tag:blogger.com,1999:blog-79178282822334858762024-03-05T03:32:19.434-03:00Blaise PascalSebastian Latorrehttp://www.blogger.com/profile/06560434053585385214noreply@blogger.comBlogger19125tag:blogger.com,1999:blog-7917828282233485876.post-67481257313633542532015-07-15T03:19:00.001-03:002015-07-15T03:19:56.153-03:00Pascal English 2<div style="background-color: white;">
Born in 1623 in Clermont, France, Blaise Pascal is one of the most well known mathematicians of all times. His mother, Antoinette, died when he was only three, leaving his father to raise the sickly Blaise and his two sisters, Gilberte and Jacqueline. After the death of his wife, Étienne moved the family to Paris. (Davidson) He did not trust his son's education to the local schools and took it upon himself to teach Blaise at home. He felt he could teach his son as well as any schoolteacher could.</div>
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Although he devoted the majority of his adult life to religion and philosophy, Pascal's genius lies in mathematics and science. Étienne was an accomplished mathematician who refused to allow his son to study mathematics. This was because he, being a mathematician himself, felt that it would take away from his other studies since math was such a fulfilling subject and it ``fills and greatly satisfies the mind.'' (Cole) Étienne wanted his son to first learn the humanities and later learn math and science.</div>
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Pascal's interest in math began with the curiosity about this subject which he was not taught. To his many questions about math, Étienne replied with vague answers. He told his son that math ``was the way of making precise figures and finding the proportions among them.'' (Cole) Pascal took this statement and began to make his own discoveries about math. According to his sister Gilberte, Pascal ``discovered'' geometry on his own. At the young age of twelve, he was drawing geometric figures on the floor of his playroom and it is said that he discovered, on his own, the fact that the interior angles of a triangle add up to the sum of two right angles (Euclid's 32nd proposition of book I). According to Gilberte, it was around this time that her father walked in to find his son drawing figures on the floor. Etienne watched his son and realized the genius of the boy. The proud father presented his son with a copy of Euclid's <i>Elements</i> and from this time on allowed him to continue his studies in mathematics. (Bishop)</div>
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Pascal's father then brought him into the society of mathematicians with whom he was associated with. The <i>Académie libre</i> met every week to discuss current topics in science and math. (Bishop) Members of this group, headed by Mersenne, included other reknowned mathematicians such as Desargue, Roberval, Fermat and Descartes. (Davidson) At these meetings, Pascal was introduced to the latest developments in math. Soon he was making his own discoveries and publishing his own results. By the age of sixteen, he published his <i>Essai pour les Coniques</i> (1640) In the same year, the family moved to Rouen. Two years later, Pascal began working on his calculating machine which was completed in 1644. (Krailsheimer)</div>
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1646 marked the beginning of Pascal's spiritual transformation. When Étienne injured his hip, the two bonesetters he called on were Jansenist converts who had devoted their lives to helping others. They taught the Pascals about Jansenism and Blaise, who found Jansenist ideas to be similar to his own beliefs, soon adopted the strict doctrines of the religion. (Bishop)</div>
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The same year, Pascal found a new interest in physics. A family friend introduced the Pascals to Torricelli's experimet involving a tube of mercury turned upside down in a bowl also filled with mercury. They found that the mercury fell to a certain point in the tube and stopped. Pascal continued to conduct the experiment many times with variations. The results of his experiments and his conclusions were published in 1651 as <i>Traite du vide</i> (Treatise on the vacuum). (Davidson).</div>
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In the summer of 1647, Pascal fell ill due to being overworked. He and Jacqueline moved back to Paris. The next few years were eventful for Pascal. He composed a treatise on conic sections in 1648 which is now lost. In 1649, he was granted rights to manufacture his calculating machine, which he perfected five years before. In 1651, his father died. Three months after his death Jacqueline joined the nuns at Port-Royal.</div>
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1654 marked an important year in the life of Pascal. His work on probability theory and the arithmetic triangle took a lot of his time. Pascal's work on probability theory is widely known due to his correspodence with Fermat. (Renyi) It was in this year that he published <i>Traite du triangle arithmetique</i>. After another religious conversion in 1654, in which Pascal fully commit himself to God, his writings were primarily of a philosophical nature. In 1656, he finished the <i>Provinciales</i>, a series of letters on religion. (Krailsheimer) In 1657, he began the<i>Apologie</i> of which the <i>Pensees</i> is all he was able to complete before his death. In the latter half of 1661 Pascal fell ill and by June of the next year, he was so ill he moved in with Gilberte. Blaise Pascal died of an undiagnosed illness on August 19, 1662.</div>
Sebastian Latorrehttp://www.blogger.com/profile/06560434053585385214noreply@blogger.comtag:blogger.com,1999:blog-7917828282233485876.post-20332120098536899432015-07-15T03:16:00.001-03:002015-07-15T03:17:24.920-03:00Bailse Pascal English<div align="justify" style="background-color: white;">
<b>Blaise Pascal</b> was the third of <a href="http://www-history.mcs.st-and.ac.uk/Mathematicians/Pascal_Etienne.html" style="text-decoration: none;">Étienne Pascal</a>'s children and his only son. Blaise's mother died when he was only three years old. In 1632 the Pascal family, Étienne and his four children, left Clermont and settled in Paris. Blaise Pascal's father had unorthodox educational views and decided to teach his son himself. <a href="http://www-history.mcs.st-and.ac.uk/Mathematicians/Pascal_Etienne.html" style="text-decoration: none;">Étienne Pascal</a> decided that Blaise was not to study mathematics before the age of 15 and all mathematics texts were removed from their house. Blaise however, his curiosity raised by this, started to work on geometry himself at the age of 12. 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 <a href="http://www-history.mcs.st-and.ac.uk/Mathematicians/Euclid.html" style="text-decoration: none;">Euclid</a>.</div>
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At the age of 14 Blaise Pascal started to accompany his father to <a href="http://www-history.mcs.st-and.ac.uk/Mathematicians/Mersenne.html" style="text-decoration: none;">Mersenne</a>'s meetings. <a href="http://www-history.mcs.st-and.ac.uk/Mathematicians/Mersenne.html" style="text-decoration: none;">Mersenne</a> belonged to the religious order of the Minims, and his cell in Paris was a frequent meeting place for <a href="http://www-history.mcs.st-and.ac.uk/Mathematicians/Gassendi.html" style="text-decoration: none;">Gassendi</a>,<a href="http://www-history.mcs.st-and.ac.uk/Mathematicians/Roberval.html" style="text-decoration: none;">Roberval</a>, <a href="http://www-history.mcs.st-and.ac.uk/Mathematicians/Carcavi.html" style="text-decoration: none;">Carcavi</a>, Auzout, <a href="http://www-history.mcs.st-and.ac.uk/Mathematicians/Mydorge.html" style="text-decoration: none;">Mydorge</a>, Mylon, <a href="http://www-history.mcs.st-and.ac.uk/Mathematicians/Desargues.html" style="text-decoration: none;">Desargues</a> and others. Soon, certainly by the time he was 15, Blaise came to admire the work of <a href="http://www-history.mcs.st-and.ac.uk/Mathematicians/Desargues.html" style="text-decoration: none;">Desargues</a>. At the age of sixteen, Pascal presented a single piece of paper to one of <a href="http://www-history.mcs.st-and.ac.uk/Mathematicians/Mersenne.html" style="text-decoration: none;">Mersenne</a>'s meetings in June 1639. It contained a number of <a href="https://www.blogger.com/null"><span style="color: green;">projective geometry</span></a> theorems, including Pascal's mystic hexagon.</div>
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In December 1639 the Pascal family left Paris to live in Rouen where Étienne had been appointed as a tax collector for Upper Normandy. Shortly after settling in Rouen, Blaise had his first work, <i>Essay on<a href="https://www.blogger.com/null"><span style="color: green;">Conic Sections</span></a></i> published in February 1640.</div>
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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 <a href="http://www-history.mcs.st-and.ac.uk/Mathematicians/Schickard.html" style="text-decoration: none;">Schickard</a> had manufactured one in 1624.</div>
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There were problems faced by Pascal in the design of the calculator which were due to the design of the French currency at that time. There were 20 sols in a livre and 12 deniers in a sol. The system remained in France until 1799 but in Britain a system with similar multiples lasted until 1971. 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. However production of the machines started in 1642 but, as Adamson writes in [<a href="https://www.blogger.com/null">3</a>],</div>
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<i>By </i>1652<i> fifty prototypes had been produced, but few machines were sold, and manufacture of Pascal's arithmetical calculator ceased in that year.</i></div>
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Events of 1646 were very significant for the young Pascal. In that year his father injured his leg and had to recuperate in his house. He was looked after by two young brothers from a religious movement just outside Rouen. They had a profound effect on the young Pascal and he became deeply religious.</div>
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From about this time Pascal began a series of experiments on atmospheric pressure. By 1647 he had proved to his satisfaction that a vacuum existed. <a href="http://www-history.mcs.st-and.ac.uk/Mathematicians/Descartes.html" style="text-decoration: none;">Descartes</a> visited Pascal on 23 September. His visit only lasted two days and the two argued about the vacuum which <a href="http://www-history.mcs.st-and.ac.uk/Mathematicians/Descartes.html" style="text-decoration: none;">Descartes</a> did not believe in. <a href="http://www-history.mcs.st-and.ac.uk/Mathematicians/Descartes.html" style="text-decoration: none;">Descartes</a> wrote, rather cruelly, in a letter to <a href="http://www-history.mcs.st-and.ac.uk/Mathematicians/Huygens.html" style="text-decoration: none;">Huygens</a> after this visit that Pascal</div>
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<i>...has too much vacuum in his head.</i></div>
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In August of 1648 Pascal observed that the pressure of the atmosphere decreases with height and deduced that a vacuum existed above the atmosphere. <a href="http://www-history.mcs.st-and.ac.uk/Mathematicians/Descartes.html" style="text-decoration: none;">Descartes</a> wrote to <a href="http://www-history.mcs.st-and.ac.uk/Mathematicians/Carcavi.html" style="text-decoration: none;">Carcavi</a> in June 1647 about Pascal's experiments saying:-</div>
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<i>It was I who two years ago advised him to do it, for although I have not performed it myself, I did not doubt of its success ...</i></div>
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In October 1647 Pascal wrote <i>New Experiments Concerning Vacuums</i> which led to disputes with a number of scientists who, like <a href="http://www-history.mcs.st-and.ac.uk/Mathematicians/Descartes.html" style="text-decoration: none;">Descartes</a>, did not believe in a vacuum.</div>
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<a href="http://www-history.mcs.st-and.ac.uk/Mathematicians/Pascal_Etienne.html" style="text-decoration: none;">Étienne Pascal</a> died in September 1651 and following this Blaise wrote to one of his sisters giving a deeply Christian meaning to death in general and his father's death in particular. His ideas here were to form the basis for his later philosophical work <i>Pensées</i>.</div>
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From May 1653 Pascal worked on mathematics and physics writing <i>Treatise on the Equilibrium of Liquids</i> (1653) in which he explains Pascal's law of pressure. Adamson writes in [<a href="https://www.blogger.com/null">3</a>]:-</div>
