my computer,” he said.
They walked a few yards to his glass-topped desk, on which sat a sleek laptop computer connected to a thirty-six inch monitor. In less than a minute of searching he found a cartoon drawing that would demonstrate his point and put it up on the screen.
Both kids smiled broadly and barely managed not to laugh when they saw it.
“Dad couldn’t draw
that?” broadcast Ryan. “Really?”
“We’re lucky Dad has such a powerful computer,” replied Regan sarcastically.
“So this brings us to Flatland,” continued Mr. Resnick, unaware that his kids were teasing him telepathically. “Flatland exists in a 2D universe. So think of Flatland as a giant piece of flat notebook paper. And Flatlanders—who appear as circle-people in the figure—are totally, well … flat. Flatlanders have no idea there is such a thing as up or down. They can only look and move in sideways directions. So if a Flatland dad suggested to his kids there might be another direction to move in, other than back and forth and sideways, they would tell him he was crazy. Impossible, they would say. There is no such direction, they would say. To us 3D beings, the up direction is obvious. But to the poor 2D Flatlanders, no matter how much you told them about the up direction and described what it was like, they couldn’t even begin to imagine it.”
“Like we can’t even begin to imagine what direction the fourth dimension would be in,” said Regan.
“Exactly,” said Mr. Resnick happily. “And since their universe exists in only two dimensions, Flatlanders are completely unable to lift themselves off the page. Not even a billionth of an inch. Just like we’re unable to move even a billionth of an inch in the direction of the fourth dimension. Whatever direction that is. But unlike people living in the line universe, at least Flatlanders can move past each other.”
Stranded (A stand-alone SF thriller) (The Prometheus Project Book 3) Page 5