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antinomy of Russell
One day, the barber in Saville village put up a sign: "All the men in the village who don't cut their own hair are cut by me, and I only cut their own hair." So someone asked him, "Who will cut your hair?" The barber was speechless at once.
Because if he cuts his own hair, then he belongs to the kind of person who cuts his own hair. However, the sign says that he doesn't cut such people's hair, so he can't cut it himself. If another person cuts his hair, he is the one who doesn't cut his own hair, and the signboard clearly States that he will cut all men who don't cut their own hair, so he should cut his own hair. It can be seen that no matter what the inference is, what the barber said is always contradictory.
This is a famous paradox called "Russell Paradox". This was put forward by the British philosopher Russell, who expressed a famous paradox about set theory in a popular way.
1874, the German mathematician Cantor founded set theory, which soon penetrated into most branches and became their foundation. By the end of19th century, almost all mathematics was based on set theory. At this time, some contradictory results appeared in the set theory, especially the paradox reflected in the barber story put forward by Russell in 1902, which was extremely simple, clear and popular. As a result, the foundation of mathematics has been shaken passively, which is the so-called third "mathematical crisis".
Since then, in order to overcome these paradoxes, mathematicians have done a lot of research work, which has produced a lot of new achievements and brought about a revolution in mathematical concepts.
Neumann
Neumann (1903~ 1957) is a Hungarian-American mathematician and a member of the American Academy of Sciences.
Born in the family of a Jewish banker, Neumann is a rare child prodigy. He mastered calculus at the age of 8, and read Function Theory at the age of 12. On the road of his growth, there was an interesting story: in the summer of 19 13, Mr. Max, a banker, published a revelation that he was willing to hire a tutor for Neumann, the eldest son of 1 1 year-old, with the salary of 10 times that of ordinary teachers. Although this seductive revelation has made many people feel heartbroken, no one dared to teach such a well-known child prodigy ... After he received his Ph.D. in physics and mathematics at the age of 2 1, he began multidisciplinary research, first in mathematics, mechanics and physics, then in economics and meteorology, then in atomic bomb engineering, and finally, he devoted himself to the research of electronic computers. All this makes him an out-and-out scientific generalist. His main achievement is mathematical research. He has made great contributions to many branches of higher mathematics, and his most outstanding work is to open up a new branch of mathematics-game theory. 1944 published his outstanding book game theory and economic behavior. During the Second World War, he made important contributions to the development of the first atomic bomb. After the war, he was praised as the father of electronic computers by using his mathematical ability to guide the manufacture of large electronic computers.
Gauss
Gauss (C.F. Gauss,1777.4.30-1855.2.23) is a German mathematician, physicist and astronomer, who was born in a poor family in zwick, Germany. His father, Gerhard Di Derrych, worked as a berm, a bricklayer and a gardener. His first wife lived with him for more than 10 years and died of illness, leaving no children for him. Di Derrych later married Luo Jieya, and the next year their child Gauss was born, which was their only child. My father is extremely strict with Gauss, even a little excessive, and often likes to plan his life for the young Gauss based on his own experience. Gauss respected his father and inherited his father's honest and cautious character. 1806 De Derrych died, by which time Gauss had made many epoch-making achievements.
In the process of growing up, the young Gauss mainly focused on his mother and uncle. Gauss's grandfather, a stonemason, died of tuberculosis at the age of 30, leaving two children: Gauss's mother Luo Jieya and his uncle Flieder. Flieder Rich is intelligent, enthusiastic, intelligent and capable, and has made great achievements in textile trade. He found his sister's son clever and clever, so he spent part of his energy on this little genius and developed Gauss's intelligence in a lively way. A few years later, Gauss, who was an adult and achieved great success, recalled what his uncle had done for him and felt deeply important for his success. He thought of his prolific thought and said sadly that "we lost a genius" because of his uncle's death. It is precisely because Flieder Rich has an eye for talents and often persuades his brother-in-law to let his children develop into scholars that Gauss did not become a gardener or a mason.
