COMPUTING SCIENCE

# First Links in the Markov Chain

Probability and poetry were unlikely partners in the creation of a computational tool

# Mathematical Theology

By most accounts, Markov was a nettlesome character, abrasive even with friends, fiercely combative with rivals, often embroiled in public protests and quarrels. We get a glimpse of his personality from his correspondence with the statistician Alexander Chuprov, which has been published in English translation. His letters to Chuprov are studded with dismissive remarks denigrating others’ work—including Chuprov’s.

Markov’s pugnacity extended beyond mathematics to politics and public life. When the Russian church excommunicated Leo Tolstoy, Markov asked that he be expelled also. (The request was granted.) In 1902, the leftist writer Maxim Gorky was elected to the Academy, but the election was vetoed by Tsar Nicholas II. In protest, Markov announced that he would refuse all future honors from the tsar. (Unlike Anton Chekhov, however, Markov did not resign his own membership in the Academy.) In 1913, when the tsar called for celebrations of 300 years of Romanov rule, Markov responded by organizing a symposium commemorating a different anniversary: the publication of *Ars Conjectandi* 200 years before.

Markov’s strongest vitriol was reserved for another mathematician, Pavel Nekrasov, whose work Markov described as “an abuse of mathematics.” Nekrasov was on the faculty of Moscow University, which was then a stronghold of the Russian Orthodox Church. Nekrasov had begun his schooling at a theological seminary before turning to mathematics, and apparently he believed the two vocations could support each other.

In a paper published in 1902 Nekrasov injected the law of large numbers into the centuries-old theological debate about free will versus predestination. His argument went something like this: Voluntary acts—expressions of free will—are like the independent events of probability theory, with no causal links between them. The law of large numbers applies *only* to such independent events. Data gathered by social scientists, such as crime statistics, conform to the law of large numbers. Therefore the underlying acts of individuals must be independent and voluntary.

Markov and Nekrasov stood at opposite poles along many dimensions: A secular republican from Petersburg was confronting an ecclesiastical monarchist from Moscow. But when Markov launched his attack on Nekrasov, he did not dwell on factional or ideological differences. He zeroed in on a mathematical error. Nekrasov assumed that the law of large numbers *requires* the principle of independence. Although this notion had been a commonplace of probability theory since the time of Jacob Bernoulli, Markov set out to show that the assumption is unnecessary. The law of large numbers applies perfectly well to systems of dependent variables if they meet certain criteria.

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