Chapter 21 Appendix Pascal's Life and Scientific Contributions

France in the seventeenth century was basically still a country of feudal serfdom, but new capitalist production relations had begun to grow within the feudal matrix.The needs of production technology have raised a series of scientific issues for advanced scientists in the field of natural struggle; the needs of ideology have raised a series of ideological issues for advanced thinkers in the field of ideological struggle.On these two fronts, Pascal, the author of this book, occupies an important historical position. Pascal was born on June 19, 1623 in the city of Clermont-Ferrand in the state of Auvergne, France; his father, Etienne Pa-scal, was the president of the court of Clermont City , known for his knowledge.When Pascal was eight, his family moved to Paris.After moving to Paris, Equina often communicated with scientists, writers and artists in the society at that time, and often took Pascal to participate in various academic gatherings.Pascal grew up in an environment with a strong academic atmosphere, and received strict education from his father instead of the popular scholastic education at that time; this created favorable conditions for his later academic and ideological activities.

The young Pascal showed his interest in studying nature and his outstanding talent.At the age of eleven he wrote a dissertation on the problem of acoustics, inquiring into the reasons why vibrating bodies cease to produce sound as soon as they are touched.This article made such a deep impression on his father that his father stopped teaching him geometry for fear that his intellectual development would be too early to be conducive to his growth.But Pascal studied geometry alone and mastered a lot of geometric knowledge. In 1639, when Pascal was sixteen years old, he wrote the famous paper "On Conic Sections", which proposed the theorem named after him.This Pascal's theorem, Pascal called it "mysterious hexagon", that is, the intersection of three sets of corresponding sides of any inscribed hexagon of a circle or ellipse is on a straight line. "Theory of Conic Sections" inherited and developed the work of mathematician Desarques (1593-1662), leading to more than 400 inferences; Descartes was greatly impressed after reading it.In this way, Pascal, together with Descartes and Desargues, opened up modern geometry.From then on, Pascal made his mark in the scientific circles, and together with famous scientists and thinkers at that time, Descartes, Hobbes, Gassendi, Desargues, Fermat (Eermat, 1601-1665), Mersenne (Mersenne, 1588) -1648), Roberval (Roberval, 1602-1675) and others established contacts; Pascal's scientific work and ideological development in his life are closely related to these people.

In 1641, when Pascal was eighteen years old, he began to design computers; he had drafted fifty models, and finally made the first computer in the history of the world based on the rotation principle of the gear train, which could calculate six-digit numbers by hand. Addition and Subtraction.The success of computer manufacturing was a major event in international science at that time.It was also at this time that Aquinas was treated by a Jansenian doctor for his disease, so the whole family accepted the Jansen teachings. This is the so-called "first conversion" of Pascal. Thereafter Pascal began to work on atmospheric pressure; on this question he completed the work begun by Galileo and carried out by Galileo's disciple Torricelli (1608-1647).The fact that air has weight has been known by no later than 1630; Galileo also knew that air has weight and did experiments to measure the weight of air, but he did not link the height of the mercury column with atmospheric pressure. study. In 1632, Galileo mentioned in his book 035 that the water pump can only pump water to a certain height. This proposition theoretically includes the problem of atmospheric pressure, but his thinking is still limited to " The traditional concept of "nature is afraid of a vacuum" failed to give a correct explanation for this phenomenon. In 1643, Torricelli experimented with a mercury column and realized the change of air pressure under different climatic conditions.Torricelli's experiment opened up a new era of human fluid mechanics research, it conclusively proved that the atmosphere is pressurized, and established the basic method of measuring atmospheric pressure.But Torricelli's concept of air pressure is vague and unclear, and the law of air pressure change has not yet been determined. In 1646, at the age of twenty-three, Pascal repeated Torricelli's experiments.Pascal carefully studied the change of the mercury column at various altitudes, thus obtaining a clear scientific concept of the law of air pressure and its change. In 1647, Pascal asked his brother-in-law Perier to conduct repeated experiments on the mercury column at the top and at the foot of the mountain to observe the changes in the height of the mercury column.Pascal had already known that the air at the foot of the mountain was thicker than that at the top of the mountain, so the conclusion should be that the height of the mercury column is lower at high places than at low places, that is, the air pressure decreases with the increase of height. On September 19, 1648, Birière conducted an experiment according to Pascal's design on Puy de Dome (Puy de Dome, 1400 meters above sea level) in Auvergne; The height difference was 3.15 hours, which made the experimenters present at that time very amazed.This experiment shocked the entire scientific community and was recognized by the scientific community (it also marked the transfer of the scientific center from Italy to Northwest Europe in the middle of the seventeenth century).On the basis of this experiment, Pascal wrote his "Liquid Equilibrium" and "Atmospheric Gravity"