In the history of mathematics, few people are as lucky as Gauss to have a mother who strongly supports his success. Luo Jieya didn't get married until she was 34, and she was 35 when she gave birth to Gauss. He has a strong personality, intelligence and a sense of humor. Since his birth, Gauss has been very curious about all phenomena and things, and he is determined to get to the bottom of it, which is beyond the scope of a child's permission. When the husband reprimands the child for this, he always supports Gauss and resolutely opposes the stubborn husband who wants to make his son as ignorant as he is.
Luo Jieya sincerely hopes that his son can do a great career and cherishes Gauss's talent. However, he didn't dare to put his son into mathematics research that couldn't support his family at that time. When Gauss/Kloc-was 0/9 years old, although he had made many great achievements in mathematics, she still asked her friend W.Bolyai (father of J. Bolyai, one of the founders of non-European geometry): Will Gauss have any future? W Bolyai said that her son would be "the greatest mathematician in Europe", and she was so excited that tears came to her eyes.
At the age of seven, Gauss went to school for the first time. Nothing special happened in the first two years. 1787 gauss 10 years old, he entered the class of learning mathematics, which was founded for the first time. Children had never heard of such a course as arithmetic before. The math teacher is Buttner, who also played a certain role in the growth of Gauss.
A story widely circulated all over the world said that when Gauss 10 was old, he worked out the arithmetic problem that Butner gave students by adding up all the integers from 1 to 100. As soon as Butner finished describing the topic, Gauss worked out the correct answer. However, this is probably an untrue legend. According to the research of E·T· Bell, a famous mathematical historian who has studied Gauss, Butner gave the children a more difficult addition problem: 81297+81495+81693+…+/kloc-0.
Of course, this is also a summation problem of arithmetic progression (the tolerance is 198 and the number of terms is 100). As soon as Butner finished writing, Gauss finished the calculation and handed in the small slate with the answers. E. T. Bell wrote that in his later years, Gauss often liked to talk to people about it, saying that only his answers were correct at that time, while other children were wrong. Gauss didn't explicitly say how he solved the problem so quickly. Mathematical historians tend to think that Gauss had mastered arithmetic progression's summation method at that time. It is unusual for a child as young as 10 to discover this mathematical method independently. The historical facts described by Bell according to Gauss's own statement in his later years should be more credible. Moreover, this can better reflect the characteristic that Gauss paid attention to grasping more essential mathematical methods since he was a child.
Gauss's computing ability, mainly his unique mathematical method and extraordinary creativity, made Butner sit up and take notice of him. He specially bought the best arithmetic book from Hamburg for Gauss, saying, "You have surpassed me, and I have nothing to teach you." Then Gauss established a sincere friendship with bartels, Butner's assistant, until bartels's death. They studied together and helped each other, and Gauss began real mathematical research.
1788 1 1 year-old gauss entered the liberal arts school. In his new school, all his lessons are excellent, especially classical literature and mathematics. On the recommendation of bartels and others, Duke zwick of Bren summoned Gauss, who was 14 years old. This simple, clever but poor child won the sympathy of the Duke, who generously offered to be Gauss' patron and let him continue his studies.
The Duke of Bren zwick played an important role in Gauss's success. Moreover, this role actually reflects a model of modern European scientific development, indicating that private funding was one of the important driving factors for scientific development before the socialization of scientific research. Gauss is in the transition period of privately funded scientific research and socialization of scientific research.
1792, Gauss entered Caroline College in zwick, Bren to continue his studies. 1795, the duke paid various fees for him and sent him to the famous German family in Gottingen, which enabled Gauss to study diligently and start creative research according to his own ideals. 1799, Gauss finished his doctoral thesis and returned to his hometown of Brun-zwick. Just as he fell ill for worrying about his future and livelihood-although his doctoral thesis was successfully passed, he was awarded a doctorate and obtained a lecturer position, but he failed to attract students, so he had to go back to his hometown-and the Duke reached out to help him. The Duke paid for the printing of Gauss's long doctoral thesis, gave him an apartment, and printed Arithmetic Research for him, so that the book was published in 180 1 year. It also bears all the living expenses of gauss. All this moved Gauss very much. In his doctoral thesis and Arithmetic Research, he wrote sincere dedication words: "To Dagong" and "Your kindness freed me from all troubles and enabled me to engage in this unique research".
