Lauren Ipsum: A Story About Computer Science and Other Improbable Things Page 4

  MOTH-CIRCLE (how-big?):

  Go forward how-big? inches,

  make a mark,

  turn right one degree,

  repeat three hundred sixty times.

  Make a MOTH-CIRCLE (one).

  The turtle went bzzaap and zzzrbt and whuzzzsh and then it started to draw. It moved one inch, made a dot, then turned a tiny bit, then moved one inch, then made another dot . . .

  “Whoops. It’s making a huge circle! Let me try a small number.” Laurie didn’t have a small number handy, so she borrowed one she had heard from Tortoise: one thirty-second of an inch.

  “That’s better,” Laurie said.

  “Let me see,” Tinker said. “Wow, look at the little guy run!”

  “That was fun,” said Laurie. “I didn’t know you could just make up new ways to do things.”

  “Of course you can. Often you aren’t the first to think of something, but if it works, who cares? Now, for my end of the trade.”

  “Did you find the shortest path?” Laurie asked.

  “Not exactly. The bad news is that what you are trying to do is impossible.”

  “It’s impossible?”

  “Well, highly improbable. There are many different ways to visit all the towns. It seems like you could write an algorithm for the turtle to try each one and find the shortest, right?”

  “Sure, why not?” said Laurie.

  “There are twenty-one towns in Userland. How many paths do you think there are?” Tinker said.

  “I don’t know,” said Laurie. “A hundred?”

  “Way more.”

  “Um, a million?” Laurie said.

  “More like a million million times that!” said Tinker.

  “But how can that be?”

  “Let’s say there are only three towns: A, B, and C,” Tinker said. “You are already standing in A, so you have to worry only about B and C. How many ways can you go?”

  “Well,” she said, “I could go from B to C, or go to C and then B. That’s two.”

  “That’s right! But BC is the same as CB, just backward. Every path has a mirror image, so with three towns there is really only one possible path that visits them all. What if there were four towns, A, B, C, and D?”

  Laurie counted on her fingers. “I could go BCD, or BDC, or CBD, or CDB, or DCB, or . . . DBC. Six! No, three.”

  “That’s three times as many. Add another town, and you have twelve times as many,” Tinker said. “Add a sixth town and there are sixty different paths through all of them. With seven towns there are three hundred sixty paths. As you add more towns, the number of paths gets very big!”

  3 towns: 2 ÷ 2 = 1

  4 towns: 2 × 3 ÷ 2 = 3

  5 towns: 2 × 3 × 4 ÷ 2 = 12

  6 towns: 2 × 3 × 4 × 5 ÷ 2 = 60

  7 towns: 2 × 3 × 4 × 5 × 6 ÷ 2 = 360

  8 towns: 2 × 3 × 4 × 5 × 6 × 7 ÷ 2 = 2,520

  9 towns: 2 × 3 × 4 × 5 × 6 × 7 × 8 ÷ 2 = 20,160

  “For twenty-one towns you have to multiply one times two times three times four, all the way up to twenty. It makes a HUGENORMOUS number!”

  2 × 3 × 4 × 5 × 6 × 7 × 8 × 9 × 10 × 11 × 12 × 13 × 14 × 15 × 16 × 17 × 18 × 19 × 20 ÷ 2 =

  1,216,451,004,088,320,000

  “!” said Laurie.

  “Indeed!” Tinker said. “All of that ‘one times two times three’ stuff takes too long to write. So you can use the exclamation point as a shorthand.”

  20! ÷ 2 = 1,216,451,004,088,320,000

  “But that’s . . .” Laurie said, counting the commas, “over one million million million paths!”

  “One of those umpty-million paths is the shortest,” Tinker said. “I don’t know of any way to find it quickly.”

  “I’ll be old before we check them all! Isn’t there a better way to do it?”

  “Ah, that’s the good news!” Tinker said. “I deal only in Exact answers. But there is a brilliant Composer who lives in Permute, named Hugh Rustic. He deals in Good Enough answers. I send him all of my hardest cases. I’ll write an IOU that you can take to him.”

