A Dream Abroad
"So you see, the curve of the function gets steeper as it approaches zero. What do we call that?" The young professor looked expectantly at the class, who stared back at him vacantly. He may as well have been speaking Swahili.
"Anyone?" Paul sighed. This was not going well. "Okay, let me try this again."
He erased the diagram he had been drawing and sketched quickly, until the shape of a grinning cat familiar to children everywhere.
"Hey, that's the Cheshire Cat!" The girl hadn't said that much the entire semester.
Paul continued sketching, and whole scene from Alice in Wonderland appeared on the board.
"Now, does anyone recognize this?" He pointed to the girl who had raised her hand. "Wendy?"
"Yeah, it's the part where Alice wants to get into the little door but can't because she's too big!" The girl's eyes sparkled as she leaned forward on her desk.
"That's right, now, how does Alice get through the door?"
"She gets small..." A few mixed voices.
Paul started to sketch the beginning of a curve. Soon the math would start. "That's right! She got very, very small. But, what if this happened instead: what if Alice just kept getting smaller and smaller as she ran towards the door? James?"
"Well, how fast is she getting smaller?"
"Hmm...interesting question. Why does it matter?"
"Because if she is getting smaller faster than she is running to the door then..."
Paul leaned forward. "Then what?"
"Won't she like...never get there?"
Glee. Sheer joy. "Yes. Precisely. She'll never get there. The function-, "he drew quickly, "-simply does not exist there." Done. The graph of the function describing Alice's shrinking and running was up. "And we call that? Shelley?"
Shelley hesitated. "...an a-simple?"
Close enough. "Well, an asymptote, but yes, that's exactly it!"
The rest of day proceeded in a blur, and Paul's moods stayed high. After the last bell he simply sat at his desk, thinking. He had reached them. And he had felt so good while doing it. Why? Why had it been so different?
"Nice move in there, sir."
Paul looked up from his musings and saw one of his newer students, Steven something. Just moved here last fall.
"Oh, hi, Steve. What do you mean?"
"It's Steven, sir. And I meant the Alice story."
Paul smiled. "Are you telling me a strapping lad like you is a fan of fairy tales?"
The boy didn't smile. "I do, actually. I like fairy tales, and ghost stories, and epic fairy-tales. I even like calculus examples that use them. What made you tell that story?"
"Well, Lewis Carroll was actually a mathematician and..."
"I know all that. I know a great deal about Mr. Carroll. What I am asking you is why you decided to tell the story like that."
Paul straightened. That was not a tone he was used to receiving from his students. "I wanted the students to understand the example."
"Right, and it worked. None of the rest of it worked. Most teachers would have thrown up their hands, and you tell a fairy tale. Why?"
Paul sighed. "You like stories? Here, here's a story for you: once upon a time, I was going to be a mathematician. I went to school, I worked real hard, and eventually got my Ph.D. And then when it came time to publish, I found that I simply had nothing to say. When I had started school, I had seen the beauty in it all, the incredible dreams hidden in the equations."
The boy started at the mention of the word "dreams".
"Finally, I gave it up. Came to teach at my old middle school. But I never forgot the beauty I glimpsed, the amazing things hidden in the equations. I just couldn't make them happen myself."
He looked up and met the boy's eyes, which seemed far older than the 13 years his file claimed.
"When I tell a story, though, it gleams through again. The kids get it. They understand."
"Well, sir, I think you may have missed your calling."
Paul laughed. "What makes you say that?"
"You are a maker of dreams, not a dissector of equations."
Paul looked at the boy hard. "How can you know that?"
"Just know that I know it, and listen. I have a proposition for you. Just listen, and I can make all your dreams come true..."
Paul started to laugh again. "I don't know, kid. I have some pretty outlandish dreams."
Steven looked down and a shadow fell over his face...which began to shift and change. He raised his eyes and grinned, rot and decay breathing out with his words. "Sir, you ain't seen nothing yet!"
"Did you have to be so dramatic?" Paul's jaw clattered as he talked, the shiny bone gleaming in the crypt's darkness.
Steven looked over and grinned. "Yes. You aren't the only one who likes a good story!"