The Cinderella Theorem Read online

  I opened Arthur’s file and read the list of things proven to make him happier: disco music, chocolate chip cookies, Gwenivere, working with his hands, and cold, cold milk. I looked at past attempts to raise his level. Mostly Calo had just played disco music, while they both danced around in the throne room under Arthur’s disco ball. Judging from the past reports, it seemed to be taking Calo longer and longer to bring about a Happy rating with this technique. Probably because he was doing the same thing every time.

  I got a Happy Plan form out of my desk and completed it, outlining my plan for Arthur, along with a list of supplies I’d need. I showed it to Calo.

  He smiled. “Creative.” He pushed in his desk chair. “Let’s go see if it’ll work.”

  ~~~

  Arthur met us at the door of his castle. “I’ve been waiting for you all afternoon. Hello, Princess,” he said, taking my hand. “Wonderful to see you.” Turning to Calo he said, “And I’ve got my monitor here, so we can see how things are going. Should we go to the throne room?” He looked from Calo to me and then back to Calo, as if unsure of who exactly to ask.

  “The kitchen, actually.” I answered.

  “The kitchen? How interesting.” He gave his monitor to Calo and led the way.

  The kitchen was large, warm, and oddly sunny for a room in the basement of a castle. I ignored the obvious flouting of mathematical laws like the refraction and reflection of light and took a CD player out of my bag. “Some music while we work,” I said, as I pulled out the ingredients for chocolate chip cookies.

  “Are those chocolate chips?” Arthur pointed.

  I nodded. “I thought we’d make some cookies today.”

  Calo sat down on a stool in the corner with Arthur’s monitor and a clipboard for taking notes.

  “Excellent idea, Princess. I’ve never baked before.” Arthur looked absolutely giddy. We had a good time baking and eating the dough before we made the cookies. Arthur was fond of scooping the dough out of the bowl and rolling it in his hands to make what he called “the perfect ball of cookie dough.” And the music was entertaining. I know very little about disco music, but Arthur had an amazing wealth of knowledge on the subject. For instance, did you know that the soundtrack of Saturday Night Fever is generally considered to be more popular than the movie itself? And he knew the words to every song. When the first batch of cookies had cooled enough to eat, I reached into my bag and pulled out a thermos of milk. As we dunked our cookies into the cold, cold milk, a chime sounded from Calo’s corner.

  “Congratulations, Princess!” Arthur said while I tried to figure out what the noise was.

  “What?” I asked.

  “You made me Happy.” He was smiling. “That’s the noise the monitor makes when Happiness is achieved.”

  “Nice work, Lily,” Calo called as he started packing his things.

  Arthur and I had just started doing the dishes when two things happened all at once: Calo’s back pocket started ringing, and a servant brought a letter in for Arthur, a black envelope addressed with gray writing.

  I turned to see if Calo would know the envelope was from Levi, but he hadn’t noticed. Strangely enough, he was talking into a make-up compact. Calo nodded and then closed the compact.

  “It’s a compact phone. Like the mirror phone at your house, but smaller. Doug from The Observatory called. It seems that Morgan heard about us coming here and is jealous; her levels are dropping pretty quickly. I’m going to head over there to see what I can do.” He paused. “Uh...I don’t think you should come, Lily. I mean, well, you know how she is. Can you make it back to HEA by yourself?”

  “I don’t think so.” I hadn’t paid much attention on the way over. I was busy thinking about what I was going to do with Arthur. “I remember something about a bridge.”

  “I’ll put your bike on auto-pilot then, and Grimm can—” He stopped. “King Arthur? Is everything alright?”

  Arthur was reading the letter with a look of growing disdain and anger. “That sycophant!” He spat out. “Implying that my kingdom can be–well!” He stopped and stalked out of the kitchen. “He’ll receive a response back from me, he will!” He paused in the doorway. “You can see yourselves out, I suppose?”

  “Certainly, sir.” Calo answered. “But, are you sure you’re alright?”

