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.

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

The best paradoxes raise questions about what kinds of contradictions can occur-what species of impossibilities are possible.

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.

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

People tend to be clueless about prices. Contrary to economic theory, we don't really decide between A and B by consulting our invisible price tags and purchasing the one that yields the higher utility, he says. We make do with guesstimates and a vague recollection of what things are “supposed to cost.”