1806, the duke was unfortunately killed while resisting the French army commanded by Napoleon, which gave Gauss a heavy blow. He was heartbroken and had a deep hostility towards the French for a long time. The death of Dagong brought economic hardship to Gauss, the misfortune that Germany was enslaved by the French army, and the death of his first wife, all of which made Gauss somewhat disheartened, but he was a strong man who never revealed his predicament to others and did not let his friends comfort his misfortune. It was only in the19th century that people learned his state of mind at that time when sorting out his unpublished mathematical manuscripts. In a discussion of elliptic functions, a subtle pencil word was suddenly inserted: "For me, it is better to die than to live like this."
The generous and kind benefactor died, so Gauss had to find a suitable job to support his family. Because of Gauss's outstanding work in astronomy and mathematics, his reputation has spread all over Europe since 1802. The Academy of Sciences in Petersburg constantly hinted that since the death of Euler in 1783, Euler's position in the Academy of Sciences in Petersburg has been waiting for a genius like Gauss. When the Duke was alive, he strongly discouraged Gauss from going to Russia. He was even willing to increase his salary and set up an observatory for him. Now, Gauss is facing new choices in his life.
In order not to lose Germany's greatest genius, B.A.Von Humboldt, a famous German scholar, joined other scholars and politicians to win Gauss the privileged positions of professor of mathematics and astronomy at the University of Gottingen and director of the Gottingen Observatory. 1807, Gauss went to Kottingen to take office, and the whole family moved here. Since then, he has lived in Gottingen except for a scientific conference in Berlin. The efforts of Humboldt and others not only made the Gauss family have a comfortable living environment, and Gauss himself could give full play to his genius, but also created conditions for the establishment of the Gottingen School of Mathematics and Germany to become the world's science center and mathematics center. At the same time, it also marks a good beginning for the socialization of scientific research.
Gauss's academic position has always been highly regarded by people. He has the reputation of "prince of mathematics" and "king of mathematicians", and is considered as "one of the three (or four) greatest mathematicians in human history" (Archimedes, Newton, Gauss or Euler). People also praised Gauss as "the pride of mankind". Genius, precocity, high yield, enduring creativity, ..., almost all praise words in the field of human intelligence are not too much for Gauss.
Gauss's research field covers all fields of pure mathematics and applied mathematics, and has opened up many new fields of mathematics, from the most abstract algebraic number theory to intrinsic geometry, leaving his footprints. He is the backbone of18-19 century in terms of research style, methods and even concrete achievements. If we imagine mathematicians in the18th century as a series of high mountains, then the last awe-inspiring peak is Gauss; If mathematicians in the19th century are imagined as rivers, then their source is Gauss.
Although mathematical research and scientific work did not become enviable occupations at the end of18th century, Gauss was still born at the right time, because with the development of European capitalism, governments all over the world began to pay attention to scientific research. With Napoleon's emphasis on French scientists and scientific research, Russian czars and many monarchs in Europe began to look at scientists and scientific research with new eyes. The socialization process of scientific research was accelerating and the status of science was constantly improving. As the greatest scientist at that time, Gauss won many honors, and many world-famous scientists regarded Gauss as their teacher.
1802, Gauss was elected as a communication academician and a professor at Kazan University by the Academy of Sciences in Petersburg, Russia; 1877, the Danish government appointed him as a scientific adviser, and this year, the Hanover government of Germany also hired him as a government scientific adviser.