  “I am fine. Forgive me, Princess, for losing my temper in your presence.” He bowed and left.

  “Is he going to be okay?” I asked Calo. “He was so happy before. Did that letter ruin—?”

  Calo cut me off by pointing at the monitor on the counter. Arthur’s level was still Happy. I stared at it, confused, for a moment. Then I followed Calo out of the castle.

  It had started to rain. The drops were hard and angry. The wind was whipping around the castle, through the trees. Calo pulled a wand out of his pocket. “Hopefully you’ll get back before this gets too bad,” he said loudly, tapping my bike. I could barely hear him over the wind and rain. “See you later,” he called as he rode off.

  My bike nudged my elbow.

  “Alright,” I muttered.

  Lightning shot across the sky as I got on and started pedaling. The storm was getting worse; Rain came down in sheets. I was completely soaked and sure that HEA’s CD player was ruined. Since I could barely see in front of me, I was glad to have the auto-pilot. Even if I had known how to get home, I would never have been able to find it.

  I started to make an equation to figure out my percentage of visibility in the storm. I looked up to estimate how far I could see in feet, but I saw something much worse than minimal visibility.

  The stream under the bridge had swollen well beyond its banks, and as I watched, the bridge tore apart and washed away.

  I barely had time to begin mathematically determining how to get over the stream, when I realized there was a more pressing problem.

  The bike would not slow down. I applied the brakes: nothing happened. And nothing I tried could keep the bike from heading right into the flooded stream.

  12

  Objects in Motion

  Newton’s first law (objects in motion stay in motion unless acted on by an outside force) flitted through my mind briefly as I flung myself off the bike. Never before have I experienced one of his laws in such a dangerous way. I hit the ground, rolled onto my back, and looked to see what happened to my bike. It was being washed downstream.

  “Stupid auto-pilot,” I muttered. I stood up and mathematically analyzed my situation.

  Torrential rains + auto-pilot bike + no knowledge of where I am = one lost, wet Lily, who will be walking wherever she goes.

  I was also muddy, cold, and completely soaked. I began to walk along the flooded stream, in hopes of finding another (stronger) bridge. In a desperate attempt to keep my mind focused on anything but how wet I was, I recited the squares. “One squared is one. Two squared is four. Three squared is nine...”

  At “fifteen squared is two hundred twenty-five,” I saw a muddy path to my right. I headed straight for it.[34] I had no idea where the path was going. But being on it had to be better than wandering aimlessly by a swollen stream. It wasn’t until “twenty-three squared is five hundred twenty-nine” that I realized my faith in the path was based on my knowledge of paths in the real world. In the real world, paths go somewhere. They move in a predictable manner. You travel for a while, then when you decide to take a turn, you take it. Steady. Predictable.

  At “twenty-three squared is five hundred twenty-nine,” I came to a fork in the path.

  An actual fork.

  The path ended. Trees were everywhere. I stood in the pouring rain and looked at the little, shiny fork that some picnicker had probably left behind. “This is in no way helpful. A path is supposed to go somewhere,” I mumbled, turning around. “I wish I knew what to do.”

  “About time, too,” said a voice behind me.

  I turned back to the wall of trees. It was Glenni. Floating as usual, she wore a plaid rain slicker, complete with a pl
aid hat and plaid galoshes, and she carried a plaid umbrella. She snapped her fingers, and another umbrella materialized. She lazily shoed it to me with her wand.

  “What is the point of having a fairy godmother if you never call on her?” She looked severely at me. “It is my job after all.”

  “Glenni! What are you doing here?” I quickly opened the umbrella.

  Glenni sighed. “Did you or did you not just make the following wish: ‘I wish I knew what to do’?”

  What? “Uh...yes. I said that.”

  “A fairy godmother is summoned by her godchildren when they make wishes.” She said tiredly, as if she had already explained this point to me–several times.

  “Oh.” I paused. “But I didn’t mean to make a wish.”

