Understand the growth experiences of Galileo and Newton and their scientific achievements, and write an article related to their own growth experiences

On February 15, 1564, Galileo Galilei was born in a dilapidated noble family in the city of Pisa on the west coast of Italy. It is said that his ancestor was a very famous doctor in Florence, but by the generation of his father Galileo Fansandu, the family situation was declining. Fansandu was a very talented composer. He published several pastoral and instrumental works during his lifetime. He was also good at mathematics and was proficient in Greek and Latin. However, beautiful music could not fill the belly of his family. His mathematics Talent cannot get him a good position. About not long after little Galileo was born, Fansandu opened a small shop selling woolen fabrics in Florence, not far from Pisa. This was completely a last resort. But in order to maintain the life of his family, Fansandu had to go into business against his will.

Little Galileo was the eldest son of Fansandu, and his father had great hopes for his son. He found that little Galileo was very smart and had been full of strong curiosity about everything since he was a child. Not only that, this child was very clever and he seemed to never be idle. He was either painting pictures or playing the piano, and he often did many clever things for his younger brothers and sisters. Motorized toy, fun to play with.

Little Galileo first entered the school of the Florenbrossa monastery. In this school, he concentrated on studying philosophy and religion. For a while, little Galileo wanted to be a missionary dedicated to the church in the future. But after Fansandu heard about this situation, he immediately took his son home. He persuaded Galileo to study medicine, which was a path he had already planned for his son's future.

When he was 17 years old, Galileo entered the famous University of Pisa. According to his father's wishes, he became a medical student. The University of Pisa is an old university with a rich collection of books in the school library, which is very suitable for Galileo. However, Galileo did not have much interest in medicine. He rarely attended classes. Once in class, he would raise various questions about the content of the professors' lectures. , making it difficult for the professors to answer. In the eyes of the professors, Galileo was a very unpleasant and bad student. However, Galileo was not interested in medicine. He studied mathematics, physics and other natural sciences tirelessly, and viewed with suspicion those theories that have been regarded as classics since ancient times.

You must know that the era when Galileo lived was the famous Renaissance era in European history, and Italy was the birthplace of the Renaissance. At that time, many large cities in Italy, such as Florence, Genoa and Venice, developed into centers of East-West trade. Business houses, handicraft workshops and the earliest banks were built, and the germination of capitalist production relations appeared. Coupled with the development of trade and the invention of printing, new ideas spread faster than ever before. As a result, people began to waver in the religious theology and traditional dogmas that had bound their minds for thousands of years.

By chance, Galileo listened to a lecture by the court mathematician Matthew Leach. Galileo was deeply fascinated by this young mathematician's profound knowledge, rigorous logic, and especially his method of proving mathematical problems. His eyes lit up, as if he had discovered a magical world. This was the mathematical kingdom he had dreamed of! He was so excited that he immediately found the court mathematician Matthew Leach and asked him many puzzling questions.

Matthew Leach originally came to Pisa from Florence with the Grand Duke of Tuscany. He taught mathematics to the page boys in the palace. He did not expect that there would be an enthusiastic audience, and he proposed The questions are very interesting and fully demonstrate his superior wisdom and profound knowledge.

When Matthew Leach heard that Galileo was a medical student at the University of Pisa, he couldn't help blurting out: "Ah, Galileo, you have a genius, you will become an outstanding mathematician."

Galileo's face turned red. He talked about his boredom with medicine, his father's expectations of him, and his distress because he could not study as he wished.

"Don't be discouraged." Matthew Leach said kindly: "You should study hard on your own. If you have any difficulties, I will be your loyal friend at any time."

Listen With the encouragement of Matthew Leach, Galileo studied mathematics and physics more diligently. He read every book borrowed from the court mathematician with great concentration and absorbed it like a sponge absorbing water. However, he was not the kind of person who was superstitious about books. Those authoritative conclusions that people thought were truths often brought unexpected questions to Galileo's mind. He often felt distressed by this and fell into deep thinking.