Gauss's life is a typical scholar's life. He has always maintained the frugality of a farmer, making it hard to imagine that he is a great professor and the greatest mathematician in the world. He has been married twice, and several children have annoyed him. However, these have little influence on his scientific creation. After gaining a high reputation and German mathematics began to dominate the world, a generation of Tianjiao completed the journey of life.
Descartes
Generation of analytic geometry
After the 16th century, due to the development of production and science and technology, astronomy, mechanics, navigation and other aspects put forward new needs for geometry. For example, the German astronomer Kepler found that the planet orbits the sun along an ellipse, and the sun is at a focus of this ellipse; Italian scientist Galileo discovered that throwing objects tested parabolic motion. These findings all involve conic curves. To study these complex curves, the original set of methods obviously has been unsuitable, which led to the emergence of analytic geometry.
1637, the French philosopher and mathematician Descartes published his book Methodology. There are three appendices at the back of this book, one is called Refractive Optics, the other is Meteorology, and the other is called Geometry. At that time, this "geometry" actually referred to mathematics, just as "arithmetic" and "mathematics" in ancient China had the same meaning.
Descartes' Geometry is divided into three volumes. The first volume discusses ruler drawing. The second volume is the nature of the curve; The third volume is the drawing of three-dimensional and "super-three-dimensional", but it is actually an algebraic problem, discussing the properties of the roots of equations. Mathematicians and historians of mathematics in later generations all regard Descartes' Geometry as the starting point of analytic geometry.
As can be seen from Descartes' Geometry, Descartes' central idea is to establish a "universal" mathematics and unify arithmetic, algebra and geometry. He imagined that turning any mathematical problem into an algebraic problem was reducing any algebraic problem to solving an equation.
In order to realize the above assumption, Descartes pointed out the corresponding relationship between points on the plane and real number pairs (x,y) from the latitude and longitude system of astronomy and geography. Different values of x and y can determine many different points on the plane, so we can study the properties of curves by algebraic method. This is the basic idea of analytic geometry.
Specifically, the basic idea of plane analytic geometry has two main points: first, a coordinate system is established on the plane, and the coordinates of a point correspond to a set of ordered real number pairs; Secondly, after the coordinate system is established on the plane, a curve on the plane can be represented by an algebraic equation with two variables. From this, we can see that the use of coordinate method can not only solve geometric problems through algebraic methods, but also closely link important concepts such as variables, functions, numbers and shapes.
The emergence of analytic geometry is not accidental. Before Descartes wrote Geometry, many scholars studied using two intersecting straight lines as a coordinate system. Some people, while studying astronomy and geography, put forward that a position can be determined by two "coordinates" (longitude and latitude). All these have a great influence on the creation of analytic geometry.
In the history of mathematics, it is generally believed that Fermat, a contemporary French amateur mathematician with Descartes, is also one of the founders of analytic geometry and should share the honor of the creation of this discipline.
Fermat is an amateur scholar engaged in mathematical research, and has made important contributions to number theory, analytic geometry and probability theory. He is modest and quiet, and has no intention of publishing his "book". But from his correspondence, we know that he had written a small article about analytic geometry long before Descartes published Geometry, and he already had the idea of analytic geometry. It was not until 1679, after Fermat's death, that his thoughts and writings were published in the correspondence to friends.
Descartes' Geometry, as a book of analytic geometry, is incomplete, but it is important to introduce new ideas and make contributions to opening up a new garden of mathematics.
The Basic Content of Analytic Geometry
In analytic geometry, the coordinate system is first established. As shown above, two perpendicular straight lines with a certain direction and measurement unit are called a rectangular coordinate system oxy on the plane. Using the coordinate system, a one-to-one relationship can be established between points in the plane and a pair of real numbers (x,y). In addition to rectangular coordinate system, there are oblique coordinate system, polar coordinate system, spatial rectangular coordinate system and so on. There are also spherical coordinates and cylindrical coordinates in the spatial coordinate system.
Coordinate system has established a close relationship between geometric objects and numbers, geometric relations and functions, so that the study of spatial forms can be reduced to a relatively mature and easy-to-control study of quantitative relations. Studying geometry in this way is usually called analytic method. This analytical method is not only important for analytic geometry, but also for the study of various branches of geometry.