Two works established the theory of atmospheric pressure and the basic laws of hydrostatics. The 1648 experiment is one of the most moving in the history of the scientific revolution. It is the most important advance in the history of hydrostatics since Archimedes, and it is also long since "developed in a general revolution, and itself radically revolutionary" as new sciences battle old ideologies again A brilliant victory; it proved that the height of the column of mercury was the result of atmospheric pressure, thus shattering once and for all the old scholastic dogma that "nature fears a vacuum."Pascal's vacuum experiments have had as liberating effects on modern thought as Galileo's experiments on falling bodies; according to. (See Galileo, "Dialogue of Two World Systems", University of California Edition, 1953. Page xxiH i.) His experiments broke the shackles of medieval thought and opened up a new era of modern experimental science and thinking methods.This success marked a new climax in the struggle between two lines in the field of thought: one was that of modern experimental science begun by Galileo, and the other was that of traditional medieval scholasticism.In this way, Pascal defended and developed the line of modern experimental science with his scientific experiments and the objective laws of nature summarized by common observation and experiments.

With the success of this experiment, Pascal also summed up a set of excellent epistemology theory from the height of thinking method.In a treatise entitled "The Theory of Vacuum", Pascal sharply attacked the "philosophical authority" of the time, and put forward the following argument: (1) Sticking to the dogmas of ancient authority is by no means an attitude of pursuing truth.He said: "Our worship of the ancients today-which should not have such a large weight in various disciplines-has reached such a point that it has taken all his thoughts and myths as oracles, No one dares to come up with a new idea without danger, and one writer's clause is enough to destroy the strongest evidence."Here "a writer" refers to Aristotle; Aristotle's dogma was regarded as authoritative by scholastics in the Middle Ages.Pascal resolutely opposed this archaic fashion of scholasticism.He believed that the authority of the ancients could only be grounded in theology and history, that is, in the field of knowledge by revelation and description; Useless, only the intellect can know it."Facts cannot be denied; therefore, his conclusion is that we must not blindly follow the ancients and dogmas, and all scientific truths can only be perfected by relying on experiments and reasoning, which is "the only criterion of science".

(2) Human beings are different from animals.The abilities and skills of animals are only natural needs, they do not know why, so they can only repeat blindly and unconsciously. People can accumulate the experience of their predecessors, so they have unlimited abilities.The accumulation is endless.If the ancients lived today, with today's support, they would be as clever as today's people.This is not any special excellence of today's people, but the natural result of the progress of human history.Mankind continues on, just as an immortal man progresses forever.It is wrong to worship the ancients, because the ancients are really just babies.The knowledge of the ancients should not be despised, this is "because the knowledge they left us can be used as a stepping stone for our own knowledge".Learning from the ancients is to surpass the ancients, so one should not follow the ancients blindly.People today surpass the ancients because they have accumulated more knowledge; "we see more", "we see more than they do".Therefore, what should be worshiped is not the ancients but the present; but people are so upside down: "It becomes a crime to oppose the ancients, and it becomes a rebellion to complement the ancients, as if the ancients have left nothing for future generations to recognize. like the truth".We should not worship the ancients but the truth.Truth, though a new discovery, is older than all ancients and their opinions.

(3) The dogma that "nature is afraid of a vacuum" is absurd. Experiments in 1648 proved that the height of the mercury column was supported by atmospheric pressure, not by any "natural fear of a vacuum".Pascal asked: "What could be more absurd than saying that inanimate objects have feelings and fears, that inanimate, inanimate, or even impossibly animate objects also have feelings? And, if If the object of this fear is the vacuum, what can the vacuum frighten them? Is there anything more boring and ridiculous than this? Not only that, if there is a principle of avoiding the vacuum in them, is it true? Are they said to have hands, feet, muscles, and nerves?"