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<i>This treatise is a complete outline of a system of hydrostatics, the first in the history of science, it embodies his most distinctive and important contribution to physical theory.</i></div>
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He worked on conic sections and produced important theorems in projective geometry. In <i>The Generation of Conic Sections</i> (mostly completed by March 1648 but worked on again in 1653 and 1654) Pascal considered conics generated by central projection of a circle. This was meant to be the first part of a treatise on conics which Pascal never completed. The work is now lost but <a href="http://www-history.mcs.st-and.ac.uk/Mathematicians/Leibniz.html" style="text-decoration: none;">Leibniz</a> and <a href="http://www-history.mcs.st-and.ac.uk/Mathematicians/Tschirnhaus.html" style="text-decoration: none;">Tschirnhaus</a> made notes from it and it is through these notes that a fairly complete picture of the work is now possible.</div>
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Although Pascal was not the first to study the <a href="https://www.blogger.com/null"><span style="color: green;">Pascal triangle</span></a>, his work on the topic in <i>Treatise on the Arithmetical Triangle</i> was the most important on this topic and, through the work of <a href="http://www-history.mcs.st-and.ac.uk/Mathematicians/Wallis.html" style="text-decoration: none;">Wallis</a>, Pascal's work on the <a href="https://www.blogger.com/null"><span style="color: green;">binomial coefficients</span></a> was to lead <a href="http://www-history.mcs.st-and.ac.uk/Mathematicians/Newton.html" style="text-decoration: none;">Newton</a> to his discovery of the general <a href="https://www.blogger.com/null"><span style="color: green;">binomial theorem</span></a> for fractional and negative powers.</div>
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In correspondence with <a href="http://www-history.mcs.st-and.ac.uk/Mathematicians/Fermat.html" style="text-decoration: none;">Fermat</a> he laid the foundation for the <a href="https://www.blogger.com/null"><span style="color: green;">theory of probability</span></a>. This correspondence consisted of five letters and occurred in the summer of 1654. They considered the dice problem, already studied by <a href="http://www-history.mcs.st-and.ac.uk/Mathematicians/Cardan.html" style="text-decoration: none;">Cardan</a>, and the problem of points also considered by <a href="http://www-history.mcs.st-and.ac.uk/Mathematicians/Cardan.html" style="text-decoration: none;">Cardan</a> and, around the same time, <a href="http://www-history.mcs.st-and.ac.uk/Mathematicians/Pacioli.html" style="text-decoration: none;">Pacioli</a> and <a href="http://www-history.mcs.st-and.ac.uk/Mathematicians/Tartaglia.html" style="text-decoration: none;">Tartaglia</a>. The dice problem asks how many times one must throw a pair of dice before one expects a double six while the problem of points asks how to divide the stakes if a game of dice is incomplete. They solved the problem of points for a two player game but did not develop powerful enough mathematical methods to solve it for three or more players.</div>
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Through the period of this correspondence Pascal was unwell. In one of the letters to <a href="http://www-history.mcs.st-and.ac.uk/Mathematicians/Fermat.html" style="text-decoration: none;">Fermat</a> written in July 1654 he writes</div>
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<i>... though I am still bedridden, I must tell you that yesterday evening I was given your letter.</i></div>
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However, despite his health problems, he worked intensely on scientific and mathematical questions until October 1654. Sometime around then he nearly lost his life in an accident. The horses pulling his carriage bolted and the carriage was left hanging over a bridge above the river Seine. Although he was rescued without any physical injury, it does appear that he was much affected psychologically. Not long after he underwent another religious experience, on 23 November 1654, and he pledged his life to Christianity.</div>
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After this time Pascal made visits to the Jansenist monastery Port-Royal des Champs about 30 km south west of Paris. He began to publish anonymous works on religious topics, eighteen <i>Provincial Letters</i>being published during 1656 and early 1657. These were written in defence of his friend <a href="http://www-history.mcs.st-and.ac.uk/Mathematicians/Arnauld.html" style="text-decoration: none;">Antoine Arnauld</a>, an opponent of the Jesuits and a defender of Jansenism, who was on trial before the faculty of theology in Paris for his controversial religious works. Pascal's most famous work in philosophy is <i>Pensées</i>, a collection of personal thoughts on human suffering and faith in God which he began in late 1656 and continued to work on during 1657 and 1658. This work contains 'Pascal's wager' which claims to prove that belief in God is rational with the following argument.</div>
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<i>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.</i></div>
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With 'Pascal's wager' he uses probabilistic and mathematical arguments but his main conclusion is that</div>
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<i>...we are compelled to gamble...</i></div>
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His last work was on the cycloid, the curve traced by a point on the circumference of a rolling circle. In 1658 Pascal started to think about mathematical problems again as he lay awake at night unable to sleep for pain. He applied <a href="http://www-history.mcs.st-and.ac.uk/Mathematicians/Cavalieri.html" style="text-decoration: none;">Cavalieri</a>'s calculus of indivisibles to the problem of the area of any segment of the cycloid and the centre of gravity of any segment. He also solved the problems of the volume and surface area of the solid of revolution formed by rotating the cycloid about the x-axis.</div>
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Pascal published a challenge offering two prizes for solutions to these problems to <a href="http://www-history.mcs.st-and.ac.uk/Mathematicians/Wren.html" style="text-decoration: none;">Wren</a>, Laloubère, <a href="http://www-history.mcs.st-and.ac.uk/Mathematicians/Leibniz.html" style="text-decoration: none;">Leibniz</a>, <a href="http://www-history.mcs.st-and.ac.uk/Mathematicians/Huygens.html" style="text-decoration: none;">Huygens</a>, <a href="http://www-history.mcs.st-and.ac.uk/Mathematicians/Wallis.html" style="text-decoration: none;">Wallis</a>, <a href="http://www-history.mcs.st-and.ac.uk/Mathematicians/Fermat.html" style="text-decoration: none;">Fermat</a> and several other mathematicians. <a href="http://www-history.mcs.st-and.ac.uk/Mathematicians/Wallis.html" style="text-decoration: none;">Wallis</a> and Laloubère entered the competition but Laloubère's solution was wrong and <a href="http://www-history.mcs.st-and.ac.uk/Mathematicians/Wallis.html" style="text-decoration: none;">Wallis</a> was also not successful. <a href="http://www-history.mcs.st-and.ac.uk/Mathematicians/Sluze.html" style="text-decoration: none;">Sluze</a>, <a href="http://www-history.mcs.st-and.ac.uk/Mathematicians/Ricci.html" style="text-decoration: none;">Ricci</a>, <a href="http://www-history.mcs.st-and.ac.uk/Mathematicians/Huygens.html" style="text-decoration: none;">Huygens</a>, <a href="http://www-history.mcs.st-and.ac.uk/Mathematicians/Wren.html" style="text-decoration: none;">Wren</a> and <a href="http://www-history.mcs.st-and.ac.uk/Mathematicians/Fermat.html" style="text-decoration: none;">Fermat</a> all communicated their discoveries to Pascal without entering the competition.<a href="http://www-history.mcs.st-and.ac.uk/Mathematicians/Wren.html" style="text-decoration: none;">Wren</a> had been working on Pascal's challenge and he in turn challenged Pascal, <a href="http://www-history.mcs.st-and.ac.uk/Mathematicians/Fermat.html" style="text-decoration: none;">Fermat</a> and <a href="http://www-history.mcs.st-and.ac.uk/Mathematicians/Roberval.html" style="text-decoration: none;">Roberval</a> to find the arc length, the length of the arch, of the cycloid.</div>
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Pascal published his own solutions to his challenge problems in the <i>Letters to <a href="http://www-history.mcs.st-and.ac.uk/Mathematicians/Carcavi.html" style="text-decoration: none;">Carcavi</a>.</i> After that time on he took little interest in science and spent his last years giving to the poor and going from church to church in Paris attending one religious service after another.</div>
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Pascal died at the age of 39 in intense pain after a malignant growth in his stomach spread to the brain. He is described in [<a href="https://www.blogger.com/null">3</a>] as:-</div>
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<i>... a man of slight build with a loud voice and somewhat overbearing manner. ... he lived most of his adult life in great pain. He had always been in delicate health, suffering even in his youth from migraine ...</i></div>
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His character is described as:-</div>
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<i>... precocious, stubbornly persevering, a perfectionist, pugnacious to the point of bullying ruthlessness yet seeking to be meek and humble ...</i></div>
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In [<a href="https://www.blogger.com/null">1</a>] the following assessment is given:-</div>
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<i>At once a physicist, a mathematician, an eloquent publicist in the Provinciales ... Pascal was embarrassed by the very abundance of his talents. It has been suggested that it was his too concrete turn of mind that prevented his discovering the <a href="https://www.blogger.com/null"><span style="color: green;">infinitesimal</span></a> calculus, and in some of the Provinciales the mysterious relations of human beings with God are treated as if they were a geometrical problem. But these considerations are far outweighed by the profit that he drew from the multiplicity of his gifts, his religious writings are rigorous because of his scientific training...</i></div>
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Sebastian Latorrehttp://www.blogger.com/profile/06560434053585385214noreply@blogger.comtag:blogger.com,1999:blog-7917828282233485876.post-50178169305514366752015-07-15T03:13:00.003-03:002015-07-15T03:13:31.961-03:008 Frases Baise Pascal 2<div class="q" style="background: url(http://www.proverbia.net/images/separador.gif) 50% 100% no-repeat rgb(255, 255, 255); border: 0px; color: #222222; font-family: 'Open Sans', Helvetica, sans-serif; font-size: 16px; font-stretch: inherit; line-height: 19.2000007629395px; margin: 0px 0px 0.2em; padding: 20px 0px; vertical-align: baseline;">
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Para quienes no ansían sino ver, hay luz bastante; mas para quienes tienen opuesta disposición, siempre hay bastante oscuridad.</blockquote>
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Las cuerdas que amarran el respeto de unos por otros son, en general, cuerdas de necesidad.</blockquote>
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Sólo conviene la mediocridad. Esto lo ha establecido la pluralidad, y muerde a cualquiera que se escapa de ella por alguna parte.</blockquote>
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Descripción del hombre: dependencia, deseo de independencia, necesidad.</blockquote>
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Sólo hay dos clases de personas coherentes: los que gozan de Dios porque creen en él y los que sufren porque no le poseen.</blockquote>
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<span style="border: 0px; color: #666666; font-family: inherit; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; line-height: inherit; margin: 0px; padding: 0px; vertical-align: baseline;">Más frases sobre: </span><a href="http://www.proverbia.net/citastema.asp?tematica=83" style="border: 0px; color: #000099; font-family: inherit; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; line-height: inherit; margin: 0px; padding: 0px; vertical-align: baseline;" title="Frases célebres de Dios">Dios</a></div>
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Los hombres creen buscar sinceramente el reposo, y en realidad no buscan sino agitación.</blockquote>
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La conciencia es el mejor libro moral que tenemos.</blockquote>
