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.

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

Kelly was aware that there is one type of favorable bet available to everyone; the stock market.

Use "entropy" and you can never lose a debate, von Neumann told Shannon - because no one really knows what "entropy" is.

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.

The best strategy is one that offers the highest compound return consistent with no risk of going broke.

In The Tricky Art of Co-Existing, Sandi Toksvig navigates life's little dilemmas with wit and not-so-common sense. You'll learn the strange history of common courtesy and the one true secret of social success: how to not drive everyone around you crazy.