Newton1643 65438+1October 4th (julian calendar1642 65438+February 25th) was born in a yeoman family in Thorpe, urs, a small town in the east of England. My father died of pneumonia eight or nine months before he was born. Thin since childhood, withdrawn and stubborn. At the age of 3, my mother remarried and was raised by my grandmother. 1 1 years old, her stepfather died, and her mother went home to farm with three younger brothers and sisters. In the unfortunate family life, Newton's grades in primary school were very poor. He "showed no talent except designing machinery."
Newton loved nature since childhood and liked to use his head and hands. When he was 8 years old, he saved some change to buy a hammer and a saw to do manual work. He especially likes to carve sundials and use the projection of sticks on them to show the time. Legend has it that he carved sundials everywhere in the corner and windowsill of his house. He also made a sundial and put it in the middle of the village. It was called "Newton Clock" and was used for several years after Newton's death. He also made bicycles with pedals; Make a dripping clock with a small wooden barrel; Flying homemade kites with small lanterns (people think comets appear); Made a mill model powered by a little mouse, and so on. The most vivid example of his observation of nature is his first experiment when he was 15 years old: in order to calculate the wind and speed, he chose to jump with the wind and against the wind when the wind was strong, and then measured the distance difference between the two jumps. When Newton was studying in Grantham Middle School, he stayed in Clark Pharmacy in Grantham Town, which cultivated his habit of doing scientific experiments, because the pharmacy was a chemical laboratory at that time. Newton arranged natural phenomena in his notes, including color matching, clocks and watches, astronomy, geometry and so on. These flexible learning methods laid a good foundation for his later creation. Newton once stopped studying and farming because of his poor family. During this period, he spent all his time teaching himself. He can't let go of herding sheep, shopping and farming, and he doesn't even know that sheep have eaten other people's crops. His uncle, a priest, once found Newton studying mathematics and supported him to continue his studies. 1661June was admitted to Trinity College, Cambridge University. As a "fee-reducing student" who receives subsidies, he must undertake the task of serving some rich children. Professor isaac barrow of Trinity College (1630 ~ 1677) was the first professor to give a new lecture on natural science (Lucas lecture) by reforming the educational model. Known as "the best scholar in Europe", he was particularly fond of Newton, which made him read many excellent works of predecessors. Newton was elected as Barrow's assistant in 1664, and graduated from the university in 1665.
From 1665 to 1666, Newton returned to his hometown during the two years of plague epidemic in London. Newton was brilliant in the past two years and made many inventions. /kloc-0 returned to Cambridge university in June 667, and obtained the master's degree in July 668. 1669, Barrow recommended 26-year-old Newton to replace Professor Lucas, 1672 became a member of the Royal Society, and 1703 became the lifelong president of the Royal Society. 1699 Director of Mint. 170 1 year, he resigned from Cambridge university. He was knighted on 1705 for his contribution to the reform of the currency system. Newton died in Kensington on 1727, and his body was buried in Westminster Abbey.
Newton's great achievements are inseparable from his efforts and diligence. His assistant H. Newton said, "He seldom goes to bed before two or three o'clock, and sometimes works until five or six o'clock. I often live in the laboratory for five or six weeks in spring and autumn until I finish my experiments. " He has a habit of persisting for a long time and concentrating on solving a problem completely. When answering people's questions about his insight into things, he said "keep thinking". This is his main feature. There are many stories about this: when he was young, he once led a cow up the mountain and read a book, only to find that there was only one rope in his hand when he got home; Cooking eggs regularly while reading will cause the watch and eggs to boil together in the pot; Once, he invited a friend to dinner at home, but he worked in the laboratory and forgot to eat or sleep. Repeatedly urged, he still didn't come out. When a friend finished eating a chicken and there was a pile of bones left on the plate, Newton remembered, but after seeing the bones on the plate, he suddenly said, "I thought I didn't eat, so I have already eaten."