The establishment of analytic geometry introduced a series of new mathematical concepts, especially the introduction of variables into mathematics, which made mathematics enter a new development period, which is the period of variable mathematics. Analytic geometry has promoted the development of mathematics. Engels once commented on this: "The turning point in mathematics is Descartes' variables. With the change of books, the movement entered mathematics; With variables, dialectics has entered mathematics; With variables, differential and integral will immediately become necessary, ... "
Application of analytic geometry
Analytic geometry is divided into plane analytic geometry and space analytic geometry.
In plane analytic geometry, besides studying the properties of straight lines, we mainly study the properties of conic curves (circle, ellipse, parabola and hyperbola).
In spatial analytic geometry, besides the properties of plane and straight line, cylinder, cone and surface of revolution are mainly studied.
Some properties of ellipse, hyperbola and parabola are widely used in production or life. For example, the reflective surface of the spotlight bulb of a movie projector is elliptical, the filament is at one focus, and the movie door is at another focus; Searchlights, spotlights, solar cookers, radar antennas, satellite antennas and radio telescopes are all made by using the principle of parabola.
Generally speaking, analytic geometry can solve two basic problems by using coordinate method: one is to satisfy the trajectory of a given condition point and establish its equation through coordinate system; The other is to study the curve properties expressed by the equation through the discussion of the equation.
The steps to solve the problem by using coordinate method are as follows: firstly, establish a coordinate system on the plane and "translate" the geometric conditions of the trajectory of known points into algebraic equations; Then use algebraic tools to study the equation; Finally, the properties of algebraic equations are described in geometric language, and the answers to the original geometric problems are obtained.
The idea of coordinate method urges people to use various algebraic methods to solve geometric problems. Previously regarded as a difficult problem in geometry, once algebraic methods are used, it becomes unremarkable. The coordinate method also provides a powerful tool for the mechanization proof of modern mathematics.
Liu Hui
(born around AD 250) is a very great mathematician in the history of Chinese mathematics, and also occupies an outstanding position in the history of world mathematics. His masterpieces "Notes on Arithmetic in Nine Chapters" and "Arithmetic on the Island" are the most precious mathematical heritages in China.
Nine Chapters Arithmetic was written at the beginning of the Eastern Han Dynasty. * * * has solutions to 246 problems. In many aspects, such as solving simultaneous equations, calculating four fractions, calculating positive and negative numbers, and calculating the volume and area of geometric figures, it is among the advanced in the world. However, because the solutions are primitive, it lacks necessary proofs, and Liu Hui has made supplementary proofs for them. These proofs show his creative contributions in many aspects. The solution of linear equations is improved. In geometry, the "cyclotomy" is put forward, that is, a method to find the area and circumference of a circle by using inscribed or circumscribed regular polygons. He scientifically obtained the result of pi = 3.14 by using cyclotomy. Liu Hui put forward in cyclotomy that "it is fine to cut, and it is too small to cut."
In the book Island Calculations, Liu Hui carefully selected nine measurement problems, which were creative, complex and representative, and attracted the attention of the West at that time.
Liu Hui's thought is agile, his method is flexible, and he advocates both reasoning and intuition. He is the first person in China who explicitly advocates using logical reasoning to demonstrate mathematical propositions.
Liu Hui's life is a life of hard work for mathematics. Although his status is low, his personality is noble. He is not a mediocre man who seeks fame and reputation, but a great man who never tires of learning. He has left precious wealth to our Chinese nation.
Leibniz
Leibniz was the most important mathematician, physicist and philosopher in Germany at the turn of 17 and 18 centuries, and a rare scientific genius in the world. He read widely and dabbled in encyclopedias, making indelible contributions to enriching the treasure house of human scientific knowledge.
