## Saturday, August 10, 2013

### Pushkin poetry, Markov chains

A Markov chain is a mathematical process that can be used to answer questions such as these:
If the current letter I am reading is a vowel, what is the probability
that the next letter will be a vowel?  A consonant?
Answers from these may be combined to create more lengthy predictions -- about the 3rd letter after a given one, or the 10th -- and so on.
A recent article by Brian Hayes in American Scientist (brought to my attention by Greg Coxson) alerted me to the fact that it is 100 years since the Russian mathematician A. A. Markov (1856 - 1922) announced his findings about these transition probabilities -- and, moreover, his work was based on analysis of poetry; the poetry was Eugene Onegin, a verse-novel in iambic tetrameter by Alexander Pushkin (1799-1837). Markov's analyis dealt with Pushkin's novel as a long string of alphabetic characters and he tabulated the categories of vowels and consonants for about 20,000 letters. (For a host of details, visit Hayes' careful and interesting article.)
The text of  Eugene Onegin does not contain mathematical ideas and so, as a sample, I simply present here the first "Pushkin sonnet" of Chapter 1 (translated into English by Babette Deutsch); this stanza contains the word "one" twice.  And perhaps, despite the lack of mathematics, you may be intrigued by the tale and will seek to read more.

from Chapter One  (of Eugene Onegin by Alexander Pushkin, translated by Babette Deutsch)

Makes haste to live and cannot wait to feel.  K Vyasemsky

1

"My uncle's shown his good intentions
By falling desperately ill;
His worth is proved; of all inventions
Where will you find one better still?
He's an example, I'm averring;
But, God, what boredom -- there, unstirring,
By day, by night, thus to be bid
To sit beside an invalid!
Low cunning must assist devotion
To one who is but half-alive:
You puff his pillow and contrive
Amusement while you mix his potion;
You sign, and think with furrowed brow --
'Why can't the devil take you now?' "

There exist a number of translations of Eugene Onegin, most more recent than this old one from my bookshelf -- found in a 1936 Modern Library Edition of The Poems, Prose, and Plays of Alexander Pushkin. Tchaikovsky created an opera from Pushkin's tale, and several films also have told versions of the story.  At this link, you may read online a highly praised translation by Charles Johnston.
Recent years have seen a variety of computer programs that generate poems using Markov chains.  Using Google with the phrase "Markov Chain poetry" will get you to several. This link, for example, offers a Markov chain poetry generator of snowballs.