Ren é Descartes (March 31, 1596 – February 11, 1650), born on March 31, 1596FranceANDRE –LoireTouraine (now Descartes, named after Descartes), died on February 11, 1650SwedenStockholm，FrancePhilosopher, mathematician, physicist.He was rightmodern mathematics He has made important contributions to the development ofanalytic geometryFather.
He's stillModern Western PhilosophyOne of the founders of thought is modern timesIdealismAnd put forward the proposition of "universal suspicion".HisPhilosophical thoughtIt deeply influenced the following generations of Europeans, and“Rationalism”Philosophy laid the foundation.
Descartes is best known for his achievements as a mathematician.He invented it in 1637modern mathematics One of the basic tools of——Coordinate system, willgeometryCombined with algebra, analyticgeometry。At the same time, he also deduced thatCartesian theoremIsogeometric formula.It is worth mentioning that the legendaryCardioidThe equation was also proposed by Descartes.
In physics, Descartes applied his coordinate geometry to the study of opticsLaw of refractionA theoretical deduction has been made.In the second chapter of his Philosophical PrinciplesSecond natureThe form of the law completely expressesLaw of inertia, and clearly put forward for the first timeLaw of conservation of momentum。All these laid a certain foundation for the later research of Newton and others.
Turainella Sea, France (now Descartes, Anders Loire)
date of birth
March 31, 1596
Date of death
February 11, 1650
University one is graduated from
Université de Poitiers
Occupation
Physicist, mathematician, philosopher
Representative works
Methodology, Geometry, Refraction, Principles of Philosophy, etc
Key achievements
One of the founders of modern western philosophy, who founded analytic geometry It is the first time to put forward a theoretical demonstration of the law of light refraction Mechanics developed the theory of relativity of Galileo's motion Developed the theory of cosmic evolution, vortex theory and other theories Famous representatives of modern dualism and idealism
Descartes' Marriage: andSpinoza、Newton、LeibnizSimilarly, Descartes never married.He had an illegitimate daughter, but unfortunately she died prematurely, regretting for her life.
Key achievements
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Descartes on French stamps
Descartes' contribution to science is multifaceted.Descartes not only opened up a new path in the field of philosophy, but also was a scientist who had the courage to explore. He had commendable innovations in physics, physiology and other fields, especially in mathematicsanalytic geometry, which opens theModern mathematicsThe door ofHistory of ScienceIt has epoch-making significance.
Descartes' Study of Light Sensitivity and Vision[20]
But hisPhilosophical thoughtandMethodologyAnd plays a more important role in his life activities.His philosophy thought had a great influence on the later development of philosophy and science.
Philosophical aspects
Descartes is widely regarded asModern Western PhilosophyHe was one of the founders of the Chinese Academy of Sciences. He was the first to establish a complete philosophy system.In philosophy, Descartes is adualismAndRationalismThe.Descartes believed that human beings should be able to use mathematical methods - that is, rationality - to carry out philosophical thinking.He believed that reason was more reliable than sensory perception.(He gave an example: when people dream, they think they are in a real world, but in fact it is just an illusion. See Zhuangzhou Dreams of a Butterfly.).He came fromlogic、geometryandAlgebra4 rules found in:
Article 1: What one does not clearly recognize, he will never take it as true acceptance.That is to say, be careful to avoid rash judgments and preconceptions. In addition to the things clearly presented in his mind that he cannot doubt at all, do not put more things into his judgments.
Article 2: Divide each difficult problem he examines into several parts according to the possible and necessary degree, so as to properly solve them one by one.
Article 3: Thinking in order starts with the simplest and easiest object to know, and gradually rises bit by bit until you know the most complex object;Even those things that have no priority should be given an order.
Article 4: In any case, we should make a comprehensive investigation as far as possible, review as widely as possible, and make sure that there is no omission.
Descartes applied this method not only to philosophical thinking, but also to geometry, and foundedanalytic geometry。
Thus, Descartes first thought that suspicion was the starting point, that knowledge of sensory perception could be doubted, and that people could not trust their own senses.