Newton's achievements were most completely summarized by Engels in England in the18th century: "Newton founded scientific astronomy because he invented the law of universal gravitation, scientific optics because he decomposed light, scientific mathematics because he founded binomial theorem and infinite theory, and scientific mechanics because he knew the nature of force". (For details of Newton's achievements in establishing the law of universal gravitation and classical mechanics, please refer to the relevant items in this manual). The achievements in mathematics, optics and philosophy (methodology) are emphatically introduced here.
(1) Newton's Mathematical Achievements
Since17th century, the original geometry and algebra have been difficult to solve many new problems raised by production and natural science at that time, such as: how to find the instantaneous velocity and acceleration of an object? How to find the tangent of the curve and the length of the curve (planetary distance), the area swept by the vector diameter, the minimum value (such as perihelion, apohelion, maximum range, etc.). ), volume, center of gravity, gravity, etc.; Although Newton had made some achievements in logarithm, analytic geometry and infinite series before, he could not solve these problems satisfactorily or universally. The greatest influences on Newton at that time were Descartes' Geometry and Varis's arithmetica infinitorum. Newton unified various special methods for solving infinitesimal problems since ancient Greece into two algorithms: downstream calculus (differential) and countercurrent calculus (integral), which are embodied in the application of infinite polynomial equation in 1669, stream calculus and infinite series in 167 1 and infinite series in 1676. The so-called "flow" is an independent variable that changes with time, such as x, y, s, u, etc. The "flow number" is the speed of flow change, that is, the rate of change, writing, etc. There is a difference between the "differential rate" and the "variable rate" he said. At the same time, he first published his binomial expansion theorem in 1676. Newton discovered other infinite series and used them to calculate areas, integrals, solve equations and so on. 1684, Leibniz introduced and lengthened S as the symbol of calculus from the tangent study of curves, and the calculus founded by Newton was rapidly popularized in mainland countries.
The appearance of calculus has become another important branch in the development of mathematics besides geometry and algebra-mathematical analysis (Newton called it "analysis by the method of infinite polynomial equation"), and further developed into differential geometry, differential equation, variational method and so on, thus promoting the development of theoretical physics. For example, J Bernoulli of Switzerland seeks the solution of the steepest descent curve, which is the initial problem of variational method, and no mathematician in Europe can answer it within half a year. 1697, Newton overheard it one day, and it was solved in one fell swoop that night, and it was published anonymously in the Journal of Philosophy. Bernoulli said in surprise, "I recognized the lion from this claw."
(2) Newton's achievements in optics.
Newton's optics is another classic of science (1704). The subtitle of the book is "Papers on Reflection, Refraction, Bending and Color of Light", which reflects his optical achievements.
The first is geometric optics and color theory (prism spectrum experiment). From 1663, the lens was ground and the telescope was made by ourselves. In a letter to the Royal Society, he reported: "I made a triangular glass prism at the beginning of 1666 to test the famous color phenomenon. To this end, I darkened the room ... "Then he described in detail the prism dispersion experiment he conducted by opening a small hole to introduce sunlight. From Aristotle to Descartes, the color theory of light holds that white light is pure and uniform, which is the true color of light. "Colored light is a variant of white light. Newton carefully noticed that sunlight is not the five colors that people often say, but seven colors between red, yellow, green, blue and purple, and intermediate colors such as orange and indigo. Strangely, the prism is not round but oblong, and then he tested the effects of "parts with different thicknesses of glass", "windows with different sizes", "putting the prism outside and then passing through the hole" and "uneven or occasionally irregular glass". Put the two prisms upside down to "eliminate the influence of the first prism"; Take "the light from different parts of the sun, see what kind of influence it will have in different incident directions"; And "calculate the refractive index of each color light" and "observe whether the light will move along the curve after passing through the prism"; Finally, a "decisive experiment" was made: monochromatic light was taken out of the ribbon formed by the prism through the small hole on the screen, and then projected onto the second prism to obtain the refractive index of nuclear color light (then called "refractive index"), thus it was concluded that "white light itself is a non-uniform mixture of colored lights with different refractive indexes". This amazing conclusion overturns the previous theory and is the result of Newton's careful observation and repeated experimental thinking. In the process of studying this problem, Newton also affirmed that neither galileo telescope (concave lens or convex lens) nor Kepler telescope (two convex lenses) can avoid chromatic aberration caused by objective lens dispersion. He found that a carefully polished metal mirror can be magnified 30 ~ 40 times as an objective lens. 167 1 year, he sent this mirror to the royal society for preservation. Up to now, the giant astronomical telescope still adopts Newton-like basic structure. Grinding and polishing precision optical mirrors by Newton method is still the main means of optical processing in many factories.
