A Pair of Paradoxes

| March 11, 2010
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.
  • 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 (barryevans9@yahoo.com) sometimes thinks it's all a paradox. Especially in Old Town Eureka, where he lives.

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Dear Barry, By now, all of your loyal readers are aware that you live in Old Town Eureka. You mention it in the italic biography at the bottom of your column over 76 percent of the time. We know that your wife also lives in Old Town, that your genes live there, and that you frequent Old Town Coffee and "Steve and Dave's bar in Old Town, where you live." After three weeks of not announcing your neighborhood of residence in the print media, you slipped back into that old mainstay this week. You must have been suffering writers' block in January, when every column came with an "Old Town Eureka" caveat. Sometimes it was embedded in a witticism, as in "Barry Evans yadda yadda in Old Town Eureka, where he lives." Usually it was just a concise conclusion: "He lives in Old Town Eureka." That is, when it wasn't "blah blah Old Town yadda yadda, in Old Town, where he lives." Why don't you share more original and more substantive facts and opinions about yourself? I can learn more about you from a simple Google search than what you usually share, besides that you live in Old Town. Why not try something like: "Barry Evans sometimes thinks it's all a paradox, especially in conversation with his Relatives: Phillip B Evans, Rogers Louisa Evans, and Philip Barry Evans." Or "Barry Evans sometimes thinks it's all a paradox, especially since he was abandoned as a baby and educated at the orphanage boarding schools run by the Shaftesbury Homes, first at Fortescue House School in Twickenham." Or: "Barry Evans sometimes thinks it's all a paradox. He became a minicab driver in Leicestershire, where in 1997 he was found dead in a dilapidated bungalow at the age of 53." I suspect you got in the habit of writing these biographies during your "four-year stint as a National Public Radio commentator." That's the kind of stuff I like. Devote more column inches to interesting anecdotes like that one, and fewer to mentioning that you still live in Old Town. If you must mention that you live in Old Town, consider making your column about Old Town, and then the fact that you live there will become a sort of credential. Best regards, Nathaniel Page

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Posted by Nathaniel Page on 03/15/2010 at 8:22 AM

It's true I was born an orphan, in Old Town Eureka (where I live) (did I mention that?). This rest is lies, all lies I tell you. Barry Evans

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Posted by barry evans on 03/15/2010 at 9:49 AM
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