There is no doubt that nature itself is inanimate, and it has no fear of a vacuum. The so-called "nature is afraid of a vacuum" is just an interpretation of nature by the ancients under their understanding conditions at that time. This paper not only contains his very valuable methodology, that is, knowing the truth cannot be based on belief and dogma, but must rely on reason for observation and experimentation; it also contains his view of historical progress, that is, human knowledge is constantly accumulating, History is constantly moving forward.The article is full of fighting spirit, and severely criticizes the stubborn thoughts under the cover of feudal Confucian classics.But at the same time, it can also be seen that although the thesis broke the historical superstition with its declaration of praising the present rather than the past, liberated people's minds, and put forward the theory of scientific method, it became a chapter in the history of thought and science in the seventeenth century. A monumental declaration of importance; yet, in addition to the positives, it also reveals the germs of a negative thought that certainty is impossible.This ideological contradiction was further expressed in the book "Silu" ten years later.

In connection with this experiment, Pascal also imagined an inverse experiment, that is, to measure the height of the mountain by the change of the barometer; the work of this inverse experiment was later completed by the French scientist Mariotte (1620-1684). Pascal also explained the siphon phenomenon with atmospheric pressure, and found that changes in air pressure were related to climate conditions, which had great enlightenment significance for the later development of meteorology. After conducting the air pressure test, Pascal turned to study the general law of liquid balance, and discovered the most basic principle of hydrostatics, that is, the pressure on any point of the fluid in the closure is equally transmitted in all directions with the same intensity. ; This is the famous "Pascal's theorem".The discovery of this theorem has great theoretical and practical value, and it laid the foundation of modern fluid mechanics.

After a period of research in fluid mechanics, Pascal returned to mathematical work.The Italian mathematician Cava-lieri (Cava-lieri, 1598-1647), who was at the same time as Pascal and earlier, suggested that the area of ​​a triangle can be calculated by dividing it into countless parallel straight lines.Pascal made important new contributions on this basis.He pointed out that what Gavalieri called straight lines were actually tiny rectangles, which led to the ideas of limits and infinitesimals.This monumental research opened up the modern mathematical method and cleared the way for the later calculus of calculus.

