An IAS officer I knew had a younger colleague who would often drift into his office for a chat. The colleague had the annoying habit of picking up and reading pretty much any file or paper on the desk, even those marked “Secret”. Gentle reprimands had no effect. So the officer—incidentally, a mathematician by training—found another way to get the message across.
He got a red file with “TOP SECRET” written prominently across the top. He put just one sheet inside, with these words on it: “Some people are in the habit of reading papers, like this one, that are not meant for them.” He set the file down on his desk, in full view. Sure enough, it wasn’t long before the colleague wandered in. Sure enough, he picked up the file and read the words. I wish I had been there to see his face. What did he think: Was the note meant for him? What do you think?
Somehow that story always reminds me of Raymond Smullyan, mathematician and puzzle-crafter extraordinaire. He once welcomed his logic students to class with this on the blackboard: “Please do not erase. Because if you do, those who follow won’t know that they shouldn’t erase.”
I’ll leave you to digest that, as I suspect Smullyan did for his students.
Smullyan was one of a kind: a mathematician and maker of puzzles, but a logician above all. He saw the world, it seemed to fans like me, as a glorious patchwork of inferences and contradictions, dead ends and shining reason—and logic was the tool that took you through it all. And pouring from that fertile imagination came a fountain of delightful, deep, sometimes delicate, sometimes devious ideas and koans and puzzles. Never straightforward, always designed to make you think that one extra step, maybe two, they have charmed generations of puzzle lovers the world over. Because they are not trivial. Not straightforward. Each demands attention, thought and concentration, and when you “get” it, it’s a satisfaction like no other.
Consider what he once asked Martin Gardner: “Is ‘No’ the right answer to this question?”
Well, is it? Are you nodding to say “Yes”? Well, then the right answer is “Yes”, not “No”. Except that in that case your answer should have been “No”, because you didn’t answer “No”… but then you would indeed have answered “No”, in which case you should have said “Yes”.
Good luck trying to pin that one down. What’s going on here, of course, is the old but always amusing logical trap of self-reference (see my column “Disobey This Command”). Entire mathematical edifices rise from there.
But Smullyan had plenty more up his sleeve, shooting off in all kinds of directions. His aphorisms make you scratch your head in bemused wonder. His puzzles are like children’s stories, but ones that push buttons in corners of your mind you never knew existed. And the best way to enjoy him is to simply read him and ruminate for yourself, not have a columnist bash you over the head with heavy-handed “explanations”. In that spirit, some Smullyan gems:
u While introducing him, someone called Smullyan “unique”. Smullyan interrupted to say: “Forgive me sir, but I happen to be the only person in the universe who is, in fact, not unique.”
u “There are two rules for success”, he once said. “The first: Never tell all you know.”
u Bunty and Babli went out for dinner and asked for a fish dish. It turned out to have two different-sized pieces of fish on it. Babli promptly helped herself to the larger piece and wolfed it down. Bunty was upset. “Yo Babli,” he said. “You’re a rude one! Why did you take the big piece? The way I was brought up, I would choose the smaller one!” Babli retorted: “Well, in that case you’ve got your choice, so why are you complaining?”
u You are lost on a curious island that’s populated by two tribes. One always tells the truth, the other always lies, and they always intermarry. Searching for Bunty and Babli’s restaurant, you come to a fork in the road. There’s a married couple standing there—so you know one is a liar and one a truth-teller, but you don’t know which is which. You can ask either one only one question—any more and one of them will kill you. Can you find your way to B&B’s restaurant?
u You ask them two questions. The couple confers on how best to murder you. He pours arsenic into your water bottle. She cuts a hole in it with her Swiss army knife. Wracked by indecision, unable to drink, you die thirsty. No more lying, now: when the cops arrive, the husband says you never touched the arsenic, so he can’t be guilty. The wife says she didn’t let you drink the poisoned water, so she’s not guilty. Still, you’re dead. Who is guilty, really?
u Perhaps you’ve read Shakespeare’s Merchant Of Venice and remember Portia’s use of portraits to eliminate suitors. Smullyan’s variant goes like this: Portia lays out three boxes—lead, silver and gold. Gold has these words: “My picture is in here.” Silver: “My picture is not in here.” Lead: “My picture is not in the gold box.” Portia tells the prospective suitor: “Dude, at most one of those statements is true.” Which box should he choose?
u Finally, my favourite Smullyan-ism. He was once asked: Do you believe in astrology? “Of course not!” he shot back. “I’m a Gemini!”
Raymond Smullyan: dead at 97 on 6 February. We’ll miss you. And that’s the truth.
Once a computer scientist, Dilip D’Souza now lives in Mumbai and writes for his dinners. A Matter Of Numbers explores the joy of mathematics, with occasional forays into other sciences.
Comments are welcome at email@example.com. Read Dilip’s Mint columns at www.livemint.com/dilipdsouza