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<span style="border: 0px; color: #666666; font-family: inherit; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; line-height: inherit; margin: 0px; padding: 0px; vertical-align: baseline;">Más frases sobre: </span><a href="http://www.proverbia.net/citastema.asp?tematica=16" style="border: 0px; color: #000099; font-family: inherit; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; line-height: inherit; margin: 0px; padding: 0px; vertical-align: baseline;" title="Frases célebres de Conciencia">Conciencia</a></div>
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Aquel que duda y no investiga, se torna no sólo infeliz, sino también injusto.</blockquote>
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El mundo está lleno de buenas máximas; sólo falta aplicarlas.</blockquote>
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La justicia sobre la fuerza, es la impotencia, la fuerza sin justicia es tiranía.</blockquote>
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<span style="border: 0px; color: #666666; font-family: inherit; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; line-height: inherit; margin: 0px; padding: 0px; vertical-align: baseline;">Más frases sobre: </span><a href="http://www.proverbia.net/citastema.asp?tematica=3" style="border: 0px; color: #000099; font-family: inherit; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; line-height: inherit; margin: 0px; padding: 0px; vertical-align: baseline;" title="Frases célebres de Justicia">Justicia</a></div>
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Ni la contradicción es indicio de falsedad, ni la falta de contradicción es indicio de verdad.</blockquote>
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Cuando leemos demasiado deprisa o demasiado despacio, no entendemos nada.</blockquote>
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Una de las principales enfermedades del hombre es su inquieta curiosidad por conocer lo que no puede llegar a saber.</blockquote>
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La moral es la ciencia por excelencia; es el arte de vivir bien y de ser dichoso.</blockquote>
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La naturaleza tiene perfecciones para demostrar que es imagen de Dios e imperfecciones para probar que sólo es una imagen.</blockquote>
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No vivimos nunca, sino que esperamos vivir; y disponiéndonos siempre a ser felices, es inevitable que no lo seamos nunca.</blockquote>
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<span style="border: 0px; color: #666666; font-family: inherit; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; line-height: inherit; margin: 0px; padding: 0px; vertical-align: baseline;">Más frases sobre: </span><a href="http://www.proverbia.net/citastema.asp?tematica=4" style="border: 0px; color: #000099; font-family: inherit; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; line-height: inherit; margin: 0px; padding: 0px; vertical-align: baseline;" title="Frases célebres de Felicidad">Felicidad</a></div>
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A fuerza de hablar de amor, uno llega a enamorarse. Nada tan fácil. Esta es la pasión más natural del hombre.</blockquote>
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La desgracia descubre al alma luces que la prosperidad no llega a percibir.</blockquote>
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<span style="border: 0px; color: #666666; font-family: inherit; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; line-height: inherit; margin: 0px; padding: 0px; vertical-align: baseline;">Más frases sobre: </span><a href="http://www.proverbia.net/citastema.asp?tematica=166" style="border: 0px; color: #000099; font-family: inherit; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; line-height: inherit; margin: 0px; padding: 0px; vertical-align: baseline;" title="Frases célebres de Desgracia">Desgracia</a></div>
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He hecho esta carta más larga de lo usual porque no tengo tiempo para hacer una más corta.</blockquote>
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Los mejores libros son aquellos que quienes los leen creen que también ellos pudieron haberlos escrito.</blockquote>
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<span style="border: 0px; color: #666666; font-family: inherit; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; line-height: inherit; margin: 0px; padding: 0px; vertical-align: baseline;">Más frases sobre: </span><a href="http://www.proverbia.net/citastema.asp?tematica=232" style="border: 0px; color: #000099; font-family: inherit; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; line-height: inherit; margin: 0px; padding: 0px; vertical-align: baseline;" title="Frases célebres de Libros">Libros</a></div>
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Sebastian Latorrehttp://www.blogger.com/profile/06560434053585385214noreply@blogger.comtag:blogger.com,1999:blog-7917828282233485876.post-44217938594220874522015-07-15T03:12:00.003-03:002015-07-15T03:12:48.963-03:007 Frases de Baise Pascal 1<div class="q" style="background: url(http://www.proverbia.net/images/separador.gif) 50% 100% no-repeat rgb(255, 255, 255); border: 0px; color: #222222; font-family: 'Open Sans', Helvetica, sans-serif; font-size: 16px; font-stretch: inherit; line-height: 19.2000007629395px; margin: 0px 0px 0.2em; padding: 20px 0px; vertical-align: baseline;">
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Si no actúas como piensas, vas a terminar pensando como actúas.</blockquote>
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Prefiero equivocarme creyendo en un Dios que no existe, que equivocarme no creyendo en un Dios que existe. Porque si después no hay nada, evidentemente nunca lo sabré, cuando me hunda en la nada eterna; pero si hay algo, si hay Alguien, tendré que dar cuenta de mi actitud de rechazo.</blockquote>
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Vale más saber alguna cosa de todo, que saberlo todo de una sola cosa.</blockquote>
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El primer efecto del amor es inspirar un gran respeto; se siente veneración por quien se ama.</blockquote>
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Sólo conozco dos tipos de personas razonables: las que aman a Dios de todo corazón porque le conocen, y las que le buscan de todo corazón porque no le conocen.</blockquote>
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<blockquote style="border: 0px; font-family: inherit; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; line-height: 1.4em; margin: 0px; padding: 0px; quotes: none; vertical-align: baseline;">
El corazón tiene razones que la razón ignora.</blockquote>
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<span style="border: 0px; color: #666666; font-family: inherit; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; line-height: inherit; margin: 0px; padding: 0px; vertical-align: baseline;">Más frases sobre: </span><a href="http://www.proverbia.net/citastema.asp?tematica=227" style="border: 0px; color: #000099; font-family: inherit; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; line-height: inherit; margin: 0px; padding: 0px; vertical-align: baseline;" title="Frases célebres de Corazón">Corazón</a></div>
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<li style="border: 0px; display: inline; font-family: inherit; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; line-height: inherit; list-style-type: none; margin: 0px 0.2em; padding: 0px; vertical-align: baseline;"><a class="twitter-button" data-text="El+coraz%C3%B3n+tiene+razones+que+la+raz%C3%B3n+ignora%2E" href="http://www.proverbia.net/cita.asp?id=2510" rel="nofollow" style="background-color: #bbbbbb; background-image: url(http://www.proverbia.net/images/ic_twitter_2.png); background-position: 50% 50%; background-repeat: no-repeat; background-size: 65%; border-radius: 4px; border: 0px; color: #000099; display: inline-block; font-family: inherit; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; height: 24px; line-height: 1em; margin: 0px; padding: 1px; vertical-align: baseline; width: 24px;" title="Tuitear frase"></a></li>
<li style="border: 0px; display: inline; font-family: inherit; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; line-height: inherit; list-style-type: none; margin: 0px 0.2em; padding: 0px; vertical-align: baseline;"><a class="facebook-button" data-text="El+coraz%C3%B3n+tiene+razones+que+la+raz%C3%B3n+ignora%2E" href="http://www.proverbia.net/cita.asp?id=2510" rel="nofollow" style="background-color: #bbbbbb; background-image: url(http://www.proverbia.net/images/ic_facebook_2.png); background-position: 50% 50%; background-repeat: no-repeat; background-size: 65%; border-radius: 4px; border: 0px; color: #000099; display: inline-block; font-family: inherit; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; height: 24px; line-height: 1em; margin: 0px; padding: 1px; vertical-align: baseline; width: 24px;" title="Compartir frase en Facebook"></a></li>
</ul>
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<blockquote style="border: 0px; font-family: inherit; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; line-height: 1.4em; margin: 0px; padding: 0px; quotes: none; vertical-align: baseline;">
El hombre está dispuesto siempre a negar todo aquello que no comprende.</blockquote>
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<span style="border: 0px; color: #666666; font-family: inherit; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; line-height: inherit; margin: 0px; padding: 0px; vertical-align: baseline;">Más frases sobre: </span><a href="http://www.proverbia.net/citastema.asp?tematica=81" style="border: 0px; color: #000099; font-family: inherit; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; line-height: inherit; margin: 0px; padding: 0px; vertical-align: baseline;" title="Frases célebres de Comprensión">Comprensión</a></div>
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<blockquote style="border: 0px; font-family: inherit; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; line-height: 1.4em; margin: 0px; padding: 0px; quotes: none; vertical-align: baseline;">
La grandeza de un hombre está en saber reconocer su propia pequeñez.</blockquote>
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<span style="border: 0px; color: #666666; font-family: inherit; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; line-height: inherit; margin: 0px; padding: 0px; vertical-align: baseline;">Más frases sobre: </span><a href="http://www.proverbia.net/citastema.asp?tematica=479" style="border: 0px; color: #000099; font-family: inherit; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; line-height: inherit; margin: 0px; padding: 0px; vertical-align: baseline;" title="Frases célebres de Grandeza">Grandeza</a></div>
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<blockquote style="border: 0px; font-family: inherit; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; line-height: 1.4em; margin: 0px; padding: 0px; quotes: none; vertical-align: baseline;">
¿De qué le sirve al hombre ganar el mundo si pierde su alma?</blockquote>
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<span style="border: 0px; color: #666666; font-family: inherit; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; line-height: inherit; margin: 0px; padding: 0px; vertical-align: baseline;">Más frases sobre: </span><a href="http://www.proverbia.net/citastema.asp?tematica=476" style="border: 0px; color: #000099; font-family: inherit; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; line-height: inherit; margin: 0px; padding: 0px; vertical-align: baseline;" title="Frases célebres de Alma">Alma</a></div>
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<blockquote style="border: 0px; font-family: inherit; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; line-height: 1.4em; margin: 0px; padding: 0px; quotes: none; vertical-align: baseline;">
Cuando no se ama demasiado no se ama lo suficiente.</blockquote>
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<span style="border: 0px; color: #666666; font-family: inherit; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; line-height: inherit; margin: 0px; padding: 0px; vertical-align: baseline;">Más frases sobre: </span><a href="http://www.proverbia.net/citastema.asp?tematica=475" style="border: 0px; color: #000099; font-family: inherit; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; line-height: inherit; margin: 0px; padding: 0px; vertical-align: baseline;" title="Frases célebres de Amar">Amar</a></div>
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Nuestra imaginación nos agranda tanto el tiempo presente, que hacemos de la eternidad una nada, y de la nada una eternidad.</blockquote>
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La felicidad es un artículo maravilloso: cuanto más se da, más le queda a uno.</blockquote>
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Dos excesos: excluir la razón, no admitir más que la razón.</blockquote>
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Muy débil es la razón sino llega a comprender que hay muchas cosas que la sobrepasan.</blockquote>
