The more improbable the message, the less "compressible" it is, and the more bandwidth it requires. This is Shannon's point: the essence is its improbability.

Bernoulli's real contribution was to coin a word. The word has been translated into English as "utility". It describes this subjective value people place on money.

Shannon's most radical insight was that meaning was irrelevant.

Samuelson, however, hedged his personal bets - by putting some of his own money in Berkshire Hathaway.

At a bare minimum, understanding entails being able to detect an internal contradiction: a paradox.

There is a deep connection between Bernoulli's dictum and John Kelly's 1956 publication. It turns out that Kelly's prescription can be restated as this simple rule: When faced with a choice of wagers or investments, choose the one with the highest geometric means of outcomes.

Expectation is a statistical fiction, like having 2.5 children.