Once, Galileo strolled to the Cathedral of Pisa, which he was familiar with. He sat on a bench and stared at the beautifully carved altar and arched columns. Suddenly, in the center of the church hall, The huge lamp swayed, and it was the house repair workers who were installing the chandelier there.

This was a very ordinary thing. The chandelier swayed like a pendulum, drawing an invisible arc in the air. However, Galileo followed the swinging chandelier intently as if he had been electrocuted. At the same time, he pressed the pulse of his left wrist with his right hand and counted the number of pulse beats per swing of the chandelier to calculate the time of the swing of the chandelier.

As a result of this calculation, Galileo discovered a secret. This is that the time it takes for the chandelier to swing once is always the same regardless of the size of the arc.

At first, the chandelier swung vigorously, and gradually it slowed down, but the number of pulse beats was the same every time it swung.

Galileo's mind was spinning. He thought that the book clearly stated that the pendulum passed through a short arc faster than a long arc. This was the ancient Greek philosopher Aristotle. No one has doubted De's statement. Is there something wrong with my eyes or something else.

He ran back to the university dormitory like a madman, closed the door and repeated the experiment. He found ropes and chains of different lengths, as well as iron balls and wooden balls that he didn't know where to get. On the roof, on the branches outside the window, I repeat it again and again obsessively, recording the swing time with the hourglass. In the end, Galileo had to boldly conclude that Aristotle's conclusion was wrong. What determines the swing period is the length of the rope and has nothing to do with the weight of the object at its end. Moreover, the vibration periods of pendulum ropes of the same length are the same. This is the law of motion of the pendulum discovered by Galileo.

Needless to say, Galileo was very happy. But at that time, who would believe the scientific discovery of a medical student, not to mention that his conclusion denied the authoritative statement of the famous Aristotle.

At this moment, Fansandu's shop became increasingly depressed. Hearing that Galileo did not study medicine according to his own wishes, but was obsessed with irrelevant experiments all day long, so he severely His father decided to stop Galileo from going to college and let him go home and work as a clerk.

Galileo was so discouraged that he left the University of Pisa and returned to Florence. But the path he chose was unshakable.

Believe in science

In a not-so-busy street in Florence, there is a shop with a small appearance and light business. This is the woolen fabric shop opened by Fansandu. Every day, when pedestrians pass by here in a hurry, you can always see the red-haired Galileo sitting at the counter in a daze, or playing with some inexplicable things there like scales, iron blocks, and plates as if no one else is around. Yeah; and more often than not, he was immersed in books. He was so focused on reading that he couldn't even hear his father shouting loudly.

Since returning home, Galileo had to work as a clerk in his father's shop against his will, but he never forgot mathematics and physics in his heart. Without the minimum learning conditions and no teachers to ask for advice, he tried every means to find some books on natural sciences and studied hard on his own with tenacious perseverance. His favorite books were Euclid's Elements and the works of Archimedes.

"Elements" is the earliest geometric work handed down in the world, and the works of the Greek scientist Archimedes contain a wealth of mathematical and mechanical knowledge, especially some of the physical experiments, which are very important to Galileo had great appeal.

When it came to experiments, Galileo was the most interested. When he was still at the University of Pisa, he started making a "pulse meter", which he designed based on the movement patterns of a pendulum. It could be used to measure the patient's pulse beat and was very popular with doctors. welcome. Now, in his father's shop, there are no conditions for experiments, but he still uses some daily utensils to conduct experiments. Although doing so will inevitably be scolded by his father, he still does it.

He was inspired by Archimedes' experiment of testing the king's crown. While repeating the experiment, he thought of the use of this method. At that time, the navigation industry in European countries was on the rise. The navigation industry drove the development of shipbuilding, machinery manufacturing, mining, and metallurgy, which in turn raised many new questions for science and technology. Galileo then turned his attention to the study of the physical and mechanical properties of alloys. Soon, he found by measuring the weight of an object in water that the weight lost by an object put into water was exactly equal to the weight of the water it displaced. On the basis of this important discovery, Galileo invented a specific gravity scale that could easily measure the specific gravity of various alloys. He also wrote a paper describing in detail the construction principles and usage of the hydrometer. This incident soon spread in Florence and other cities.

