30 March 2013 – The story starts in the early 20th century with one of those obscure academic squabbles that usually don’t amount to much. A mathematician and theologian named Pavel Nekrasov argued that since independent events follow the law of big numbers and social phenomena such as crime statistics do as well, then humans must have free will.
Andrei Markov, one of the great mathematicians of the day, thought Nekrasov’s argument was hogwash. After all, he noted, just because independent variables follow a certain mathematical law doesn’t mean that directed activity can’t do so as well.
To prove his point, he performed a mathematical analysis of Eugene Onegin, Pushkin’s famous novel in verse, and showed that the combinations of vowels and consonants followed the law of big numbers as well. A vowel, would most likely be followed by a consonant and vice versa, in proportions that became more stable as you analyzed more text.
And so, Markov succeeded in showing that dependent variables could yield distinct probabilities. It was the kind of interesting, but relatively useless insight that … Read more