  Chapter 7. Read Me

  Laurie and Xor were halfway to Permute when a creature with red skin and horns and a black leather jacket pulled up on a red motorcycle. On the back of the bike was a huge bag full of packages and envelopes.

  “Hello, who are you?” Laurie asked.

  “I’m a daemon. Who else would I be? Hold on, there’s a message for you in here somewhere.” He rummaged around in his bag and handed Laurie a plain envelope. When she opened it, all she found inside was the strangest nonsense:

  LOREM IPSUM, ESXIHU! SIT AMET, CONSECTETUR ADIPISICING ELIT, SED DO EIUSMOD TEMPOR INCIDIDUNT UT LABORE ET DOLORE MAGNA ALIQUA. UT ENIM AD MINIM VENIAM, QUIS NOSTRUD EXERCITATION . . .

  “Are you sure this is for me?”

  “Are you sure you are you?”

  “Well . . . yes.”

  “Then that’s for you,” said the daemon. “I never make a mistake of identity.”

  “But how can you be sure?”

  “How can you be sure you are you?”

  “Because I’m right here!”

  “See? It’s only logical.”

  “But I can’t read it,” Laurie said. “What does it say?”

  “How old are you, that you can’t read?” said the daemon. “That’s a real shame.”

  “But—”

  “Did you know that kids in some countries start reading when they are only 12 months old?”

  “I can read—I just can’t read this. It’s gibberish!”

  “That,” said the daemon, putting his riding gloves back on, “sounds like a whole lot of Not My Problem.”

  “But—”

  “Do you accept delivery? Or do I have to bounce it?”

  “Well, yes, but—”

  “Look, Miss Well-Yes-But. I’m a mail delivery daemon. I work for the Colonel. My job is to deliver messages. What the message says is Not My Problem. Good day!” The daemon sped away, his tires spitting dirt and gravel all over her.

  “Ooh!” Laurie was so mad that she actually stamped her foot. “That little d-d—”

  “What is it, Laurie?” asked Xor, who had been napping in her pocket.

  “I think it’s a message for me,” she said. “But I don’t understand it at all.”

  “A secret message!” Xor said, rubbing his little claws together. “It’s lucky for you that my mother’s half-brother is a Cryptosaurus.”

  “A what-asaurus?”

  “A Cryptosaurus. We know everything there is to know about secret messages. Let’s see what we’ve got here.” Xor crawled onto the message for a closer look. The paper was white, so of course his skin turned black.

  “Hmm. This is a hard one. I don’t recognize these letters at all.”

  “Why are you looking at it upside down?” Laurie asked him.

  “Of course, well, uh, sometimes you can see patterns in secret messages that way.” He turned the right way around.

  “Now, um, let’s read it through slowly and look for clues. Con-sec-te-tour a-dee-peace-ick-ing el . . .” Xor’s skin rippled as he moved across the letters. “. . . dew-is ow-tay . . .”

  “Hey, Xor, wait a second.” Laurie had noticed something odd. “Back up just a little.”

  “Like this?”

  “Yeah. Now, think really hard about blending in.”

  “Okay. What do you see?” he said.

  “Your skin. I think I can read it.”

  When Xor was lined up just right, LOREM IPSUM ESXIHU in black on white became LAUREN IPSUM GREETINGS in white on black.

  “You are unhiding the message!”

  “Really? I mean, see? I told you I could do it.”

  “You are wonderful, Xor! Can you get closer to the paper?”

  “If I were any closer, I’d be behind it!”

  Word by word, they unscrambled the message. But even then it didn’t make much sense:

  LAUREN IPS
UM, GREETINGS! WITHOUT A DOUBT, YOU ARE THE MOST INTERESTING VISITOR TO USERLAND IN A LONG TIME. BUT YOU HAVE MANY LABORS AND SETBACKS AHEAD IF YOU KEEP DOING WHAT YOU ARE DOING. REMEMBER, THE MAP IS NOT THE TERRITORY!

  YOUR HUMBLE SERVANT,

  COLONEL TRAPP

  “Labors and setbacks? The map is not the territory? What does that even mean?” Laurie asked.