Life story
Leibniz was born in a scholarly family in Leipzig, eastern Germany. He was widely exposed to ancient Greek and Roman culture and read the works of many famous scholars, thus gaining a solid cultural foundation and clear academic goals. /kloc-When he was 0/5 years old, he went to the University of Leipzig to study law, and also read extensively the works of Bacon, Kepler, Galileo and others, and made in-depth thinking and evaluation on their works. After listening to the course of Euclid's Elements, Leibniz became interested in mathematics. /kloc-at the age of 0/7, he studied mathematics for a short time at the University of Jena and obtained a master's degree in philosophy.
At the age of 20, he published his first mathematical paper, On the Art of Combination. This is an article about mathematical logic, and its basic idea is to attribute the truth argument of the theory to the result of a calculation. Although this paper is not mature enough, it shines with innovative wisdom and mathematical talent.
Leibniz joined the diplomatic community after receiving his doctorate from Altdorf University. During his visit to Paris, Leibniz was deeply inspired by Pascal's deeds and determined to study advanced mathematics, and studied the works of Descartes, Fermat, Pascal and others. His interest has obviously turned to mathematics and natural science, and he began to study the infinitesimal algorithm, independently established the basic concepts and algorithms of calculus, and laid the foundation of calculus together with Newton. 1700 was elected as an academician of the Paris Academy of Sciences, which contributed to the establishment of the Berlin Academy of Sciences and served as its first president.
Originating calculus
/kloc-In the second half of the 7th century, science and technology in Europe developed rapidly. Due to the improvement of productivity and the urgent needs of all aspects of society, the calculus theory based on the concept of function and limit came into being through the efforts of scientists from all over the world and the accumulation of history. The idea of calculus can be traced back to the method of calculating area and volume proposed by Archimedes and others in Greece. 1665 Newton founded calculus, and Leibniz also published his works on calculus in 1673- 1676. In the past, differential and integral were studied separately as two kinds of mathematical operations and two kinds of mathematical problems. Cavalieri, Barrow, Wallis and others have obtained a series of important results of finding area (integral) and tangent slope (derivative), but these results are isolated and incoherent.
Only Leibniz and Newton really communicated the integration and differential, and clearly found the internal direct connection between them: differential and integral are two reciprocal operations. And this is the key to the establishment of calculus. Only by establishing this basic relationship can we build a systematic calculus on this basis. And from the differential and quadrature formulas of various functions, the algorithm program of * * * is summed up, which makes the calculus method universal and develops into the calculus algorithm represented by symbols.
However, there has been a heated debate in mathematics about the priority of the creation of calculus. In fact, Newton's research on calculus was earlier than Leibniz's, but the publication of Leibniz's results was earlier than Newton's. Leibniz's paper in Journal of Teachers published in 1684 10, "A wonderful type of calculation for seeking minimax", is regarded as the earliest published calculus document in the history of mathematics. Newton's first and second editions of Mathematical Principles of Natural Philosophy published in 1687 also wrote: "Ten years ago, I was with the most outstanding geometer G.
△ jules verne, a French science fiction novelist, carefully read more than 500 kinds of books and materials in order to write Adventures on the Moon. He wrote 104 science fiction novels in his life. There are 25,000 reading notes.
△ Darwin, a British naturalist and founder of the theory of evolution, traveled around the world with the research ship Beagle. He traveled overseas, studied biological remains, recorded 500,000 words of precious materials, and finally wrote the book The Origin of Species, which caused a sensation in the world, and founded the theory of evolution.
△ Chekhov, a great Russian writer, paid great attention to accumulating life materials and wrote down some things he heard, saw or thought in a notebook at any time, which was called a "life manual". Once, Chekhov heard a friend tell a joke, and he burst into tears. Laughing, he took out his "life handbook" and begged, "Please say it again and let me write it down."
