Blaise Pascal
French mathematician and philosopher who left many important results in mathematics, physics, and literature.
He began to work on geometry at the age of 12, and wrote a paper on projective geometry when he was 16. Thus mathematics became one of his major fields of study. When he was 19 years old, he invented a mechanical calculator, called "Pascaline". A small number of machines were actually manufactured but only a few were sold.
In 1653, he worked on hydrostatics and wrote Treatise on the Equilibrium of Liquids which contains Pascal's Law of pressure. Then in 1654, his correspondence with Fermat prepared the ground for mathematical theory of probability. Later, in his religious essay, he applied a game theoretic consideration to his apologetic argument for the existence of God (Pascal's wager).
In 1654 also, his Treatise on the Arithmetical Triangl was completed. Pascal's triangle is the following figure:
1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
1 5 10 10 5 1
This figure is related to the binomial expansion of (a+b)(a+b) ..., and the numbers in the figure are nothing but binomial coefficients in a certain order: For instance, "2" in the third line is a sum of the two numbes "1" and "1" immediately above, and likewise "3" in the fourth line is a sum of "1" and "2" immediately above. This triangle has various applications to mathematical problems, including probability and games.
Late in this year 1654, he had some religious experience and turned to Christianity (Jansenist sect). "Pascal's wager" appears in Pensees, No. 233; its most intriguing part is stated thus:
Let us weigh the gain and the loss in wagering that God is. Let us estimate these two chances. If you gain, you gain all; if you lose, you lose nothing. Wager, then, without hesitation that He is. . . . there is an eternity of life and happiness. . . . there is here an infinity of infinitely happy life to gain, a chance of gain against a finite number of chances of loss, and what you stake is finite.The structure of this argument may be reconstructed by the following diagram.
(1) Belive in God and lead a life of faith:
Either God exists; then there is a finite probability that you gain infinitely happy life;Or God does not exist; then you lose at most finite happiness.(2) Don't believe in God and lead a life of non-faith:
Either God exists; then you are going to be damned (presumably, infinitely unhappy);Or God does not exist; then you gain at most finite happiness.Which alternative, (1) or (2), are you going to bet on? You must make a bet, according to Pascal.