  “I once heard of a king who wanted to make a perfect map of his territory,” said Xor.

  “Why did he want to do that?”

  “Kings always want something silly, like a book about everything or a chariot with no weak parts,” he said. “This king decided that he wanted a perfect map as large as his kingdom. That way, the royal cartographers could fit everything in, down to the last pebble and flower. It took seven whole years to finish it. But it was a disaster!”

  “Why? What happened?” Laurie asked.

  “As a map, it didn’t work very well. To measure the distance between two places, you had to travel exactly that distance,” the lizard explained. “By that time you were already there.”

  “Where did they even put such a big map?”

  “That was the other thing. King Borges had only one kingdom, so there was nowhere to put the map except right where it was. It was a huge bother, what with the map sitting on top of people’s houses, and none of the crops could grow. The people finally overthrew the king and tore up the map. They say you can still see huge pieces of paper blowing around in the desert.”

  Chapter 8. More Than One Way to Do It

  Permute was a small village not far from Symbol. Hugh Rustic’s shop was easy to find. Its sign was even bigger and fancier than Tinker’s.

  “Hello, Mister Rustic?” Laurie called as she stepped inside the shop. “Mister Tinker back in Symbol owes me an algorithm, and he said I should talk to you about it.”

  Rustic was a tall, loud, messy-looking man with a big red beard. He didn’t look anything like the elegant Eponymous or the neat and proper Tinker.

  He certainly didn’t look how Laurie thought a Composer should look! But Tinker had recommended him, so Laurie handed him the IOU.

  “I’m, um, trying to find the shortest path through all the towns. Can you help me?”

  “Wonderful! Interesting!” Rustic said. “Tinker sent you to the right place, miss. Improbable we can do right away. Impossible, by Tuesday at the latest.”

  “But if it’s impossible—” Laurie began.

  “Only improbable,” corrected Rustic.

  “If it’s improbable, how do you do it?”

  “By shifting your point of view,” said Rustic. “Instead of looking for an answer that fits your problem, you imagine an answer and look for a problem to fit it.”

  “But you can’t just change the problem, can you?”

  “Why, of course you can! Worrying about the problem is a waste of time! What you really want is an answer, right?”

  “Maybe, but I don’t understand how,” Laurie said.

  “How do you buy the best tomato?” he said.

  “Well, I . . . what?”

  “Let’s say you’re at the market. You want the best, most perfect tomato. But to find the best tomato, you’d have to compare them all, right? You’d look at each and every one, turn it around, maybe squeeze it a bit. For every tomato in the whole market.”

  “No one does that!” said Laurie. “Well, old Mrs. Harris does do that. But my mom says she’s a little batty. I just pick a good one.”

  “See? You already know how to do things the Hugh Rustic way. You don’t waste your time looking for the best tomato when there are plenty that are Good Enough.”

  “So instead of trying to find the shortest path through all of the towns in Userland,” Laurie said, “we look for one that’s short enough?”

  “Why not?” asked Rustic. “Out of all the zippity-million paths, I bet there are a whole lot that are pretty short. You need to find only one of them, and that’s much easier.”

  Rustic pulled out a large map and placed it on the counter.

  “Here is where we are,” he said, pointing to Permute, “and this is where you started, am I right? Let’s put some pencils here to stand in for Mount Upper Bound, and a little spoon there for Lower Bound Valley.” The map also had markers for Bach and Recursion Junction, as well as many other places Laurie hadn’t been to yet.

  “Now for the fun part,” said Rustic. “Let’s ask the ants.”

  “Ask the ants? What are you talking about? Ants can’t read maps!” Laurie said. At the mention of insects, Xor was suddenly alert.

  “Who says they can’t? Next you’ll try to tell me that turtles can’t draw circles,” Rustic said.

  “So you teach the ants to read maps?”

  “Not exactly. Ants are good at finding their way home already. The idea is to get them to work for us.” He opened a jar of honey and put a tiny daub of the sweet stuff on each town.

  A minute passed. Nothing happened. Then a little ant crawled onto the table. It smelled the honey and zig-zagged its way onto the map. It nibbled from one bit of honey, then wandered around until it walked into another one.