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El espíritu cree naturalmente y la voluntad naturalmente ama; de modo que, a falta de objetos verdaderos, es preciso apegarse a los falsos.</blockquote>
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Estando siempre dispuestos a ser felices, es inevitable no serlo alguna vez.</blockquote>
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El hombre tiene ilusiones como el pájaro alas. Eso es lo que lo sostiene.</blockquote>
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La razón obra con lentitud, y con tantas miras, sobre tantos principios, que a cada momento se adormece o extravía. La pasión obra en un instante.</blockquote>
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La virtud de un hombre no debe medirse por sus esfuerzos, sino por sus obras cotidianas.</blockquote>
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Por muchas riquezas que el hombre posea y por grandes que sean la salud y las comodidades que disfrute, no se siente satisfecho si no cuenta con la estimación de los demás.</blockquote>
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Sebastian Latorrehttp://www.blogger.com/profile/06560434053585385214noreply@blogger.comtag:blogger.com,1999:blog-7917828282233485876.post-75448278704315430132015-07-15T03:12:00.000-03:002015-07-15T03:12:08.412-03:006 Critica y recepcion <div style="background-color: white; color: #252525; font-family: sans-serif; font-size: 14px; line-height: 22.3999996185303px; margin-bottom: 0.5em; margin-top: 0.5em;">
En una época en la que ya se insistía en la separación de la fe y el saber, Pascal representó, en su vida y en su obra, el principio de la unidad de todo el ser. Para él, dedicarse tanto a problemas de ciencias naturales como a cuestiones filosóficas y teológicas no suponía contradicción de ninguna clase; todo le servía para lograr una directa profundización de sus conocimientos. Su percepción de la «intelligence/raison du coeur» – solo la conjunción de la razón con el corazón puede constituirse en base del conocimiento humano– como forma más esencial del conocimiento omnímodo es considerada por sus adeptos como concepción visionaria y ejemplar por los tiempos de los tiempos.</div>
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Hasta el día de hoy, a Pascal se le considera un locuaz <a class="mw-redirect" href="https://es.wikipedia.org/wiki/Apolog%C3%ADa_del_cristianismo" style="background: none; color: #0b0080; text-decoration: none;" title="Apología del cristianismo">apologista</a> del cristianismo y defensor de una profunda ética cristiana. Por eso, algunos críticos del cristianismo, como el<a href="https://es.wikipedia.org/wiki/Jean_Meslier" style="background: none; color: #0b0080; text-decoration: none;" title="Jean Meslier">abate Meslier</a> o <a href="https://es.wikipedia.org/wiki/Voltaire" style="background: none; color: #0b0080; text-decoration: none;" title="Voltaire">Voltaire</a>, lo atacaron pronto como eximio oponente. <a href="https://es.wikipedia.org/wiki/Friedrich_Nietzsche" style="background: none; color: #0b0080; text-decoration: none;" title="Friedrich Nietzsche">Friedrich Nietzsche</a> durante toda su vida reflexionó sobre Pascal. Para él, Pascal es «el <i>lógico</i> admirable del cristianismo»;<sup class="reference" id="cite_ref-9" style="line-height: 1em; unicode-bidi: -webkit-isolate;"><a href="https://es.wikipedia.org/wiki/Blaise_Pascal#cite_note-9" style="background: none; color: #0b0080; text-decoration: none; white-space: nowrap;">9</a></sup> «Pascal, a quien casi amo, porque me ha enseñado infinitas cosas: el único cristiano lógico».<sup class="reference" id="cite_ref-10" style="line-height: 1em; unicode-bidi: -webkit-isolate;"><a href="https://es.wikipedia.org/wiki/Blaise_Pascal#cite_note-10" style="background: none; color: #0b0080; text-decoration: none; white-space: nowrap;">10</a></sup> Es posible hallar juicios que expresan tanto admiración como rechazo: Nietzsche veía en Pascal, como también en <a href="https://es.wikipedia.org/wiki/Arthur_Schopenhauer" style="background: none; color: #0b0080; text-decoration: none;" title="Arthur Schopenhauer">Schopenhauer</a>, algo así como un adversario digno. También veía una relación de contenido entre ambos: «sin la fe cristiana», opinaba Pascal, «vosotros mismos seréis, así como la naturaleza y la historia, ‘un monstre et un chaos‘». Esta profecía la hemos <i>cumplido</i>: después de que el siglo XVIII, débil y optimista, hubiera <i>embellecido</i> y <i>racionalizado</i> al ser humano […], en un sentido esencial es <i>Schopenhauer</i> el primero, que vuelve a <i>retomar</i> el movimiento de<i>Pascal</i> […] <i>nuestra incapacidad de conocer la verdad</i> es consecuencia de nuestra <i>corrupción</i>, de nuestra <i>decadencia</i> moral: dice Pascal. Y eso mismo en el fondo dice Schopenhauer.»<sup class="reference" id="cite_ref-11" style="line-height: 1em; unicode-bidi: -webkit-isolate;"><a href="https://es.wikipedia.org/wiki/Blaise_Pascal#cite_note-11" style="background: none; color: #0b0080; text-decoration: none; white-space: nowrap;">11</a></sup> En Pascal Nietzsche puede localizar su crítica del cristianismo: «El cristianismo no merece perdón por haber aplastado a personas como Pascal. […] ¿Qué es lo que combatimos en el cristianismo? El que él quiera quebrar a los fuertes, que quiera desalentarlos, aprovechar sus malos momentos y su cansancio, transformando su orgullosa seguridad en inquietud y cargos de conciencia […] hasta que los fuertes sucumben en los excesos del autodesprecio y del automaltrato: esa manera lúgubre de sucumbir, cuyo ejemplo más afamado lo ofrece Pascal.»<sup class="reference" id="cite_ref-12" style="line-height: 1em; unicode-bidi: -webkit-isolate;"><a href="https://es.wikipedia.org/wiki/Blaise_Pascal#cite_note-12" style="background: none; color: #0b0080; text-decoration: none; white-space: nowrap;">12</a></sup></div>
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Críticos modernos como <a href="https://es.wikipedia.org/wiki/Aldous_Huxley" style="background: none; color: #0b0080; text-decoration: none;" title="Aldous Huxley">Aldous Huxley</a>, al que en general se considera relativamente reservado, han ido más lejos en su crítica, aunque de un modo psicologizante. Pascal habría hecho virtud de su necesidad –sus achaques corporales y su incapacidad de sentir auténtica pasión– camuflándolo con palabras pías. Pero aún peor: habría usado el peso de su razón para incentivar a otros a que adoptaran la misma cosmovisión hostil a lo terrenal. Citas de Pascal como: «Desviarse del término medio es desviarse de la humanidad» y otras inducen a entenderlo simplemente como pensador moderado en el sentido aristotélico. Huxley opina que este no habría sido más que una faceta teórica de Pascal. En la vida real, es decir, en lo que probadamente se refiere a su vida cotidiana, Pascal habría sido muy consecuente –hoy se diría: fundamentalista–. Expresiones surgidas de la pluma de Pascal tales como: «la enfermedad es el estado natural del cristiano; porque sólo en la enfermedad el ser humano es como siempre <i>debería</i> ser» expresarían la postura sombría del filósofo. En base a sus formulaciones brillantes y al relato impresionante de sus experiencias espirituales, Pascal sería considerado como «pionero de una causa noble», mientras que –en lo que se refiere a su aspecto filosófico cristiano– no habría sido más que un asceta enfermo. Según Huxley, y a diferencia de Nietzsche, Pascal no habría luchado en contra de sus dolencias, sino que las habría usado como indicios bienvenidos de que la vida terrenal carecía de valor.</div>
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Al plano filosófico se refieren la reinstanciación por <a href="https://es.wikipedia.org/wiki/Karl_L%C3%B6with" style="background: none; color: #0b0080; text-decoration: none;" title="Karl Löwith">Karl Löwith</a> de la crítica de Voltaire y su tratamiento de la «Apologética» o la interpretación crítica de su obra en la historia de la ontología funcional moderna por <a class="new" href="https://es.wikipedia.org/w/index.php?title=Heinrich_Rombach&action=edit&redlink=1" style="background: none; color: #a55858; text-decoration: none;" title="Heinrich Rombach (aún no redactado)">Heinrich Rombach</a>.<sup class="reference" id="cite_ref-13" style="line-height: 1em; unicode-bidi: -webkit-isolate;"><a href="https://es.wikipedia.org/wiki/Blaise_Pascal#cite_note-13" style="background: none; color: #0b0080; text-decoration: none; white-space: nowrap;">13</a></sup> Teológicamente relevante es por ejemplo la gran interpretación de <a href="https://es.wikipedia.org/wiki/Hans_Urs_von_Balthasar" style="background: none; color: #0b0080; text-decoration: none;" title="Hans Urs von Balthasar">Hans Urs von Balthasar</a> en su obra <i>Herrlichkeit</i>.<sup class="reference" id="cite_ref-14" style="line-height: 1em; unicode-bidi: -webkit-isolate;"><a href="https://es.wikipedia.org/wiki/Blaise_Pascal#cite_note-14" style="background: none; color: #0b0080; text-decoration: none; white-space: nowrap;">14</a></sup>Los intérpretes recién nombrados no hacen comentarios puntuales sobre cuestiones seleccionadas de la persona o la obra, sino que se ocupan del conjunto del legado de su obra. Existe una amplia investigación sobre Pascal, no solamente en Francia, sino también, por ejemplo, en Estados Unidos o en Japón.</div>
Sebastian Latorrehttp://www.blogger.com/profile/06560434053585385214noreply@blogger.comtag:blogger.com,1999:blog-7917828282233485876.post-4680170908285135842015-07-15T03:10:00.001-03:002015-07-15T03:10:51.268-03:005 Resumen Cronologico<div class="separator" style="clear: both; text-align: center;">
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Sebastian Latorrehttp://www.blogger.com/profile/06560434053585385214noreply@blogger.comtag:blogger.com,1999:blog-7917828282233485876.post-7789327228482445372015-07-15T03:08:00.005-03:002015-07-15T03:08:32.466-03:004 Los PenseesA consecuencia de su temprano deceso, Pascal no pudo terminar la gran Apologética que tenía planeada. Solo dejó notas y fragmentos, alrededor de 1000 papeles en unos 60 fajos, que en 1670 fueron la base para la publicación por amigos jensenistas de una edición titulada Pensées sur la religion et autres sujets («Pensamientos sobre la religión y otros temas»). Esta primera edición tiene gran mérito, ya que los editores —algo poco usual en esa época— trataban de publicar y hacer asequible una obra pese a estar inconclusa. Sin embargo resulta problemática porque los editores no se guiaron por el texto original, pese a que este se encontraba disponible como manuscrito autógrafo, si bien solo en forma de fajos de papeles, sino que usaron una de las dos copias que los Périer habían mandado hacer de los fajos poco después de la muerte de Pascal. Resulta más problemática aún por el hecho de que los textos conservados fueron abreviados con arreglo a diversos criterios y que —a diferencia de la copia utilizada, que había conservado básicamente el orden de los papeles y los fajos— se introdujo un orden nuevo, supuestamente más lógico, de los fragmentos.
Las ediciones modernas son el resultado de una paciente labor filológica en los siglos XIX y XX. Esta comienza en 1842, cuando el filósofo Victor Cousin, en un informe dirigido a la Academia francesa, hiciera ver la necesidad de una nueva edición de los Pensées, en vista de las evidentes deficiencias de la primera edición, que hasta entonces todos los editores habían reproducido en lo esencial, aunque casi siempre con abreviaciones y reestructuraciones adicionales. De hecho, aún en 1844, Prosper Faugère intentó por primera vez realizar una edición completa basada en los papeles originales de Pascal, reordenándolos sin embargo libremente en capítulos y secciones de acuerdo a criterios de contenido. Este principio se continuó aplicando y supuestamente perfeccionando por parte de otros editores posteriores, llegando a ser el más conocido de ellos Léon Brunschvicg con su edición de 1897–1904.
Alrededor de 1930, los investigadores abandonaron el prejuicio establecido de que los papeles de Pascal en último término no habían tenido orden alguno. En cambio reconocieron que al menos 27 fajos (es decir, alrededor de 400 papeles) correspondían a otros tantos capítulos en las intenciones de Pascal y ciertamente mostraban un orden interno. También otros fajos se evidenciaron como más homogéneos y más ordenados de lo que hasta entonces se había pensado, de modo que se pasó (especialmente Louis Lafuma, 1952) a ediciones cuyo texto corresponde al original autógrafo y cuya estructura se orienta en gran medida según las copias, o mejor dicho según la mejor de ellas (en 1710–1711 el sobrino de Pascal, Louis Périer, con la mejor de las intenciones, había reordenado todos los papeles, pegándolos en grandes pliegos).
Sin embargo, aún las ediciones más recientes no son más que aproximaciones hipotéticas. Necesariamente sigue sin responder la pregunta de cómo habría sido la obra si Pascal la hubiera podido terminar (y de si acaso la hubiera podido terminar en vida).
