The soul flies on a rainy night

The night sky is shrouded in rolling dark clouds, and the whole sky is so dark that you can’t see your fingers; gusts of strong wind roar past, as if being shaken by a huge madman The branches swayed this way and that; heavy rain poured down, and the whole universe was filled with the sound of wind and rain, making this late summer night even more boring and breathless!

At this time, on a road On a small road, a carriage left Paris, France, speeding towards the suburbs in the rain. The sound of horse hooves and the sound of splashing water from racing wheels were all lost in the sound of wind and rain. The two people sitting in the car hope to reach their destination quickly and rescue the critically ill scientist Pascal. Lightning flashed in the sky, reflecting the words on the road sign: Go to the theological center Pili Al. Then, several deafening thunders resounded through the sky!

Blaise Pascal

Located in the theological center on the outskirts of Paris, it is a magnificent church-like building. It is a place dedicated to cultivating talents who study theology. The two pointed bell towers are hidden in the heavy rain. The carriage stopped at the door of the theological center, and jumping out of the carriage were Pascal's old servant Le Verrier and the famous doctor Peso invited by him. The two hurried down the corridor and into Pascal's bedroom. When Le Verrier saw Pascal dying. He rushed to the bed, shook Pascal's arm, and called his master's name. Pascal, who was lying on his back, suddenly opened his eyes, looked at the doctor standing beside the bed, pointed at the experimental instruments scattered on the table, and pointed at the statue of a god hanging on the wall, then tilted his head slowly and feebly. He turned to one side and stopped breathing. The clock tower rang with bursts of bells. The bells were sad and trembling, passing through the rain clouds and spreading to all directions. Dr. Peso glanced at the calendar on the wall: August 19, 1662, and the clock pointed at zero o'clock. Then he sighed and said, "You are too young to die at the age of 39." But the doctor was puzzled by what Pascal meant by pointing here and there before he died. When the doctor further examined Pascal's body, he found that there was a hand-wide belt around his waist, which was covered with iron thorns. The tips of the thorns were pointed at the muscles. In some places, the flesh was bloody; Inflammation and suppuration, pungent smell. A cloud of doubt arose in Dr. Peso's mind, and he asked Le Verrier: "What's going on?"

The 65-year-old servant Le Verrier sadly recalled the past: "June 1623 AD. Pascal was born in Clermont-Ferrand. His father was a tax collector in his hometown. He was very good at mathematics. Under his father's education, Pascal studied hard and got good grades when he was 13 years old. He sat at the table every day, writing, calculating, and studying non-stop. As a result, he discovered the law of binomial expansion coefficients-Pascal's triangle. When he was less than 16 years old, he discovered a basic principle of projective geometry. He used After more than a year of research on this principle, more than 400 inferences were derived. These were considered a great contribution to the mathematics world at that time, and a young man was emerging.

When he was 19 years old, He has grown into a promising young man. Seeing that his father had to perform very complicated calculations every day and it was very hard, he decided to develop a calculator to replace his father's labor. After research, he used a gear to represent numbers. Properly matched, the gear representing the lower digit rotates once for every ten turns, which solves the carry problem and creates a hand that can perform addition and subtraction operations. Shake the calculator. (In a sense, this is the world's first digital calculator!) I remember that on the first day when I used the machine, Pascal's residence was surrounded by people who came to visit, all coming to see what it could do. A machine that improved manual efficiency several times. Soon, this kind of machine was widely used throughout France." At this point, Le Verrier was proud of his master's many achievements, and his sadness disappeared. : The doctor kept nodding his head as he listened, expressing his admiration for Pascal's achievements.

"I heard that Pascal also studied some law. Do you understand the process of this matter?" the doctor asked.

"Understood. I have been a servant in Pascal's family since I was 20 years old. I watched Pascal grow up and know many things." Le Verrier continued talking happily. [5]

The inspiration of the bucket

“I remember one day when Pascal was 23 years old, I brought a bucket full of water into the house. This phenomenon attracted Pascal. He wouldn't let me carry the bucket away. When the water ran out, he asked me to carry more water and observe again. In those days, he was too busy to eat or sleep. ." Le Verrier looked proud when he talked because he also participated in this experiment. He looked at the doctor and continued.

