The Undying Novena

Abstract

At first, I was highly suspicious of the stated birthdate of this letter and its claimed continuity. If no one ever broke the chain, I naively reasoned, then the exponential growth of mail would have overwhelmed the earth and stripped the world's forests for paper. (Today's electronic novena would similarly swamp the Internet with e-mail.) However, I soon realized that it is possible that the chain has never completely died out, although many individuals have broken their part of it. Despite its claim, the letter is a type of chain letter, whose life can be modeled as a branching process [2]. In this stochastic process, each parent may give birth to four offspring creating four branches. Of course, some of the branches may die out as individuals break the chain. As long as one branch survives, however, the chain survives another generation. Since a novena requires nine consecutive days of prayer, we assume that a new generation occurs after every nine days-time sufficient for both the post office and the recipient to handle the letter before sending it onward. To investigate the purported lifetime of the novena, let's assume that a person either breaks the chain, with probability p, or continues it as instructed, with probability 1 p. Then the mean number of offspring from each person is m = 4(1 p). Thus, each recipient of the novena sends out, on average, m novenas. Each of these m recipients sends out, on average, m novenas, and so on. Thus, in the nth generation there are, on average, 4mn novena recipients stemming from the four original recipients in generation zero.