The second part of optics describes various experiments of Newton's ring phenomenon when light shines on stacked convex lens and flat glass. He did all the experiments that modern experiments can think of and made accurate measurements, except for the reason why the ring came into being. He explained the interference phenomenon as "burst" or "coincidence" in light propagation, that is, it is periodic, sometimes "easy to reflect" and sometimes easy to spread. He even measured the size of this equal interval For example, there is a burst interval of colored light between yellow and orange, which is 1/89000 inches (that is, the current 2854× 10-65438).
The third part of optics is "kink" (he thinks that light is absorbed), that is, diffraction and birefringence experiments and his 3 1 topic. These diffraction experiments include more than 10 experiments, such as hair, leaves and monochromatic narrow beam "light band" (now called diffraction pattern) formed by sharp splitting. Newton has reached the door of an important discovery, but missed it. His 3 1 question is very enlightening, which shows that Newton did not make absolute affirmation before the experimental facts and physical thoughts matured. In the first and second chapters of Optics, Newton regarded light as a material flow, that is, a group of particles with different speeds and sizes emitted by a light source. In birefringence, he assumes that these light particles are oriented and anisotropic. Because the wave theory at that time could not explain the straight-line progress of light, he tended to the particle theory, but he thought that particles and waves were hypothetical. He even thinks that the existence of ether is unfounded.
In fluid mechanics, Newton pointed out that the viscous resistance of fluid is directly proportional to the shear rate, and this resistance is directly proportional to the separation speed between parts of liquid. Those that conform to this law (such as air and water) are called Newtonian fluids. In terms of heat, Newton's cooling law is that when the surface of an object forms a temperature difference with its surroundings, the heat lost per unit time and area is directly proportional to this temperature difference.
In acoustics, he pointed out that the speed of sound is directly proportional to the square root of atmospheric pressure and inversely proportional to the square root of density. He once regarded sound propagation as an isothermal process, but later P.S. Laplace modified it as an adiabatic process.
(3) Newton's philosophy and scientific method.
Newton's great achievements in science, coupled with his simple materialistic philosophy and a set of physical methodology system that has begun to take shape, have had a great impact on the development of physics and even the whole natural science, and on the development of industrial revolution, social and economic changes and mechanical materialism in the18th century. Only a few outlines have been drawn here. Newton's philosophical views are inseparable from his basic achievements in mechanics. He tried to explain all natural phenomena from the perspective of mechanics, which formed Newton's spontaneous materialism in philosophy and led to the prevalence of mechanism. In fact, Newton regarded all phenomena such as chemistry, heat and electricity as "things related to attraction or repulsion". For example, he first expounded the chemical affinity and described the chemical displacement reaction as the competition between two kinds of gravity; It is considered as "heat generated by exercise or fermentation"; Powder explosion is also a process of violent collision, decomposition and thermal expansion of particles such as sulfur and carbon.