"The bucket gave Pascal a great inspiration. Later he told me that the deeper the hole in the side wall of the bucket is from the water surface, the greater the pressure and the greater the speed of water flowing out. After a while One day, Pascal designed and made a complete wooden barrel. The lid was sealed on the barrel and a small hole was opened in the center of the lid. After the barrel was filled with water, there was no abnormality in the barrel. A long thin iron pipe is inserted into the small hole of the wooden barrel to make the joint watertight. Then a few cups of water are poured from the top of the pipe to raise the water level in the pipe by several meters. When the water in the pipe reaches a certain height, Do you think it's strange that the barrel cracked? Later, Pascal summarized the rules and wrote a paper, which is called Pascal's law.

I heard that someone is using this law to develop a hydraulic press!" Le Verrier paused and added: "Oh, he also developed mathematical induction. He also likes literature very much. The two literary works he wrote, "Thoughts" and "Letters to Foreigners," are recognized as literary masterpieces in Europe!" Since doctors are busy treating patients every day, they are very interested in Pascal, a talented and scientific person. Although I have heard about the deeds of the legendary figure, I have not heard about it in detail. After listening to Le Verrier's introduction today, I not only have more respect for Pascal, but also respect the old servant of Le Verrier. But about the belt and Pascal. He was still confused about his actions before his death, so he asked in a more respectful tone: "Can you please tell me about the belt Pascal was wearing? Thank you. ”

Although Le Verrier felt that the doctor had spoken to him in a more polite tone, his expression changed when he heard the doctor ask about it...[6]

Belt Mystery

"The occurrence, development and result of an event are related to each other to a certain extent, are you right?" What surprised the doctor was that the experienced old servant Jing He was very impressed by his ability to speak such philosophical words, and he nodded in agreement hurriedly.

"Most people living in our time believe in religion and respect the Bible. . Copernicus published "On the Revolutions of the Celestial Spheres" in 1543, advocating the heliocentric theory. Indeed, in that era, whoever said that the sun did not move around the earth and that the earth was not stationary would definitely conflict with the church; it would also conflict with Aristotle's theory of motion that everyone recognized. , in this respect, Copernicus was a very brave man. "

The doctor felt that this old servant had spent time with the great man Pascal and was already a knowledgeable person. However, he was eager to continue the conversation, so he asked: "Then What’s the other side? Why didn’t the church ban the books written by Copernicus?”

“Copernicus wrote at the beginning of his book: Copernicus dedicated it to Pope Paul III, He also quoted the opinions of the ancient Pythagoreans, who believed that the earth was in motion. As for issues that were inconsistent with the Bible, he avoided talking about them, and so on. Later, in order to defend and develop the heliocentric theory, Galileo wrote the book "Dialogue". It was not until he was sentenced to death by the church in 1632 that the church truly discovered that the works of Copernicus and Galileo were in direct opposition to the church's views. This was very important to the church. Said it was absolutely prohibited. Pascal was born and grew up in this social background. As Pascal continued to contribute to scientific research, he always felt the ghosts of the Church and God lingering in his thoughts. Many scientific theories and laws of things are very contradictory to religious teachings. The more I study them, the more difficult I feel to move forward.

He once told me that he was very distressed. Sometimes he doubted whether he was following in the footsteps of Galileo, he also doubted whether his research direction was wrong, and so on. Later, he decided to reconcile religious belief with mathematical rationalism and become one. In fact, he still mainly believes in religion in his thoughts. Pascal's life experience proved that this would not work. Therefore, he was tired of mathematics and physics and decided to give up scientific research and study theology exclusively. In order to concentrate on practicing religion, he not only moved from his residence to the theological center, but also specially made a spiked belt to wrap around his waist. Once he discovered that he had any evil thoughts such as being ungrateful to God or wanting to concentrate on studying science, he would Then he punched the belt to sting the flesh.