Descartes emphasized that the purpose of science is to benefit mankind and make man the master and ruler of nature.He objectedScholastic philosophyAnd theology, proposing a "systematic method of doubt" for everything.So he won't say "I see, so I am" or "I listen, so I am".From this he learned a truth: what we cannot doubt is "our doubt".[24]
He believes that the above two entities are finite entities, and juxtaposing them shows thatmetaphysicsorOntologyYes, he is typicaldualismThe.Descartes takes this asmetaphysicsFrom this, he concluded that "I" must be something independent of the body and thinking.
Descartes also tried to prove thatThe existence of God。Descartes believes that we all have the concept of perfect entity. Since we cannot get the concept of perfection from imperfect entity, there must be a perfect entity - God - to let us get the concept.That is, God is the creator of limited entities and the ultimate reason.From the two points obtained, Descartes continues to infer that since perfect things (gods) exist, we can determine that the previous devil hypothesis is not tenable, because a perfect thing cannot allow such demons to deceive people, so we can be sure that "the world really exists" through constant suspicion,And the mathematical logic after proof should be correct.In the real world, there are many characteristics that can be perceived by reason, that is, their mathematical characteristics (such as length, width, and height). When our reason can clearly recognize a thing, it must not be illusory, and it must be as we know it.That is, Descartes willReasoning methodandDeductive methodApplied to philosophy, it believes that a clear concept is truth, and proposes“Innate ideas”。
Descartes' view of natural philosophyAristotleHis theory is completely opposite.He believes that all material things are machines governed by the same mechanical laws, even the human body.At the same time, he also believed that there was a spiritual world besides the mechanical world. This dualistic view later became the fundamental thinking method of Europeans.
Although Descartes provedreal world He believes that there are two different entities in the universe, namely thinking (mind) and the external world (matter), both of which come from God, and God exists independently.He believes that only talents have souls, and human beings are dualistic beings who can think and occupy space.Animals belong only toMaterial world。
Descartes emphasized that thought is an unquestionable starting pointEuropean PhilosophyHas had an important impact.“I think, so I am”The controversy arises from the so-called existence of God and animalsmonism（chimpanzee、octopus、parrot、dolphin, elephants, etc.), and the main idea of doubt is indeed very useful for research.
Methodology
Descartes wanted to introduce him in a book entitled "The World"Scientific research achievementsBut when the book was almost finished in 1633, he learned that the Italian church announcedGalileoGuilty, because he supportsCopernicusOfHeliocentric theory。Although DescartesNetherlandsNot receivedCatholicismThe persecution of authority, but he still decided to be cautious and put the books in the trunk, because in the book he defendedCopernicusThe theory of.But in 1637, he published the most famous book, Methodology of Correct Thinking and Discovery of Scientific Truth, which is usually referred to as Methodology for short.
Descartes pointed out in his Methodology that there are four steps to research the problem:
1. Never accept any truth that I do not know, that is, try to avoid recklessness and prejudice. It can only be a truth that is very clear and certain according to my own judgment, without any doubt.That is to say, as long as you have not experienced the problem personally, you can doubt any authoritative conclusion.This is the famous theory of "suspecting everything".For example, Aristotle once concluded that women have two fewer teeth than men.But this is not the case.
2. What can be studiedComplex problems, try to break down into a number of relatively simple small problems and solve them separately one by one.
3. Arrange these small problems from simple to complex, starting with problems that are easy to solve.
4. Replace allProblem solvingAfter that, we will make a comprehensive inspection to see whether it is complete and whether the problem has been completely solved.
Before the 1960s, the Westscientific researchMethods, from machinery toHuman anatomyThe research of《Talk about methods》The rapid development of western modern scienceFacilitation。However, there are also some defects, such as the human body function, which is only a mechanical synthesis of various parts, but the interaction between them is not thoroughly studied.untilApollo 1 With the appearance of the moon landing project, scientists found that some complex problems cannot be resolved and must be treated with complex methods, which led to the emergence of system engineering, and the methodology was replaced by comprehensive methods for the first time.The emergence of systems engineering has greatly influenced many large-scale western countriesTraditional sciencePlayed a considerable role in promoting, such asenvironmental science，meteorology, biology, artificial intelligence, etc.