  “When an ant finds food, she leaves a little scent message for the others that come after her,” Rustic said. “Ants follow the scent of food and also the scent of other ants. Lots of ants can try lots of different paths at the same time. Eventually they’ll settle on a quick route to all of the food and back to their nest.”

  The first ant continued on to Bach. Another appeared and went directly to Recursion Junction instead. Still others went all the way across to Probability Bay, Permute, Notation, and other towns. Soon the map had dozens of ants going every which way, collecting bits of honey and leaving scents for their sisters.

  After a few minutes it was clear that some paths were more popular than others. The lines of ants got wider and wider, until there was just one ant superhighway that marched all around the map and back to the nest. Hugh Rustic copied it to a piece of paper before the honey disappeared.

  “Ah, there you go!” he said, handing Laurie his sketch.

  “Thank you, Mister Rustic! Is this really the shortest way?”

  “It’s a short way. That’s as much as I can promise.”

  Chapter 9. Don’t Repeat Yourself

  Laurie and Xor set out from Permute with their new map. They finally knew where they were, where they were going, and how to get there. It was all right there on paper.

  “The places on this map have funny names,” said Laurie. “Truncate. What’s that?”

  “To Truncate is to make something shorter by cutting off part of it. The town of Truncate has very precise borders,” Xor said.

  “Oh. So what’s Axiom?” Laurie asked.

  “An Axiom is a rule that you pretend is true even if you don’t know why it’s true,” said Xor.

  “Really?”

  “Surely. My cousin Nand taught me all about it. She’s a Euclidosaurus.”

  “You’re making stuff up again, Xor.”

  “No, it’s just one of those things,” the lizard shrugged, turning gray-green. “Either you believe in Axioms or you don’t.”

  “Oh yeah? I bet you don’t know what a Furfnoodle is,” Laurie said.

  “It’s a . . . I mean, um. I give up. What is it?”

  “A Furfnoodle is a kind of bird,” she said. “With long, blue feathers! And it loves eating little lizards.”

  “Really?” Xor looked worried and checked the sky for blue feathers.

  “No. But if I ever see a big, blue bird that loves to eat lizards, I’m going to call it a Furfnoodle.”

  “You really shouldn’t make up words like that,” said Xor.

  “If you can make up words, so can I,” Laurie said.

  “I was telling the truth, Laurie.”

  “It’s even fun to say!” she said. “Furfnoodle.”

  “But—”

  “Furfnooooodle!” she sang.

  “Look, it’s not safe—”
>
  “Furfnoodle. Furfnoodlefurfnoodle. Furf. Nood. Ull!”

  There was a bloop sound, and a tiny mouse-looking creature appeared on the path in front of them.

  “Furfnoodle!” it said in a tiny mouse voice. It ran around them a few times, then zipped off into the weeds, still screaming. “Furfnoodle! Furfnoodle!”

  “What on Earth was that?!” Laurie said.

  “That,” said Xor, “was a baby Jargon.”

  “Where did it come from? It just blooped out of the air.”

  “You made it with . . . that word.”

  “I made it?”

  “I tried to warn you,” Xor said. “Where did you think Jargon came from?”

  “What’s so special about Furf—that word?”

  “It’s a name that only means something to you. That’s what a Jargon is,” Xor said. “You made it. It’s yours.”

  “But why?”

  “No one knows,” he said. “It’s one of those Axiom things. You have to be careful with names. They have a power all their own.”

  Chapter 10. A Well-Timed Entrance

  Probability was a little town on the edge of the sea. It was surrounded only by a rough wooden fence, nothing like the high stone walls of Symbol, and the main entrance seemed to be unguarded. Laurie was walking through the gates, when—

  “Excuse me, dear! Hello, on your left.” An elderly lady was sitting in the shade just inside. She held a large book on her lap. Her name tag read Jane Hecate, Border Security.

  “Oh! I didn’t see you there,” said Laurie.

  “That’s all right, dear. But before you come in I have to make sure you are on the List.”

  Laurie had played this game before. “My name is Eponymous Bach, and my password is—”