Los 27 capítulos mencionados muestran el camino que Pascal quería seguir en la argumentación de su apologética del cristianismo. La apologética se divide en dos: «Primera parte: La miseria del hombre sin Dios. Segunda parte: La felicidad del hombre con Dios» (Laf. 6). Primero, los capítulos bajo los títulos de «Vanidad», «Miseria», «Aburrimiento», «Contradicciones», «Distracción», etc., presentan una imagen dramática del estado de la humanidad, ejecutada con brillantes formulaciones paradójicas e irónicas, dedicándose a continuación a los filósofos en la búsqueda del «más alto bien» para encontrar la solución de las aporías de la existencia humana en el cristianismo. En esta parte, la demostración utiliza ampliamente la exégesis de los padres de la Iglesia, transmitida por Port-Royal —si bien en una forma «moderna», muy historizante— por lo que no pertenece al ámbito de la investigación histórica crítica moderna. El objetivo de la apologética de Pascal es la conversión de los ateos o dudosos.
En el material anexo de los Pensées, es decir en los demás fajos de papeles, hallamos los grandes textos antropológicos elaborados «Desproporción del ser humano» (Laf. 199) acerca de la situación del ser humano entre lo infinitamente pequeño y lo infinitamente grande, «Dispersión» (Laf. 136) acerca de la evasión del pensar sobre la situación real, caracterizada por la miseria y la muerte, entre otros. La unidad del pensamiento de Pascal desde sus escritos matemáticos hasta sus escritos teológicos se expresa plenamente en el famoso fragmento acerca de los tres órdenes de los cuerpos, del espíritu y del amor o la santidad (Laf. 308). Sin haber sido asignada a alguno de los 27 capítulos, se encuentra allí también la llamada «Apuesta de Pascal», según la cual la fe en Dios no solo es acertada sino también racional, porque: «Si ganan, lo ganan todo y si pierden, no pierden nada» (Laf. 418).Sebastian Latorrehttp://www.blogger.com/profile/06560434053585385214noreply@blogger.comtag:blogger.com,1999:blog-7917828282233485876.post-81256680481429139552015-07-15T03:08:00.001-03:002015-07-15T03:08:01.433-03:003 El entorno Port RoyalEn otoño de 1654, Pascal sufrió un trastorno depresivo. Volvió a acercarse a Jacqueline, visitándola con frecuencia en el convento y se mudó a otro barrio para alejarse de sus amigos mundanos. Sin embargo siguió trabajando en cuestiones matemáticas y otros asuntos científicos. El 23 de noviembre, posiblemente después de un accidente con su carroza del que sin embargo no existen testimonios fidedignos, tuvo una experiencia religiosa de renacimiento que intentó registrar esa misma noche en una hoja de papel que aún se conserva, el así llamado Mémorial. La hoja, fechada "en el año de gracia de 1654, lunes 23 de noviembre, a partir de las diez y media de la noche aproximadamente hasta cerca de media hora después de la medianoche" comienza con la palabra "feu" (fuego) escrita en grandes letras mayúsculas, y relata una visión que ha experimentado. Incluye los fragmentos "¡Dios de Abraham, Dios de Isaac, Dios de Jacob, no el de los filósofos y los sabios!" y añade más adelante "El Dios de Jesucristo: sólo por los caminos que enseña el Evangelio se le puede hallar".7
Después se retiró por completo de la sociedad parisina para dedicarse por completo a su devoción. Sus únicas relaciones humanas pasaron a ser los «ermitaños» jansenistas (solitaires); se trataba de sabios y teólogos que se habían establecido en el entorno del convento Port-Royal des Champs y a los que visitaba con frecuencia. Alrededor de 1655 desarrolló aquí el diálogo legendario con su nuevo confesor A. Le Maître de Sacy (Conversation avec M. de Saci sur Épictète et Montaigne), en el que, entre los dos polos del escepticismo de Montaigne y la ética estoica de Epicteto, ya ofrece un esbozo de la antropología, que posteriormente desarrollaría en los Pensées.
La sanación, ocurrida en 1656, de su sobrina Marguerite Périer, que después de visitar Port Royal se había curado de un abceso en el ojo, contribuyó más a fortalecer la fe de Pascal. Al mismo tiempo, en docto diálogo con los solitaires, especialmente con Antoine Arnauld y Pierre Nicole, empezó a redactar escritos de motivación religiosa y teológica. A la par, como siempre, también se dedicaba a cuestiones prácticas, así por ejemplo en 1655 a la didáctica del aprendizaje de la lectura, para la escuela que mantenían los solitaires.
Blaise Pascal.
En el momento de su conversión (como indica el Mémorial), Pascal se vio implicado en una situación, en la que la devoción ortodoxa y el moralismo riguroso de los jansenistas se habían convertido en una molestia para los jesuitas, más relajados y conciliadores, pero también conscientes de su poder. Cuando en 1655 se desató abiertamente el conflicto, porque a Arnauld, en su calidad de jansenista, se lo expulsó de la facultad de teología de la Sorbonne en París, Pascal tomó partido y en 1656/57 redactó una serie de folletos satíricos polémicos anónimos. Estos tuvieron una resonancia explosiva y en 1657 incluso fueron publicados en Holanda en forma de libro, bajo el título de Lettres provinciales, ou Lettres de Louis de Montalte à un provincial de ses amis et aux R. R. PP. Jésuites sur la morale et la politique de ces pères (Cartas provincianas, o cartas de L. de M. a un provinciano amigo así como a los RR. PP. jesuitas sobre la moral y la política de estos padres). Se trata de dieciocho cartas supuestamente escritas por un personaje ficticio de nombre Montalte de viaje en París, de las que las primeras diez están dirigidas a un amigo ficticio en su provincia de origen, las siguientes seis a los padres jesuitas de París, mientras que las últimas dos se dirigen en especial al padre confesor del rey. En estas cartas, Montalte, primero en el papel de joven noble, ingenuo y no versado en teología, describe como los jesuitas le explican su teología de manera sabihonda y desdeñosa; después, aprendida la «lección», empieza a discutir con ellos, reduciendo al absurdo sus enseñanzas de manera aguda e hilarante. Pascal ridiculizó y atacó así la teología en cierto sentido amistosa y práctica, pero tendencialmente oportunista y muchas veces capciosa –la famosa casuística– de los jesuitas y desenmascara sus ansias de poder sumamente terrenales. Las Lettres provinciales tuvieron un éxito notorio y durable, aunque fueron prohibidas a partir de la número cinco, puestas en el índice al aparecer como libro y hasta quemadas por el verdugo en 1660, señalando a largo plazo el principio del fin de la omnipotencia jesuita, al menos en Francia. Por su claridad y precisión se las considera entre las obras maestras de la prosa francesa, que otorgaron a su autor un lugar entre los clásicos de la literatura francesa.
Fueron menos divulgados los cuatro escritos polémicos, con los que Pascal (junto a Arnauld y Nicole) intervino en 1658 en un conflicto entre párrocos parisinos de orientación jansenista y los jesuitas.
Lápida de Blaise Pascal en la iglesia de Saint-Étienne-du-Mont (París).
En lo inmediato, sin embargo, los jesuitas mantuvieron el control de la situación con la ayuda del Rey y del Papa, lo que ensombreció los siguientes años para Pascal. Porque mientras muchos de sus correligionarios cedían bajo la presión de las represalias que tomaba la autoridad o daban pasos tácticos, él permaneció indoblegable.
En medio de esta situación, en 1658 empezó a trabajar de manera más sistemática en una gran apologética de la religión cristiana. Con este fin había escrito unas primeras notas en 1656. Sus líneas principales se pueden encontrar en el escrito redactado en 1657 pero no terminado Écrits sur la grâce (Escritos sobre la Gracia), en el que explica la forma jansenista de la noción de gracia de San Agustín como término medio entre la noción casi fatalista de predestinación del calvinismo y la noción optimista de gracia de los jesuitas, asignándole a la libre voluntad del hombre el decidir sobre su salvación. Porque para Pascal rige: «Aquel que nos creó sin nuestro concurso, no puede salvarnos sin nuestra participación».
Aparte de su trabajo en los Pensées, volvió a emprender también estudios matemáticos. Así, en 1658, calculó la superficie de la cicloide con los métodos de Cavalieri, así como el volumen del sólido de rotación que resulta de una rotación de la ciclode alrededor del eje de las x. Después de haber hallado la solución él mismo, organizó una competencia sobre el problema, lo que le significó recibir numerosas propuestas (insuficientes) así como desarrollar una intensa polémica con un descontento.
En 1659 apareció su escrito Traité des sinus des quarts de cercle (Tratado de los senos de los cuadrantes circulares). Cuando Gottfried Leibniz leyó esta obra en 1673 en París, recibió de ella un impulso decisivo para desarrollar el cálculo infinitesimal considerando el razonamiento específico por parte de Pascal, que Leibniz empleó de manera más general, interpretando el círculo de Pascal como círculo de curvatura en determinados puntos de una función o curva cualquiera. Leibniz dice que en ello había visto una luz que el propio autor no vio. De allí se origina el concepto de triángulo característico.8
Su salud deteriorada empeoró cada vez más deprisa en esos años, probablemente a consecuencia de su modo de vida extremadamente ascético, que lo debilitaba más. Por ejemplo, en 1659, no pudo trabajar durante numerosas semanas. A pesar de ello, en ese año fue miembro de un comité que trataba de poner en marcha una nueva traducción de la Biblia. En 1660 pasó varios meses de convalecencia en un palacete perteneciente a su hermana mayor y a su cuñado cerca de Clermont.
A principios de 1662, junto a su amigo Roannez, fundó una empresa de carrozas (Les carosses à cinq sous («Las carrozas de cincuenta centavos»), marcando el comienzo del transporte público local en París.
En agosto enfermó gravemente, hizo vender sus enseres domésticos donándolos para fines de caridad y murió, a la edad de solo 39 años, un año después de la muerte de su hermana Jacqueline, en casa de los Périer en París.Sebastian Latorrehttp://www.blogger.com/profile/06560434053585385214noreply@blogger.comtag:blogger.com,1999:blog-7917828282233485876.post-6378633404526926182015-07-15T03:07:00.002-03:002015-07-15T03:07:29.508-03:002 periodo parisinoA partir de mayo de 1647 volvió a vivir con Jacqueline y poco después también con su padre, principalmente en París, donde contactó a los principales jansenistas, pero también continuó con sus investigaciones. Sus ideas no fueron bien recibidas por numerosos teólogos e investigadores, entre ellos Descartes con el que se reunió repetidas veces en París a fines de septiembre de 1647. Por ello a partir de entonces formuló sus especulaciones sobre el vacío y el éter de una forma más indirecta, particularmente en un tratado sobre la presión atmosférica, demostrando su dependencia de la altura del lugar en cuestión, por medio de experimentos que hizo realizar a su cuñado Périer en el Puy de Dome en 1648. También en 1648, en otro tratado, fundamentó la ley de los vasos comunicantes.
Pocos años antes (en 1644), Torricelli había publicado su experimento por el que el peso del aire de la atmósfera mantenía el mercurio en un tubo, con vacío en su parte superior, demostrando que el aire ejerce una presión debido a su peso. Pascal no estaba convencido de esa teoría, y seguía siendo partidario de la teoría del Horror vacui. Para confirmarlo, pidió a su cuñado que escalase el volcán Puy de Dôme hasta su cima, y se comprobó que el mercurio sube más en la base de la montaña que en su cima. Tras el experimento, Pascal abandonó la teoría del Horror vacui y se convirtió a la teoría de la causa mecanicista.4
Cuando, en la primavera de 1649, los desórdenes de la Fronda dificultaron la vida en París, los Pascal se refugiaron hasta otoño de 1650 en casa de los Périer en Auvergne.