"I think, so I am"
Descartes' most famous thought comes from Methodology.
Latin: Cogito ergo sumEnglish: I think, there are I am. French: Je pen se, donc je suis
LiterallyOriginal Latin meaning: "I" think, so "I" is existence.
Deep meaning:CartesianPhilosophical propositionThe so-called "skeptical method" is to verify whether the source of "knowledge" is reliable.We can doubt everything around us. There is only one thing we can't doubt, that is, to doubt the existence of the "I" who is doubting.In other words, we cannot doubt "our doubts", because only in this way can we affirm our "doubts".Descartes proved the existence of God from his "I think, therefore I am".Because the subject of the thought of "I" cannot be "doubted", then there is a higher "entity" that makes "I" exist.In other words, because I exist, there must be an "existential" who makes me exist, and the "existential" who makes me exist must also be the "existential" who makes all things exist.Therefore, only God must be able to make all things exist.
This famous saying, which Descartes regarded as the starting point of his philosophical systemEastern EuropeAnd the Chinese academia in the 21st century are considered extremeSubjective idealismAnd was severely criticized.Many people even take the argument that "existence must precede consciousness", "there can be no thought without body", and think that Descartes is "putting the cart before the horse", "ridiculous".Descartes' suspicion is notSpecific thingsThe suspicion of specific principles is the absolute suspicion of human beings, the world and God.From this absolute doubt, Descartes wants to lead out the unquestionable principles of philosophy.
Physics
Descartes, relying on his genius intuition and rigorous mathematical reasoning, made a useful contribution to physics.
Read Johnny from 1619·KeplerDescartes has been paying attention to the lens theory since his optical works of;And participated in the study of the nature, reflection andRefractive indexAnd the research of grinding lens.He regards the theory of light as the wholeKnowledge systemThe most important part of.Descartes firmly believes that light is transmitted "instantaneously". In his works "On Man" and "Principles of Philosophy", he completely explained the concept of the nature of light.Descartes used his coordinate geometry to engage in optical research, and for the first timeLaw of refraction of lightProposedTheoretical demonstration。Share the honor of discovering the law of refraction of light with Snell of the Netherlands.He believes that light is the propagation of pressure in the ether. From the perspective of light emission theory, he uses the model of tennis balls hitting cloth to calculate the light in two kinds ofmediumReflection, refraction andtotal reflectionSo that the velocity component parallel to the interface is assumed to be constant for the first timeLaw of refraction；However, his assumption is wrong, and his deduction shows that lightOptically sparse mediumget intoOptically dense mediumWrong conclusion of speed increase when.He also carried outOptical analysis, explained that the cause of vision disorder is lens deformation, designedCorrected visionThe lens of.
Descartes' explanation of rainbow formation[18]
He also explained the rainbow phenomenon with the refraction law of light, and analyzed the color by the rotation speed of the element particles.
Descartes in the second chapter of Philosophical PrinciplesSecond natureThe form of the law is the first time to completely expressLaw of inertia: As long as the object starts to move, it will continue to move at the same speed and in the same straight direction until it meets the obstruction or deviation caused by some external reason.Here he emphasized what Galileo did not clearly stateInertial motionStraightness.
Descartes discovered momentumConservation principleThe original form of (momentum defined by Descartes is oneabsolute valueIt's not a vector, so his momentum conservation principle was later proved to be wrong).
Descartes put hisMechanistic theoryThe idea was applied to celestial bodies and developed the theory of cosmic evolution, forming his theory of the genesis and structure of the universe.He believes that things are easier to understand from the perspective of development rather than just from the existing form.He foundedWhirlpool theory。He thinks there are huge whirlpools and stars around the sun.
