### Blaise Pascal Bio Blaise Pascal's Thesis

Length: 8 pages Sources: 6 Subject: Education - Mathematics Type: Thesis Paper: #77340896 Related Topics: Calculus, Biography, Mathematics, Math
##### Excerpt from Thesis :

The problem, first posed by an Italian monk in the late 1400s, had remained unsolved for nearly two hundred years. The issue in question was to decide how the stakes of a game of chance should be divided if that game were not completed for some reason. The example used in the original publication referred to a game of balla where six goals were required to win the game.

If the game ended normally, the winner would take all. But what if the game stopped when one player was in the lead by five goals to three? In seeking a solution to the problem, Pascal entered into correspondence with the lawyer and mathematician Pierre de Fermat. Between the two of them they laid the foundations of modern probability theory. What Fermat and Pascal realized was that the solution came from listing all of the possibilities and then counting the proportion of the time that each player would win.

From this approach, Pascal derived more general results and developed rules of probability. While Pascal's contribution to probability theory was undoubtedly substantial, it was just the beginning. Importantly, his analysis did not stretch to more realistic situations where a finite number of equally likely possible outcomes could not be listed (Stigler 25). In the early 18th century, Jacob Bernoulli, who stressed the role of statistical sampling in dealing with uncertainty, addressed problems with a potentially infinite number of outcomes.

Through his law of large numbers, Bernoulli sought to provide a formal proof of the idea that uncertainty decreased as the number of observations increased. Another key development of that century was the discovery by Abraham De Moivre of the normal curve the fact that random drawings would distribute themselves in a bell shape around their average value. Although theories relating to risk and uncertainty have continued to develop, the contributions of Pascal, Bernoulli and De Moivre remain pivotal to our understanding of risk.

The work done by Fermat and Pascal into the calculus of probabilities laid important groundwork for Leibniz's formulation of the infinitesimal calculus (http://www.math.rutgers.edu/courses/436/Honors02/leibniz.html).After a religious experience in 1654, Pascal mostly gave up work in mathematics. However, after a sleepless night in 1658, he anonymously offered a prize for the quadrature of a cycloid. Solutions were offered by Wallis, Huygens, Wren, and others? Pascal, under the pseudonym Amos Dettonville, published his own solution. Controversy and heated argument followed after Pascal announced himself the winner.

Philosophy of Mathematics

Pascal's major contribution to the

...

Here, Pascal looked into the issue of discovering truths, arguing that the ideal of such a method would be to found all propositions on already established truths. At the same time, however, he claimed this was impossible because such established truths would require other truths to back them up -- first principles, therefore, cannot be reached.

Based on this, 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. Pascal also used De l'Esprit geometrique to develop a theory of definition. He distinguished between definitions which are conventional labels defined by the writer and definitions which are within the language and understood by everyone because they naturally designate their referent. The second type would be characteristic of the philosophy of essentialism. Pascal claimed that only definitions of the first type were important to science and mathematics, arguing that those fields should adopt the philosophy of formalism as formulated by Descartes.

In De l'Art de persuader ("On the Art of Persuasion"), Pascal looked deeper into geometry's axiomatic method, specifically the question of how people come to be convinced of the axioms upon which later conclusions are based. Pascal agreed with Montaigne that achieving certainty in these axioms and conclusions through human methods is impossible. He asserted that these principles can only be grasped through intuition, and that this fact underscored the necessity for submission to God in searching out truths.

Works Cited

Connor, James a. Pascal's Wager. New York: Harper Collins, 2006.

Hald, Anders. A History of Probability and Statistics and Its Applications before 1750. Indiana:

Wiley Publications, 1990.

Kisacanin, Branislav. Mathematical Problems and Proofs. New York: Kluwer Academic

Publishers, 2002.

Pattanayak, Ari. The…

###### Sources Used in Documents:

Works Cited

Connor, James a. Pascal's Wager. New York: Harper Collins, 2006.

Hald, Anders. A History of Probability and Statistics and Its Applications before 1750. Indiana:

Wiley Publications, 1990.

Kisacanin, Branislav. Mathematical Problems and Proofs. New York: Kluwer Academic

###### Cite this Document:

"Blaise Pascal Bio Blaise Pascal's" (2008, December 05) Retrieved June 24, 2021, from
https://www.paperdue.com/essay/blaise-pascal-bio-blaise-pascal-26110

"Blaise Pascal Bio Blaise Pascal's" 05 December 2008. Web.24 June. 2021. <
https://www.paperdue.com/essay/blaise-pascal-bio-blaise-pascal-26110>

"Blaise Pascal Bio Blaise Pascal's", 05 December 2008, Accessed.24 June. 2021,
https://www.paperdue.com/essay/blaise-pascal-bio-blaise-pascal-26110

##### Cardinal Health and Industry Competition the Pharmaceutical
Words: 827 Length: 3 Pages Topic: Business Paper #: 11627879

Cardinal Health and Industry Competition The pharmaceutical and generic drug industries are highly competitive and, simultaneously, tremendously risk oriented. Both of these characteristics are significantly present in the current outlook for Cardinal Health. The producer of generic drugs is a Fortune 500 company which, according to Leger (2012), pulls in roughly \$103 billion in revenue on an annual basis. However, the company is also the target of fierce competition from fellow

##### Cardinal Health 2 Analytics and
Words: 580 Length: 2 Pages Topic: Business Paper #: 15937881

All of these factors taken together assisted the company in attaining tis objectives of implementing an advanced by and analytics platform. Do you have any experience with your company succeeding in embracing advanced BI techniques? While working for a company that specialized in distribution sales and service, a large-scale analytics and BI platform was implemented. The goals of the new system were to better manage pricing, price optimization, inventory levels, credit

##### Cardinal Health the First Project Is for
Words: 1197 Length: 4 Pages Topic: Economics Paper #: 44682089

Cardinal Health The first project is for Micron Technology. The net present value analysis will be used to evaluate this project. The net present value (NPV) technique involves discounting future cash flows to present dollars, to take into account the firm's opportunity cost of capital. As a basic rule, projects that have a positive net present value will add value to the company above and beyond existing operations. All such projects

##### Cardinal Health Case Analysis the
Words: 580 Length: 2 Pages Topic: Business Paper #: 63532612

The paradox for Cardinal Health was the need to reign in the intellectual curiosity that BI and analytics applications can generate while staying focused just on the most critical aspects of automating and adding insight into their core businesses. The goals Cardinal Health defined prior to the implementation were to consolidate 20 different enterprise systems, improve user interfaces of their enterprise systems and resolve 2K issues. The three success

##### Cardinal Health, Its Mission and Its Current
Words: 1989 Length: 7 Pages Topic: Business Paper #: 57702437

Cardinal Health, its mission and its current situation. An environmental analysis is presented to analyze the current environment in which the company operates. A SWOT analysis summarizes the company's internal strengths, weaknesses, potential opportunities, and potential threats. The issue in the case study is overviewed, and supporting facts and significant factors are presented that support the problem. Three potential alternative solutions are given, with an evaluation of each solution's