Tuesday, January 22, 2013

The validity of someone else's solution

Within the first couple dozen pages of The Devotion of Suspect X, by Keigo Higashino, there's a murder. The main characters are sketched out in simple, broad, vivid strokes. Yasuko, with the help of her daughter, kind of accidentally kills her abusive ex-husband. We're sympathetic toward Yasuko; the jerk deserved it. Their neighbour, Ishigami, a high-school math teacher and genius, offers to help cover up the incident.

A body's discovered in due course, and the investigation gets underway. Turns out that Ishigami went to the same school as Detective Kusanagi, the cop on the case, and they have a mutual friend, Manubu Yukawa, a brilliant physicist, to whom Kusanagi often turns for advice.

And so the mathematician and the physicist — theory and practice — face off.
"You're familiar with the P = NP problem, right? Yukawa asked from behind him.

Ishigami looked around. "You're referring to the question of whether or not it is as easy to determine the accuracy of another person's results as it is to solve the problem yourself — or, failing that, how the difference in difficulty compares. It's one of the questions the Clay Mathematics Institute has offered a prize to solve."

"I figured you might be." Yukawa smiled and tipped back his glass.

Ishigami turned back to the desk.

He had always thought of mathematics at a treasure hunt. First, one had to decide where to dig; then one had to determine the proper excavation route that led to the answer. Once you had a plan, you could make formulas to fit it, and they would give you clues. If you wound up empty-handed, you had to go back to the beginning and choose another route. Only by doing this over and over, patiently, yet boldly, could you hope to find the treasure — a solution no one else had ever found.

Therefore, it would seem that analyzing the validity of someone else's solution was simply a matter of following the routes they had taken. In fact, however, it was never that simple. Sometimes you could follow a mistaken route to a false treasure, and proving that it was false could be even harder than finding the real answer.

Which was why someone had proposed the exasperating P = NP problem.
This book is a treasure, not a false one. Some readers cry foul over the ending, but I think that's because they have fallen into the kind of trap Ishigami sets for his students, mistaking this book for a geometry puzzle, when really it's an algebra problem. One would do well to remember too that Yasuko, Ishigami, the cop, and the physics professor are each trying to solve a different puzzle, with different information at hand.

The resolution is logical, it fits perfectly; it is also heart-rending.

I read this book over a weekend, and it evoked in me all the wow of when my grade 7 teacher read us The Witness for the Prosecution, and it occurs to me he may have been trying to teach us the lesson to avoid the trap, question our assumptions, watch for our blind spots, not just how to construct a perfect alibi.

The review that put this book on my radar: Reading Matters.

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