He believes that the movement of celestial bodies comes from inertia and the pressure of certain cosmic material vortex on celestial bodies. There must be a celestial body in the center of various vortices of different sizes. This hypothesis is used to explain the interaction between celestial bodies.Descartes' Ethereal vortex model of the origin of the sun for the first time relied on mechanics rather than theology to explain the celestial bodies, the sun, planets, satellitescometThe formation process of equality, compared with Kant'sNebula theoryOne century earlier, it was the most authoritative in the 17th centuryCosmology。
CartesianCelestial evolutionThe vortex model and the view of short-range action are just like his wholeideological systemOn the one hand, with rich physical ideas and rigorousscientific methodIt is characterized by oppositionScholastic philosophy, InspirationScientific thinkingThe role of promoting the progress of natural science at that time had a great impact on manynatural scientistHis thought has far-reaching influence;On the other hand, it often stays in the intuitive and qualitative stage, not starting from the quantitative experimental facts, so some specific conclusions often have many defects, and become the main opposite of Newton's physics later, leading to extensive debate.
He believed that there was a huge vortex around the sun, driving the planets to keep moving.The particle of matter is in a unified vortex, and three elements of earth, air and fire are differentiated in the movement. Earth forms planets, while fire forms the sun and stars.
He also developed the theory of cosmic evolutionWhirlpool theoryAlthough the specific theory has many defects, it still has an impact on future natural scientists.
Mathematics
Descartes' most important contribution to mathematics is the creation of analytic geometry.In the Cartesian era, algebra was still a relatively new discipline, and the thinking of geometry still occupied a dominant position in the minds of mathematicians.Descartes devoted himself to the study of the connection between algebra and geometry, and successfully connected algebra and geometry, which were completely separated at that time.In 1637, he foundedCoordinate systemLater, analytic geometry was successfully established.His achievement isCalculusThe foundation was laid by the foundation ofmodern mathematics An important cornerstone of.Analytic geometry is still importantMathematical methodone of.
Descartes not only proposed the analysisgeometryThe main thinking method of learning also points out its development direction.In his book Geometry, Descartes put logic, geometry,algebraic methodTogether, by discussing the problem of drawing, we outline a new method of analytic geometry. Since then, numbers and shapes have come together,Number axisIt is the first contact between number and shape.It is proved to the world that geometric problems can be reduced to algebraic problems, and geometric properties can also be found and proved through algebraic transformation.Descartes introduced the concept of coordinate system and line segment operation.He innovativelyGeometry'Translation' algebraequationSo that the geometric problem can be solved by algebraic method, which is called "analytic geometry" or“Coordinate geometry”。
The foundation of analytic geometry isHistory of mathematicsThe last epoch-making turn.andRectangular coordinate system The establishment of analytic geometry is the foundation of the establishment of analytic geometry.Rectangular coordinate systemThe creation of, built a bridge between algebra and geometry, which enables geometric concepts to be expressed in algebraic form, and geometric figures can also be expressed in algebraic form, so algebra and geometry are thus integrated into one family.
In addition, manyMathematical symbolDescartes first used them, includingKnown numbera. B, c, unknown numbers x, y, z, etc., as well as the representation of indexes.He also found thatConvex polyhedronThe relationship among edges, vertices and faces is called Euler Cartesian formula.And Descartes, a common calculusLeaf lineHe also found it.
Image source:[14][19]
Cartesian coordinate system
In mathematics,Cartesian coordinate system, also known asRectangular coordinate system, is an orthogonal coordinate system.The two-dimensional rectangular coordinate system is composed of two mutually perpendicular points and zero points coincidentNumber axisConstitutive.In the plane, the coordinates of any point are set according to the coordinates of the corresponding points on the number axis.In the plane, the correspondence between any point and the coordinate is similar to the correspondence between the point and the coordinate on the number axis.
useCartesian coordinates，geometryIt can be clearly expressed by algebraic formula.The rectangular coordinates of each point of a geometric shape must comply with this algebraic formula.
Cartesian coordinate system was created by French mathematician Rene Descartes.In 1637, Descartes published a masterpiece《Methodology》。This book, which specializes in studying and discussing western academic methods, provides many correct insights and good suggestions, and has made great contributions to the subsequent western academic development.
In order to show the advantages and effects of the new method and help him in scientific research, he added another book in the appendix of Methodology《geometry》。The study of Cartesian coordinate system appears in the book Geometry.
Cartesian research on coordinate system combines algebra andEuclidean geometry, for later analytic geometryCalculus, andCartographyIt has the key pioneering power.
