Religious + Atheists = Math Advances

 

Imagine if you will, a mathematician, Pavel,  in Moscow who trained as an Orthodox theologian and another man who lived in St. Petersburg.  This other, a man hated the church, a self proclaimed atheist, and constantly wrote letters to the Editor about various social matters thus gaining the nickname of "Andrei the Furious" Markov. 

The disagreement between the two arose when Pavel thought he'd come up with a mathematical proof of free will which supported the position of the church.  Andrei felt this mystical nonsense was wrapped up as mathematics. 

In 1902, Pavel applied the law of large numbers to the debate of free will versus predestination. He decided that voluntary acts are like independent events  in probability with no casual links between any of them.  The law of large numbers applies only to those independent events.  Since crime statistics conform to the law of large numbers, those voluntary acts must also be subject to the law of large numbers. 

Andrei Markov found a basic error with Pavel's thinking because Pavel assumed that the law of large numbers required the principle of independence and Andrei set out to prove that the law of large numbers applied to dependent events as long as they meet certain criteria.  

Consequently he created the Markov chain to show that random behavior could be produced mechanically but had the same features as those that Pavel used for free will.  Markov applied this first to digits and then the English language when he applied the idea to Puskin's poem Eugene Onegin. He broke it down into consonants and vowels before analyzing the placement of each.

He discovered that the letter following a consonant has a 67% chance of being a vowel and only 33% chance of another consonant. On the other hand, the letter following a vowel has almost a 13% chance of being another vowel and an 87% chance of being a consonant.  He applied his ideas to other pieces of literature to find that the author could be determined by the results and probabilities.

He presented his discovery to the Imperial Academy of Sciences in St. Petersburg in January of 1913. This move extended probability in a new direction.  It took chains of linked events and determined the next step based on the current state of the system.  

Today, Markov chains are used to identify which legislative maps have been brutally gerrymandered, how Google determines which websites are the most important, or it can teach the computer how to create human like text.  It is used to help identify genes in DNA, creating algorithms for voice recognition software, and so much more. All that is needed is to know are the probabilities for the next step in the process based on the previous step. 

Thus arising out of a disagreement between two mathematicians, we have something that extended probability to a something with so many applications.  Let me know what you think, I'd love to hear, have a great day.