Consider a circle; an equilateral triangle inscribed on it; and a chord drawn at random. What is the probability that the chord is longer than the side of the triangle? This question is known as Bertrand’s paradox – here’s the Wikipedia entry. I found it fascinating and spent some time to make this ipython notebook about it.
The best book I read in 2014 was ‘Probability Theory – The Logic of Science’ (2003) by Edwin T. Jaynes. It was recommended to me by an ex-colleague from Toronto and it turned out to be one of the most exciting scientific books I’ve read so far.
E.T. Jaynes was a physicist and one of the main figures in the development of probability theory in the 20th century. He was associated with the school of scientists that, in the tradition of Laplace, viewed probability as a system of logic – what’s commonly known as the Bayesian school of probability. This book was his attempt to summarize his view on probability theory. Unfortunately, he was not able to complete it before his death. As a result, the published version is missing some chapters from the originally planned outline and some of the later chapters in the book are not as polished as earlier ones. Still, its 700 pages make an extraordinary read.