Choosing Shoes
(and Socks)
A game of skill, luck, and the Axiom of Choice
A game of skill, luck, and the Axiom of Choice
Perhaps you have heard Bertrand Russell's analogy about the Axiom of Choice (AC). If you have a collection of pairs of shoes, you can define how to select one from each pair, e.g., "choose the left shoe". But with pairs of socks (of a classic style where left is indistinguishable from right) there is no obvious way to define how to "choose" one from each pair, without invoking the AC.
This game simplifies these ideas to a finite (or at least countable) context, and lets YOU do your best to act as a choice function.
Click screen to continue
The game consists of two rounds: a round of skill, and a round of chance.
Round 1 (skill): you must select the left shoe from each vertical pair. It will be obvious which one is the left shoe.
Round 2 (chance): you select one sock from a pair. For an arbitrary (infinite? uncountable?) collection, there is no clear-cut way to define how to do this without assuming the Axiom of Choice. So we'll see how well you do by randomly choosing elements without clear-cut instructions.
Round 1 is over.
Ready to play round 2?
Play again to try and beat your streak?