Expectation is a statistical fiction, like having 2.5 children.

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

Your second ducat, like your second million, is never quite as sweet.

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

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.

Paradox is thus a much deeper and universal concept than the ancients would have dreamed. Rather than an oddity, it is a mainstay of the philosophy of science.

Samuelson spotted a mistake in Bacheliers work. Bachelier's model had failed to consider that stock prices cannot fall below zero.