Tuesday, June 19, 2012

It is not Certain that Everything is Uncertain - Blaise Pascal's Thoughts

Blaise Pascal (1623-1662)
"It is not certain that everything is uncertain." is one of the many profound insights that philosopher and mathematician Blaise Pascal (1623-1662) published in his seminal work entiteled "Pensées" (Thoughts, published in 1669). He literally had versatile scientific interests, as he provided influential contributions in the field of mathematics, physics, engineering, as well as in religious philosophy. Blaise Pascal was a child prodigy educated by his father Étienne Pascal, a tax collector in Rouen. His mother died when he was only three years old. As the father did not like the way school was taught at that time he decided to instruct Blaise and his three siblings at home by himself. In particular he put emphasis on learning the classic languages Latin and Greek. But he considered not to teach geometry to Blaise because he felt the topic was too enticing and attractive. 

Geometry is the branch of mathematics that deals with points, lines, angles, surfaces, and solids. Blaise's father thought that if exposed to geometry and mathematics too soon, Blaise would abandon the study of classics. But, this ban on mathematics made Blaise even more curious. On his own he experimented with geometrical figures. He invented his own names for geometrical terms because he had not been taught the standard terms. He discovered that the sum of the angles of a triangle are two right angles and, when his father found out, he relented and allowed Blaise a copy of Euclid's standard textbook on mathematics. Some people believe that Blaise was twelve years old when he started attending meetings of a mathematical academy together with his father. Others suppose that he did not attend the meetings until he was about sixteen. In any case he was far younger than the adults who were there. 

Blaise Pascal invented the first digital calculator to help his father with his work collecting taxes. He worked on it for three years between 1642 and 1645. The device, called the Pascaline, resembled a mechanical calculator of the 1940s. This, almost certainly, makes Pascal the second person to invent a mechanical calculator for Wilhelm Schickard had manufactured one in 1624. First, the Pascaline was only able to do additions, but was subsequently improved also to provide the means for subtractions. There were additional problems faced by Pascal in the design of his calculator due to the French currency at that time. There were 20 sols in a livre and 12 deniers in a sol. This monetary system remained in France until 1799 (in the UK a system with similar multiples lasted even until 1971). Thus, Pascal had to solve much harder technical problems to work with this division of the livre into 240 than he would have had if the division had been 100. Although Blaise Pascal filed a patent for his machine, he was not able to make a fortune out of it. The elaborate and complex design of the machine made it's construction much too expensive to be sold in significant numbers.

In correspondence with the famous hobby mathematician Pierre de Fermat (you might remember Fermat's last theorem) Pascal laid the foundation for the modern theory of probability. This correspondence started in 1654 and consisted of five letters about the dice problem that asks how many times one must throw a pair of dice before one expects a double six.

Following a mystical experience in late 1654, Pascal had his "second conversion", abandoned his scientific work, and devoted himself to philosophy and theology. Two of his most famous works date from this period: the Lettres provinciales and the Pensées. The later consists of a collection of personal thoughts on human suffering and faith in God. This work contains also 'Pascal's wager' which claims to prove that belief in God is rational with the following argument. 
"If God does not exist, one will lose nothing by believing in him, while if he does exist, one will lose everything by not believing."
At yovisto you might watch a brief introduction into Pascal's Pensées or also a short description of his famous Pascaline.

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