This mechanical view, that is, the view that all forms of material motion are classified as mechanical motion, adopts absolute time-space view, atomism, mechanical determinism that can determine the motion state at any time in the future by initial conditions, and the law of cause and effect of things. They are necessary as the general way of thinking of the whole physics to explain the mechanical motion problems. It can be considered that Newton was the first person to establish a relatively complete system of physical causality, and causality is the cornerstone of classical physics. Newton's contribution to scientific methodology, just like his contribution to physics, especially mechanics, not only created one or two new methods, but formed a set of methodological system for studying things and put forward several methodological principles. In Newton's principle, the following scientific methods are embodied:
① Experiment-theory-application method. Newton said in the preface to Principles: "The whole task of philosophy seems to be to study various forces of nature from various moving phenomena, and then use these aspects to demonstrate other phenomena." I.B.Cohen, a historian of science, correctly pointed out that Newton "mainly compared the real world with its simplified mathematical representation repeatedly". Newton was a master who engaged in experiments and summarized practical materials, and also an expert who applied his theory to practical problems such as celestial bodies, fluids and gravity.
② Analysis-comprehensive method. Analysis is from the whole to the part (such as differential and atomic view), and synthesis is from the part to the whole (such as integral, including the synthesis of heaven and earth, the establishment of three laws of motion, etc. Newton said in Principles: "In natural science, just like in mathematics, when studying difficult things, we should always use analytical methods first and then comprehensive methods. Generally speaking, from result to cause, from special cause to common cause, until the most common cause is proved, this is the method of analysis; The comprehensive method assumes that the reasons have been found and have been defined as principles, and then these principles are used to explain their phenomena and prove the correctness of these explanations. " ③ Inductive and deductive method. The above analytical synthesis method and inductive deduction method are combined with each other. Newton began with observation and experiment. "Draw a common conclusion from it by induction", that is, get concepts and laws, then deduce various conclusions by deduction, and then test, explain and predict through experiments. Most of these predictions were later confirmed. At that time, Newton's law was called axiom, which indicated that the general conclusion drawn by induction could be used to deduce other conclusions. ④ Physical-mathematical methods. Newton put the concepts and laws within the scope of physics into mathematics as much as possible. Einstein said: "Newton was the first to successfully find the basis clearly expressed by a formula." On this basis, he logically and quantitatively deduced a wide range of phenomena with mathematical thinking, which is consistent with experience. " "Only the form of differential law can fully meet the requirements of modern physicists for the law of cause and effect, and the definition of differential law is one of Newton's greatest intellectual achievements." Newton called his book Mathematical Principles of Natural Philosophy to illustrate this point.
Newton's methodological principles are concentrated in the four principles in the third chapter of Principles, "Inference Rules in Philosophy", and are not quoted here. To sum up, it can be called the principle of simplicity (rule 1), the principle of causality (rule 2), the principle of universality (rule 3) and the principle of no proof (rule 4). Some people also argue that Newton's thought in the next paragraph is called structural principle: "The purpose of natural philosophy is to discover the functions of various structures in nature and reduce them to some universal laws and regulations as far as possible-establish these laws through observation and experiment, and then deduce the cause and effect of things."
Newton's philosophy and methodology system was praised by Einstein as "the program of every worker in the field of theoretical physics". This is an open plan to guide the progress of generations of scientists. But Newton's philosophy and methodology inevitably have obvious limitations and incompleteness of the times, which is the highest achievement of science in its infancy. Newton only made a preliminary systematic study of the simplest mechanical motion of matter at that time, absolutized space-time and matter, and tried to extrapolate particle theory to all fields (for example, even he could not explain the "Newton's ring" he discovered), which was his achilles heel. When Newton saw that the "first cause" of things was not necessarily mechanical, he raised the question of "these things are so orderly" ... whether there seems to be an omnipresent God (optics, question 29), and turned to the "scientific" research of theology for a long time, which consumed a lot of energy. However, Newton's historical limitations, like his historical achievements, are all teaching materials that inspire future generations to keep moving forward.