En otoño de 1651 murió Pascal padre. Poco después y contraviniendo los deseos tanto del fallecido como también de Blaise, Jacqueline se incorporó al convento estrictamente jansenista de Port Royal en París.
Ahora, Pascal por primera vez dependía nada más que de sí mismo. Ya que, si bien no era rico, sí tenía una situación acomodada y era noble, comenzó a frecuentar la sociedad de París, trabando amistad con el joven duque de Roannez, con el que compartía el interés por la filosofía. Éste lo llevó de viaje en 1652, junto a algunos de sus amigos librepensadores, entre ellos Antoine Gombaud, conocido como el "caballero de Méré", oportunidad en la que Pascal se introdujo en la filosofía moderna, aprendiendo además el arte de las conversaciones sociales. Gracias a que frecuentaba el salón esteta de Madame de Sablé, se compenetró también con las «bellas letras» de su época.5 Incluso llegó brevemente a pensar en comprar un cargo y en casarse. Sin embargo, una obra que se le adjudicó por mucho tiempo, al amoldarse en cierto sentido a esta fase mundana de su vida, el anónimo Discours sur les passions de l’amour (Discurso acerca de las Pasiones del Amor), no es de su autoría.
En 1653 escribió un tratado sobre la presión atmosférica, en el que por primera vez en la historia de la ciencia se hace una descripción completa de la hidrostática.
Junto a sus nuevos conocidos, especialmente con el Chevalier de Méré, Pascal también tenía discusiones acerca del modo de ganar en los juegos de azar, un pasatiempos típicamente de nobles. Esto lo llevó en 1653 a dedicarse a la teoría de la probabilidad, estudiándola en 1654 en su intercambio epistolar con el juez de Toulouse y destacado matemático Pierre de Fermat. Analizaron principalmente los juegos de dados. Al mismo tiempo, Pascal se ocupó de otros problemas matemáticos, publicando diversas obras en 1654: el Traité du triangle arithmétique acerca del llamado triángulo de Pascal y los coeficientes binomiales, en el que también por primera vez formuló explícitamente el principio de la demostración por inducción matemática,6 el Traité des ordres numériques acerca de los órdenes de los números y Combinaisons sobre combinaciones de números.Sebastian Latorrehttp://www.blogger.com/profile/06560434053585385214noreply@blogger.comtag:blogger.com,1999:blog-7917828282233485876.post-15412319811809560372015-07-15T03:06:00.002-03:002015-07-15T03:06:53.753-03:001Blaise Pascal (Pronunciación en francés: /blɛz paskal/; Clermont-Ferrand, 19 de junio 1623-París, 19 de agosto de 1662) fue un polímata, matemático, físico, filósofo cristiano y escritor francés. Sus contribuciones a la matemática y a la historia natural incluyen el diseño y construcción de calculadoras mecánicas, aportes a la teoría de la probabilidad, investigaciones sobre los fluidos y la aclaración de conceptos tales como la presión y el vacío. Después de una experiencia religiosa profunda en 1654, Pascal abandonó la matemática y la física para dedicarse a la filosofía y a la teología.
Infancia y juventud[editar]
Nació el 19 de junio de 1623 en el seno de una familia noble en Clermont (hoy en día Clermont-Ferrand) en la zona de Auvernia, del Macizo Central francés. Su padre, Étienne Pascal, tras haber recibido una formación como jurista en París, era un magistrado de alto rango (maître des requêtes)1 que se desempeñaba como juez vicepresidente de la oficina de recaudación tributaria de Auvernia en Clermont. Por otra parte, Étienne Pascal destacaría más tarde como matemático. Su madre, Antoinette Begon provenía de una familia burguesa de comerciantes acomodados que también aspiraba a la Noblesse de robe. Blaise Pascal tenía dos hermanas, Gilberte y Jaqueline. A la primera, tres años mayor que Blaise, se le conoce mucho más, puesto que fue ella quien escribió la primera biografía publicada sobre su hermano. Al nacer Jaqueline, su hermana dos años menor, la madre no logró recuperarse de aquel parto complicado y el puerperio, de modo que Pascal perdió su madre a la temprana edad de tres años.
En 1631, Étienne Pascal se trasladó con su familia a París, conservando en Clermont su puesto en la oficina de recaudación de impuestos. También llevó a una niñera que estaba a cargo del cuidado de sus tres hijos huérfanos de madre.2 Blaise tenía para entonces ocho años y el objetivo de su padre era abrirle en la capital francesa mayores posibilidades que las existentes en la provincia para su educación y despliegue de capacidades, a todos los hijos, pero particularmente para Blaise, quien llamaba mucho la atención por sus facultades mentales, superiores a las promedio.
Resulta sorprendente que Pascal no haga ninguna mención de esta temprana pérdida. Al respecto, su hermana Gilberte Pascal escribirá en la biografía:
...al morir mi madre en 1626, cuando mi hermano no tenía más que tres años, mi padre, al quedarse solo, se entregó con mayor dedicación al cuidado de la familia; y como Blaise era su único hijo varón, esta cualidad y las demás que en él observó [las grandes pruebas de inteligencia que observó en él] le llenó hasta tal punto de afecto paternal que decidió no encargar a nadie la tarea de su educación y tomó la resolución de instruirle él mismo, como en efecto hizo, pues mi hermano no tuvo nunca otro maestro que mi padre...3
En 1640, su padre fue nombrado Comisario Real y jefe de la recaudación de impuestos para Normandía con asiento en Ruan. Aquí, en 1642, Pascal inventó para él la roue pascaline, «rueda de pascal» o Pascalina, considerada como una de las calculadoras más antiguas. Inicialmente solo permitía realizar adiciones, pero en el curso de los diez años siguientes añadió mejoras, siendo finalmente capaz de hacer restas. Pascal la hizo patentar, pero no se cumplieron sus expectativas de hacerse rico comercializando su invento por medio de una pequeña empresa de su propiedad. Las máquinas, trabajosamente confeccionadas una a una y a mano, eran demasiado caras como para poder venderse en volúmenes mayores y solo llegó a fabricar cincuenta, de las que subsisten nueve.
En Ruan, ciudad con universidad, corte de justicia (Parlement) y ricos comerciantes, la familia Pascal pertenecía a la sociedad, aunque el padre se había hecho enemigos por su rigor en el ejercicio de su cargo. Pascal y su hermana menor Jacqueline, con dotes literarias, cuyos intentos poéticos fueron apoyados por el dramaturgo Pierre Corneille, se movían en este ambiente elegante. Su hermana Gilberte se casó en 1641 con un pariente joven, Florin Périer, traído desde Clermont-Ferrand por el padre para que fuera su ayudante.
En 1646, durante la convalecencia del padre después de un accidente, la familia, que hasta entonces no había sido muy religiosa, entró en contacto con las enseñanzas del obispo reformista holandés Jansenio, que defendía en el seno de la iglesia católica una noción de gracia divina basada en San Agustín, similar a las ideas de Calvino. El padre, el hijo y las hijas se hicieron devotos y Jacqueline incluso decidió hacerse monja, mientras que Pascal, que sufría fenómenos de parálisis en las piernas con permanentes dolores, interpretó su enfermedad como signo divino y empezó a llevar una vida ascética.
A principios de 1647 demostró el fervor de su nueva devoción forzando al arzobispo de Ruan a castigar a un seminarista, que ante él y amigos suyos había defendido una visión de la religión que les había parecido demasiado racionalista.
Sin embargo, el propio Pascal nunca consideró que su devoción fuera un obstáculo para seguir dedicándose a sus estudios en ciencias naturales y matemática. Así, por ejemplo, ya en 1646 repitió con éxito los ensayos que Evangelista Torricelli había realizado en 1643 para demostrar la existencia del vacío, la que hasta entonces se había considerado como imposible, publicando en 1647 sus resultados en el tratado Traité sur le vide (Tratado sobre el vacío).Sebastian Latorrehttp://www.blogger.com/profile/06560434053585385214noreply@blogger.comtag:blogger.com,1999:blog-7917828282233485876.post-23793019205716656592009-06-20T13:40:00.007-04:002009-06-21T14:17:46.805-04:00Biografía<a href="http://www.csus.edu/indiv/c/craftg/Hist127/pascal.jpg"><img style="margin: 0px 0px 10px 10px; float: right; width: 323px; height: 313px;" alt="" src="http://www.csus.edu/indiv/c/craftg/Hist127/pascal.jpg" border="0" /></a><span style="font-size:130%;"><br /></span><div align="justify"><span style=";font-family:lucida grande;font-size:130%;" ><span class="blsp-spelling-error" id="SPELLING_ERROR_0">Blaise</span> Pascal nació el 19 de junio de 1623 en <span class="blsp-spelling-error" id="SPELLING_ERROR_1">Clermond</span>-<span class="blsp-spelling-error" id="SPELLING_ERROR_2">Ferrand</span> en Francia. Su padre no lo envío a la <span class="blsp-spelling-corrected" id="SPELLING_ERROR_3">escuela</span>, sino que él mismo lo educo. <span class="blsp-spelling-corrected" id="SPELLING_ERROR_4">También</span> no quiso que <span class="blsp-spelling-error" id="SPELLING_ERROR_5">Blaise</span> estudiara <span class="blsp-spelling-corrected" id="SPELLING_ERROR_6">matemáticas</span> hasta que tenga la edad de 15 años <span class="blsp-spelling-corrected" id="SPELLING_ERROR_7">pudiese</span> estudiarla. Como medida saco todos los libros relacionados con la <span class="blsp-spelling-corrected" id="SPELLING_ERROR_8">matemáticas</span> pero <span class="blsp-spelling-corrected" id="SPELLING_ERROR_9">Pascal</span> <span class="blsp-spelling-corrected" id="SPELLING_ERROR_10">empezó</span> a estudiarla a escondidas de su padre desde los 12 años.