In addition, Pascal is also engaged in various scientific research and technical design.The seventeenth century was called "the century of genius" in some works on the history of science.In his youth, Pascal stood among the geniuses of the seventeenth century with his brilliant scientific contributions.But the ranks of geniuses of the "century of genius" did not emerge out of nowhere, they were stimulated by the new capitalist mode of production.Overseas voyages stimulated the founding of astronomy, hydraulic engineering stimulated the emergence of hydrodynamics, and the introduction of machinery "was, to the great mathematicians of the time ... the actual fulcrum and stimulus which enabled the creation of modern mechanics."Without this social and material foundation, the founding ceremony of modern science would not have been held in the seventeenth century. Pascal's rich scientific research work was carried out under the condition of continuous illness and extremely weak body.From the age of eighteen, he had not been sick for a day, and at the age of twenty-four he was paralyzed by a stroke.During this period, he lived with his father and sister Jacqueline, and under the influence of both of them, he gradually paid attention to the problems of thought and belief. His father died in 1651, and his younger sister entered the Poloyar Monastery.During the two or three years from this time to 1654, Pascal (28-31 years old) lived alone in Paris, living a secular life.The surviving Essay on Love, which most scholars attribute to Pascal, and to this period of secular life; the whole text is imbued with the spirit of Epicureanism, and shows that his Jansenism thinking is in crisis.At this time, he made friends with the atheists, free thinkers, and scholars of human nature Des Barreaux (Des Barreaux, 1602-1673), Miton (Mere, 1610-1684) and others, and was particularly influenced by Mere. At the same time, he delved deeply into the history from Epictetus (50-135?) to Montaigne (1533-1 592) et al.In science, in philosophy, in contemplative life and in secular life, he explored the truth of the world and the happiness of life, and he never returned.The secular life of this period gave him the opportunity to observe various social life and human phenomena in depth, thus providing various materials for the later "Thinking Records".Another aspect of secular life, gambling, induced him to study probability theory. Pascal and Fermat are the founders of the discipline of probability theory.According to Leibniz, seventeenth-century mathematicians began to formulate the theory of probability by calculating the odds in gambling.Murray, Pascal's friend and gambler, raised the following question: How should the chances of winning or losing be calculated when gambling is interrupted at any certain stage?This question caused a sensation among scholars at the time; Pascal was thus introduced into the study of probability theory.Pascal once informed Fermat of his research, and the two came up with their own answers.Leibniz read Pascal's research results when he lived in Paris from 1672 to 1676, and he was deeply aware of the importance of this "new logic" and conducted serious research.After Pascal, Fermat and Leibniz, successive generations of mathematicians such as Huygens, Jabernoy, De Mafort, Labras and others have continued to study and develop probability theory.The discipline created by Pascal has been widely used in many departments of modern science and technology, and it has also greatly inspired modern theoretical science and philosophical thought. Its important significance and value have been proved by later scientific practice . The period of Pascal's secular life was also the period of his rich scientific creation. His two works "Atmospheric Gravity" and "Liquid Equilibrium" were both published in 1653; the following year he completed a series of research work on number theory and probability theory, and the famous "Pascal's triangle" still used in algebra today " (that is, the triangular arrangement method of binomial coefficients) was proposed in this year. On November 23, 1654, Pascal was in distress while riding a carriage. Both horses fell to their deaths in the Seine River in Paris, but Pascal himself survived miraculously.The accident stimulated him to undergo a peculiar inner experience, which has been called a "second conversion" by some of Pascal's researchers.Afterwards, Pascal entered the Beau-Royal Monastery and devoted himself to the truth of the universe and life for the rest of his life, and he pursued it in the midst of fierce struggle and pain. The style of the Jansenists emphasized reason, and the basic line Pascal followed was also rational rather than scholastic, philosophical and thinking rather than theological and dogmatic.Several important works written in the later years of his short life——1655 The "Conversation with Mr. Chassy" in 1656-1657, the "Letters to Foreigners" in 1656-1657, and the "Thinking Records" written in 1658-all reflect this ideological characteristic. Since the suppression of the Fronde, Jesuit activity in France has intensified.In the sharp struggle on the French ideological front in the seventeenth century, that is, the theoretical struggle of the Jansenists against the Jesuits, Pascal, as an outstanding defender of the Jansenists, wrote eighteen letters attacking Jesus as a layman. Will letter.These eighteen letters became an important historical document of the anti-Jesus church ideology rule at that time, which inspired the emerging humanism.This "Letter to Other Provinces" and the later "Silu" have become classic works in the history of ideology and culture with their polemical sharpness, profound thoughts, and smooth and meaningful writing. They have a profound influence on later generations. Even during the period of indulging in philosophical and religious meditation, he did not give up his scientific research work.His "Mathematical Triangle Theory" was published in 1665 after being revised by Fermat. In the book, the proof method of mathematical induction was established for the first time. The scientific problem that he studied the most and contributed the most in his later years was the problem of the cyclochoid.The study of cycloids provided a brilliant example of "movement and dialectics entering mathematics" due to the development of industrial technology in the seventeenth century, and laid the foundation for the later work of Newton and Leibniz.The cycloid was the most famous curve in mathematics at that time, and Descartes, Torricelli, Fermat and others had studied it diligently; he solved the quadrature problem that was considered to be the most difficult at that time.With the solution of this problem, he raised a series of other problems to challenge the scientific community. Huygens and others participated in the challenge, and he also announced his own solutions to these problems.These studies directly contributed to the birth of differential calculus.His scientific deeds were once hailed by the encyclopedic scientist D'Alembert (1717-1783) in the eighteenth century as an intermediate link between the work of Archimedes and that of Newton. It is in line with historical facts. In his later years, Pascal was a staunch fighter against the Jesuits.When Po-Royal was on the verge of failure after several severe blows by the ruling authorities, some representatives of the Jansen faction were inclined to compromise, but he insisted on continuing to fight. For this reason he almost broke with his Pou-Royal friends, and ended his genius and short life in pain and disease. Pascal died in Paris on August 19, 1662, at the age of thirty-nine.The debate between the Jansenists and the Jesuits, as a narrow theological debate, has long since become a thing of the past; But beyond the scope of theology, it has left a worthy legacy in the history of thought.Regarding his life activities, his sister Gilberte (Mrs. Birière) once wrote a biography of Pascal for the Poloyar version of "Thoughts", readers can refer to it. The philosophical viewpoints and ideological methodologies of each era are always summed up based on the scientific achievements and political struggles at that time.The formation of the world outlook and methodology of thinkers in the seventeenth and eighth centuries was closely related to their scientific work (and in this historical stage, mainly mathematical science).However, in addition to being restricted by their scientific knowledge and scientific methods, their world outlook and methodology are also restricted by the characteristics of their times and political characteristics.Pascal was born in an era when the domination of theological thought was about to collapse but had not yet collapsed, so his theoretical system often used theological thought materials; his social status belonged to the middle-class civil opposition in early modern times, so he could not Avoid a lot of idealistic and agnostic views.These are things we should pay attention to, analyze and criticize while affirming his historical contribution.