Anecdotes
Spider Weaving Web and Establishment of the Plane Rectangular Coordinate System
It is said that one day, Descartes was ill in bed and was seriously ill. However, he still thought about a problem repeatedly: geometry is intuitive, andalgebraic equationIt is relatively abstract. Can we combine geometric figures with algebraic equations, that is, can we use geometric figures to express equations?To achieve this goal, the key is how to hook the points that make up the geometric figure with each group of "numbers" that meet the equation. He pondered hard and tried to figure out how to link "points" and "numbers".Suddenly, he saw one on the corner of the roofspider, pulling the silk down.After a while, the spider climbed up along the silk again and pulled the silk on the top left and right.The "performance" of spiders made Descartes' thinking suddenly clear.He thought that the spider could be regarded as a point.He can move up, down, left and right in the room. Can you determine each position of the spider with a set of numbers?He also thought that the two adjacent walls in the room intersected three lines with the ground. If the corner of the wall on the ground is taken as the starting point and the three lines intersected are taken as three number axes, then the position of any point in the space can find three numbers in order on the three number axes.Conversely, given a set of three ordered numbers, you can also find a point P corresponding to it in space. In the same way, a set of numbers (X, Y) can represent a point on the plane, and a point on the plane can also be represented by a set of two ordered numbers, which is the prototype of the coordinate system.
Descartes' sign rule was first introduced by Descartes in his works《La Géométrie》It is a method for determining the number of positive or negative roots of a polynomial.
If the unary real coefficientpolynomialIf arranged in a descending power manner, the number of positive roots of the polynomial is either equal to the number of changes in the sign of the adjacent non-zero coefficient, or is a multiple of 2 less than it.Such as 5,3,1 or 4,2,0.The number of negative roots is the number of changes in the sign of the polynomial obtained by changing the coefficients of all odd degree terms, or a multiple of 2 less than it.
Special case: Note that if the polynomial is known, onlyReal root, the number of positive roots can be completely determined by this method.Since the repeatability of zero roots is easy to calculate, the number of negative roots can also be calculated.Then the symbols of all roots can be determined.
Euler Cartesian formula
Euler Cartesian formula is a formula in geometry.
The content of the formula is:Convex polyhedron, setVIs the vertex number,EIs the number of edges,FIs the number of faces, thenV−E+F=2。
The name comes fromLatinOffolium, which means "leaf".
Characteristics of curves: usingImplicit functionY 'can be calculated by the derivation rule of
The point can be obtained by using the point oblique equation of the straight line（
）Tangent equation at:
Horizontal and vertical tangents: when
The tangent of the Cartesian leaf line is horizontal.So:
When
The tangent line of Cartesian leaf line is vertical.So:
This can be explained by the symmetry of the curve.As you can see, the curve has two horizontal tangents and twoverticalTangent.Cartesian leaf line is symmetric about y=x, so if the horizontal tangent has coordinates（
）Then there must be a corresponding vertical tangent line with the coordinates（
The slope of this asymptote is - 1, and both the x and y intercept are - a.
Cartesian and Christian cardioid (i.eCardioid）'s story
Cardioid
Christian cardioid
There is no rigorous evidence to prove that the cardioid was invented by Descartes.
The heart line has oneCuspOfEpicycloid。In other words, when a circle rolls along another circle with the same radius, the track of a point on the circle is the heart line.
Cardioid is a kind of epicycloidnIs 2.It can also be expressed in polar coordinates:r= 1 + cosθ。The perimeter of such heart line is 8, and the area enclosed is
Its equation in polar coordinates is to be investigated, and here is only for reference.
Four heart lines facing different directions
The story of mathematics tells the love story of the mathematician Descartes.Descartes was born in France in 1596,Continental EuropeburstBlack DeathWhen he wandered toSwedenHe met Kristina, an 18-year-old princess from a small principality in Sweden, and later became her math teacher. Their love for each other grew from their daily relationship. The princess's father, the king, became furious when he learned about it, ordered Descartes to be executed, and then exiled to France because of her daughter's plea. Princess Christine was also put under house arrest by her father.Descartes contracted the Black Death shortly after he returned to France. He wrote to the princess every day. Christine had never received a letter from Descartes because he was intercepted by the king.Descartes died after he sent the thirteenth letter to Christine, which contained only one short formula: r=a (1-sin θ).The king couldn't understand it. He felt that they didn't always talk about each other, so he mercifully handed the letter to Christine, who was always unhappy. When the princess saw it, she immediately understood the lover's intention. She immediately started to draw the figure of the equation. When she saw the figure, she was very happy. She knew that the lover still loved her. The figure of the equation was the shape of a heart.The princess built it on paperPolar coordinate system, use a pen to trace the point of the equation, see the heart line represented by the equation, and understand Descartes' deep love for himself.This is also known as the "heart-shaped line".