△ In the room of Jack London, an American writer, strings of small pieces of paper are hung everywhere, whether on curtains, clothes hangers, cabinets, bedside and mirrors. When you look closer, it turns out that wonderful words, vivid metaphors and useful information are written on the pieces of paper. He hung pieces of paper in all parts of the room. It is to see and remember whenever and wherever you sleep, dress, shave and pace. He also carried a lot of pieces of paper in his pocket when he went out. He studied so hard and accumulated information that he finally wrote such fascinating works as Love Life, Iron Shoe and Waves.
(1), Edison had more than 1000 inventions in his life. Where did the time for these countless experiments come from? Is from often even
Out of the extreme tension of working for two days and three days. Later, he kept squeezing out time, so he would never be exhausted.
The experimental time. And became a scientist.
(2) Lu Xun disciplined himself with the motto "Time is life" and engaged in proletarian literature and art for 30 years, depending on time.
Like life, pen ploughing never stops.
(3) Balzac worked hard for 16 or 17 hours every day, even though his arm ached with fatigue.
Pain, tears in my eyes, not willing to waste a moment.
(4) Edison grasped every "today" for scientific invention and worked for more than ten hours every day, except
In order to eat, sleep and exercise, I have almost never been idle. Extending working hours every day is equivalent to prolonging life. Therefore,
On his 79th birthday, the local people called themselves 135 years old. Edison lived at the age of 85, and only published in the US Patent Office.
There are 1328 invention patents recorded, and there is an invention every 15 days on average.
(5) Qi Baishi, a master of Chinese painting, insists on painting every day and never stops except for physical discomfort. 85 years old
In, one day, after painting four paintings in succession, he painted another one specially for yesterday, and wrote an inscription: "Yesterday was stormy, and I was in a mood."
Restless, never painting, make up for it now, and don't spend a day without teaching. "
(6), "Don't teach a day to be idle", all those who have achieved something will do it. Please look at Lu Xun's last year (1936
Years), from January to October (1died on October 26th), stayed in bed for 8 months, and wrote essays and other articles.
Chapter 54, translated three chapters of the second part of Dead Soul and made two notes, replied to more than 270 letters, and gave a lot of information.
In 2000, the author read the manuscript and kept a diary when he was ill. Three days before his death, he wrote a preface to a translated novel. Six years before his death
Lu Xun has been living near Hongkou Park in Shanghai, only a few minutes' walk from his residence to the park, but
Never played in the park. This is Lu Xun, who "spends all other people's coffee drinking time at work".
Celebrity case-tolerance
During the Spring and Autumn Period, Chu Zhuangwang won the championship.
One night, I held a candlelight party with my beloved princess and gave a big feast to the ministers. The wine was half drunk when suddenly a strong wind blew out the candle. A military commander wanted to flirt with Princess Ai in the dark, and Princess Ai tore off the red tassel from his helmet. Princess Ai suggested that the King of Chu immediately light a lamp to see which guy had lost the red tassel from his helmet and severely punish him. A friend's wife should not be bullied, let alone a leader's wife. Unexpectedly, King Zhuang was magnanimous and ordered all the generals to take off the red tassels on their helmets before lighting the lamps. Soon, the king of Chu used personal expedition to go to war with the enemy, and was trapped in a tight encirclement. His soldiers would flee in all directions, and the king of Chu's life was in danger. Suddenly, a desperate battle emerged to protect deus ex, the king of Chu, and retrieve a life. The king of Chu said excitedly, "Everyone else fled for their lives, only Aiqing was willing to lay down his life to save the driver. What's your name? Which unit is it? " The general should answer, "I was the one who molested your wife at the candlelight party that day!" "
(Legend, because I can't tell the source! ) Edison made the first light bulb. He asked one of his disciples to take it to test, but he broke it! Disciples are ashamed. However, when Edison made the second light bulb, despite the opposition of others, he still gave it to the disciple to experiment. Edison said, "The greatest tolerance is to give him another chance!" "
On the day of the report, Lincoln came to the report office to take the exam. When he came to the report office, he found that the person in the prison was the one he had offended, and he finished the exam with a heavy burden. When he asked about the thing that had offended him, the man said, "Did you? I don't remember. "