Blaise Pascal 17th Century Western Philosopher Biographical Overview Pascal was born on June 19, 1623 in Clermont, France. In 1626 his mother passed away when he was three years old. In 1631, the family moved to Paris. Pascal was a child prodigy educated by his father, who was a local judge in tax court. In 1646 his family converted to Jansenism religion. Pascal was a French physicist, mathematician, and religious philosopher. His health was never good and he died on August 19, 1662 at the age of 39. Accomplishments Physicist Pascal invented the hydraulic press and the syringe (not hypodermic). On the hydraulic press - at one end of the system is a piston with a small cross- sectional area driven by a lever to increase the force. - small-diameter tubing leads to the other end of the system. Hydraulic force increase Hydraulic Press Syringe Physicist Pascal’s Law applies to the hydraulic press. Physicist Pascal refuted Aristotle’s followers who insisted that nature abhors a vacuum. - Pascal gave reasoning to why a genuine vacuum could and did exist above the mercury in the barometer. - He detailed basic rules describing to what degree various liquids could be supported by air pressure. - He also provided reasons why it was indeed a vacuum above the column of liquid in a barometer tube. Mathematician Pascal invented the first digital calculator, the Pascaline. Pascaline Mathematician Pascal’s Triangle was developed through his discovery work done on Binomial coefficients. (a+b)n (where n = 0,1,2,3…), we get the Pascal’s Triangle. Pascal’s Triangle Mathematician Pascal Theorem was developed from his discovery work done on conic sections in projective geometry. Mathematician In Geometry, Pascal looked into the issue of discovering truths. - Pascal argued that the procedure used in geometry was as perfect as possible, with certain principles assumed and other propositions developed from them. - Nevertheless, there was no way to know the assumed principles to be true. Also in Geometry he developed a theory of definition. - Only definitions with conventional labels were important to science and math, arguing that those fields should adopt the philosophy of formalism. Religion Pascal's Wager charted new territory in probability theory and was one of the first attempts to make use of the concept of infinity, and marked the first formal use of decision theory. E means Existence. ∞ means infinite. f1, f2, and f3 means finite. p is your positive, non-infinite probability for God's existence): E(wager for God) = ∞*p + f1*(1 − p) = ∞ That is, your expected utility of belief in God is an infinite force. On the other hand, wagering against God is: E(wager against God) = f2*p + f3*(1 − p) This is finite. Rationality requires you to perform the act of maximum expected utility. Therefore, rationality requires you to wager for God. Publications Essai pour les coniques (Essay on Conics) 1639 - Reasoning text and geometric drawings explaining conic sections. Experiences nouvelles touchant le vide ("New Experiments with the Vacuum") (1647) - Reasoning why a genuine vacuum could and did exist above the mercury in the barometer. Traité du triangle arithmétique ("Treatise on the Arithmetical Triangle") (1653) - Foundation of probability theory as the originator of the concept of expectation and its use recursively to solve the ‘Problem of Points’, as well as the justification for calling the arithmetical triangle ‘Pascal’s triangle’. Lettres provinciales (Provincial letters) (1657 or 1658) - Letters defending Jansenists against the Jesuits by attacking casuistry, a popular ethical method used by Catholic thinkers. He denounced casuistry as the mere use of complex reasoning to justify moral laxity and all sorts of sins. Publications De l'Esprit géométrique ("On the Geometrical Spirit") (1657 or 1658) - The issue of discovering truths and he developed a theory of definition. Écrit sur la signature du formulaire ("Writ on the Signing of the Form") (1661) - Exhorting the Jansenists not to give in. Pensees ("Thoughts") (incomplete at death) - Written in defense of the Christian religion. Long Term Significant’s Pascal has been given to the SI unit of pressure, to a programming language, Pascal’s law, Pascal's triangle and Pascal's wager. Pascal’s law is still used today in Physics. Pascal’s triangle and probability theory is still used today in Mathematics. The calculator is still used today for computation. Probability theory is it is extremely important today in economics, especially in actuarial science, in the way we regard uncertainty, risk, decision-making, and an individual's and society's ability to influence the course of future events . Bibliography "Blaise Pascal." From Wikipedia, the free encyclopedia. 23 Jan. 2009. Wikimedia Foundation, Inc. 23 Jan 2009 <http://en.wikipedia.org/wiki/Blaise_Pascal#Philosophy_of_mathematics> Hajek, Alan. "Pascal’s Wager." Stanford Encyclopedia of Philosophy. 4 Jun. 2008. Stanford University. 23 Jan. 2009 <http://plato.stanford.edu/entries/pascal-wager/#4> "Pascaline." 1642 France. The History of Computing Project. 5 Aug. 2007. 23 Jan. 2009 <http://www.thocp.net/hardware/pascaline.htm> Pascal's Law and Bernoulli's Principle." Boomer.org. 23 Jan 2009 <http://boomeria.org/physicslectures/pascal/pascal.html> "Pascal’s Theorem." Sci-Tech Dictionary: Pascal’s theorem. 2008. Answers Corporation. 23 Jan 2009 "Pascal’s Triangle." IES Inc. 23 Jan 2009 <http://www.ies.co.jp/math/java/misc/PascalTriangle/PascalTriangle.html> "Pascal’s Triangle." Site Suggestions. 2009. Drexel University. 23 Jan. 2009 <http://mathforum.org/workshops/usi/pascal/pascal.links.html> Glossary Jansenism: branch of Catholic Gallican thought which arose in the frame of the Counter-Reformation and the aftermath of the Council of Trent (1545-1563). Hydraulic Press: a hydraulic mechanism in which a large lifting or compressive force applied by a piston to a small area is transmitted through water to another piston having a large area. Pascal’s Law: when pressure is applied to a contained fluid, the force is transmitted equally in all directions. Pascaline: the first digital calculating machine. Pascal’s Triangle: is a geometric arrangement of the Binomial coefficients in a triangle. Pascal's Theorem: when one inscribes a simple hexagon in a conic, the three pairs of opposite sides meet in collinear points. Pascal's Wager: even though the existence of God cannot be determined through reason, a person should "wager" as though God exists. Questions 1. Did you plan to do further research and developed of the syringe? 2. Did you plan to do further research with hydraulic pressure? 3. What more would you have said in the Pensees?
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