After the death of the king, Christina ascended the throne and immediately sent people to look for her sweetheart everywhere in Europe. The man of Wuneisi died, so she left her alone in the world
It is said that this world-renowned love letter is still kept in the European Descartes Memorial Hall.
In history, Descartes and Christina did have friendship.But Descartes came to Sweden on October 4, 1649 at the invitation of Christina, who had become the Queen of Sweden at that time.Descartes and Christina mainly talked about philosophical problems rather than mathematics.
It is recorded that due toChrisina von Schweden Due to tight schedule, Descartes could only discuss philosophy with her at five o'clock in the morning.Descartes' real cause of death was cold weather and overworkpneumonia, not the Black Death.[12]
analytic geometry
Cartesian geometry
The RenaissanceEuropean scholars inheritedancient GreekThe geometry of, also accepted the algebra introduced from the East.With the development of learning technology, describing motion with mathematical methods has become the central issue that people care about.Descartes analyzed the advantages and disadvantages of geometry and algebra, and said he would "seek another method that includes the advantages of these two sciences without their disadvantages".
In Volume I of Geometry (a part of Methodology), he used the distance from a point on the plane to two fixed straight lines to determine the distance of points, and used coordinates to describe points in space.He further created analytic geometry, which shows that geometric problems can not only be reduced to algebraic forms, but also be discovered and proved through algebraic transformation.
Descartes transforms geometric problems into algebraic problems and proposes the unification of geometric problemsGraphing method。To this end, he introduced the concepts of unit line segment, as well as addition, subtraction, multiplication, division and square root of line segment, so as to link line segment and quantity. Through the relationship between line segments, "find two ways to express the same quantity, which will form an equation", and thenSolution of the equationThe relationship between the represented line segments is plotted.
In Volume II, when Descartes used this new method to solve the Pappus problem, he defined a starting point for it with a straight line as the baseline on the plane, and then selected another line intersecting it. They are equivalent to the x axis, the origin, and the y axis, respectively, to form aOblique coordinate system。Then the position of any point on the plane can be uniquely determined by (x, y).The Pappus problem is reduced to a quadratic indefinite equation with two unknowns.Descartes pointed out that the degree of equation is independent of the choice of coordinate system, so curves can be classified according to the degree of equation.
Geometry puts forward the main ideas and methods of analytic geometry, marking the birth of analytic geometry.Since then, human beings have entered the stage of variable mathematics.
In Volume 3, Descartes pointed out that the equation may have as many roots as its degree, and also proposed the famous Cartesian sign rule: the maximum number of positive roots of the equation is equal to the number of sign changing times of its coefficient;The maximum number of negative roots (he calledRhizoid）It is equal to the number of times the sign remains unchanged.Descartes also improvedWeidaCreativeSemiotic system, denote known quantity with a, b, c,..., denote quantity with x, y, zUnknown quantity。
The emergence of analytic geometry has changed the trend of separating algebra and geometry since ancient Greece, unifying the opposite "number" and "shape", and combining geometric curves with algebraic equations.Descartes' ingenuity is moreCalculusThe foundation was laid by the establishment of, thus opening up a wide range of variable mathematics.
just asEngelsSaid: "The turning point in mathematics is Descartes' variable. With variable, movement enters mathematics; with variable,DialecticsEntered mathematics;With variables, differentiation and integration become necessary immediately. "
Psychology
Descartes' viewpoints and major discoveries in psychology had a great impact on later psychology.
