When I announced this newsletter, I said it would be a work-in-progress, not a serialization of a finished, polished story. This week, it seems, is when I follow through on that promise.
In the first edition of this newsletter, I shared a scene in which the protagonist learns about the game of life. Now, seven weeks later, I’m sharing that same scene again, but rewritten (with different characters) and expanded (to almost twice the length!).
I’ve known since week two that I would have to rewrite the opening. When I first drafted the scene, I was imagining a story organized around a loving and supportive relationship between the protagonist and her mother. But once I adopted the search for superstability as an organizing theme for the story, I felt I had to change Mira’s relationship with her parents. It seemed that her interest in the mathematics of stability could be best explained if her non-mathematical life was chaotic, unstable, and uncertain. That would include her relationship with her parents. Instead of opening with the protagonist and her mother, I’ve introduced a new mentor figure to help eight-year-old Mira navigate the pages of Scientific American: Mira’s Uncle Mark.
I’ve also used this rewrite as an opportunity to linger a bit longer with Mira as she learns Life, to give readers a greater chance of grasping its rules. This scene is the primary opportunity for readers to learn how Life works, so I want to make sure it offers a satisfactory explanation without being too didactic. If after reading this scene you have no idea how Life works, please let me know! (A quick response to this email will do — just copy-paste “I read the scene and I’m still confused!”). If it needs to be clearer, I’ll come back and do another pass over it.
Having said that, I suspect the scene is now too long, so I may cut it back down in a later draft. But that’s what this process is all about! It gets longer before it gets shorter.
Mira is sitting at the kitchen table eating a bowl of cereal. When she hears a knock, she jumps down from her chair, runs down the hall, and unlatches the front door.
“Uncle Mark! You’re here!”
She holds her arms up, a signal. He laughs and lifts her up with a whoof of effort.
“You’re getting too big for this. Soon you’ll be too tall for me to lift!”
Feet back on the floor, Mira asks: “Did you bring the magazine?”
Uncle Mark reaches behind him and pulls a copy of Scientific American from his back pocket, somewhat squished from being folded in half, but still glossy.
“Just arrived this morning.”
Mira hops up into her seat at the kitchen table. Uncle Mark sits across from her and flips through the magazine, opening it to the Mathematical Games column.
“Are you going to read today, or do you want me to read?”
“You read,” Mira says.
Mira stops Uncle Mark frequently and makes him explain the hard words. Not “topological” or “orthogonal”, which appear frequently in the column and which he taught her a long time ago, but unusual words like “sporadic” and “solitaire,” “desiderata” and “dissection.”
“It says we need something small and flat and round to use as counters.” Uncle Mark looks around the kitchen.
Mira jumps up.
“I have something. But you have to promise not to tell.”
A minute later, she is back. She drops two small handfuls of plastic-wrapped stacks of candy on the table.
Uncle Mark laughs. “Where did you get those?”
She stretches up on tiptoe and whispers in his ear.
“So your mother has a secret candy stash, does she? She always did have a sweet tooth. When she was little she used to eat whole packets of sugar, the kind they give you at the diner with a cup of coffee.”
Together they unwrap the hard, pastel-colored tablets shaped like miniature hockey pucks. They sort the yellow and purple ones into separate piles and leave the rest jumbled together.
Uncle Mark takes a sheet of graph paper out of his jacket pocket and smooths it on the table. Using the edge of the magazine as a guide, he darkens every other line with a pencil to create a looser grid over the printed blue one. In the pencil grid, each cell is just large enough to hold a single candy.
“Are you ready for the rules?” he asks.
Mira nods.
“A cell with a candy on it is ‘alive.’ A cell without a candy is ‘dead.’ See how each cell is surrounded by eight other cells? Those are the cell’s ‘neighbors.’ If a live cell has two or three live neighbors in the current generation, it will stay alive in the next generation. If it has more than three or fewer than two live neighbors, it will die — either from overcrowding, or isolation. If an empty cell has exactly three neighbors, then it will become alive in the next generation. So you should put a candy on it. Got it?”
Mira shakes her head.
“Ok, we’ll do an example. Put three candies in a row. What’s going to happen to them?”
After the blinker, Uncle Mark described one shape after another: a row of four crackers; two sets of two crackers askew from each other, like the letter z; four crackers arranged in the shape of an L.
At first, Mira makes mistakes. She lays down a candy only to see Uncle Mark shake his head.
“Hmmm, that’s not what Gardner says,” he comments, looking from the magazine to the graph paper with its pastel candies and squinting as he tries to work out where the pattern had gone wrong. “Let’s try that one again.”
Mira lays the last candy in a pattern of four blinkers. Mira had started this one with three candies and one centered below, like a squat T. At nine generations, some using as many as twenty candies, this is the longest pattern Mira has played. She pauses.
|
|
|
|
| Stack of four | Z | L | T |
“I bet it’s called Life because the starting pattern is like a seed. And applying the rule is like watering the seed to make it grow. Only it’s like a seed from a surprise mix, because you never know what you’re going to get.”
