The Equation That Couldn't Be Solved by Mario Livio

The Equation That Couldn't Be Solved by Mario Livio

Author:Mario Livio
Language: eng
Format: epub, pdf
Publisher: Simon & Schuster
Published: 2004-12-31T16:00:00+00:00


Shaken, Not Stirred

Finding the love of your life through mathematics is not the only process where permutations are thrust into the limelight. Lotteries commonly provide such situations, and nowhere more dramatically so than in the 1970 Vietnam era draft lottery.

On November 26, 1969, President Richard Nixon signed an executive order that instructed the Selective Service to establish a random selection sequence for induction. The executive order stipulated that the lottery would be based on birth dates, but it provided no specific instructions on the precise method of drawing the dates.

This was not the first time in history when a draft was supposed to be based on some sort of lottery. The biblical story of the judge Gideon is particularly intriguing. God first told Gideon, “The troops with you are too many to give the Midianites into your hand. Israel would only take the credit away from me, saying, ‘My own hand has delivered me.’ Now therefore proclaim this in the hearing of the troops, ‘Whoever is fearful and trembling, let him return home.’ ” Thus Gideon sifted them out; twenty-two thousand returned, and ten thousand remained.

In the second “lottery” stage, God imposed on Gideon a second selection criterion. Gideon was asked to take his troops down to the water to drink. He was then told to choose only those three hundred who lapped the water, “putting their hands to their mouths,” and to release all the rest “who knelt down to drink water” directly, “as a dog laps.” Clearly, Gideon’s “lottery” was far from a random selection—all the possible permutations of the pool of candidates were not treated equally. Many interpretations have been suggested for the peculiar choice of the second criterion. The simplest is that the entire scheme was used merely to select a small number of people, in order to amplify the impression of the miraculous victory. More elaborate explanations relate the kneeling to practices used in the worship of other gods, or the use of the hands (rather than drinking directly from the stream) to a demonstration of being considerate and not greedy.

Oddly enough, even though conducted thousands of years later, the 1970 draft lottery also suffered from problems with randomization.

The procedure itself was simple enough. The officials tucked scraps of paper with the 366 dates of the year (including February 29) into capsules. One by one, these capsules were drawn from a bowl on December 1, 1969. Every man born between 1944 and 1948 was assigned a draft number corresponding to the order in which his birth date was picked. For instance, the first date drawn was September 14, and all men with that birthday were assigned no. 1. Men born on June 8 (the last capsule drawn) were assigned no. 366. Clearly, every drawing represents a permutation of the 366 dates. The smaller his draft number, the higher the chances that a man would actually be drafted. The table below shows the average lottery numbers by month obtained in the 1970 lottery.



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