Descartes' Interpretation of Reflex Regulation[23]
He is moderndualismandidealismA famous representative of theory.His reflexes andReflecting arcThe important discovery of "animal is machine" provides an important basis for the assertion.And put forward the hypothesis of response stimulus.
But Descartes' concept of reflection is mechanical. He emphasizes the difference between human beings and animals. Animals have no hearts, but people have hearts. Such inference is a typical manifestation of dualism.
In addition, the theory of mind mind interaction is also CartesianBody mind relationshipAnother typical expression of the upper dualism, he believes that human body is composed ofPhysical entityThe human mind is composed ofSpiritual entityConstitutive.The mind and human body can influence, cause and effect each other.
He believes that there are six kinds of primitive emotions: surprise, love, hatred, desire, joy and sorrow. Other emotions are all branches or combinations of these six primitive emotions.
Illustration of Descartes' La Geometry[17]
CartesiandualismAlthough the psychological thought was theoretically wrong, it played a very important role in promoting and making progress in the social background at that time. He used dualism to get rid of the absolute control of theology over science and guide people's thoughts toRational thinkingAnd specific research, so his contribution to psychology can not be ignored.
Self writer Thomas Aquinas (1225 – 1274) put forward the concept of instinct and believed that animals have instinct, but human beings do not have instinct.He argues that human beings have dual natures - material and non-material, or physical and mental (intellectual) - but the laws governing human material natures are different from those governing animals. The reason for this difference comes from the view that "man is a special product created by God".Many early scientists argued about the profound similarities between animal motivation and human motivation.On the surface, both humans and animals are manipulated by the same laws, but there seems to be differences.Descartes put forward an explanation that can reconcile these two views: in the willAction levelThe body behavior under can be explained mechanically (instinct), but the behavior related to such things as moral conduct is under the control of the will. Descartes argues that the body and spirit (will, soul) interact, and the position where the action occurs isPineal gland。Some kind of physical behavior, such asa sexual behaviorIt happens under the control of spirit rather than some simple mechanical products.This dual view can echo the views of scientists and the Catholic Church at the same time.It was of positive significance at that time.[13]
Character's Life
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childhood
Rene Descartes was born on March 31, 1596, in the Tulainera Sea, Anders Loire Province, France.He came from a lower noble family, and his father Joachim wasRyanOfBrittanyA member of Parliament and a judge of the District Court.
When he was more than one year old, his mother suffered frompulmonary tuberculosisWhen he died, he was also infected, resulting in weakness and illness.Because Descartes was ill since childhood, but his family was rich, so the school allowed him to study early in bed.[1]
After his mother died, his father moved to another country and remarried, leaving Descartes to his grandmother to bring him up. Since then, the father and son have rarely seen each other, but his father has always provided financial help to enable him to receive a good education and pursue his own interests without worrying about financial resources.Therefore, he has formed the habit of lifelong meditation and withdrawn personality.Seeing that he has the temperament of a philosopher, his father affectionately called him "little philosopher".
In 1606 or 1607, his father hoped that Descartes would become a theologian in the future, so he sent Descartes to the most famousAristocratic school——Study at the Royal Henley College of the Jesuit Church in Lafleche[2]。In order to take care of his weak body, the school authorized him not to acceptschool regulationsYou don't have to go to school in the morning. You can read in bed.Therefore, he developed the habit of being quiet and good at thinking when he was young.He studied in the school for 8 years and accepted the traditionalcultural education, learnedClassical literatureHistory, theology, philosophy, law, medicine, mathematics and other natural sciences.He learned mathematics and physics, including Galileo's work.[3]However, he was disappointed with what he learned, because in his opinion, the subtle arguments in the textbooks were actually ambiguous or even contradictory theories, which only made him suspicious and unable to obtain solid knowledge. The only consolation for him was mathematics.
Here is an interesting story about the philosopher Descartes on the stars.Once Descartes sat on the steps in front of his house, staring at the darkhorizon。A passer-by approached him and asked, "Hey, smart man, how many stars are there in the sky?" He replied, "Fool! Nobody can embrace that boundless thing..."[4]
youth
After graduating in December 1616, he followed his father's wish to become a lawyer and enteredUniversité de Poitiers Studying law and medicine, deeply interested in various knowledge, especially mathematics, and gainedIndustrialistDegrees and diplomas.[5]
After graduation, Descartes has been rightCareer choiceUndeterred, he also decided to travel around Europe and concentrate on seeking the wisdom in the "World Book".
