The Unfinished Game by Keith Devlin

Devlin, Keith. The Unfinished Game: Pascal, Fermat, and the Seventeenth-Century Letter that Made the World Modern. New York: Basic Books, 2008.

The Unfinished Game is a book about math, history and how ideas can change the way we live. The title refers what is also called the problem of points. When a game of chance is ended prematurely, what is the fairest way to divide the pot?

The prevailing idea before Blaise Pascal and Pierre de Fermat is that it is impossible to tell the future, and that made it hard rightly to divide the potential winnings. These mathematicians didn’t work out a way to predict the future, but they did figure out how to calculate the likelihood of different potential outcomes. The fair way to split the pot was in proportion to each player’s probability of winning.

Settling a debate amongst gamblers isn’t and especially important, but the concept of probability they created, along with its correct calculation, gave birth to something we do all time: manage risk. By estimating the likelihood of various events, we can make decisions generally increase our successes and reduce our losses. The insurance industry is built on understanding probability and decisions we make every day about what investments to make, what activities to undertake, even what to wear, are informed by our estimates of the probability of some future condition.

This concept of probability is common now. It can be daunting to think of how revolutionary it was at the time.

An interesting revealed in the book is how Pascal and Fermat worked out these ideas. It was through friendly correspondence. While much is made of the contentious debates and battles of ideas, much of our increase in knowledge comes from the cooperation of curious and committed colleagues. Both men were brilliant thinkers, but they weren’t haughty or difficult, though Fermat didn’t get along with everyone as well as he did with Pascal. For all the great math they considered in their letters, the correspondence is characterized by humility and grace.

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Pascal's Wager by James A. Connor

Blaise Pascal had a great impact on mathematics. He laid the foundations of our mathematical understanding of probability. A computer programming language was named for him.

Pascal was also a deeply religious man and philosopher. His book Pensées is read as a devotional by many Christians. His argument that the belief in God is rational is widely known.

James A. Connor takes the name of that argument for the name of his biography of the man, Pascal’s Wager. Connor considers both Pascal’s life in science and math and his religious convictions.

For many, there is no conflict in scientific study and religious devotion, but there was for Pascal. He was a Jansenist, though somewhat at odds with the leaders of the movement because of his interests in science and philosophy. The Jansenists were deeply concerned with sin and living a life of penitence; to pursue anything else was to embrace worldliness. Pascal loved the discoveries he made by reason and experiment, but he also longed for a life of purity and closeness to God.

Pascal was seen as a bit of a mathematical prodigy, especially in his youth when his father led a secular life by the standards of the day. He published a pamphlet on conic sections when he was 16 years old. He invented a calculating machine, the Pascaline, when he was 19. He was still fairly young by modern standards when he developed a theory of probability in a series of letter he exchanged with Pierre Fermat.

He had a mystical experience in 1654 that changed his focus in life. He told know one about it, but wrote a note about it that he kept pinned in his coat to carry with him the rest of his life. The note was discovered by his nephew shortly after his death.

After his experience, he devoted more of his time to supporting Jansenism, which his entire family had come to follow, especially his sister, Jacqueline, a nun. Jansenists were in conflict with other Catholics over their views on original sin and election, especially with the Jesuits. Pascal became an apologist for Jansenism, and especially mocked the Jesuits in The Provincial Letters.

Politics and religion were deeply linked in 17^th Century France, and the conflict between Pascal’s sect and the wider French Catholic church became a conflict with Louis XIV. He felt that the Jansenist leaders capitulated to the king and the Jesuits, which brought him into conflict with them as well.

Though religious debates had been part of his entire life, this heating up of the conflict to such a level occurred toward the end of his life. He expressed his devotion to God in self-imposed poverty and care for the poor; which in one case took the form of establishing the first public transportation system. He did not abandon math, though, and published a paper on the cycloid as well. He had been sick most of his life and passed away in 1662 at the age of 39.

Connor’s book is approachable for most readers. Though Pascal’s fame today probably rests more on his accomplishments as a mathematician, Connor shows how his life was shaped by his religion and both the religious and secular traditions of his time (Connor is a former Jesuit priest).

If you’re interested in this book, you may also be interested in

Chance by Amir Aczel

The Drunkard’s Walk by Leonard Mlodinow

How Not to Be Wrong by Jordan Ellenberg

The Language of God by Francis S. Collins

On a Grander Scale by Lisa Jardine

The Unfinished Game by Keith Devlin

Connor, James A. Pascal’s Wager: The Man Who Played Dice with God. San Francisco: HarperSanFrancisco, 2006.