In the summer of 1589, Galileo, who had spent 4 years of self-study in a shop in Florence, received encouragement from the court mathematician Matthew Leach, especially the recommendation of the noble Marquis of Gatbolto. He finally secured a position as professor of mathematics and science at the University of Pisa. At this time, he was only 25 years old.

Now, Galileo no longer has to worry about life. Although the salary is not high, he can concentrate on the scientific research he yearns for in addition to completing daily teaching. Not long after this, Galileo conducted the free fall experiment introduced at the beginning of this article. The iron ball he dropped from the Leaning Tower of Pisa (it was later rigorously proven that Galileo did not come to the Leaning Tower of Pisa to conduct the experiment) not only proved Objects of different weights have the same speed when falling from the same height. More importantly, this bold conclusion overturns Aristotle's authoritative conclusion. In the eyes of those conservative and rigid-minded people, this move was tantamount to digging their ancestral graves. Aristotle's followers and Galileo began to be at odds with each other. After a semester at the University of Pisa, Galileo lost his position again. The reason was that he had offended a relative of the Grand Duke, Giovanni.

This Giovanni was an uneducated man. He claimed to have invented a dredger and came to ask Galileo for advice. When Galileo carefully observed the model of the dredger, he bluntly told him that the design did not comply with scientific principles and could not be used at all. Giovanni was frustrated. Not only did he not accept Galileo's opinion, but he stubbornly insisted on launching the experiment. As a result, the ship sank. Facts proved that Galileo's judgment was completely correct, but the angry Giovanni turned his anger on Galileo, spread rumors, and attacked him as an "insidious person." Those followers of Aristotle who had been dissatisfied for a long time took the opportunity to attack him violently, causing uproar in the city. In this atmosphere, Galileo could no longer stay at the University of Pisa.

Galileo once again turned to the Marquis of Getterbotu for help. This nobleman who cherished talents once again extended a hand of friendship. He used his influence to recommend Galileo to the University of Padua. Padua is a small city with a strong academic atmosphere in northern Italy, not far from the beautiful coastal city of Venice. , under the jurisdiction of the Republic of Venice. In 1592, at the age of 28, Galileo was appointed professor of mathematics, science and astronomy at the University of Padua.

Since then, Galileo ushered in a golden age in his life.

Afterwards, Galileo continued his scientific research at the court in Florence, but his astronomical discoveries and his astronomical writings clearly reflected Copernicus' heliocentric views. As a result, Galileo began to attract the attention of the church. Beginning in 1616, Galileo began to be brutally persecuted by the Roman Inquisition for more than 20 years.

Galileo's later life was very miserable. His daughter Celeste, who took care of him, died before him. The grief of losing his beloved daughter made Galileo blind. Even under such conditions, he still did not give up his scientific research work.

At 4 o'clock in the morning on January 8, 1642, the great Galileo, a warrior who fought for science and truth all his life, passed away at the age of 78. On the eve of his death, he repeated this sentence: "The pursuit of science requires special courage."

Young Newton

January 4, 1643, in Lincoln, England Newton was born in a yeoman family in the county town of Walsop. Newton was a premature baby, weighing only three pounds at birth, and his midwives and his relatives were worried about whether he would survive. No one expected that this seemingly insignificant little thing would become a scientific giant that shocked the past and the present, and lived to the age of 84.

Newton's father died three months before he was born. When he was two years old, his mother remarried a priest and left Newton to be raised by his grandmother. When she was 11 years old, her mother's step-husband passed away, and her mother returned to Newton with her son and two daughters. Newton was taciturn and stubborn since he was a child. This habit may come from his family situation.

From about the age of five, Newton was sent to public schools. Newton was not a child prodigy when he was a boy. He had ordinary qualifications and average grades like Newton in his childhood. But he liked reading and read books that introduced various simple mechanical model making methods, and was inspired by them to make some weird things by himself. Gadgets such as windmills, wooden clocks, folding lanterns and more.

