Pascal on God…
Presently, I am reading this fascinating book called “Against the Gods: The remarkable story of risk” by Peter Bernstein. Have been usually lazy, and it took me a while to get to page 69. But now that I am past page 69, I think this is probably the most interesting page I have read for sometime. So interesting, that I am in fact going to put it down here. Before I get down to that, here’s a synopsis of the premise of the book.
Bernstein’s proposition: What is it that distinguishes the thousands of years of history from what we think of as modern times? The answer goes beyond the progress of science, technology, capitalism and democracy. The revolutionary idea that defines the boundary between modern times and the past is the mastery of risk: the notion that the future is more than a whim of the gods and that men and women are not passive before nature. The book tells the story of a group of thinkers whose remarkable vision revealed how to put the future at the service of the present. By showing the world how to understand risk, measure it, and weigh its consequences, they converted risk-taking into one of the primary catalysts that drive modern western society. By defining a rational process of risk-taking, thee innovators provided the missing ingredient that has propelled science, and enterprise into the world of speed, power, communication and sophisticated finance that marks our own age. Their discoveries about the nature of risk, and the art and science of choice, lie at the core of our modern market economy that nations around the world are hastening to join.
…. Blaise Pascal who the author discusses in some detail was one of the leading mathematicians of his age. Not just that, he was also an occasional philosopher, and later on in life yielded to his religious convictions that were essentially anti-intellectual. One of his contemporaries was Pierre De Fermat (of the Fermat’s last theorem fame), a lawyer in Toulouse. Fermat’s erudition was awesome. He spoke all the principal European languages, wrote poetry in some of them, and he was a busy commentator on the literature of the Greeks and Romans. Moreover, he was a mathematician of rare power. He was an independent inventor of analytical geometry, contributed to the early development of calculus, did research on the weight of the earth, and he worked on light refraction and optics. In the course of what turned out to be an extended correspondence with Pascal , he made a significant contribution to the theory of probability.
The question they answered was the one posed by Luca Paccioli, a Franciscan monk and mathematician, in 1494, and a contemporary of Leonardo Da Vinci. The question was this.
“A and B are playing a fair game of “balla” (some kind of dice game, I think). They agree to continue until one has won six rounds. The game actually stops when A has won five and B three. How should the stakes be divided? The puzzle, which came to be known as the problem of the points was more significant than it appears. The resolution of how to divide the stakes in an uncompleted game marked the beginning of a systematic analysis of probability – the measure of our confidence that something is going to happen.
Anyway Pascal and Fermat together answered this puzzle, Pascal approaching it from a geometric perspective, Fermat from a pure algebra standpoint. (Recall the Pascal’s triangle?)…
Anyway, more than mathematics was involved here for Pascal, who was so deeply involved with religion and morality. After Pascal renunciated mathematics and physics, and took up residence in the monastery of Port-Royal, Paris, he put together his thoughts about life and religion and published them under the title Pensees. In the course of his work on that book, he filled two pieces of paper on both sides with what came to be known as “Pascal’s wager”, which asks, “God is, or he is not. Which way should we incline? Reason cannot answer.”
Here, drawing on his work in analyzing possible outcomes of the game of balla, Pascal frames the question in terms of a game of chance. He postulates a game that ends at an infinite distance in time. At that moment, a coin is tossed. Which way would you bet – heads (God is) or tails (God is not)?
Ian Hacking, historian asserts that Pascal’s line of analysis to answer this question is the beginning of the theory of decision-making. “Decision theory”, as Hacking describes it, “is the theory of deciding what to do when it is uncertain what will happen.” Making that decision is the essential first step in any effort to manage risk.
Sometimes we make decisions on the basis of past experience, out of experiments we or others have conducted in the course of our lifetime. But we cannot conduct experiments that will prove either the existence or absence of God. Our only alternative is to explore the future consequences of believing in God or rejecting God. Nor can we avert the issue, for by the mere act of living we are forced to play this game.
Pascal explained that belief in God is not a decision. You cannot awaken one morning and declare, “Today I think I will decide to believe in God.” You believe or you do not believe. The decision, therefore, is whether to choose to act in a manner that will lead to believing in God, like living with pious people and following a life of “holy water and sacraments”. The person who follows this precept is wagering that God is. The person who cannot be bothered with that kind of thing is wagering that God is not.
The only way to choose between a bet that God exists and a bet that there is no God down that infinite distance of Pascal’s coin-tossing game is to decide whether an outcome in which God exists is preferable –more valuable in some sense-than an outcome in which God does not exist, even though probability may be only 50-50. This insight is what conducts Pascal down the path to a decision – a choice in which the value of the outcome and the likelihood that it may occur will differ because the consequences of the two outcomes are different. “
If God is not, whether you lead your life piously or sinfully is immaterial. But suppose that God is. Then if you bet against the existence of God by refusing to live a life of piety and sacraments you run the risk of eternal damnation; the winner of the bet that God exists has the possibility of salvation. As salvation is clearly preferable to eternal damnation, the correct decision is to act on the basis that God is. “Which way should we incline?” The answer was obvious to Pascal.