May be the Odds be Ever in Your Favor

Probability Theory is maybe one of the lesser known branches of mathematics for most people. However, I believe it to be one of the most important branches of math for the average person to understand. Before I begin to explain why I think this, I am going to start that the discoveries made by the mathematician being highlighted in this article were revolutionary for his time and still are. They broke the common way to think, and ultimately helped move along the idea that the individual controls their life. The notion that came from the poem “Invictus”, “I am the master of my fate and I am the captain of my soul” came from this era of philosophy. It is my position that math is a social thing, as it philosophy. The political and economic spheres impact the math and the philosophy at the time, so to understand Blaise Pascal we must have an understanding of 17th Century France.

During this time the kings were Henry IV, Louis XIII, and Louis XIV, each of them having a more absolutist rule than the last. Meaning that what the word of the king became more powerful, and the voice of the people shrunk in importance. This is 100 Years before the French Revolution, so all of the things that started the revolution began in this time. In addition to the increase of an absolutist rule, the catholic church was the official church in France. So if you went against the word of the king, you were also disobeying the Church and God.
The notion that we have today, that each persons voice matters, was more than revolutionary when it was birthed. Interestingly the group of philosophers at the time were known as the Rationalists: Francis Bacon (Scientific Method ), Rene Descartes ( Geometry ), John Locke, Spinoza, Immanuel Kant, Diderot, David Hume. Those are not all of them, but they are the major players at the time in France, Austria, England, and Spain. They were the beginners of the French Enlightenment where the concept of reason takes over social thought as opposed to blind faith or passiveness. It encouraged people to have an active role in their lives.

So this was the world that Blaise Pascal was born into in 1623. The general social thought was changing which would lead to a revolution in the British Colonies ( U.S ) and France. Pascal’s father was as mathematician and accountant by trade, who home-schooled Pascal. Funny though, he did not teach Pascal math. He believed it would be too distracting for his son and would prevent him from learning a trade. So he sent his son to live with his uncle and learn a trade. However Pascal rebelled and taught himself geometry. His father, seeing how much his son enjoyed math gave in and taught his son. This was the beginning to Blaise Pascal as a protege child. His first invention was a calculator to help is father with work. He added a few more inventions to the list, and developed the field of hydrodynamics in physics, where his name is used as a unit of pressure.

In mathematics however Blaise Pascal is best known as the ( or one of ) the fathers of Probability Theory (is the field of math that attempts to quantify randomness). It started in a way to solve problems in gambling and games of chance. For example, how do you split the pot when you can’t finish a game? This question gave rise to the concept of Expected Value ( predicted value of a variable, found by summing up all possible values multiplied by the probability of the occurrence ). He did this work with another famous mathematician and lawyer by trade Pierre de Fermat. In math, we use Fermat’s notation but it was the methods of Pascal that we use today.
Another of his famous works is known as Pascals triangle ( pictured below ).

To understand this, these are are all probability calculations. The number on top is how many things you are choosing from and the bottom number is how many you are choosing.
So for example if you are choosing what how many different pairs of socks you can wear, and you don’t care about mismatching two socks and you have 5 pairs of socks. It would be a 5 on top and a 2 on bottom.
This is used in something known as the Binomial Theorem ( it is used in working with polynomials ).

One day Pascal woke up and denounced math. He claimed that it was for children and a waste of his time. He sold everything he owned except for his bible and lived with the homeless, devoting his life to Christianity and the catholic religion. In doing this he came up with what is known as Pascals Wager. It is not an argument for the existence of god, rather an argument for a belief in god. It goes as follows:
There are 4 cases and 4 possible outcomes. You either believe in God or you don’t, and God exists or he doesn’t exist.

Case 1: God exists and you believe → +infinity good.
Case 2: God exists and you don’t believe → -infinity bad.
Case 3: God doesn’t exist and you believe → + some good or no change.
Case 4:God doesn’t exist and you don’t believe → +some good or no change.

It was called a wager, because it is a gamble, ( again pulling from the culture around him and his math background) The values in the middle can be thought of the expected values from the probabilities of God existing or not.

Even though Pascal had denounced his math, the concept of a expected value made it’s way to his theology. So what does this mean, if we take away the math, if we take away the equations and calculations, what does this mean?
It is my opinion, that this gives all of the control back to someone, or simply calls for accountability.
What do I mean by this? Randomness is thought of as rare, but that isn’t the case. Randomness is just that, random. Anything can happen at any time. A tree falls onto your car when it is park, and we see that as a rare event and we say it was random. However trees fall often, it isn’t an anomaly. This that appear to be random, are things that we had direct control of, they are the sum of the experiences and actions we took previously. My favorite way to explain this is meeting a new friend. Often we meet people and they have a huge impact on our lives, and we think it was so random that we met them. However you probably made a choice to become more friendly, or you wanted more positive people in your life or a bunch of other things could have happened that made you talk to or meet a new person.
This also applies to every bad that happens to you. It is just the sum of everything that happened previously. (Disclaimer, of course not EVERYTHING).