  Glenni raised her eyebrows. “Do you mean that you do not wish to know what you are to do here, at the fork in the road?”

  “No…I mean, yes, I do want to know what I should do. But I didn’t mean to summon you. I was just wondering.”

  Glenni shook her hands in an impatient gesture. “Wishing, wondering–the point is you need help.” She glanced at me. “And soon I’d say. You’ll be growing gills to help you breathe in all this water if you don’t get dry.”

  I started to laugh, but then I stopped myself. I realized that it was probably entirely possible in Smythe’s SFL to grow gills when you’re wet. Not wishing to delay, I asked, “So what am I supposed to do?”

  Glenni pointed to the fork. “Pick it up.”

  Breathing deeply (in case I lost lung capability), I bent over and picked up the fork.

  Six doors appeared around the path: two to the left, two to the right, and two in front of me, at the dead end of the path. Each door was a different color–red and orange to the left, yellow and green in front, and blue and purple to the right. “Well,” I managed. “I guess it’s not just a lost picnic fork.”

  Glenni floated over to me. “The blue door will take you to shelter.” Then she disappeared.

  Ignoring the fact that disappearing people no longer surprised me, I looked at the blue door. It was just a door; no wall connected it to anything. I could walk completely around it. There was no reason to believe that going through that door would take me anywhere than three feet off the muddy path. No reason, that is, other than the door was in Smythe’s SFL, and was probably another portal device like my bathtub.

  I kept standing in the rain, wishing Glenni had been more specific about where the door would take me. I didn’t dare voice my wish out loud though; I would have to be more careful about what I said from now on. It seemed like Glenni had to drop whatever she was doing and whisk herself away every time one of her godchildren made a wish. That could get annoying fast. And I seem to recall something about not wanting to upset fairies. Didn’t Rapunzel’s hair just grow and grow because they didn’t invite all the fairies to her christening or something?

  I considered taking a different door, but the variability of what they could lead to was too great to logically consider actually using one. Glenni had said the blue one led to shelter; therefore, using the knowledge that is available, one can only determine that the others do or do not lead to shelter. Each non-blue door had a 50% chance of leading to shelter. The blue door had a 100% chance. But what did Glenni consider shelter? What if it was so completely fairy-godmothery that it lacked any kind of shelter aspect in a mathematical definition?

  Finally, I remembered that Glenni had given me a calculus book, which showed enough mathematical sense for me. I opened the door.

  There was no rain on the other side–only sunshine and clear skies. I quickly went through and shut the door behind me. As it closed, I realized I probably should have left it opened in case wherever I had come was dangerous. I looked around this bright land of sunshine; it was very clean. While folding my umbrella, I noticed there was no litter anywhere, and the sunshine made everything seem sparkly and new. There was another path through the woods to my left. I decided to take it.

  Traveling this sunny path was such a completely different experience. I dried out a little and warmed up. Whoever lives in this area must always be happy. How could you be unhappy in sunshine like this? I was blissfully warm and happy and unaware of how far I had traveled when I saw a castle right in front of me. A sudden turn in the path had taken me out of the woods and into a clearing where it stood.

  I did not recognize the castle. I considered that both good and bad. Good that it was not Morgan’s castle, but bad that Glenni hadn’t sent me back to my own castle. Who could live here? I mentally listed some possible characters. King Median or Midas or whatever and his golden touch ice cream would probably have a castle (kings usually do). Sleeping Beauty. That princess with the frog. But also, Potio Bane, the scary apple lady. She seemed like she had a castle, what with all of that clapping to summon her servants and her general attitude.

  After several minutes of mathematical wondering (this time in much warmer, dryer conditions), I concluded that I could trust Glenni. The calculus book, the path of sunshine, and the floating math alarm clock were all things highly in her favor. I walked to the door, took a deep breath (happily noting that I still just had regular, human breathing), and knocked twice, using the shoe-shaped doorknocker.

  A pretty and vaguely familiar lady answered the door. “Princess Lily? Come in,” she was obviously surprised. I followed her into an entryway. “But whatever are you doing here?” Her dress was simple, but still elegant. “You’re all wet!”

