- This is great! If my friend's wallet has more money in it than my wallet, I win their money-while if it has less money than mine, I lose my money. Since I stand to win more than I stand to lose, the odds are in my favor.
Paradox: a seemingly contradictory statement that may nevertheless be true.
The story goes that in 1943, the Swedish Broadcasting Company announced that a civil defense test would be held one day of the following week, starting Sunday and ending Saturday. In order to test the efficiency of the Civil Defense units, the actual day of the test would be kept secret until it actually happened -- i.e. it would be unexpected. Suppose you were in charge of one of the units, and you were trying to figure out in advance which day the test would take place. You might reason thus:
"If by Friday evening, I haven't been advised of the test, it must take place the next day, Saturday (the last possible day). But hang on -- it's supposed to be a secret! So Saturday's eliminated, meaning it must be scheduled for between Sunday and Friday. Now, if Thursday evening arrives with no test being announced, it must happen on Friday or Saturday, and since I've eliminated Saturday, it's going to happen on Friday. But then it wouldn't be a secret -- so it can't happen on Friday!"
You can probably see where this is going: Each of the remaining days, from Thursday back to Sunday, can be eliminated by the same logic. So you conclude, with unimpeachable logic, that the test can't possibly take place, and you relax -- until at dawn on Wednesday, when the test is announced. It is, as promised, unexpected. The announcement is now seen to be perfectly logical, even though you previously proved that it couldn't be. How come?
The second paradox involves the case of Alice and Bart, who are equally well-off. They're having a coffee together, and on a whim decide to bet on the contents of their wallets: Whoever has the least cash receives the contents of the other's wallet. Alice reasons, "The most I can lose is the contents of my wallet. But, since neither of us know how much is in the other's wallet, I have a 50/50 chance of winning, and if I win, I'll gain more than the contents of my wallet. Since I stand to win more than I stand to lose, the odds are in my favor!"
Bart reasons exactly the same way, concluding that the odds are in his favor. How can the odds favor both of them?
A good paradox is like a good joke. If someone has to explain it, it takes the bite out of it, and sometimes the best jokes are the ones we don't "get" right away. If you're like me, you'll be doing something completely different, and suddenly start chuckling. (This usually happens to me while listening to a serious talk in a crowded lecture theater.) So forgive me if I stop this column right here.
Barry Evans (firstname.lastname@example.org) sometimes thinks it's all a paradox. Especially in Old Town Eureka, where he lives.