Pascal

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Pascal

  1. 1. Blaise Pascal1623-1662
  2. 2. The Beginning• Born in Clermont-Ferrand, France, June 19, 1623• His father, Etienne, was a royal tax officer• Probably grew up in wealthy circumstances• He was taught by his father with an unorthodoxapproach– First learned methods of reason and judgment -discovering the why behind facts.– At age 12, Pascal was allowed to learn Latin, but notmathematics.
  3. 3. Pascal’s greatest achievements…• By age 12, he proved Euclid’s theorems (The Elements) onhis own!• By 16, Had published a book on conic sections• Invented projective geometry• Proved that vacuums could be created• Invented the syringe and hydraulic lift• Unified and proved much in fluid mechanics• Came up with the basis for much of modern insurance andprobability work, together with Pierre de Fermat• Cleared up many question concerning cycloids
  4. 4. 1642- Pascal’s Adding Machine•Many prototypes were constructed•Never had a large market, probably because of price
  5. 5. The faith of the man…• Christ was the center of his theology– “In [Jesus] is all our virtue and all ourhappiness. Apart from Him there is only vice,misery, error, darkness, death, despair.”• He converted to Jansenism, a branch ofCatholicism, in 1646– They rediscovered Augustine and opposedsemi-Pelagianism– Major beliefs sound quite similar to Reformers– Stressed moral purity
  6. 6. The faith of the man…Provincial Letters-These were Jansenist lettersthat were written in opposition to the JesuitsPensées (“Thoughts”) - chapters include discussion on• mathematics & reason• fundamentals of Christianity• proofs for Jesus ChristWritings...General distinguishing belief:Man cannot do any act trulypleasing to God without thegrace of God. (regeneration)God’s grace effectivelyaccomplishes His will.
  7. 7. His mathematics applied to faith…His work with probability produced what hasbecome known as Pascal’s wager• It demonstrates a method of coming to a “reasonable” decision.– Either God is or God is not. One has no choice but to“wager” on which of these statements is true, where thewager is in terms of one’s actions.– Which way should one act?• In complete indifference to God or• In a way compatible with the (Christian) notion of God.
  8. 8. His mathematics applied to faith… (cont.)• Which way should one act?– If God is not, it does not matter much.– If God is,• wagering that there is no God will bring damnation while• wagering that God exists will bring salvation.– Because the outcome of the latter is infinitely more desirablethan the former, the outcome of this “decision-problem” isclear, even if one believes that the probability of God’sexistence is small:• The reasonable person will act as if God exists."If God does not exist, one will lose nothing by believing in Him, whileif He does exist, one will lose everything by not believing." -Pascal
  9. 9. Development of Calculus• From 1653-1654 he wrote– Traité du triangle arithnétique– Traité des ordres numériques (published in 1665)– Traité de la sommation des puissancesnumériques• Here Pascal laid down the principles ofdifferential and integral calculus
  10. 10. Pascal,a man who lived and worked in light of theexistence of a Sovereign, Personal God whorevealed Himself in the person of the Lord JesusChrist,grew gravely ill in 1659 and died in August 1962
  11. 11. Pascal & Beyond• Unlike the Protestant Reformers, Pascal’s religious order saw anunscriptural dichotomy between secular and ecclesiastical activities.Instead of doing all to the glory of God, Pascal felt an unnecessarytension between his mathematical studies and his faith.• Pascal’s independent discovery of Geometry’s postulates testifiesthat mathematics is a discovery of the works of God and not merelyan invention of man.– “One could believe that calculus was a work of art produced by thefree will of man if one could believe the possibility of a symphonyarising from the scores of a number of composers who supposed theywere writing only tone poems for solos or chamber groups. Thissymphony comes together without changing even the key, though theartists wrote during hundreds of years in different corners of the globewithout the knowledge of each other’s work.” - Zimmerman Truth and theTranscendent
  12. 12. Pascal & BeyondMany discoveries even occurred simultaneously in the history ofmathematics despite great distances and slow communication– Law of Inverse Squares by Newton and Halley– Logarithms by Burgi and Napier/Briggs– Calculus by Newton on the island and Leibniz on the continent– Two geometries of Russian Lobachevski and Hungarian Bolyai– Modern vector calculus by both Hamilton and Grassman– Contradiction Hypothesis by H.A. Lorentz and Fitzgerald– The double Theta functions by Gopel and Rosehain– The rectification of the semi-cubal parabola by Van Heauraet, Neil, and Fermat– Geometric law of duality by Oncelet and Gergone– Principle of Least Squares by Gauss and Legendre“It seems to be my fate to concur in nearly all my theoretical works withLegendre”- Gauss quoted in Bell’s Men of Mathematics

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