Lauren Ipsum: A Story About Computer Science and Other Improbable Things Read online

  “Well, okay. I can carry you in my pocket,” Laurie said. “Have you heard of Hamilton?”

  “I don’t know. Can you eat it?”

  “Never mind. Let’s go.”

  Chapter 2. Sense and Sensibleness

  Laurie and Xor soon reached the little town of Bach. It was very confusing at first, because the name “Bach” appeared on everything: Bach Street, Bach Avenue, Bach Plaza—even the sidewalk was labeled sidebach. They finally found Bach Haus down Bach Way.

  Laurie knocked on the enormous front door. A tall lady with frizzy white hair and an elegant coat answered. “Hello, what can I do for you?” she asked.

  “Are you Eponymous Bach? I’m Laurie. I was told you can help me.”

  “If I can’t help solve your problem, I can at least give it a name. Do come in and have some tea.”

  The house was impressive on the outside, but on the inside it was a mess! Strange machines were shoved against the walls, cobwebs hung down from the corners, tools were scattered on the floor, and piles and piles of paper with scribbled notes were everywhere. A violin was stuffed into a flowerpot. Xor jumped out of Laurie’s pocket to hunt some insects.

  “Um, so you’re a composer?” Laurie asked.

  “That’s right,” said Eponymous.

  “What kind of music do you compose?”

  “Oh, I don’t compose music,” Eponymous said. “I Compose Ideas!”

  “You compose . . . ideas? How?”

  “I put little ideas together to make bigger ones. Then I put those ideas together to make bigger and bigger ones! And then I put my name on them. You shouldn’t let any ideas escape without a name,” she said. “That’s Bach’s First Law of Eponymy. I made it myself, you see.”

  “Is that why all the streets are named after you?” Laurie asked.

  “Yes, I used to put my name on Things. But it’s much better to have your name on an Idea. That’s my Second Law of Eponymy.”

  “But why is an idea better?” Laurie asked. “You can’t see an idea.”

  “Because good ideas never wear out! You put your name on a birthday cake, but it doesn’t last very long, does it?”

  “No. You eat it right away,” Laurie said. Birthday cakes don’t last long at all!

  “You can also put your name on a mountain,” said Eponymous. “But even a mountain falls down eventually. It makes a terrible noise, too! No, the best way to make something last forever is to take away everything but the ideas.” She pointed to a portrait of a man with curly hair and a funny coat. “Look over there,” she said.

  “That’s my friend Andy Ampère. One day, he noticed that when he put electricity through two wires, they would bend a little toward each other. So he called it Andy’s Magical Wire Bender, and he went around selling it to people who make paper clips.”

  “That’s pretty neat!” said Laurie.

  “Yes, but I told Andy to keep going, to take away all of the Things until he had an Idea worth putting his name on. He realized he could use his machine to measure electricity by looking at how much the wires bent. That was truly new—a new law of nature. Nobody uses Andy’s Magical Wire Bender anymore, but Ampère’s Law will always be current.”

  “But why do you put your name on everything?”

  “Names are very important! A thing without a name is like a pot without a handle. Just try telling a story about turtles without using the word turtle.”

  “Well,” said Laurie, always ready to argue a point, “you could say a Green Round animal with a Shell instead of turtle.”

  “Hrmph,” Eponymous hrmphed, “That’s not a very easy name, but I suppose it will do. So how can I help you, child?”

  “I’m looking for a path back to Hamilton. The Wandering Salesman said I just have to go everywhere I’ve never been before, and eventually I’ll find my way home. But . . .”

  “But what, dear?”

  “I don’t know, something about what he said doesn’t make sense.”

  “It might make sense, but it may not be sensible,” said Eponymous.

  “Isn’t that the same thing?” asked Laurie.

  “Many things make sense but are not sensible at all! You can go from the front door to the back door by walking through the house, right?”

  “Sure.”

  “You can also walk around the outside of the house, or even all the way around the planet, to do the same thing. Many ways make sense, but only some are sensible.”