  “There was a storm,” I said, and noticing a delicate crown on her head, I added, “my lady.”[35]

  “A storm!” She looked outside.

  “It was near King Arthur’s,” I helpfully supplied.

  “Oh,” she nodded knowingly, “that does explain it.” I shivered involuntarily in my cold, wet clothes. “Stay here. I’ll bring you something warm to put on.”

  As she left, I found myself wondering primarily two things.

  (1) Who is she?

  And (2) how does the fact that the storm was at King Arthur’s explain anything?

  I looked around the room I was standing in. Again, for a castle made of stone with few windows, there seemed to be an awful lot of sunlight. It was beginning to seem as if the Smythian architects knew a way to magically suspend the laws about light refraction. Which, I further reflected, they probably did.

  On one wall, there hung a mirror (probably the mirror phone). Under the mirror, sat a table with letters piled on it. Next to the table was an umbrella stand. I added mine to it and examined the pile of letters.

  Looking through another person’s mail generally equals highly rude behavior, very bad manners, and practically mail tampering, but it also equals way to find out whose house you are in. I looked at few of the letters in the stack. They were all addressed to Cinderella. Some of them gave her additional titles. Princess Cinderella, Her Royal Highness, or (my favorite) Cinderella, A Charming Princess for a Charming Prince.

  So I was at Cinderella’s castle.

  I immediately wished (again, not out loud) that I knew more about her story. What did I know about her? She gave me a pair of glass magic dancing shoes at my presentation. I paused to consider how impossible glass shoes are. Without the additional magic that must be in them, I don’t see how they could physically work. And glass is see-through; why would you want to have everyone see your feet? It’s like being barefoot.

  I shook my head to stop myself from thinking about the shoes, and I racked my brain for anything else I might know about Cinderella. I recalled she had sent one of the letters I received after Morgan vanished me on Monday. It was a nice letter. What else? Perhaps, she had a stepmother? Although, that’s just basic fairy tale probability. Always guess a wicked stepmother.

  Cinderella came back into the hall carrying some clothes and a comb. “These should fit you.” She handed the stack to me. “They’re one size fits all.” She pointed to a little door. “You can change in the powder room.”

 
I thanked her (using her name) and went into the powder room. Cinderella had given me a dress, undergarments, socks and shoes. Looking at them, however, I had some trouble figuring out what exactly was meant by “one size fits all.” They were much too big for me. However, appearances do not mean the same thing in Smythe’s SFL as they do in a normal (mathematical) setting, so I took off my own wet clothes, and began putting on the huge, dry ones. Oddly (or perhaps I should have expected it), the minute the clothes were in place they shrunk to my size. I can only assume, following this principle, that if I had been larger than the clothes that they would have grown once I got into them. But how would a larger person get in them? Perhaps that’s why they were so big to begin with? I quickly combed through my hair, gathered my wet things, and went back out into the hall.

  “Oh, here.” Cinderella came toward me. “Let me have those wet clothes. We’ll put them in the dryer.” She pointed to another door off the hallway. “Go right through there. I’ve got all the tea things set up. Help yourself; I’ll only be a minute.” She left again.

  I went through the door. The room was sunny, of course, and looked like a living room. Although, it was probably called a parlor or drawing room or something that sounds more like a fairy tale. “Living room” doesn't really convey a magical feeling. A tea tray sat on the coffee table: sugar, milk, little lemon wedges, several spoons, and a pot. There was also a tray of cookies.

  I looked at the tea tray for a moment. “Yeah, I don’t know what to do with that,” I said softly as I sat down. I will just say I wanted to wait for her to start. After all, I am only a guest. Doesn’t the hostess have to do a “hosting” thing with the tea?

  In a few moments, Cinderella returned. “Your clothes will be dry in half an hour. In the meantime,” she sat down, “you and I can have a nice visit. Wouldn’t you like some tea?” She shifted in her seat so she could better serve.