Once Upon a Number by Paulos John Allen

Author:Paulos, John Allen [Paulos, John Allen]
Language: eng
Format: mobi
Publisher: Basic Books
Published: 2012-01-31T21:00:00+00:00

A PARABLE OF FURIOUS FEMINIST AND THE STOCK MARKET

I wrote this parable a week after the precipitous decline in the stock market in October 1997. It takes place in a benightedly sexist village of uncertain location. In this village there are 50 married couples, and each woman knows immediately when another woman’s husband has been unfaithful but never when her own has. The strict feminist statutes of the village require that if a woman can prove her husband has been unfaithful, she must kill him that very day. Assume also that the women are statute-abiding, intelligent, aware of the intelligence of the other women, and, mercifully, that they never inform other women of their philandering husbands. As it happens, all 50 of the men have been unfaithful, but since no woman can prove her husband has been so, the village proceeds merrily and warily along. Then one morning the tribal matriarch from the far side of the forest comes to visit.

Her honesty is acknowledged by all and her word taken as law. She warns darkly that there is at least one philandering husband in the village. Once this fact, only a minor consequence of what they already know, becomes common knowledge, what happens?

The answer is that the matriarch’s warning will be followed by 49 peaceful days and then, on the 50th day, by a massive slaughter in which all the women kill their husbands. To see this, assume there is only one unfaithful husband, Mr. A. Everyone except Mrs. A already knows about his infidelity, so when the matriarch makes her announcement only Mrs. A learns something new from it. Being intelligent, she realizes that she would know if any other husband were unfaithful. She thus infers that Mr. A is the philanderer and kills him that very day.

Now assume there are only two unfaithful men, Mr. A and Mr. B. Every woman except Mrs. A and Mrs. B knows about both cases of infidelity, Mrs. A knows only of Mr. B’s, and Mrs. B knows only of Mr. A’s. Mrs. A thus learns nothing from the matriarch’s announcement, but when Mrs. B fails to kill Mr. B the first day, she infers that Mr. A must also be guilty. The same holds for Mrs. B, who infers from the fact that Mrs. A has not killed her husband on the first day that Mr. B is also guilty. The next day Mrs. A and Mrs. B both kill their husbands.

If instead there are exactly three guilty husbands, Mr. A, Mr. B, and Mr. C, then the matriarch’s announcement would make no impact the first day, but by a reasoning process similar to the one just described, Mrs. A, Mrs. B, and Mrs. C each would infer from the inaction of the other two on the first two days that their husbands also were guilty and kill them on the third day. By a process of mathematical induction we can conclude that if all 50 husbands were unfaithful, their intelligent wives finally would be able to prove it on the 50th day, the day of the righteous bloodbath.

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