Due to long-term ideological distress, poor health, and various serious illnesses, he was unwilling to actively treat them, so he tortured himself on the wrong path and destroyed himself. No matter what a person does, he will not be able to do it without a firm and correct idea, and neither will he be able to achieve harmony and swing. "The doctor opened his eyes wide and listened to Le Verrier's incisive analysis word for word. He understood the mystery of the belt; he also understood Pascal's actions before his death. They refer to two opposite things, science and Religions have never been able to be reconciled together, and it is a pity to die!

The rain stopped in the courtyard, the wind stopped, and the sky was bright. The trees, houses, grass, and sky seemed to have taken a bath. A refreshing feeling. Everything in the universe is constantly moving with a new look. [6]

The meaning of the tombstone

One day in late autumn five years later, Lao Le. Weyer used a cane and led his six-year-old grandson to Pascal's tomb in slow steps. With infinite nostalgia, he paid homage to the owner in the tomb. The grandson asked curiously: "Grandpa, on that big stone tablet." What is it written on? Is it a table carved on it?" "It is written on the stone:

The tomb of the writer, mathematician, and physicist Pascal

1623.6.19-1662.8.19

“The tombstone is engraved with a table, and a piece of paper is engraved on it, which means it is approximately equivalent to a piece of paper with an area of ??1 cm and a mass of 1 The pressure of a gram of material on the tabletop is an internationally accepted unit of pressure, called 1 Pascal, which is often said to be '1 Newton of pressure per square meter.'"

"Why not the statue in front of the tombstone? Is it engraved on the stone tablet? Why is the pressure unit called Pascal?" The little grandson didn't understand the second half of Fang's answer.

“In order to commemorate Pascal’s contribution, the world customized the pressure unit after his name.

The results of his scientific research are engraved on the stone tablet, and the statues of gods cannot and cannot be engraved on the same stone tablet. "Old Le Verrier didn't care whether his grandson understood it or not, and slowly led him away. At this time, bursts of crickets chirped in the grass in the cemetery. [6]

Triangle Pascal's father thought that studying mathematics was harmful to the body, so he hid all the mathematics books at home and did not allow his friends to talk about mathematics in front of Pascal. He only let Pascal read a lot. His father's approach aroused Pascal's interest in mathematics. One day he asked his father what geometry was, and his father simply said, "Geometry is." "Teach people to make correct and beautiful pictures when drawing." So Pascal took chalk and drew various shapes on the ground. As he drew, the 12-year-old Pascal discovered that the sum of the interior angles of any triangle is 180 degrees. When he told his father about this discovery, his father was so excited that he burst into tears and took out all his mathematics books for Pascal to read. Under his father's careful education, Pascal became proficient in Euclidean geometry at a very young age and independently studied it. He discovered Euclid's first 32 theorems, and the order was completely correct. Later, through continuous self-study and exploration, Pascal became a very accomplished mathematician, physicist and philosopher.

At that time. The 12-year-old Pascal seemed to be talking to himself or telling his father something important: "The sum of the three interior angles of a triangle is two right angles. ” [2] Question: How did Pascal prove it? Let’s take a look:

The four corners of a rectangle are all right angles, and the sum of the four angles of a rectangle must be 360°. Put the edges of the rectangle opposite When the angle line is divided into two, it becomes two right-angled triangles. The sum of the interior angles of each right-angled triangle is 360 divided by 2, which is equal to 180 degrees. Any right-angled triangle can be regarded as a rectangle cut, so any right-angled triangle. The sum of the interior angles must be 180 degrees. Any acute triangle can be divided into two right triangles along the height. The sum of the two right triangles is 18180=360 degrees, and two of the right angles join together to form a straight line, so The sum of the three interior angles of an acute triangle is 360-90-90=180 degrees. The same principle can be used to explain that the sum of the interior angles of an obtuse triangle is also 180 degrees.