Pascal had poor health, especially after the age of 18, and he died just two months after his 39th birthday. Pascal was born in Clermont-Ferrand , which is in France's Auvergne region. He lost his mother, Antoinette Begon, at the age of three. Pascal had two sisters, the younger Jacqueline and the elder Gilberte.

The newly arrived family soon hired Louise Delfault, a maid who eventually became an instrumental member of the family. The young Pascal showed an amazing aptitude for mathematics and science. Particularly of interest to Pascal was a work of Desargues on conic sections. It states that if a hexagon is inscribed in a circle or conic then the three intersection points of opposite sides lie on a line called the Pascal line. Pascal's work was so precocious that Descartes was convinced that Pascal's father had written it.

When assured by Mersenne that it was, indeed, the product of the son and not the father, Descartes dismissed it with a sniff: "I do not find it strange that he has offered demonstrations about conics more appropriate than those of the ancients," adding, "but other matters related to this subject can be proposed that would scarcely occur to a year-old child. In France at that time offices and positions could be—and were—bought and sold.

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But in Richelieu, desperate for money to carry on the Thirty Years' War , defaulted on the government's bonds. In , in an effort to ease his father's endless, exhausting calculations, and recalculations, of taxes owed and paid into which work the young Pascal had been recruited , Pascal, not yet 19, constructed a mechanical calculator capable of addition and subtraction, called Pascal's calculator or the Pascaline.

Partly because it was still quite cumbersome to use in practice, but probably primarily because it was extraordinarily expensive, the Pascaline became little more than a toy, and a status symbol , for the very rich both in France and elsewhere in Europe. Pascal continued to make improvements to his design through the next decade, and he refers to some 50 machines that were built to his design.

The triangle can also be represented:. Pascal concludes with the proof,. From this discussion, the notion of expected value was introduced. The work done by Fermat and Pascal into the calculus of probabilities laid important groundwork for Leibniz ' formulation of the calculus.

## Pascal, Blaise

The work was unpublished until over a century after his death. Here, Pascal looked into the issue of discovering truths, arguing that the ideal of such a method would be to found all propositions on already established truths. At the same time, however, he claimed this was impossible because such established truths would require other truths to back them up—first principles, therefore, cannot be reached. Based on this, Pascal argued that the procedure used in geometry was as perfect as possible, with certain principles assumed and other propositions developed from them.

Nevertheless, there was no way to know the assumed principles to be true.

### by Voltaire

He distinguished between definitions which are conventional labels defined by the writer and definitions which are within the language and understood by everyone because they naturally designate their referent. The second type would be characteristic of the philosophy of essentialism. Pascal claimed that only definitions of the first type were important to science and mathematics, arguing that those fields should adopt the philosophy of formalism as formulated by Descartes.

In De l'Art de persuader "On the Art of Persuasion" , Pascal looked deeper into geometry's axiomatic method , specifically the question of how people come to be convinced of the axioms upon which later conclusions are based. Pascal agreed with Montaigne that achieving certainty in these axioms and conclusions through human methods is impossible.

He asserted that these principles can be grasped only through intuition, and that this fact underscored the necessity for submission to God in searching out truths. Pascal's work in the fields of the study of hydrodynamics and hydrostatics centered on the principles of hydraulic fluids. His inventions include the hydraulic press using hydraulic pressure to multiply force and the syringe. He proved that hydrostatic pressure depends not on the weight of the fluid but on the elevation difference. He demonstrated this principle by attaching a thin tube to a barrel full of water and filling the tube with water up to the level of the third floor of a building.

This caused the barrel to leak, in what became known as Pascal's barrel experiment. By , Pascal had learned of Evangelista Torricelli 's experimentation with barometers.

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Having replicated an experiment that involved placing a tube filled with mercury upside down in a bowl of mercury, Pascal questioned what force kept some mercury in the tube and what filled the space above the mercury in the tube. At the time, most scientists contended that, rather than a vacuum , some invisible matter was present. This was based on the Aristotelian notion that creation was a thing of substance, whether visible or invisible; and that this substance was forever in motion.

Furthermore, "Everything that is in motion must be moved by something," Aristotle declared. How so? As proof it was pointed out:.

Following more experimentation in this vein, in Pascal produced Experiences nouvelles touchant le vide "New experiments with the vacuum" , which detailed basic rules describing to what degree various liquids could be supported by air pressure. It also provided reasons why it was indeed a vacuum above the column of liquid in a barometer tube. The weather was chancy last Saturday Several important people of the city of Clermont had asked me to let them know when I would make the ascent I was delighted to have them with me in this great work First I poured 16 pounds of quicksilver I repeated the experiment two more times while standing in the same spot I attached one of the tubes to the vessel and marked the height of the quicksilver and Taking the other tube and a portion of the quick silver I repeated the experiment five times with care Pascal replicated the experiment in Paris by carrying a barometer up to the top of the bell tower at the church of Saint-Jacques-de-la-Boucherie , a height of about 50 metres.