</span></div><span style="font-size:130%;"><br /></span><div align="justify"><span style="font-size:130%;">Pascal trabajó en las secciones cónicas y desarrolló importantes teoremas en la geometría </span><span class="blsp-spelling-error" id="SPELLING_ERROR_11" style="font-size:130%;">proyectiva</span><span style="font-size:130%;">. En su correspondencia con </span><span class="blsp-spelling-error" id="SPELLING_ERROR_12" style="font-size:130%;">Fermat</span><span style="font-size:130%;"> dejó la creación de la Teoría de la Probabilidad. Aunque parezca poco creible, a esa edad descubrió que la suma de los ángulos internos de un triángulo es 180 grados. Cuando su padre descubrió que su hijo estudiaba geometría a escondidas y además que la disfrutaba tanto, le permitió leer los libros de </span><span class="blsp-spelling-error" id="SPELLING_ERROR_13" style="font-size:130%;">Euclides</span><span style="font-size:130%;"> y así Pascal comenzó su formación matemática de una manera rigurosa. A los catorce años asistía con mucha frecuencia a las reuniones que organizaba un monje llamado </span><span class="blsp-spelling-error" id="SPELLING_ERROR_14" style="font-size:130%;">Mersenne</span><span style="font-size:130%;">, quien invitaba a científicos y filósofos a entablar discusiones y reflexiones en su celda. Fue ahí donde Pascal conoció a matemáticos de la talla de </span><span class="blsp-spelling-error" id="SPELLING_ERROR_15" style="font-size:130%;">Fermat</span><span style="font-size:130%;"> y </span><span class="blsp-spelling-error" id="SPELLING_ERROR_16" style="font-size:130%;">Desargues</span><span style="font-size:130%;"> de los que fue un excelente alumno. A los dieciséis años Pascal era ya uno de los miembros más destacados de ese círculo de estudio. A la edad de 16 años Pascal presentó sólo un trozo de papel con escritos a las reuniones </span></div><span style="font-size:130%;"><br /></span><div align="justify"><span style="font-size:130%;">Pascal fue un científico universal, su manera de estudiar, entender y describir la naturaleza sirvió de ejemplo a muchos otros científico que durante los siglos posteriores siguieron sus pasos. </span></div><span style="font-size:130%;"><br /></span><div align="justify"><span style="font-size:130%;">Blaise Pascal murió el 19 de agosto de 1662 en París. Tenía tan sólo 39 años y murió con intensos dolores producidos por un tumor maligno en el estómago que se le propagó hasta el cerebro. </span></div>Sebastian Latorrehttp://www.blogger.com/profile/06560434053585385214noreply@blogger.com0tag:blogger.com,1999:blog-7917828282233485876.post-27127105513477262182009-06-19T15:59:00.001-04:002009-06-24T22:13:31.327-04:00Apuesta de Pascal<span style="font-size:130%;">Es un argumentos creado por Blaise Pascal en una discusión sobre la creencia en la existencia de Dios, basado en el supuesto de que la existencia de Dios es una cuestión de azar. El argumento plantea que, aunque no se conoce de modo seguro si Dios existe, lo racional es apostar que sí existe. </span><blockquote><span style="font-size:130%;"><br />La razón es que, aún cuando la probabilidad de la existencia de Dios fuera extremadamente pequeña, tal pequeñez sería compensada por la gran ganancia que se obtendría, o sea, la gloria eterna.<br /><br /></span></blockquote><span style="font-size:130%;"> Básicamente, el argumento plantea cuatro escenarios: </span><ul><li><span style="font-size:130%;">Puedes creer en Dios, si existe, entonces irás al cielo.<br /></span></li><li><span style="font-size:130%;">Puedes creer en Dios, si no existe, entonces no ganarás nada.</span></li><li><span style="font-size:130%;">Puedes no creer en Dios, si no existe, entonces tampoco ganarás nada.</span></li><li><span style="font-size:130%;">Puedes no creer en Dios, si existe, entonces irás al infierno.</span></li></ul><table style="border: 1px solid rgb(170, 170, 170); margin: 0.5em 0.5em 0.5em 1em; padding: 0.5em; background: rgb(249, 249, 249) none repeat scroll 0% 50%; -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial; border-collapse: collapse; width: 302px; height: 125px;font-size:95%;" border="2" cellpadding="4" cellspacing="0"><tbody><tr><th><span style="font-size:130%;"><br /></span></th> <th><span style="font-size:130%;">Dios existe (Dios)</span></th><td style="vertical-align: top; font-weight: bold;"><span style="font-size:130%;">Dios no existe (¬Dios)</span></td> </tr> <tr> <th><span style="font-size:130%;">Creer en Dios (Creer)</span></th> <td><span style="font-size:130%;">+ ∞ (CIELO)</span></td> <td> <center><span style="font-size:130%;">0</span></center> </td> </tr> <tr> <th><span style="font-size:130%;">No creer en Dios (¬Creer)</span></th> <td><span style="font-size:130%;">− ∞ (INFIERNO)</span></td> <td> <center><span style="font-size:130%;">0</span></center></td></tr></tbody></table><span style="font-size:130%;"><br />La apuesta de Pascal fue expresada por él, de la siguiente manera:<br /></span><blockquote><span style="font-size:130%;"><i><br />Usted tiene dos cosas que perder: la verdad y el bien, y dos cosas que comprometer: su razón y su voluntad, su conocimiento y su bienaventuranza; y su naturaleza posee dos cosas de las que debe huir: el error y la miseria. Su razón no está más dañada, eligiendo la una o la otra, puesto que es necesario elegir. He aquí un punto vacío. ¿Pero su bienaventuranza? Vamos a pesar la ganancia y la pérdida, eligiendo cruz (de cara o cruz) para el hecho de que Dios existe. Estimemos estos dos casos: si usted gana, usted gana todo; si usted pierde, usted no pierde nada. Apueste usted que Él existe, sin titubear.</i></span></blockquote>Cristian Barrientoshttp://www.blogger.com/profile/07726512189146889457noreply@blogger.comtag:blogger.com,1999:blog-7917828282233485876.post-90899479502499723892009-06-19T14:53:00.007-04:002015-07-14T16:37:47.389-03:00Estudios sobre la presión atmosférica<div style="text-align: justify;">
En el año 1646, Pascal ya conocía los experimentos de Evangelista Torricelli con barómetros. Tras replicar la creación de un barómetro de mercurio, para lo cual se coloca un tubo de mercurio boca abajo en un recipiente lleno de ese metal, Pascal comenzó a cuestionarse qué fuerza era la que hacía que parte del mercurio se quedase dentro del tubo y qué era lo que llenaba el espacio por encima del mercurio hasta el final del tubo.<br />
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<span style="text-align: justify;">En 1647 Pascal publicó </span><i style="text-align: justify;">Experiences nouvelles touchant le vide</i><span style="text-align: justify;"> ("Nuevos Experimentos sobre el Vacío"), en donde detallaba una serie de reglas básicas que describían hasta qué punto varios líquidos podían estar soportados por la presión del aire. También ofrecía razones por las que lo que había por encima de la columna de líquido era realmente un vacío.</span><br />
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El 19 de septiembre de 1648, tras muchos meses de preparación, Pascal realizó junto con Florin Périer, el marido de la hermana mayor de Pascal, el experimento esencial para la teoría de Pascal. El relato, escrito por Périer, dice así:</div>
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"El clima incierto el pasado sábado (...) [pero] alrededor de las cinco de la mañana (...) se hizo visible el Puy-de-Dôme <a href="http://es.wikipedia.org/wiki/Puy-de-D%C3%B4me" style="color: #3366ff;" title="Puy-de-Dôme"></a> (...) por lo que decidí hacer un intento. Varias personas importantes de la ciudad de Clermont me pidieron que les hiciera saber cuándo haría la ascensión (...) estaba encantado de tenerles conmigo en este gran trabajo (...)"</div>
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<span style="font-size: 100%;">"(...) a las ocho llegamos a los jardines de la Orden de los Mínimos, que tiene la menor elevación en la ciudad (...) Primero vertí dieciséis libras de <a href="http://es.wikipedia.org/wiki/Mercurio_%28elemento%29" title="Mercurio (elemento)">mercurio</a> (...) en un recipiente (...) luego tomé diversos tubos de cristal (...) cada uno de cuatro pies de largo y herméticamente sellados en un extremo y abiertos en el otro (...) luego los coloqué en el recipiente [de mercurio] (...) I observé que el mercurio ascendía hasta 26" y 3½ líneas por encima del mercurio del recipiente (...) Repetí el experimento dos veces más estando sobre el mismo lugar (...) con el mismo resultado en cada ocasión (...)"</span></div>
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<span style="font-size: 100%;">"Adherí uno de los tubos al recipiente y marqué la altura del mercurio y (...) solicité al Padre Chastin, de la Orden de los Mínimos (...) que vigilase si ocurría algún cambio a lo largo del día (...) Tomando el otro tubo y una parte del mercurio (...) anduve hasta la cima del Puy-de-Dôme</span><span style="font-size: 100%;">, unas 500 brazas más alta que el monasterio, en dónde el experimento (...) mostró que el mercurio alcanzaba una altura de sólo 23" y 2 líneas (...) Repetí el experimento cinco veces con cuidado (...) cada uno en diferentes puntos de la cima (...) y resultó la misma altura del mercurio (...) en cada caso (...)"</span></div>
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Pascal replicó el experimento en París, transportando el barómetro hasta lo alto del campanario de la iglesia de<span style="font-weight: bold;"> </span>Saint-Jacques-de-la-Boucherie, a una altura de unos cincuenta metros. El mercurio cayó unas dos líneas. Estos y otros experimentos de Pascal fueron aclamados por Europa por establecer el principio y el valor del barómetro.<br />
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</span>Sebastian Latorrehttp://www.blogger.com/profile/06560434053585385214noreply@blogger.comtag:blogger.com,1999:blog-7917828282233485876.post-36570958593250434292009-06-19T14:47:00.001-04:002009-06-24T11:26:08.884-04:00"Principio de Pascal"<span style="font-weight: bold;font-size:130%;" ><strong style="font-weight: normal;">El principio o Ley de Pascal </strong></span><span style="font-size:130%;">q</span><span style="font-size:130%;">ue se resume en la frase: «el incremento de <a href="http://es.wikipedia.org/wiki/Presi%C3%B3n" title="Presión">presión</a> aplicado a una superficie de un <a href="http://es.wikipedia.org/wiki/Fluido" title="Fluido">fluido</a> incompresible (líquido), contenido en un recipiente indeformable, se transmite con el mismo valor a cada una de las partes del mismo».<strong style="font-weight: normal;">
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<br /></strong></span><span style="font-size:130%;">El principio de Pascal puede ser interpretado como una consecuencia de la ecuación fundamental de la hidrostática y del carácter altamente incompresible de los líquidos. En esta clase de fluidos la densidad es prácticamente constante, de modo que de acuerdo con la ecuación:</span><span style="font-weight: bold;font-size:130%;" >
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<br /><img class="tex" alt=" p = p_0 + \rho.g.h \," src="http://upload.wikimedia.org/math/0/b/e/0bede8b5e609fef9d2ce0fbddd7ef74e.png" />
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<br />Donde:
<br /><img class="tex" alt="p \," src="http://upload.wikimedia.org/math/5/a/3/5a34bb082daf037b3c4b14c13af6855b.png" />, presión total a la profundidad <img class="tex" alt="h \," src="http://upload.wikimedia.org/math/7/c/4/7c4073ca34bcc95361750a3f1fddc7a8.png" />.
<br /><img class="tex" alt="p_0 \," src="http://upload.wikimedia.org/math/2/a/f/2af989a335eb062bdb809d9900b31ff1.png" />, presión sobre la superficie libre del fluido.
<br /><img class="tex" alt="\rho \," src="http://upload.wikimedia.org/math/a/b/4/ab4c699d5daae16f90abf620d960811a.png" />, densidad.
<br /><img class="tex" alt="g \," src="http://upload.wikimedia.org/math/f/3/1/f31f123f5b510e1c58b2be1990dcada8.png" />, gravedad.
