Mathematics and Free Will
Persi Diaconis, a statistician who himself has an interesting biography, related at lunch today an interesting aspect of the history of Markov chains.
Apparently, when Communism came into power in Russia, a biologist named Trofim Lysenko became rather influential. He had theories that rejected Mendelian genetics and Darwinian evolution because they did not sufficiently allow for Free Will. His ideas, particularly the emphasis on Free Will, became known as Lysenkoism and they reached their peak under Stalin, who apparently was a big fan. However, even before Stalin, Lysenkoism was taking a prominent political role and controlling research done not only in biology or chemistry, but even mathematics. For example, analysts were ordered not to study smooth functions because they apparently did not have enough "Free Will". If you dared to say that was a ridiculous motivation, you of course lost your job or got demoted.
Markov, at that time, was a probabilist. Directives came from above that probability should only be studied for independent variables, since only independent variables had enough "free will" to exhibit the true theorems of probability, like the Law of Large Numbers or the Central Limit Theorem. Markov, to say the least, was not happy with this dictum. So he developed the theory of Markov chains, which do not involve completely independent variables. His groundbreaking paper on the subject proved that they obey rules like the Law of Large Numbers and the Central Limit Theorem, the very things Lysenkoists had argued made independent variables more "pure", or whatever. The very last line of Markov's paper said "It is possible to do probability without free will."
It's pretty crazy to think that such an important mathematical subject as Markov chains was foremost a political statement.
Apparently, when Communism came into power in Russia, a biologist named Trofim Lysenko became rather influential. He had theories that rejected Mendelian genetics and Darwinian evolution because they did not sufficiently allow for Free Will. His ideas, particularly the emphasis on Free Will, became known as Lysenkoism and they reached their peak under Stalin, who apparently was a big fan. However, even before Stalin, Lysenkoism was taking a prominent political role and controlling research done not only in biology or chemistry, but even mathematics. For example, analysts were ordered not to study smooth functions because they apparently did not have enough "Free Will". If you dared to say that was a ridiculous motivation, you of course lost your job or got demoted.
Markov, at that time, was a probabilist. Directives came from above that probability should only be studied for independent variables, since only independent variables had enough "free will" to exhibit the true theorems of probability, like the Law of Large Numbers or the Central Limit Theorem. Markov, to say the least, was not happy with this dictum. So he developed the theory of Markov chains, which do not involve completely independent variables. His groundbreaking paper on the subject proved that they obey rules like the Law of Large Numbers and the Central Limit Theorem, the very things Lysenkoists had argued made independent variables more "pure", or whatever. The very last line of Markov's paper said "It is possible to do probability without free will."
It's pretty crazy to think that such an important mathematical subject as Markov chains was foremost a political statement.