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The mercury dropped two lines. In the face of criticism that some invisible matter must exist in Pascal's empty space, Pascal, in his reply to Estienne Noel , gave one of the 17th century's major statements on the scientific method, which is a striking anticipation of the idea popularised by Karl Popper that scientific theories are characterised by their falsifiability : "In order to show that a hypothesis is evident, it does not suffice that all the phenomena follow from it; instead, if it leads to something contrary to a single one of the phenomena, that suffices to establish its falsity.

Pascal introduced a primitive form of roulette and the roulette wheel in his search for a perpetual motion machine. For after all what is man in nature? A nothing in relation to infinity, all in relation to nothing, a central point between nothing and all and infinitely far from understanding either. The ends of things and their beginnings are impregnably concealed from him in an impenetrable secret. He is equally incapable of seeing the nothingness out of which he was drawn and the infinite in which he is engulfed. In the winter of , Pascal's year-old father broke his hip when he slipped and fell on an icy street of Rouen; given the man's age and the state of medicine in the 17th century, a broken hip could be a very serious condition, perhaps even fatal.

Following a mystical experience in late , he left mathematics and physics and devoted himself to reflection and writing about philosophy and theology. He had suffered from ill-health throughout his life and his new interests were ended by his early death two months after his 39th birthday. Blaise Pascal was brother to Jacqueline Pascal and two other sisters, only one of whom, Gilberte, survived past childhood. Young Pascal showed immediate aptitude for mathematics and science, perhaps inspired by his father's regular conversations with Paris' leading geometricians, including Roberval, Mersenne, Desargues, Mydorge, Gassendi , and Descartes.

It is not true, as some have said, that he had reinvented the theorems of Euclid to that point. Still, it was an astonishing performance; and it seemed so marvelous to his father that he no longer sought to hold Blaise back in the study of mathematics. Particularly of interest to the young Pascal was the work of Desargues. Following Desargues's thinking, at age 16 Pascal produced a treatise on conic sections, Essai pour les coniques Essay on Conics. Most of it has been lost, but an important original result has lasted, now known as "Pascal's theorem. The Zwinger museum, in Dresden, Germany , exhibits one of his original mechanical calculators.

Though these machines stand near the head of the development of computer engineering, the calculator failed to be a great commercial success. Pascal continued to make improvements to his design through the next decade and built a total of 50 machines.

In addition to the childhood marvels recorded above, Pascal continued to influence mathematics throughout his life. It should be noted, however, that Yang Hui, a Chinese mathematician of the Qin dynasty, had independently worked out a concept similar to Pascal's triangle four centuries earlier. In , prompted by a friend interested in gambling problems, he corresponded with Fermat on the subject, and from that collaboration was born the mathematical theory of probabilities.

## Blaise Pascal - New World Encyclopedia

This was the introduction of the notion of expected value. The work was unpublished until over a century after his death. Here Pascal looked into the issue of discovering truths, arguing that the ideal such method would be to found all propositions on already established truths. At the same time, however, he claimed this was impossible because such established truths would require other truths to back them up—first principles cannot be reached.

Based on this, Pascal argued that the procedure used in geometry was as perfect as possible, with certain principles assumed and other propositions developed from them. Nevertheless, there was no way to know the assumed principles to be true. In De l'Art de persuader, Pascal looked deeper into geometry's axiomatic method, specifically the question of how people come to be convinced of the axioms upon which later conclusions are based.

Pascal agreed with Montaigne that achieving certainty in these axioms and conclusions through human methods is impossible. He asserted that these principles can only be grasped through intuition, and that this fact underscored the necessity for submission to God in searching out truths. He distinguished between definitions which are conventional labels defined by the writer and definitions which are within the language and understood by everyone because they naturally designate their referent.

The second type would be characteristic of the philosophy of essentialism. Pascal claimed that only definitions of the first type were important to science and mathematics, arguing that those fields should adopt the philosophy of formalism as formulated by Descartes. Pascal's work in the fields of the study of fluids hydrodynamics and hydrostatics centered on the principles of hydraulic fluids. His inventions include the hydraulic press using hydraulic pressure to multiply force and the syringe. By Pascal had learned of Evangelista Torricelli's experimentation with barometers.