Drunkard's Walk - Leonard Mlodinow [22]
Before his death, Gerolamo Cardano burned 170 unpublished manuscripts.1 Those sifting through his possessions found 111 that survived. One, written decades earlier and, from the looks of it, often revised, was a treatise of thirty-two short chapters. Titled The Book on Games of Chance, it was the first book ever written on the theory of randomness. People had been gambling and coping with other uncertainties for thousands of years. Can I make it across the desert before I die of thirst? Is it dangerous to remain under the cliff while the earth is shaking like this? Does that grin from the cave girl who likes to paint buffaloes on the sides of rocks mean she likes me? Yet until Cardano came along, no one had accomplished a reasoned analysis of the course that games or other uncertain processes take. Cardano’s insight into how chance works came embodied in a principle we shall call the law of the sample space. The law of the sample space represented a new idea and a new methodology and has formed the basis of the mathematical description of uncertainty in all the centuries that followed. It is a simple methodology, a laws-of-chance analog of the idea of balancing a checkbook. Yet with this simple method we gain the ability to approach many problems systematically that would otherwise prove almost hopelessly confusing. To illustrate both the use and the power of the law, we shall consider a problem that although easily stated and requiring no advanced mathematics to solve, has probably stumped more people than any other in the history of randomness.
AS NEWSPAPER COLUMNS GO, Parade magazine’s “Ask Marilyn” has to be considered a smashing success. Distributed in 350 newspapers and boasting a combined circulation of nearly 36 million, the question-and-answer column originated in 1986 and is still going strong. The questions can be as enlightening as the answers, an (unscientific) Gallup Poll of what is on Americans’ minds. For instance:
When the stock market closes at the end of the day, why does everyone stand around smiling and clapping regardless of whether the stocks are up or down?
A friend is pregnant with twins that she knows are fraternal. What are the chances that at least one of the babies is a girl?
When you drive by a dead skunk in the road, why does it take about 10 seconds before you smell it? Assume that you did not actually drive over the skunk.
Apparently Americans are a very practical people. The thing to note here is that each of the queries has a certain scientific or mathematical component to it, a characteristic of many of the questions answered in the column.
One might ask, especially if one knows a little something about mathematics and science, “Who is this guru Marilyn?” Well, Marilyn is Marilyn vos Savant, famous for being listed for years in the Guinness World Records Hall of Fame as the person with the world’s highest recorded IQ (228). She is also famous for being married to Robert Jarvik, inventor of the Jarvik artificial heart. But sometimes famous people, despite their other accomplishments, are remembered for something they wished had never happened (“I did not have sexual relations with that woman”). That may be the case for Marilyn, who is most famous for her response to the following question, which appeared in her column one Sunday in September 1990 (I have altered the wording slightly):
Suppose the contestants on a game show are given the choice of three doors: Behind one door is a car; behind the others, goats. After a contestant picks a door, the host, who