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.

The story of the Kelly system is a story of secrets - or if you prefer, a story of entropy.

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.

Carl Friedrich Gauss, often rated the greatest mathematician of all time, played the market. On a salary of 1,000 thalers a year, Euler left an estate of 170,587 thalers in cash and securities. Nothing is known of Gauss's investment methods.

There were many at Bell Labs and MIT who compared Shannon's insight to Einstein's. Others found that comparison unfair - unfair to Shannon.

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

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