On The Improbability of Art

In my work as a psycholinguist, I have opportunity to compute the exact chance probability (given a distribution of words in a very large corpus of human-created text) of a particular sentence; i.e. to compute how probable it is that you would come across a particular sentence by chance. (I have a fun job!) Even very ordinary and very short (three-word) sentences have (to me) astoundingly low probabilities, easily below 1 in 10,000,000,000 and often ten orders of magnitude less probable. Weirder sentences would be much less likely. 

 I enjoy then thinking about the absurd improbability of any really long set of words. Any normal length novel is so improbable as to be incalculably unlikely (of course, novels and sentences do not come about by chance, so the calculation is perhaps somewhat misleading...this doesn't really make any difference to my point, but I won't get into that here). It is no wonder that I enjoy the musings of the Soviet statistician Andrei Kolmogorov (1956, from this interesting article on his life in Nautilus magazine) “Is it possible to include [Tolstoy’s War and Peace] in a reasonable way into the set of ‘all possible novels’ and further to postulate the existence of a certain probability distribution in this set?” His point, of course, was that it is not. Art is vanishingly improbable and therefore singular. Perhaps that is one reason why we like it.