Legend has it that after Newton figured out the mechanical principles of the windmill, he made a model of a mill. He tied a mouse to a wheeled treadmill, and then placed a wheel in front of it. Grains of corn happen to be out of reach of mice. The mouse wanted to eat the corn, so it kept running, so the wheel kept turning; once again when he was flying a kite, he hung a small light on the rope. At night, the villagers looked at it and suspected that it was a comet; he also made a small water clock. . Every morning, the small water clock will automatically drip water on his face to urge him to get up. He also liked painting and sculpture, and especially carving sundials. He placed sundials he carved everywhere in the corners and windowsills of his home to observe the movement of the sun's shadow.

When Newton was 12 years old, he entered Grantham Middle School not far from home. Newton's mother originally wanted him to become a farmer, but Newton himself had no intention of doing this and loved reading instead. As he grew older, Newton became more and more fond of reading, meditating, and doing small scientific experiments. When he was studying at Grantham High School, he stayed at the home of a pharmacist, which exposed him to chemical experiments.

Newton did not have outstanding academic performance in middle school. He just loved reading and was curious about natural phenomena, such as color, the movement of sun and shadow in the four seasons, especially geometry, Copernicus' heliocentric theory, etc. He also keeps reading notes by category, and likes to make creative gadgets, tricks, inventions, and experiments.

At that time, new Christian ideas were permeating British society. Newton's family had two relatives who were both priests, which may have affected Newton's religious life in his later years. From these ordinary environments and activities, it is not obvious that the young Newton was a child with outstanding talents and extraordinary talents.

Later, due to the pressure of life, his mother asked Newton to drop out of school and work at home to support the family. But Newton buried himself in his books whenever he had the chance, and often even forgot to work. Every time his mother asked him to go to the market with his servant to familiarize himself with the business, he would beg the servant to go to the street alone while he hid behind the bushes and read a book.

Once, Newton's uncle became suspicious and followed Newton to the town. He found his nephew lying on the grass with his legs stretched out and he was concentrating on a mathematical problem. Newton's studious spirit moved his uncle, so his uncle persuaded his mother to let Newton resume school and encouraged Newton to go to college. Newton returned to school again, eagerly absorbing the nutrition from the books. It is said that one time, he went to the countryside to play, and then rested under an apple tree. Suddenly, an apple fell from the tree. He thought it was strange, why did the apple fall from top to bottom instead of rising from bottom? He returned home to study with this question, and later he discovered through demonstration that the earth has gravity and can attract objects. Subsequently, "Newton's Physics of Gravitation" appeared.

School years

In 1661, 19-year-old Newton entered Trinity College, Cambridge, as a reduced-fee student. He paid for his tuition with the income from doing chores for the college. In 1664, he became a scholarship student. Recipient, received his bachelor's degree in 1665.

In the mid-17th century, the education system of Cambridge University was still permeated with a strong flavor of medieval scholasticism. When Newton entered Cambridge, some scholastic courses were still taught there, such as logic, ancient Chinese, grammar, and ancient times. History, theology, etc. Two years later, a new trend emerged at Trinity College. Lucas created an original lecture course, which provided for the teaching of natural science knowledge, such as geography, physics, astronomy and mathematics.

The first professor of the lecture, Isaac Barrow, was a learned scientist. This scholar had a unique insight and saw that Newton had profound observation and keen understanding. So he taught Newton all his mathematical knowledge, including methods of calculating the area of ??curved figures, and led Newton to the research field of modern natural sciences.

During this learning process, Newton mastered arithmetic and trigonometry, and read Kepler's "Optics", Descartes's "Geometry" and "Principles of Philosophy", and Galileo's "The Two Worlds" "Systematic Dialogue", Hooke's "Micrographia", as well as the history of the Royal Society and early philosophical transactions, etc.

