Introduction:
Discouraged by his father not to study mathematics because it might strain his brain, it had the paradoxical effect of igniting a study of geometry and eventually other mathematics. Unaided by any book, he proved on his own that the sum of the angle measures of a triangle is 180°, unleashing a passion for the subject of mathematics. He went on to prove fascinating theorem in geometry. Pascal’s theorem states that if a hexagon is inscribed in a circle (or conic) then the three intersection points of opposite sides lie on a line (called the Pascal Line).
Description: First Computing Machine
In 1642, at age 18, Pascal invented the first computing machine in history. Designed for the arithmetic of addition and subtraction, it became the forerunner of our powerful present-day computer. The Pascaline calculating device, about the size of a shoebox, is shown here.
Theory of Probability
The most significant contribution that Pascal made to mathematics was the creation with Pierre Fermat of the theory of probability in 1654. The theory grew out of the desire to compute probabilities in games of chance. What seemed like pure chance became structured under a theory that brought theorems and rules and eventually led to today’s powerful branch of mathematics called statistics. In chapters 4 and 6 of The Faith Equation, we make extensive use of the theory of probability and statistics.
Pascal’s Triangle
Though not actually developed by Pascal he made extensive use of a triangular array of numbers that came to be know as Pascal’s Triangle.
Perhaps you see how to write one row of numbers given the rows above. Write 1’s on the outside. Each remaining number is the sum of the two numbers above it. The array of numbers in Pascal’s Triangle is rich in importance to mathematics. One use is to provide the coefficients of the expansion of (a+b)n . Another is to the binomial distribution in probability and yet another involves the famous Fibonacci sequence.
Pascal’s Contribution to Religion and Philosophy
The life of Blaise Pascal exemplifies one of paradox, the topic covered in chapters 2 & 3 of The Faith Equation. Some writers called him a religious neurotic because his religious writings interrupted his mathematics scholarship. Pascal is condemned for “drifting” off into religion because it misdirected him from mathematics. They think of Pascal in terms of the mathematics he might have discovered, most notably he could have been the one to invent the calculus instead of Leibniz or Newton. I prefer to laud him for using a great brain on a broader range of life than mathematics. I embrace the idea of integrating science (mathematics) and religion, each bringing insight to the other and it seemed to me that Pascal balanced his mathematics with his pursuit of religious wisdom.
He lived a short life, 39 yrs from 1623 – 1662, in which most of the years up to 1654 were centered by mathematics. Pascal became converted to a religious belief called Jansenism. This led to what is called his first conversion to Christianity. His second conversion came after reading his Bible the night of Nov 23, 1654. He wrote his memorial, a delineation of his faith, and had it sewn into his clothing. This began two religious writings, one called the Provinical Letters and another called Pensées (Thoughts). Not published in Pascal’s lifetime, but later reconstructed from accumulated notes, this book was an apologetic defense of Christianity.
I have read Pensées and found it very stimulating. For the most part, it is a collection of “one-liners” very much in the style of the book of Proverbs.
You will encounter numbered paragraphs, like verses in the Bible. I think many of these are excellent quotes, or what my men’s reading group calls “nuggets”. I list a few of them as follows.
#10. People are generally better persuaded by the reasons which they have themselves discovered than by those which have come into the mind of others.
#245. There are three sources of belief: reason, custom, inspiration. The Christian religion, which alone has reason, does not acknowledge as her true children those who believe without inspiration. It is not that she excludes reason and custom. On the contrary, the mind must be opened to proofs, must be confirmed by custom and offer itself in humbleness to inspirations, which alone can produce a true and saving effect.
#253. Two extremes: to exclude reason, to admit reason only.
Pascal’s Pensées is widely considered to be a masterpiece, and a landmark in French literature. Read and study the Pensées. It is a wealth of wisdom.
Perhaps the most famous argument for faith in Christianity is the so-called Pascal’s Wager, covered in Pensées, #233, and abbreviated as follows:
#233. Belief is a wise wager. Granted that faith cannot be proved, what harm will come to you if you gamble on its truth and it proves false? If you gain, you gain all; if you lose, you lose nothing. Wager, then, without hesitation, that He exists.”
I have a dear friend who believes in God, but not the afterlife or heaven. I have frequently used a form of Pascal’s Wager to convince him that he may as well believe. If you believe and there is no afterlife, you have lost nothing. But, if you believe and there is an afterlife, consider the wonder you will find there and the joy and hope it gives you in this life. Make the wager; you can’t lose.
One more reference to a nugget in Pensées, #706, supports my arguments in Ch 4 of The Faith Equation for the reliability of the Bible based on prophesy.
#706. The prophecies are the strongest proof of Jesus Christ [the Holy Bible]. It is for them also that God has made most provision; for the event which has fulfilled them is a miracle existing since the birth of the Church to the end. So God has raised up prophets during sixteen hundred years, and, during four hundred years afterwards, He has scattered all these prophecies among all the Jews, who carried them into all parts of the world. Such was the preparation for the birth of Jesus Christ, and, as His Gospel was to be believed by all the world, it was not only necessary that there should be prophecies to make it believed, but that these prophecies should exist throughout the whole world, in order to make it embraced by the whole world.