Critical Infrastructure Protection in Homeland Security: Defending a Networked Nation, 2nd Edition

Appendix A Math: Probability Primer

The publication of Geronimo Cardano's (1501–1576) Ars Magna in 1545 is generally recognized as the beginning of modern mathematics even though his most important works were not published until after his death [1]. Cardano's mathematics was somewhat at odds with Isaac Newton's (1642–1727) deterministic universe in which an apple falls from its tree in exactly the same way every time it falls. Its path is predictable in every detail.

Newton's deterministic model cast a shadow over Cardano's nondeterministic model for over a century. It was perfect for explaining some phenomena but completely inadequate to describe many other everyday phenomena. For example, Newtonian mathematics failed to explain accidents, diseases, and games of chance. Newton's model could not predict when the apple would fall. On the other hand, Cardano turned uncertainty and games of chance into a practical application of mathematics. According to Wikipedia, “Cardano was notoriously short of money and kept himself solvent by being an accomplished gambler and chess player. His book about games of chance, Liber de ludo aleae (‘Book on Games of Chance'), written around 1564 but not published until 1663—[during Newton's life ]—contains the first systematic treatment of probability, as well as a section on effective cheating methods.”¹

Cardano's ideas were developed even further by a young genius named Blaise Pascal (1623–1662). Pascal built and sold 50 mechanical calculators ...