Other tests based on compression or Kolmogorov complexity.
Now Kolmogorov joined the critics and turned against Luzin.
But Kolmogorov's interests inclined him in more philosophical directions, too.
Thanks to Kolmogorov, though, we can explain when and why we don't.
For Kolmogorov, his ideas neither eliminated chance,
nor affirmed a fundamental uncertainty about our world;
It was through Luzitania that Kolmogorov's evaluation of probability took on a more personal turn.
At that moment, Kolmogorov decided to change his concentration to mathematics,
where one proof would suffice.
Kolmogorov believed that the frequency of stress deviation from the classical
meters offered an objective“statistical portrait” of a poet.
The most basic notion of Kolmogorov's theory was the“elementary event,” the outcome
of a single experiment, like tossing a coin.
Kolmogorov objected, taking a radical probabilistic view
of social interactions in which people acted as statistical samples of larger groups.
To measure the artistic merit of texts, Kolmogorov also employed a letter-guessing method to evaluate
the entropy of natural language.
In the face of his own political conformity, Kolmogorov presented a radical and, ultimately, foundational revision of probability theory.
The moral dimension of Kolmogorov's decision aside,
he had played the odds successfully and gained the freedom to continue his work.
During the Second World War, the Russian government asked Kolmogorov to develop methods for increasing the effectiveness of artillery fire.
Kolmogorov showed that the great circle has a measure zero,
since it is a line segment and its area is zero.
After switching his major, Kolmogorov was initially drawn into the devoted mathematical
circle surrounding Nikolai Luzin, a charismatic teacher at Moscow University.
Studying Pushkin, Pasternak, and other Russian poets, Kolmogorov argued that they had manipulated meters to give“general
coloration” to their poems or passages.
Kolmogorov conceived complexity as the length of the shortest description of an object,
or the length of an algorithm that produces an object.
Kolmogorov stressed that every true work of art was a unique creation,
something unlikely by definition, something outside the realm of simple statistical regularity.
It is oddly appropriate that a chance event drove Kolmogorov into the arms of probability theory,
which at the time was a maligned sub-discipline of mathematics.
Music and literature were deeply important to Kolmogorov, who believed he could analyze them probabilistically to gain
insight into the inner workings of the human mind.
Kolmogorov drew analogies between probability and measure, resulting
in five axioms, now usually formulated in six statements, that made probability a respectable part of mathematical analysis.
As a young man, Kolmogorov was nourished by the intellectual ferment of post-revolutionary Moscow, where literary experimentation,
the artistic avant-garde, and radical new scientific ideas were in the air.
In 1944 and 1945, the government awarded Kolmogorov two Orders of Lenin for his wartime contributions,
and after the war, he served as a mathematics consultant for the thermonuclear weapons program.
Kolmogorov privately remarked that, from the viewpoint
of information theory, Soviet newspapers were less informative than poetry, since political discourse employed a large number of stock phrases and was highly predictable in its content.
It is one of the many intellectual innovations dreamed up by Andrei Kolmogorov, a mathematician of startling breadth
and ability who revolutionized the role of the unlikely in mathematics, while carefully negotiating the shifting probabilities of political and academic life in Soviet Russia.