Shelf life: How a book of puzzles helped Chris Hannay figure out life

Share

Is there a book you return to again and again, a work that would make life on a desert island bearable? Each weekend, until Labour Day, Globe writers will share their go-to tomes – be it novel, poetry collection, cookbook – and why the world is just a little better for them.

So you're walking along in a garden when you come across three humans just hanging out. This being a world in which everyone either lie all the time (people called Knaves) or always tell the truth (Knights), your first thought is: I wonder what type of people these people are?

You go up to the first one, let's call them A, and you ask: "Are you a Knight or a Knave?"

A mumbles quietly and you can't hear what they say.

B, with a wry smile, pipes up: "A said they're a Knave."

C, with an eye roll, says: "Don't listen to B, B is lying."

Now the challenge: who's what?

This is known as a "Knight and Knave" logic puzzle. They were popularized by Raymond Smullyan, a famed American mathematician and university professor whose bushy white beard and mane made him look like Gandalf or Dumbledore.

As a kid, I was always trying to puzzle things out. (So my mom tells me.) When I was about eight years old, my mom got me What Is The Name Of This Book: The Riddle of Dracula and Other Logical Puzzles.

The core of the 250 or so problems in the book are based on an eternal human fascination: whether someone is lying or telling the truth.

In the spirit of eight-year-old Chris, let's puzzle this one out.

First, we can figure out pretty quickly that B is a liar. In Knight-and-Knave land, no one claims to be a Knave. Saying "I am a Knave" is tantamount to saying "I am lying right now" which leads to a paradox: If the person is indeed lying, they are actually telling the truth, which contradicts what they said. Conversely, if they are telling the truth that they are lying right now, then they are actually lying – again a contradiction.

So A never said they were a Knave, which means B is a liar. C, then, is a Knight for claiming truthfully that B is lying. (And A? We'll never know – there's not enough information in the puzzle to know what they are.)

Here's another riddle: Why would someone bother rereading the same puzzle book over more than 20 years? Surely they know all the solutions by now?

What Is The Name Of This Book is more than, say, a book of crosswords with all the answers filled in. While Smullyan is spinning you tales of Knight-and-Knave land, and others inspired by the works of Lewis Carroll and Shakespeare, he's also teaching fundamental principles of logical reasoning. Revisiting the book over the years, I've found, helps remind me how to think things through.

The problem of the three people in the garden was puzzle 26 in the book. Let's flip ahead to number 110.

Here, Smullyan introduces us to a person (either a Knight or a Knave) who, when asked if they are a Knight, exclaims: "If I am a knight, then I'll eat my hat!"

This is a conditional statement – if this, then that – and it's part of the foundation of computer programming. Conditional statements are assumed to be true unless proven false. So if I say, "If you mow my lawn, then I'll give you $20," that promise is considered true unless you mow my lawn and I do not give you $20. If you do not mow my lawn, the promise is considered by logicians to still be true, whether or not I give you $20 anyway.

Back in Smullyan's world, then, it's impossible for a Knave to say, "If I am a Knight, then …" because the first part of the statement would be false (a Knave is not a Knight, you did not mow my lawn), and therefore the entire sentence is considered to be true. But that doesn't make sense – Knaves don't say true things. Therefore, the person who said "If I am a knight, then I'll eat my hat!" is not a Knave. A Knight said that. And since what Knights say is true, he will eat his hat.

Smullyan could be a little silly.

Let's skip ahead to the end of the book.

By this point, the problems have steadily increased in complexity to include Normals (people who sometimes lie and sometimes tell the truth), Zombies (who speak a language you don't understand) and Vampires (whose sanity is in question, and they may not know whether they're lying).

The book, too, has become more sophisticated, moving seamlessly through simple riddles to the basics of programming logic to questions about the nature of truth.

And, I hope, I've become more sophisticated in the decades since I first cracked open the book. Now I am an editor of political coverage. I am preoccupied every day with questions of whether someone is telling the truth, what exact word choices a politician made and what evidence is required to prove or disprove an allegation. I read reporters' stories and examine their logic, their story flow, their factual accuracy.

In Smullyan's final puzzle, number 271, he presents a statement: "This sentence can never be proved."

The sentence is a paradox that can only be resolved with the realization that there is no clear definition of what it means to prove something. You can define a certain system, with a certain set of rules, but you will always run into things that you know to be true, but you can't prove them.

In real life, not every problem has a solution. And by the end of the book, neither do these.