Read Online Stranded (A stand-alone SF thriller) (The Prometheus Project Book 3) by Douglas E. Richards - Free Book Online Page A
Authors: Douglas E. Richards
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on the board.
“So here you see a Flatlander eyeing a bank vault.”
“How is that a bank vault?” protested Ryan. “It’s just a square. And it’s not enclosed.”
“Good point,” said Mr. Resnick. “It doesn’t have a roof. Why do you think that is?”
Regan’s eyes widened. Could it be that this was finally beginning to make some kind of bizarre sense to her? “Because it can’t have a roof,” she said. “Because you can’t have any height in Flatland. A roof has to go over something. But there is no such thing as over or under in Flatland.”
“You’ve got it,” said her father. “But it doesn’t need a roof. Flatlanders have no way to see what’s inside the vault. And they can’t climb over the line blocking them from the money. So unless they can break through one of the walls there is no way they can get into this vault. But we live and move in the third dimension. So we could get the money. Easily ,” he said. “We could just reach in from above and grab it. Everyone in Flatland would think the theft was impossible. Like magic. But what seems impossible in one dimension can be laughably easy in a higher dimension.”
Ryan scratched his head. “So everything you’re saying about Flatland would be true for us also.”
His father nodded. “Yes. That’s exactly the point of this thought experiment.”
“So someone living in the fourth dimension could rob one of our locked vaults,” said Ryan. “Just as easily as we could steal from a Flatland vault.”
“Very good,” said Mr. Resnick, nodding enthusiastically. “Even if our vault had four walls, a floor and a ceiling that were all made of three-foot-thick steel. The Flatlanders can’t possibly imagine that their vault is wide open from above. To them there is no above. Same with us. Our sealed vault seems absolutely closed and impenetrable to us. But it would be wide open when viewed from the fourth dimension. And when our money disappeared from a closed vault, we would think it was magic.”
“Are you understanding any of this?” asked Ryan.
“I don’t know,” replied Regan. “But Dad was right. This stuff is making my brain hurt.”
“So let’s perform a thought experiment that wasn’t in Abbott’s book,” continued Mr. Resnick.
He scribbled on the board once again and said, “Here I’ve drawn a three-dimensional object, shaped like a wedge of cheese.
“Notice how only its top edge is touching Flatland. So which part of this 3D object would the Flatlanders see?”
Regan rolled her eyes. “Dad, you drew one of the lines thicker than the rest and you have an arrow pointing to it. So I’m going to say they’d only see that.” She pointed to her father’s drawing. “Are those little circles supposed to be Flatlanders?” she said in amusement.
Mr. Resnick smiled with his eyes. “I’m afraid so. Now you see why I went into science and not art. Anyway, that’s right, the Flatlanders would see only a line. Now if you and I were standing on Flatland, we could look down over the edge and see the cheese wedge. But not Flatlanders. They can’t perceive anything above or below them. The wedge is there—they just have no way of looking in that particular direction. Are you with me?”
Both kids nodded.
“Let’s suppose that one day a few Flatlanders stumble upon this line and measure it very, very carefully. Suppose they even name it.” His eyes twinkled. “Let’s say they call it Prometheus .”
He drew a second figure next to his first.
“So now they enter this line right where I have the arrow pointing, and spread out. Notice that the precise point where they enter is part of both Flatland and the surface of the cheese wedge that is facing us.”
Mr. Resnick capped the black marker and slid it onto the tray at the bottom of the whiteboard once again.
“So now, as far as the Flatlanders know, they’re still on Flatland. They still perceive everything as being in two-dimensions. They have
“So here you see a Flatlander eyeing a bank vault.”
“How is that a bank vault?” protested Ryan. “It’s just a square. And it’s not enclosed.”
“Good point,” said Mr. Resnick. “It doesn’t have a roof. Why do you think that is?”
Regan’s eyes widened. Could it be that this was finally beginning to make some kind of bizarre sense to her? “Because it can’t have a roof,” she said. “Because you can’t have any height in Flatland. A roof has to go over something. But there is no such thing as over or under in Flatland.”
“You’ve got it,” said her father. “But it doesn’t need a roof. Flatlanders have no way to see what’s inside the vault. And they can’t climb over the line blocking them from the money. So unless they can break through one of the walls there is no way they can get into this vault. But we live and move in the third dimension. So we could get the money. Easily ,” he said. “We could just reach in from above and grab it. Everyone in Flatland would think the theft was impossible. Like magic. But what seems impossible in one dimension can be laughably easy in a higher dimension.”
Ryan scratched his head. “So everything you’re saying about Flatland would be true for us also.”
His father nodded. “Yes. That’s exactly the point of this thought experiment.”
“So someone living in the fourth dimension could rob one of our locked vaults,” said Ryan. “Just as easily as we could steal from a Flatland vault.”
“Very good,” said Mr. Resnick, nodding enthusiastically. “Even if our vault had four walls, a floor and a ceiling that were all made of three-foot-thick steel. The Flatlanders can’t possibly imagine that their vault is wide open from above. To them there is no above. Same with us. Our sealed vault seems absolutely closed and impenetrable to us. But it would be wide open when viewed from the fourth dimension. And when our money disappeared from a closed vault, we would think it was magic.”
“Are you understanding any of this?” asked Ryan.
“I don’t know,” replied Regan. “But Dad was right. This stuff is making my brain hurt.”
“So let’s perform a thought experiment that wasn’t in Abbott’s book,” continued Mr. Resnick.
He scribbled on the board once again and said, “Here I’ve drawn a three-dimensional object, shaped like a wedge of cheese.
“Notice how only its top edge is touching Flatland. So which part of this 3D object would the Flatlanders see?”
Regan rolled her eyes. “Dad, you drew one of the lines thicker than the rest and you have an arrow pointing to it. So I’m going to say they’d only see that.” She pointed to her father’s drawing. “Are those little circles supposed to be Flatlanders?” she said in amusement.
Mr. Resnick smiled with his eyes. “I’m afraid so. Now you see why I went into science and not art. Anyway, that’s right, the Flatlanders would see only a line. Now if you and I were standing on Flatland, we could look down over the edge and see the cheese wedge. But not Flatlanders. They can’t perceive anything above or below them. The wedge is there—they just have no way of looking in that particular direction. Are you with me?”
Both kids nodded.
“Let’s suppose that one day a few Flatlanders stumble upon this line and measure it very, very carefully. Suppose they even name it.” His eyes twinkled. “Let’s say they call it Prometheus .”
He drew a second figure next to his first.
“So now they enter this line right where I have the arrow pointing, and spread out. Notice that the precise point where they enter is part of both Flatland and the surface of the cheese wedge that is facing us.”
Mr. Resnick capped the black marker and slid it onto the tray at the bottom of the whiteboard once again.
“So now, as far as the Flatlanders know, they’re still on Flatland. They still perceive everything as being in two-dimensions. They have
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