Newton's time under Barrow was a critical period for his learning. Barrow was 12 years older than Newton and was proficient in mathematics and optics. He greatly admired Newton's talent and believed that Newton's mathematical talent exceeded his own. Later, Newton recalled: "Dr. Barrow was teaching courses on kinematics. Perhaps it was these courses that prompted me to study this aspect."

At that time, Newton was very big in mathematics. The degree is dependent on self-study. He studied the works of many mathematicians such as Euclid's "Elements of Geometry", Descartes's "Geometry", Wallis's "Infinite Arithmetic", Barrow's "Lectures on Mathematics" and Veda. Among them, Descartes's "Geometry" and Wallis's "Infinite Arithmetic" had a decisive influence on Newton. They quickly led Newton to the forefront of mathematics at that time - analytic geometry and calculus. In 1664, Newton was elected as Barrow's assistant. The next year, the Cambridge University Senate passed the decision to award Newton a bachelor's degree from the University.

A severe plague swept London from 1665 to 1666. Cambridge was not far from London. For fear of spreading the disease, the school was closed. Newton left school and returned home in June 1665.

Because Newton was influenced and trained in mathematics and natural sciences at Cambridge, he developed a strong interest in exploring natural phenomena. The quiet environment of his hometown allowed his thoughts to spread. The short period of time from 1665 to 1666 became the golden years of Newton's scientific career. He was full of ideas and talents in the field of natural sciences, thinking about problems that his predecessors had never thought about, and entering fields that had not been touched by his predecessors. Created unprecedented and amazing results.

In early 1665, Newton created the series approximation method and the rule for converting binomials of any power into a series; in November of the same year, he created the positive flow method (differential calculus); in January of the following year , used prisms to study color theory; in May, began to study the reflux number method (integration). Within this year, Newton began to think of studying the problem of gravity and wanted to extend the theory of gravity to the orbit of the moon. He also deduced from Kepler's laws that the forces keeping the planets in their orbits must be inversely proportional to the square of their distance from the center of rotation. The legend that Newton realized the gravity of the earth when he saw an apple falling to the ground also tells an anecdote that happened at this time.

In short, during the two years he lived in his hometown, Newton engaged in scientific creation and cared about natural philosophy issues with more energy than at any time since. His three major achievements: calculus, gravitation, and optical analysis were all conceived at this time. It can be said that Newton at this time had already begun to draw the blueprint for most scientific creations in his life.

Shortly after Easter 1667, Newton returned to Cambridge University. On October 1, he was elected as a junior fellow (junior member) of Trinity College. He received his master's degree on March 16 of the following year, and at the same time Become a principal couple (senior committee member). On October 27, 1669, Barrow resigned as professor in order to support Newton. Newton, 26, was promoted to professor of mathematics and served as the Lucas Lecture Professor. Barrow paved the way for Newton's scientific career. Without the help of Newton's uncle and Barrow, Newton, the thousand-mile horse, might not be galloping on the road of science. Barrow gave way to the wise, which has always been a legend in the history of science.

Great achievement ~ the establishment of calculus

Among Newton's all scientific contributions, mathematical achievements occupy a prominent position. The first creative achievement of his mathematical career was the discovery of the binomial theorem. According to Newton's own recollection, he discovered this theorem in the winter of 1664 and 1665 when he was studying Dr. Wallis's "Infinite Arithmetic" and trying to modify his series for finding the area of ??a circle.

Descartes' analytic geometry corresponds the functional relationships describing motion to geometric curves. Under the guidance of his teacher Barrow, Newton found a new way out based on studying Descartes' analytic geometry. The speed at any moment can be regarded as the average speed in a small time range. This is the ratio of a small distance to the time interval. When this small time interval shrinks to infinitesimal, it is the accurate value of this point. . This is the concept of differentiation.

Finding the differential is equivalent to finding the tangent slope at a certain point based on the relationship between time and distance. The distance traveled by a variable-speed moving object in a certain time range can be regarded as the sum of the distances traveled in tiny time intervals. This is the concept of integration. Finding the integral is equivalent to finding the area under the curve that relates time to velocity. Starting from these basic concepts, Newton established calculus.