  “Then I want to find a sensible way,” said Laurie. “I don’t want to walk all around the planet!”

  “So,” Eponymous said, “we have named and framed your problem: Laurie’s Quest is to find the shortest path home.”

  “But how do I do that?” asked Laurie. “Is it difficult?”

  “You’ll never know unless you try. The next town up the road is called Symbol. Have you been there before?”

  “No, I’ve never even heard of it.”

  “Then it sounds perfect. Just follow Bach Avenue out of town, and take a left at Recursion Junction.”

  “That’s great!” said Laurie. “Xor, let’s go. Oh, that’s right,” she remembered. “Do you know anything about how to find Steganosauruses?”

  Eponymous smiled. “Who’s been telling you stories like that, my dear girl? Steganosauruses don’t exist.”

  Chapter 3. Rounding Error

  As they headed out of Bach, Laurie couldn’t help but tease Xor a little. “Steganosauruses don’t exist, huh?”

  “That lady doesn’t know what she’s talking about. Her place had some really good bugs, though.”

  “Maybe she’s right.”

  “She says Steganosauruses don’t exist because she’s never seen one. But that proves my point! Steganosauruses are so good at hiding that people think they’re imaginary.”

  “That doesn’t make any sense, Xor.”

  “Who are you going to believe, me or your own eyes?” Squawk! Laurie felt something brush her shoulder. Before she knew it, a fat bird was flying away with Xor in its talons.

  “Hey!” Laurie ran after the bird as it slowly flew to a nearby branch. It was so fat it was almost spherical, about the size and shape of a coconut. There were two more just like it in the tree.

  Laurie jumped at the bird holding Xor, but it tossed the lizard to another bird, which caught him in its beak. She jumped at that one, but then Xor was thrown to another.

  The birds enjoyed playing keepaway. When their mouths weren’t full of lizard, they hopped up and down and sang a silly rhyme:

  “Faster and faster—”

  “—too fast to follow—”

  “—Round Robins throw faster—”

  “—than an unladen swallow!”

  “Give him back!” Laurie shouted. “He’s my friend!” The Round Robins only cackled and mocked her.

  “Give him back!”

  “Give him back!”

  “We think he will make—”

  “—an afternoon snack!”

  “Help!” Xor squeaked in terror. “They want to eat me!”

  “Thought he was hiding—”

  “—but bird eyes can see—”

  “—an evenly dividing—”

  “—meal for three!”

  “No!” Laurie picked up a stone and threw it at the nearest Round Robin. To her utter surprise, it didn’t fly away. The fat, nasty thing caught the stone.

  “A stone!”

  “How rude!”

  “Hardly a treasure.”

  “We’ll happily juggle it—”

  “—for your pleasure!”

  They played catch with the stone and Xor. Laurie threw another stone, and then another, but the birds caught those, too. Now the Round Robins were juggling three stones plus Xor. This wasn’t getting Laurie anywhere. She paused, thinking, another stone in her hand.

  “Gave up so soon?”

  “We love to play ball!”

  “Throw us more toys—”

  “—and we’ll catc
h them all!”

  Instead of throwing the single stone, Laurie scooped up a large handful and started tossing them in nice, easy lobs, one by one. The Robins caught each stone and juggled it. If they hadn’t been trying to eat her friend, Laurie would have been impressed.

  “What are you doing? Save me!” Xor said.

  Soon, the three Robins were having trouble keeping so many things in the air. Laurie threw the stones harder and faster, trying to knock the birds off balance. They sang for reinforcements.

  “More wings, my brothers!”

  “More beaks and more talons!”

  “We need more Round Robins—”

  “—to evenly balance!”

  Five more of the creatures flapped and flopped in to join the party of their murderous kin. They evened out the load of stones and mocked Laurie even more loudly.

  “You can’t beat us that way!”

  “We’ll have our meal!”

  “Each one will eat less—”

  “—but a deal’s a deal!”

