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In a book called Advanced Data Analysis from an Elementary Point of View by Cosma Rohilla Shalizi, page 405, the first instance of "Markov process" is accompanied by a footnote which reads

After the Russian mathematician A. A. Markov, who introduced the theory of Markov processes in the course of a mathematical dispute with his arch-nemesis, to show that probability and statistics could apply to dependent events, and hence that Christianity was not necessarily true (I am not making this up: Basharin et al., 2004).

I found it curious, how could religion have anything to do with the fact that the law of large numbers can be extended to non iid variables (because that is what Nekrasov, Markov's "arch-nemesis", was wrong about, and that argument is at the origin of the chains. They are a counterexample of Nekrasov false claim that independence is necessary for a law of large numbers). But I did not find the answer is the references math/history paper by Basharin et al.

Why would the following be true:

[Law of large numbers holds $\implies$ independence] $\implies$ Christianity is true

And what do they mean by Christianity being true or not?

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    $\begingroup$ Good question. If you can read Russian, the answer is here. Or, just use Google Translate. $\endgroup$ Jul 25, 2021 at 17:09
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    $\begingroup$ Just guessing: I suspect that the argument might go something like: We can observe the Law of Large Numbers applying in reality, and we know that requires independence, so that demonstrates that individuals independently make choices such as between good and evil, including whether to accept and work with God's grace as taught by the Orthodox Church in contrast to other ideas such as Calvinism's irresistible grace or some atheists' philosophy of mechanism. $\endgroup$
    – Henry
    Jul 26, 2021 at 1:42
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    $\begingroup$ Should this perhaps go on HSM instead? $\endgroup$
    – tox123
    Jul 26, 2021 at 4:58
  • $\begingroup$ It makes no sense to estimate probabilities for events that are completely outside of our scope , like "does god exist ?" We have not the slightest clue whether anything about the religion ideas human have has any basis. $\endgroup$
    – Peter
    Jan 18, 2023 at 14:59
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    $\begingroup$ @Peter, my own estimate is that it's about 7% likely that "god exists". Also, whatever particular pattern of coin-flips one produces is very unlikely. "Ah, probability!" :) $\endgroup$ Jan 19, 2023 at 0:45

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I'm not an expert on history or theology, but it seems that the motivation behind Nekrasov's claim is related to the Russian Orthodox's Church's doctrine of free will. If this is the only context behind the religious aspect of this work by Markov, then Shalizi's depiction "hence that Christianity was not necessarily true" is probably for humorous effect rather than for historical accuracy. But it is possible that I have missed some more explicit connection between religion and Markov/Nekrasov.


Page 9 of Basharin et al. 2004. (emphasis mine):

Nekrasov was originally a theologian by training, and later took up mathematics, eventually obtaining a professorship at Moscow University. Nekrasov was also an active member of the Moscow Mathematical Society, another prestigious mathematical school in Russia. The Moscow school often times maintained a clear tension with its sister school in St. Petersburg. Most mathematicians of the Moscow School were stout members of the Russian Orthodox Church and strong proponents of the religious doctrine of free will. Moscow members like Nekrasov tried to enlist statistics and probability to provide a foundation for their doctrine of free will. Of course, Markov, an atheist and eventual excommunicate of the Church quarreled endlessly with his equally outspoken counterpart Nekrasov.

Abstract of Seneta, "Markov and the Birth of Chain Dependence Theory." 1996. (emphasis mine):

Markov's work on chain dependence was motivated by his desire to refute a statement by Nekrasov that pairwise independence of random summands was a necessary condition for the Weak Law of Large Numbers. He did this by obtaining such a Law in 1906 for systems of dependent random variables, in particular for finite homogeneous 'Markov' chains. Nekrasov's incorrect assertion arose out of the theological doctrine of free will, with which some members of the Moscow School of Mathematics of the time were much concerned.

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    $\begingroup$ Many people had seen the determinism of Newton's physics as a serious challenge to religious belief at all while others saw it as a challenge to certain types of religious belief. In particular if everything is determined at every instant since the beginning, then where is there room for a person to exercise choice? One response to save the believe in human choice, free will, was to see the world as stochastic, not deterministic. This seems to fit with Nekrasov's view. $\endgroup$ Jul 27, 2021 at 19:16

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