March 7, 2002
OLD CHALLENGE (Dean Thomas). Describe a practical way of picking a member of the Earth's population at random.
ANSWER (Al Zimmermann). I am assuming that by "at random" you mean "at random with uniform distribution." Otherwise I could just flip a coin--heads I pick my wife, tails I pick George Bush. It's legitimately random since you can't predict in advance who will be chosen.
Presumably one wants African tribesmen, Afghani cave dwellers, and American mathematicians to have equal probability of being chosen. Likewise, newborns, the homeless, the elderly, the imprisoned, the rich and the poor should all have their fair chance of being chosen.
Start by picking a country at random, with more populous countries being more likely to be chosen. (That's easy to do.) Once the country is chosen, use census data (as available) for successively smaller geographical regions until you get to an area for which there are no subdivisions with census data. Perhaps this will be a precinct in New York City's Manhattan or the Fijian island of Tutu. Now you have to try to find or create a list of everybody who lives there, and finally pick a person at random.
QUESTIONABLE MATHEMATICS. Eric Brahinsky sends in this example of overaccuracy from rough data.
"Really dishing it out" (San Antonio Express-News, 9/14/01)
This steakhouse goes through 2,000 pounds of prime beef each week, or 285.71 pounds a day. About 100 pounds of asparagus are served each week, or 14.28 pounds a day.
Readers are invited to submit more examples of questionable mathematics.
NEW CHALLENGE (Joe Shipman). I have noticed that it takes me longer to run around a loop near my house in one direction than the other; one direction has a long slow rise and a steep downhill, where the reverse direction has a long slow downslope and a steep climb. Which direction is faster?
Copyright 2002, Frank Morgan.
Send answers, comments, and new questions by email to Frank.Morgan@williams.edu,and JoeShipman@aol.com, to be eligible for Flatland and other book awards. Winning answers will appear in the next Math Chat. Math Chat appears on the first and third Thursdays of each month. Prof. Morgan's homepage is at www.williams.edu/Mathematics/fmorgan.
THE MATH CHAT BOOK, including a $1000 Math Chat Book QUEST, questions and answers, and a list of past challenge winners, is now available from the MAA (800-331-1622).