Lauren Ipsum: A Story About Computer Science and Other Improbable Things (5 page)

“I think it’s because you told it to repeat, but not how many times,” said
Tinker.

“Well, it should stop when the circle is done,” Laurie said.

“It doesn’t really understand circles,” Tinker said. “It’s just
a toy turtle, remember? You have to teach it.”

Laurie thought a little more, then rewrote her poem:

Then she realized that she could make circles of any size she wanted. It was just like opening
the compass wider.

“This is interesting. You’re working really hard!” Tinker scratched his
head. “But as it is, it’s no good.”

“Why?”

“People want to make lots of different circles,” he said. “I’ll have
to keep a lot of algorithms of different sizes, just in case someone wants
three-and-nine-thirteenths inches or four-and-three-quarters inches.”

“Well, what if you tell the turtle how big to make the circle?” she said.
“Maybe like this.”

“And
then
,” she said, “instead of ONE-CIRCLE or
TWO-CIRCLE, you can say ANY-CIRCLE(one), or (two), or even
(one-and-eleventy-sevenths)!”

“Good idea, Laurie. That’s a lot simpler,” said Tinker. “I was worried
you were going to fill my shop with circles!”

“You know, the turtle is drawing really slowly. Not like when it was drawing the
square,” she said.

It was true. The turtle would crawl all the way to the edge of the circle, then make a mark,
then crawl all the way back to the center, 360 times. With small circles it wasn’t too bad,
but big circles took a lot longer.

“Hmm,” Tinker said. “It spends a
lot
more time running
back and forth than it does making marks. Do you think you can reduce the running
time?”

It makes sense, but it isn’t sensible.
Laurie thought and doodled,
and doodled and thought, but she couldn’t figure out how to make it more sensible. The turtle
has to go back to the center, right? How else could it know where the edge of the circle was?

Laurie let her eyes wander around the room. Xor was staring at a moth that was flying in lazy
loops around a lightbulb. His skin was slowly fading from red to yellow and back to red. The moth
went around and around. It was hypnotic. Around and around and around and . . .

Oh! If the moth doesn’t have to go to the center of the lightbulb to fly
around it in a circle, then why does the turtle need to go back to the center to draw
one?

Laurie reached for a fresh piece of paper before the idea got away.
Don’t let
a new thing out of your sight without a name.

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!”

“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!”

“!” 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.”

“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.”

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:

“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
Crypto
saurus. 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, L
OREM
I
PSUM
E
SXIHU
in black on white became
L
AUREN
I
PSUM
G
REETINGS
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:

“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.”