The game of Cats and Dogs works like this: You and your teammate are placed in separate rooms and forbidden to communicate. You are each asked a randomly chosen question: Either “Do you like cats?” or “Do you like dogs?” (Each of your questions is determined by a separate fair coin flip.)
You win if your answers agree — unless you were both asked the “cats” question, in which case you win if your answers disagree.
A little reflection should convince you that if you are allowed to meet with your partner and plot strategy before the game, then the best you can do is agree to always agree — say by both always answering “yes”. That way, you win 75% of the time, and there’s no way to do better. In particular, there’s nothing to be gained by randomizing your answers.
That, at least, is true, in a world governed by the laws of classical physics and probability theory. But in a world governed by the laws of quantum mechanics — which is to say, in the world we live in — you can in principle do better. Namely: You each carry with you one of a pair of entangled “quantum coins” (actually elementary particles, but I prefer to think of them as coins, since you’re going to use them as randomizing devices).
Continue reading ‘Cats, Dogs and Quantum Mechanics’
Here are some thoughts on last week’s absent-minded driver problem.
First a recap of the problem, with a bit more detail than last week:
Each day, Albert leaves his office (at the bottom of the map), gets on the Main Highway and attempts to drive home to his house on Second Street. If he turns too soon (onto First Street) or if he overshoots (going all the way to the north end of the Main Highway), he is mauled by dinosaurs.
Obviously, Albert’s best strategy is to go straight at the first intersection and turn right at the second. Unfortunately, both intersections look identical. Doubly unfortunately, Albert can never remember whether he’s already passed the first intersection.
Continue reading ‘Absentminded Musings’
Until last week, I had never heard of the paradox of the absent-minded driver, but I was recently told that it has some relevance to my encyclopedia article on quantum game theory. That plus the fact that I am a notoriously absent-minded driver myself made me think I should check out the original source. Here’s what I extracted:
Each day, Albert leaves his office (at the bottom of the map), gets on the Main Highway and attempts to drive home to his house on Second Street. If he turns too soon (onto First Street) or if he overshoots (going all the way to the north end of the Main Highway), he is mauled by dinosaurs.
Obviously, Albert’s best strategy is to go straight at the first intersection and turn right at the second. Unfortunately, both intersections look identical. Doubly unfortunately, Albert can never remember whether he’s already passed the first intersection.
Continue reading ‘The Absent-Minded Driver’
