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In the book "The Golden Ticket. P, NP, and the Search for the Impossible" By Lance Fortnow, It contains the following story:

After attacking the geneticists, the lead “philosophers” in Russia went after the field of probability because of its notion of independent events. Probability theory measures the chances that some events will happen, such as the probability that two dice will sum to five is one out of nine. Probability gives a way of describing independent events. For example, when you roll two dice, the value of one die does not depend on the outcome of the other. This didn’t fit well with Marxist philosophy, under which everything is interconnected and dependent on everything else. These philosophers met with Kolmogorov and challenged him: “Under Marxism there cannot be independent events.” Kolmogorov realized the importance of his next words, for it could greatly affect the course of Russian mathematics. He responded, “But, you are mistaken.” The agents believed they had Kolmogorov—to challenge the beliefs of determinacy meant an open challenge to the fundamental beliefs of Marxism, which could quickly lead to the end of Kolmogorov’s career. Kolmogorov went on, “Consider a priest that during a drought prays for rain. The following day it rains. These events are independent.” The agents couldn’t counter. Any dependence in these events would acknowledge the power of religion, which in itself would also be considered an attack on Marxist dogma. Kolmogorov had saved probability.

The book is for a wide general audience and the story is interesting. I am asking if there is more history, or more I could read about this. Marxism and genetics is well documented (See Lysenkoism) but I am looking for similar information, either on this interaction, or marxist opposition to the notion of independent events. Some work has been written on Kolmogorov's ideology with respect to soviet mathematics, including opposition to Lysenkoism, but I can't find any more information on this specific story.

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    $\begingroup$ Does the book give any source for this story? $\endgroup$ Commented Jul 27 at 14:41
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    $\begingroup$ @TorstenSchoeneberg I never thought to check but it contains notes in the end of the book on it, so I suppose I will answer my own question. $\endgroup$ Commented Jul 27 at 15:17

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The book states at the end:

Kolmogorov’s story about saving probability theory in Russia comes from discussions with Alexander Razborov and a blog post (http://ansobol.livejournal.com/12551.html). As the text indicates, this story should perhaps be considered apocryphal.

The Google translated version of the link reads:

Again the pique vest. The reason is a quote from RIA Novosti from the speech of Patriarch Kirill at the consecration of the icon on the Spasskaya Tower: For his part, Patriarch Kirill noted that we must try to look at today’s event “with a different scale of vision.”

“The face of the Savior appeared on the Spasskaya Tower. This is, of course, a symbol. And the fact that it rained today—rain is always a manifestation of God’s grace. We prayed hard for rain, but now it is coming. And let it still rain so that our parched land will be nourished,” he said.

This brings to mind a well-known (among probabilists) anecdote. Somewhere around the famous VASKhNIL session on biology, dialectical materialists also became interested in mathematics. In particular, the concept of independent events, fundamental to probability theory, was subjected to sharp criticism. In fact, Marxists said, everything in nature is interconnected - how can events be independent? Andrei Nikolaevich Kolmogorov, who was mainly targeted (after all, the founder of modern probability theory), stopped these conversations by publicly giving the following example. “Imagine,” he said, “a prolonged drought.” The village priest organizes a religious procession and serves a prayer service in the field for the sending of rain. And as soon as he finished, a clap of thunder is heard, a cloud flies in and rain pours down on the parched land. This is an example of completely independent events.

The "apocryphal" comment should be as close to an answer as one can get. If I had to conjecture, since two people have heard the story but don't authoritatively have a source of where it came from, it could be regional "folklore", or perhaps an invented teaching aid.

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