Induction Ida

Everything else fell on its own.

A roar rose from the crowd. The town quickly put up bunting, and the bakery sold out of its special festival biscuits. Strangers hugged. Soon, the dominoes were swept away. Plans for next year's Cascade began immediately. Then, the whole town went home.

The Cascade was more than just a festival for Ida. It was the place where she began to understand the world like a mathematician.

Ida's family, the Latticefords, had overseen the Cascade preparations for generations. They were known as the festival-domino-makers. Ida grew up watching her mother carefully arrange long curves of dominoes across the town square. She started helping as soon as she could walk. By age seven, Ida could lay a hundred dominoes on her own. She managed this without accidentally knocking any over. This skill was harder than it seemed. It required a particular knack: setting down the next piece without bumping the one before. You simply could not be in a hurry.

At twelve, Ida was already a careful and capable domino-setter. Yet, she wasn't a mathematician then. That transformation began the year the chain stretched nine hundred and fifty pieces long. It was the year her mother gave her the ultimate honor: she would push the first domino.

It was a tremendous honor, but also a heavy responsibility for Ida. She had spent the entire afternoon laying her own section of the chain. She checked each piece three times, making sure it stood perfectly. At twelve, she was the youngest person to push the first domino in seventeen years.

She bent down at sunset. She pushed the first domino.

It fell into the second. The second fell into the third. The third fell into the fourth.

Ida watched the chain unfold.

In those thirty seconds, Ida watched with intense focus. She saw something with the piercing clarity only a twelve-year-old sometimes possesses. Adults, she realized, often forgot this simple truth. She had pushed only one domino. The other nine hundred and forty-nine had fallen entirely on their own. She hadn't touched them. She hadn't even been close to them. The entire chain, every single piece, had toppled. This happened because the first one fell, and because each domino was placed close enough to the next one to knock it down in turn.

She thought, then and there: That is everything I need to know.

Ida walked home that night, humming a quiet tune. Her sister, Sten, then nine, didn't understand why. Sten, now known as Strong-Induction Sten, had eaten three festival biscuits. At that moment, she simply didn't care about humming.

Ida wrote down what she had figured out, in her own twelve-year-old handwriting, in a notebook her grandmother had given her. The notebook page said:

"To knock down all the dominoes, you only need to do two things:

1. Knock down the first one.

2. Make sure each domino is close enough to the next one to knock it down too.

That's it. The rest happens by itself."

That night, Ida didn't know this principle had a name. She didn't know it was hundreds of years old. She certainly didn't know mathematicians called it *induction*. They used it to prove things about every natural number. She couldn't have known that in eight years, she would arrive at the ProofQuest academy. There, she would introduce herself by saying, "I am the dominoes person." And the academy master would look up from his notes, a smile on his face, and say, "Oh good. We have been waiting for you."