The Five Greatest Applications of Markov Chains.

Eugeny Onegin (1913)

In 1913 Markov expands the 3rd edition of his book, “The Calculus of Probabilities,” to celebrate the 200 anniversary of Jakob Bernoulli’s “Ars Conjectandi.” 3rd edition closes with Markov’s famous application of chains:

“Let us finish the article and the whole book with a good example of the dependent trials, which approximately can be regarded as a simple chain.”

Markov studied sequence of 20,000 letters in A.S. Pushkin’s poem “Eugeny Onegin”.

Markov also presented this work at the physico-mathematical meeting of the Academy of Sciences in 1913.

Calculations for Eugeny Onegin

“The second question concerns an original statistical investigation which I have carried out and with which I propose to conclude my book. The character of the investigation, which embraces a sequence of 20,000 letters, is shown in the example below.”

(Jan. 15, 1913 letter to Chuprov)

All results:

- stationary probability of vowel = 0,432
- stationary probability of consonant = 0,568
- probability of a vowel following a vowel = 0,128
- probability of a vowel following a consonant = 0,663

Besikovitch on Markov’s book: “great attention is paid to the simplest numerical examples which are discussed in unusual detail. And further, it is hardly possible to find a single mistake in these examples.”

Markov on calculating: “Many mathematicians apparently believe that going beyond the field of abstract reasoning into the sphere of effective calculations would be humiliating.”

Table for Normal Distribution produced a table with up to 11 digits.
Table was used into the 1940s.

Reaction to Markov’s Application

Nikolai A. Morozov at a 1915 meeting of the Academy of Sciences in St. Petersburg called Markov’s method “a new weapon for the analysis of ancient scripts.”.
o demonstrate Morozov provided some statistics that could help identify the style of some authors.
Markov found Morozov’s experiments unconvincing, but did mention that a more advanced model and extended data set might enable author identification solely by mathematical analysis of this writings.
By 1916 Markov’s vision was nearly completely lost to glaucoma, and his analysis of texts ceased.

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