Exhaustion Edda

This is a thing many people do not enjoy hearing. Edda enjoys saying it anyway.

Her favourite example, which she uses in every introductory class, is this: a child once came to the archive looking for the oldest letter that mentions a particular variety of red apple — an apple called the Crinklecoat, which grows only in a small valley on the western border. The child had a school project. The school project was about the history of the Crinklecoat. The child wanted to know which letter in the archive was the earliest to mention the apple by name.

There was, Edda explained, no shortcut.

There was no master index of "letters mentioning Crinklecoat apples." There was no clever algorithm. There were two hundred and forty thousand letters in the archive. To find the earliest letter mentioning the Crinklecoat by name, somebody had to look through every letter.

The child said: "But that will take forever."

Edda said: "It will take about four weeks. I have a system. We will start with the oldest letters and work forward, and we will stop the moment we find the first one."

The child said: "That is still a lot of letters."

Edda said: "Yes."

They started the next morning. Edda made tea. She showed the child her cataloguing system. The child read letters. Edda read letters. They worked side by side, every morning for three weeks and four days, until they found the letter — a small note from a baker named Lull to his cousin, dated one hundred and twelve years ago, mentioning "the new Crinklecoat apples Cousin Bevin brought from the valley".

The child cried, just briefly, with relief. Edda made more tea.

The school project, when it was eventually finished, won the regional history prize.

Edda kept a copy of the project. She still has it, on a shelf in her office, between two thick blue ledgers.

This is, in mathematical terms, proof by exhaustion.

You break a problem into all of its possible cases. You check each one. When you have checked all of them, you have proved the claim — by the simple, deeply satisfying logic that there are no cases left to check.

When the ProofQuest academy asked Edda, at sixty-five, whether she would consider teaching the exhaustion technique to children, Edda said the now-famous line: "Finally. A technique that respects my actual job."

She did not retire from the archive when she accepted. The academy was willing to wait for her on the days she was needed at the archive. (She is needed at the archive most days. She likes the archive. She likes the academy too. She splits her time.)

Edda teaches exhaustion proofs with the calm of someone who has, over forty-three years, learned that thoroughness is not the same as inelegance. Some children come to her class expecting exhaustion to be boring. They leave understanding that it is, in some cases, the only honest answer.

She is also the cast member who most often reminds the others — quietly, at academy dinners — that not every claim has a clever shortcut. Sometimes you just have to check the seven hundred thousand letters. Sometimes the seven hundred thousand letters are the proof.