Mira is starting to feel confident. “I want to make my own pattern.”
“I’ll race you,” she challenges.
Uncle Mark spreads out another sheet of graph paper while Mira pushes candies around on her own sheet of graph paper, looking for a pleasing arrangement.
“There!”
She has used nine purple candies to form a letter. “‘M’ for Mira.”
“How do you know it’s not ‘M’ for Uncle Mark?” he needles her.
She grins. “Because I’m going to win.”
They begin to step the pattern forward, stopping after each step to review each other’s work. If they both have the same answer, the person who finished first gets a candy from the pile of red and orange and green and white extras. If they have different answers, they start again from the previous step and evolve it more slowly. In that case, the person who got it right takes a candy from the pile.
Mira still makes mistakes sometimes, but so does Uncle Mark. She is faster than he is. While she waits for him to finish, she admires the patterns her “M” is producing: a ghostly figure outlined by candies with a dot for a head; a delicate pattern of separated candies.
Mira wins. Uncle Mark teases her: “You win, little ‘M’. How about a rematch for big ‘M’?”
He recreates her original pattern on his graph paper and modifies it, extending the pattern upwards at the corners to turn it into a capital ‘M.’
“You’re on.”
|
|
| Mira's little M. | Uncle Mark's big M. |
The first step of the pattern is like the first step of the little ‘M’ stretched vertically by one cell. Uncle Mark gets the next step wrong because he tries to take a shortcut, reproducing the third step of the little ‘M,’ also stretched vertically by one cell. The bottom of the third steps are the same, but the tops are completely different. By the fifth step, all resemblance between the two patterns has vanished.
“Damn,” Uncle Mark shakes his head in disbelief.
Uncle Mark is the only adult who swears in front of Mira. She likes this. Sometimes, she hears other grownups swear when they talk to each other and think she can't hear. Hearing Uncle Mark swear in front of her makes her feel grown-up.
“All we did was change two cells, and the pattern is completely different. I guess it’s because everything affects everything else. It’s so sensitive.”
At the fifth step, a face appears: two eyes surrounded by a wild mass of hair which comes to points atop the head and behind the ears. At the eighth step, an unassuming hollow triangle unfolds without warning into a rag doll with boots curling up at the toes and long, drooping arms. But by the twentieth, Mira is flagging (her smaller ‘M’ lasted for only ten steps).
“When is it going to be done?”
“No idea. It could keep going forever. Gardner says there is a five-cell pattern that has been tracked for 460 generations and is still going. No one knows how it ends. It might never end.”
Mira gapes at him.
“Four hundred and sixty generations?”
“Let’s keep going for a little bit longer at least,” he cajoles.
They are evenly matched, their candy hoards the same size (if whoever is counting remembers to include the two Mira popped into her mouth after winning them). But from the twenty-sixth step, Uncle Mark pulls ahead, finishing every step before Mira.
Six steps later, Mira notices something.
“I’ve seen these patterns before.” She points at two wedge shapes positioned on either side of the growing pattern, pointing outwards. “We saw them a few steps ago. But they were closer to the center then.” She pauses. “They’ve moved!”
“Yeah.” Uncle Mark doesn’t seem surprised. She looks at him hard, squinting with mock suspicion.
He confesses. “I saw a diagram of that shape in the article, and when it appeared, I recognized it right away. It’s called a glider.”
“Cheater!”
Uncle Mark defends himself: “Silly! We hadn’t gotten to it yet. How was I supposed to know we would see a glider on the second pattern we tried?”
Mira relents. “Ok, tell me about it.”
“Gardner says it is the smallest pattern which moves. Apparently they’re called ‘spaceships.’ He says there are three other known patterns that move, but he’s kept them ‘secret as a challenge for readers.’ We could try to find one. What do you think?”
They spend the rest of the afternoon trying to build a spaceship, without success, but happy nonetheless.
I had the pleasure and honor this week of interviewing one of my college math instructors, a professor who taught what was certainly the most formative class of my college experience. I originally reached out to her asking for feedback on Mira’s office hours with her math professor. Our conversation went far beyond that scene, though.
She told me the story of her mathematical life: excelling in high school, finding her skills and interests recognized and supported in undergrad, then the many discouragements of grad school and teaching.
I know already how some of the details she shared with me will make their way into this story. I’m sure as I keep writing over the next few weeks, her story will also influence mine in ways I haven’t yet imagined.
Perhaps someday, with her permission, I’ll share a writeup of the interview. It was a rich conversation; not always happy (sometimes she described things that made me mad!), but always full of life.
Next week, I plan to share a full draft of what I’ve written so far with anyone who can commit to reading it (I estimate it’ll be ~5500 words, or a ~20-minute read) and giving feedback by Wednesday, December 14. That will give me time to incorporate everyone’s feedback before the LAST edition of this newsletter and the end of this writing project on December 21!
If you’re interested in giving feedback on the full draft, send me a quick response to this email. I hope to finish a draft of the “minimum viable story” this weekend, and will start sending it out as soon as it’s ready.
As always, thanks for your interest and support — it’s what keeps me going!
Justin