The creation of calculus is Newton's most outstanding mathematical achievement. In order to solve the problem of motion, Newton created this mathematical theory that is directly related to physical concepts. Newton called it "fluid mathematics". Some of the specific problems it handles, such as tangent problems, quadrature problems, instantaneous velocity problems, and maximum and minimum value problems of functions, have been studied before Newton. But Newton surpassed his predecessors. He stood at a higher perspective, synthesized the scattered conclusions in the past, and unified the various techniques for solving infinitesimal problems since ancient Greece into two common types of algorithms - differential and integral. The reciprocal relationship between these two types of operations was established, thereby completing the most critical step in the invention of calculus, providing the most effective tool for the development of modern science, and opening up a new era in mathematics.

Newton did not publish the research results of calculus in time. He may have studied calculus earlier than Leibniz, but the expression form adopted by Leibniz was more reasonable, and his works on calculus were published. It's also earlier than Newton.

When Newton and Leibniz argued about who was the founder of this discipline, a violent quarrel was caused. The family feud lasted for a long time, resulting in a long-standing antagonism between continental European mathematicians and British mathematicians. For a period of time, British mathematics was closed to the country, limited by national prejudices, and stagnant in Newton's "fluid mathematics". As a result, the development of mathematics lagged behind for a hundred years.

It should be said that the creation of a science is by no means the performance of one person. It must be the result of the efforts of many people and the accumulation of a large number of results, and finally summarized by one or several people. Completed. The same is true for calculus, which was independently established by Newton and Leibniz on the basis of their predecessors.

In 1707, Newton's algebra lectures were compiled and published as "Universal Arithmetic". He mainly discusses the basics of algebra and its application (by solving equations) to solving various types of problems. The book states the basic concepts and basic operations of algebra, uses a large number of examples to illustrate how to turn various problems into algebraic equations, and conducts in-depth discussions on the roots and properties of equations, leading to fruitful results in equation theory, such as: He derived the relationship between the roots of an equation and its discriminant, and pointed out that the coefficients of the equation can be used to determine the sum of the powers of the roots of the equation, which is the "Newton Power Sum Formula".

Newton contributed to both analytic geometry and synthetic geometry. He introduced the center of curvature in "Analytical Geometry" published in 1736, gave the concept of a close line circle (or curved circle), and proposed a curvature formula and a method for calculating the curvature of curves. He summarized many of his research results into a monograph "Enumeration of Cubic Curves", published in 1704. In addition, his mathematical work also involves many fields such as numerical analysis, probability theory and elementary number theory.

Newton's later years

However, due to limitations of the times, Newton was basically a metaphysical mechanical materialist. He believes that motion is only mechanical motion, and Newton's tomb is a change in spatial position; the universe, like the sun, has no development and change; relying on the action of gravity, stars are always in a fixed position...

As his scientific reputation grew, so did Newton's political status. In 1689, he was elected university representative in Parliament. As a member of Parliament, Newton gradually began to distance himself from the science that had brought him so much success. From time to time he expressed his distaste for the field he represented. At the same time, he spent a lot of time arguing about scientific priorities with famous scientists of his generation such as Hooke and Leibniz.

In his later years, Newton lived a grand life in London. In 1705, he was made a peer by Queen Anne. Newton was very wealthy at this time and was generally regarded as the greatest living scientist. He served as President of the Royal Society, and during his twenty-four years he ruled the Society with an iron fist. No one can be elected without his consent.

In his later years, Newton began to devote himself to the study of theology. He denied the guiding role of philosophy, believed in God devoutly, and immersed himself in writing books on theology. When he encountered unexplainable celestial motions, he came up with "divine first impetus." He said, “God rules over all things, and we are His servants who fear and worship Him.”

On March 20, 1727, the great Isaac Newton passed away. Like many other distinguished Englishmen, he is buried in Westminster Abbey. His tombstone is engraved with:

Let people hail such a great one

The glory of mankind once existed in the world.