  The birds were juggling 15, 20, 25 stones now. They could catch whatever Laurie threw at them, and a dozen more of the creatures were waiting to join in. How could she get Xor away from them?

  “Clever Round Robins,”

  “too many to beat!”

  “You can’t stop the Robins—”

  “—when there’s dinner to eat!”

  It was hard to concentrate with the birds singing and Xor screaming, but Laurie waited again, trying to see a pattern. A Round Robin can catch anything. . . .

  “’Round he goes!”

  “Where will he stop?”

  “Stones all a-juggle,”

  “but the lizard won’t—mmph!”

  Just as one of the birds was about to catch Xor, Laurie hit it in the beak with a nice big clod of dirt. A Round Robin can catch anything. But it can’t catch two things!

  She caught Xor as he fell and ran away as fast as she could. Stones and furious Robins flew everywhere as the flock lost its rhythm. Some tried to chase her, but they were too fat to keep up and too angry to rhyme.

  “No fair!”

  “No fair!”

  “You stole our snack!”

  “Come back!”

  “No fair!”

  “You stole . . .”

  “Are you okay?” Laurie said.

  “No . . . yes . . . maybe.” Xor was breathing hard. They both were. The little lizard didn’t look hurt, but he was scared out of his wits. “Birds!”

  “This is why you have to blend in, isn’t it?” she asked. “Birds want to eat you.”

  “I hate birds.”

  Chapter 4. What the Tortoise Said to Laurie

  Laurie took a left turn at the sign marked “Recursion Junction.” After cresting a little hill, she ended up at . . . Recursion Junction!

  “Is this the same place, Xor?” Laurie asked. “It looks like it.”

  “Try a right turn,” he said.

  She did, but after a short while they were back where they started. When she tried a second, and a third, and twenty-seventh time, they always came back to Recursion Junction.

  “It seems as though I am going somewhere else, but we always come back to the same place. What’s going on?” Laurie wondered.

  They went around . . .

  . . . and around . . .

  . . . and around . . .

  . . . and around so many times that Laurie lost count.

  Just as she was about to give up, there was a gigantic smashing sound, like a stack of plates falling to the floor.

  They both jumped in fright, and for a moment Xor accidentally turned the same color as Laurie’s shirt. They looked around for the source of the noise but couldn’t find it. To their surprise, the next turn put them on a different road.

  This road was neat and straight, and it seemed to stretch on forever. Up ahead, a man in a Greek helmet was riding on a large Round Green animal with a Shell. (Eponymous might have called the creature a turtle, though she wouldn’t have been quite right.) The two were moving slowly and steadily away.

  “Hey! Wait!” Laurie shouted, running up to them.

  “At last, someone has caught up to us!” said the animal.

  “I thought that was impossible,” said the man.

  “Hello!” the animal said to Laurie. “I am Tortoise, a humble tortoise.” He was much too large to be a mere turtle. “This is my esteemed companion, Achilles the Logician.”

  “At your service, miss!” said Achilles, bowing to her from his perch atop Tortoise.

  “Um, hello. My name is Lauren Ipsum.” She attempted a curtsey.

  “How did you get here, Miss Ipsum?” asked Tortoise.

  “I don’t really know,” Laurie said. “We were following the path to Symbol, but I got turned around at Recursion Junction.”

  “That often happens. You spent quite a bit of time chasing your tail, I imagine.”

  “But I don’t have a tail,” she said.

  “So it got away from you, did it?”

  “What?” Laurie asked. “No, I don’t—”

  “Or perhaps it was optimized away,” said Tortoise. “No matter. Most of you made it through, and that’s the important thing. You can help us resolve a question.”

  “Well, I can try,” Laurie said, not sure that she and Tortoise were having the same conversation.

  “Splendid!” said Tortoise. “The question my dear friend Achilles and I are considering is this: how long is an infinite piece of string?”

  “An infinite string? Infinite means it’s really, really, really, really, really, really long. Really,” said Laurie. Really.