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<br />La prensa hidráulica constituye la aplicación fundamental del principio de Pascal y también un dispositivo que permite entender mejor su significado.Consiste, en esencia, en dos cilindros de diferente sección comunicados entre sí, y cuyo interior está completamente lleno de un líquido que puede ser agua o aceite. Dos émbolos de secciones diferentes se ajustan, respectivamente, en cada uno de los dos cilindros, de modo que estén en contacto con el líquido. Cuando sobre el émbolo de menor sección <i>S</i><sub>1</sub> se ejerce una fuerza <i>F</i><sub>1</sub> la presión <i>p</i><sub>1</sub><i>p</i><sub>2</sub> que ejerce el líquido sobre el émbolo de mayor sección <i>S</i><sub>2</sub>, es decir:
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<br />que se origina en el líquido en contacto con él se transmite íntegramente y de forma (casi) instantánea a todo el resto del líquido. Por el principio de Pascal esta presión será igual a la presión </span> <dl><dd><span style="font-size:130%;"><img class="tex" alt="p_1 = p_2 \," src="http://upload.wikimedia.org/math/f/3/9/f39a1e7f1d0cda0b96e357a50e27adfc.png" /></span></dd></dl> <p><span style="font-size:130%;">
<br />con lo que, las fuerzas serán, siendo <i>S</i><sub>1</sub> < <i>S</i><sub>2</sub> :
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<br /></span> </p> <dl><dd><span style="font-size:130%;"><img class="tex" alt="F_1 = p_1 S_1 < p_1 S_2 = p_2 S_2 = F_2\," src="http://upload.wikimedia.org/math/d/c/0/dc03993c08223f0c87d6cd1cb8d93328.png" /></span></dd></dl> <p><span style="font-size:130%;">
<br />y por tanto, la relación entre las fuerza resultante en el émbolo grande cuando se aplica una fuerza menor en el émbolo pequeño será tanto mayor cuanto mayor sea la relación entre las secciones:
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<br /></span> </p> <dl><dd><span style="font-size:130%;"><img class="tex" alt="F_1 = F_2 \left( \frac{S_1}{S_2} \right) " src="http://upload.wikimedia.org/math/9/d/0/9d0e704d55f7f14f7c813fefa9bc8553.png" /></span></dd></dl>
<br /><strong style="font-weight: normal;"></strong>Sebastian Latorrehttp://www.blogger.com/profile/06560434053585385214noreply@blogger.comtag:blogger.com,1999:blog-7917828282233485876.post-46270356295594998632009-06-19T14:21:00.004-04:002015-07-14T16:48:21.378-03:00Orígenes de la probabilidad<div style="text-align: justify;">
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La probabilidad tiene su <span class="blsp-spelling-error" id="SPELLING_ERROR_0">or</span><span class="blsp-spelling-error" id="SPELLING_ERROR_1">ígen</span> en los estudios de las posibilidades de ganar en juegos de azar; en el siglo <span class="blsp-spelling-error" id="SPELLING_ERROR_2">XVII</span>.</div>
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En el año 1650, Dé <span class="blsp-spelling-error" id="SPELLING_ERROR_3">Méré</span> un francés, se encuentra con <span class="blsp-spelling-error" id="SPELLING_ERROR_4">Blaise</span> Pascal y le propone un problema que ya se había discutido en la Edad Media. El problema que le propone a Pascal consistía en cómo debían repartirse el premio si al suspenderse Dé <span class="blsp-spelling-error" id="SPELLING_ERROR_5">Méré</span> tenia 2 puntos y su contrincante 1 punto.</div>
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Pascal le envía cartas a otro matemático famoso de de la época: <span class="blsp-spelling-error" id="SPELLING_ERROR_6">Pierre</span> de <span class="blsp-spelling-error" id="SPELLING_ERROR_7">Fermat</span>, contándole acerca de este problema.</div>
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En el año 1654, ambos matemáticos resuelven el problema argumentando que si cada uno de los jugadores había aportado 32 doblones y como Dé <span class="blsp-spelling-error" id="SPELLING_ERROR_8">Méré</span> tiene el doble de probabilidades de ganar que su adversario, debería recibir 48 doblones.</div>
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Sobre estas investigaciones de Pascal y <span class="blsp-spelling-error" id="SPELLING_ERROR_9">Fermat</span> surgieron las bases de la probabilidad la que influye en muchos aspectos de nuestra vida actual.</div>
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A continuación una representación en <span class="blsp-spelling-error" id="SPELLING_ERROR_10">comic</span> de los problemas de Dé <span class="blsp-spelling-error" id="SPELLING_ERROR_11">Méré</span> en los juegos de azar.</div>
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Sebastian Latorrehttp://www.blogger.com/profile/06560434053585385214noreply@blogger.comtag:blogger.com,1999:blog-7917828282233485876.post-22799601300024404382009-06-19T10:27:00.001-04:002015-07-14T16:57:10.959-03:00Triangulo de Pascal<a href="http://upload.wikimedia.org/wikipedia/commons/0/0d/PascalTriangleAnimated2.gif" onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}"><img alt="" border="0" src="http://upload.wikimedia.org/wikipedia/commons/0/0d/PascalTriangleAnimated2.gif" style="float: right; height: 240px; margin: 0pt 0pt 10px 10px; width: 260px;" /></a><br />
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El <b>triángulo de Pascal</b> en matemáticas es un conjunto infinito de números enteros ordenados en forma de triángulo que expresan coeficientes binomiales. El interés del <span style="font-weight: bold;">Triángulo de Pascal</span> radica en su aplicación en álgebra y permite calcular de forma sencilla numeros combinatorios lo que sirve para aplicar el binomio de Newton<span style="font-size: 130%;">.</span></div>
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Sebastian Latorrehttp://www.blogger.com/profile/06560434053585385214noreply@blogger.comtag:blogger.com,1999:blog-7917828282233485876.post-46686299975368554322009-06-19T09:42:00.003-04:002009-06-24T22:42:32.642-04:00Relación entre el triángulo de Pascal y el binomio de Newton<span style="font-size:130%;">La expresión que proporciona las potencias de una suma <b><img style="width: 64px; height: 20px;" class="tex" alt="(a+b)^n\;" src="http://upload.wikimedia.org/math/9/d/4/9d44f23cefd1911c3b64959520e4f6e2.png" /></b> se denomina Binomio de Newton.<br /><br /><p style="border: 2px ridge rgb(255, 0, 0); font-style: italic;"><span style="font-size:100%;">Los coeficientes de la forma desarrollada de (a + b)<sup>n</sup> se encuentran en la línea «n + 1» del Triángulo de Pascal.</span></p><br /></span><p><span style="font-size:130%;">Para obtener el resultado de cualquier valor de n ∈ <b>N</b>, se procede por induccion matemática Suponiendo que es cierto para un valor de <b>n</b>, deducimos que lo es también para <b>n+1</b>. Observemos lo que sucede con n = 4.</span></p> <div class="center"> <div class="floatnone"><span style="font-size:130%;"><a href="http://es.wikipedia.org/wiki/Archivo:Tri%C3%A1ngulo_Pascal_binomio_Newton.png" class="image" title="Triángulo Pascal binomio Newton.png"><img alt="" src="http://upload.wikimedia.org/wikipedia/commons/a/af/Tri%C3%A1ngulo_Pascal_binomio_Newton.png" width="502" height="141" /></a></span></div> </div> <p><span style="font-size:130%;">El desarrollo de (a + b)<sup>4</sup> consiste en el desarrollo de (a + b) (a + b)³.</span></p> <p><span style="font-size:130%;">Si sólo se escriben los coeficientes, obtenemos la siguiente suma:</span></p> <div class="center"> <div class="floatnone"><span style="font-size:130%;"><a href="http://es.wikipedia.org/wiki/Archivo:Tri%C3%A1ngulo_Pascal_binomio_Newton_2.png" class="image" title="Triángulo Pascal binomio Newton 2.png"><img alt="" src="http://upload.wikimedia.org/wikipedia/commons/b/bf/Tri%C3%A1ngulo_Pascal_binomio_Newton_2.png" width="424" height="76" /></a></span></div> </div> <p><span style="font-size:130%;">Obviamente, aparecen las mismas cifras desplazadas en una posición: la suma consiste en añadir a un coeficiente el coeficiente situado a su derecha, y esto es justamente lo que se obtiene en el triángulo de Pascal.</span></p>Sebastian Latorrehttp://www.blogger.com/profile/06560434053585385214noreply@blogger.comtag:blogger.com,1999:blog-7917828282233485876.post-91357009965294336942009-06-19T09:10:00.005-04:002015-07-14T16:52:29.837-03:00Calculadora Pascalina<div class="separator" style="clear: both; text-align: center;">
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<span style="text-align: start;">Blaise Pascal inventó la primera calculadora mecanica,la cual fue creada en 1645, tras tres años de trabajos sobre la misma. Esta maquina solo podía sumar y restar, tenia unas ruedas en las cuales llevaban en su borde una serie de cifras que iban desde 1 hasta 10.</span></div>
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Cuando la rueda de la derecha, que representaba las unidades, daba una vuelta completa, engranaba con la rueda situada a su izquierda que representaba las decenas, y se adelantaba una muesca. mediante este proceso la calculadora arrojaba un resultado muy preciso de la operación realizada inicialmente, claro está que esto pasaba solo si se introducían los números correctos, ya que si alguno era erróneo la operación fallaría totalmente.</div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjU1A7USnEuf5EbyoyTz1naip0EMjrPdY14NkEx-p22mBrtwczNjBPw2MvUW7VmsrZghnlX9RHmzxETKAlLr43D46DcwqNdv0Gl4N3adzlmwa867dyXwtGw7LqIKz4PxoZw9VROaHLlu7EG/s1600/pascalina.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="210" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjU1A7USnEuf5EbyoyTz1naip0EMjrPdY14NkEx-p22mBrtwczNjBPw2MvUW7VmsrZghnlX9RHmzxETKAlLr43D46DcwqNdv0Gl4N3adzlmwa867dyXwtGw7LqIKz4PxoZw9VROaHLlu7EG/s320/pascalina.jpg" width="320" /></a></div>
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El primer uso de la calculadora Pascalina fue en la hacienda francesa, debido a que Pascal diseñó la Pascalina para ayudar a su padre, que era contador en dicha entidad. Debido a ello la Pascalina estaba destinada básicamente a solucionar problemas de aritmética comercial.</div>
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Se fabricaron varias versiones y Pascal en persona construyó al menos cincuenta ejemplares. Finalmente mostró al mundo su versión definitiva en el año 1649, pero lastimosamente su esfuerzo por comercializar la maquina fue un fracaso, debido a que era demasiado costosa y las personas no contaban con el dinero suficiente como para adquirirla.</div>
Cristian Barrientoshttp://www.blogger.com/profile/07726512189146889457noreply@blogger.comtag:blogger.com,1999:blog-7917828282233485876.post-47594480638500184122009-06-07T00:21:00.001-04:002009-06-24T22:41:59.728-04:00Resumen y Síntesis<span style="font-size:130%;">Blaise Pascal veia las cosas muy racionalmente, quizas fue esto lo que hizo que este fuese un gran matematico, ya que sus descubrimientos fueron muy importantes y todavia se siguen usando sus postulados, ya sea para estudiar la presión atmosférica, su triangulo llamado el triangulo de pascal y sus diversas propiedades, y la probabilidad.<br /><br />Se ve su pensamiento racional en como el postula a que Dios si existe, ya que en apuesta, él utiliza la matematica para decir que Dios existe, al ser la matemática una ciencia exacta se le puede dar esta apreciación encontrando una respuesta, con una realidad absoluta, a la existencia de Dios.<br /><br />El Triangulo de Pascal uno de los mas conocidos de sus pustulados o creaciones, cuyas propiedades, tiene relacion con el estudio para realizar ejercicios como los productos notables., ya sean cubos, cuadrados de binomio,etc.<br /><br />Pascal es un muy importante matemático puesto que sus postulados han perdurado hasta los dias de hoy, y aún son reelevantes en la actualidad, el triangulo de pascal, como se ve en el video que muestra sus múltiples utilidades, quieren decir que su trabajos y descubrimientos no fueron en vano y que su pasión por las matematicas y su curiosidad por aprenderlas hicieron de él alo muy importante.</span>pipehttp://www.blogger.com/profile/18026196392950242028noreply@blogger.com