  “Ah! So you agree with me,” Achilles said. “That means the burden of proof must be borne by the other side.”

  “The burden of Achilles on my back is more than enough!” Tortoise grumbled.

  “Friend Tortoise is wise about many things,” said Achilles. “But he is clearly wrong this time. He says that an infinite string can be exactly two inches long!”

  “But how can an infinite string be two inches long?” Laurie asked.

  “His claim is preposterous and indiscrete,” said Achilles. “We are in continuous disagreement about it.”

  “I never disagree,” said Tortoise. “I only discuss, especially with an intellect such as yours, Achilles. Your understanding has no limit.”

  “You are too kind, dear Tortoise.”

  “I mean every word,” said Tortoise. “Allow me to suggest a way to settle the question by Experiment.”

  “Please, suggest away,” said Achilles.

  “Let us build—hypothetically, of course!—an infinitely long piece of string and then measure it. Miss Ipsum can be our impartial judge.”

  “I accept. Experiment is always better than mere Theory,” Achilles said. “And an impartial judge sounds wonderful, especially when she already agrees with me!”

  “Excellent,” said Tortoise. “Miss Ipsum, imagine you have an infinite number of pieces of string. If you laid them all end-to-end, would that be infinitely long? Hypothetically?”

  “Yes, it must be,” said Laurie.

  “Infinity is infinity,” said Achilles. “It’s only logical.”

  “I wonder. Suppose we start with a piece of string one inch long,” Tortoise said. “Then add a second piece of string that is one-half inch long. How long are they together?”

  “One and a half inches,” Laurie said.

  “And that is shorter than two inches?” Tortoise asked.

  “One-half inch shorter. Unmistakably,” Achilles said.

  “We all agree thus far,” said Tortoise. “Perhaps we shall converge upon the same conclusion.”

  “I doubt that!” said Achilles. Laurie wasn’t sure what Tortoise was getting at, but she doubted it, too.

  “Achilles, would you please keep count of our hypothetical string? I want to add a third piece one-quarter of an inch long,” said Tortoise. “Is our string now one and three-quarters inches lo
ng?”

  Achilles retrieved a much-used notebook from under his helmet and scribbled some figures. “It seems so,” he said.

  “With one-quarter inch to spare?” asked Tortoise.

  “Yes,” replied Achilles. “Only one-quarter inch! You are a finger’s width away from defeat!”

  “Add an eighth-inch piece,” Tortoise said. “Do I still have some space left over?”

  “Yes, but I’ll have beaten you soon!” the Greek Logician crowed. “Your string is an eighth of an inch away from the limit, and you’ve done only four pieces!”

  “Your arithmetic is correct as always, Achilles. But in the interest of science, let us continue until the bitter end,” Tortoise said.

  “It won’t be long,” said Achilles. “What is your next move?”

  “I would like to add another piece of string, this time one-sixteenth inch long.”

  “Done!” Achilles scribbled away. “Only one-sixteenth inch left, old friend!”

  “Only that much?” said Tortoise. “Then for the next one, I would like to add a piece of string one thirty-second inch long.”

  “As you wish, poor Tortoise. One thirty-second of an inch added. There is only one thirty-second inch remaining, and an infinity of strings to go! There will be plenty of rope left to trip yourself with!” said Achilles.

  “Please add a sixty-fourth-inch piece of string,” said Tortoise, “then a one-hundred-twenty-eighth-inch piece, and a two-hundred-and-fifty-sixth-inch piece, and then a five-hundred-twelfth-inch piece, and then—”

  “Slow down, Tortoise! You are going too fast,” Achilles said. “And those are very big—no, very small numbers.” He figured and scribbled for a minute. “There is only a five-hundred-and-twelfth inch remaining. It’s too bad we’re not splitting hairs, or you could have gotten a little farther! Do you give up now?”

  “Oh. I see!” exclaimed Laurie. “Achilles, Tortoise is right.”

  “What? Don’t change your mind now when we are so close to victory!” Achilles cried.