In 1618, Descartes joined the army of Mauritz in Nassau, Netherlands.But there was an armistice between the Netherlands and Spain, so Descartes used this paragraphfree timeLearn math.[6]
During his military service and traveling around Europe, Descartes continued to pay attention to "collecting all kinds of knowledge" and "thinking about all kinds of things encountered everywhere".In Descartes' time, Latin was the language of scholars.He also signed his Latinized name Renatus Cartesius on his works as was customary at that time.Because of this, he initiatedCartesian coordinate systemAlso called Cartesian coordinate system.
Descartes' interest in combining mathematics and physics was born when he was in the Netherlands.
On November 10, 1618, he happened to be on the roadsideBulletin BoardUp, see withFlemishAsk mathematical questions.This aroused his interest, and asked people around him to translate the Flemish language he did not understand into Latin.The person beside him is Isaac Beeckman, who is eight years older than him.Beckman had high attainments in mathematics and physics and soon became his mentor.[7]Four months later, he wrote to Beckman: "You are the one who awakened me from indifference..." and told him that he had made four major discoveries in mathematics.
It is said that Descartes had three strange dreams in one night.The first dream was that Descartes was blown by a storm to a place where the wind could not reach;The second dream was that he got the key to open the treasure house of nature;The third dream is that he has opened the way to true knowledge.These three strange dreams strengthened his confidence in creating new theories.This day is a turning point in Descartes' thought, and some scholars have set this day as the birth date of analytic geometry.
In 1621, Descartes retired from the army and returned home. It was during the civil strife in France. So in 1622, at the age of 26, Descartes sold the assets left by his father and spent four years traveling in Europe, including two years in Italy, and then moved to Paris in 1625.Because the French church at that time was so powerful that it could not freely discuss religious issues.
Descartes moved to Holland in 1628 and lived there for more than 20 years.During this period, Descartes carried out in-depth research on philosophy, mathematics, astronomy, physics, chemistry, physiology and other fields, and devoted himself to philosophical research and published many important collections, and through mathematiciansMasonPriests maintain close ties with leading European scholars.
Almost all of his major works were completed in the Netherlands.
In 1628, he wrote Principles Guiding Philosophy.
In 1634Nicolaus Copernicus Theory based On the World.The book summarizes his views on philosophy, mathematics and many natural science issues.
1637, usedFrenchWrote three papers: Refraction, Meteorology and Geometry（La Géométrie）》For this purpose, he wrote a preface, Methodology for the Correct Application of Rationality and the Pursuit of Truth in Science, which is called Methodology for short in the history of philosophy（Discours de la méthode）（1637）。On June 8LeidenPublished anonymously.[15]
Principles of Philosophy（les Principes de la philosophie）（1644）。
《Meditations on First Philosophy 》（Méditations métaphysiques）(1641) made Descartes one of the most influential philosophers in Europe.
Descartes died in February 1650 at the age of 54.Never married for life.Due to the church's prevention, only a few friends buried him.He also published On Light (1664) after his death.
In 1663, his works were listed in the Vatican in Rome and Paristhe pontiffIn the list of banned books issued.However, the spread of his ideas was not hindered, and Descartes became one of the most influential masters of European philosophy and scientists in the 17th century and later.
In 1740, the ban was lifted in Paris, which was aimed at improving the popularity of France at that timeNewtonThe world system provides an alternative.
People carved the words on his tombstone: "Descartes, EuropeThe RenaissanceSince then, he has been the first person to fight for and guarantee rational rights for mankind. "
religious belief
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Cartesianreligious beliefIt has been strictly debated in the academic circle.He claims to be pious RomeCatholicismThe purpose of apostles and "meditation" is to maintain the Christian faith.But in his own time, Descartes was accused of promoting secretsDeismandatheismfaith.ContemporaryBlaise PascalSaid, "I can't forgive Descartes; he wants to leave God alone in all his philosophy. However, he can't let God touch him lightly to make the world move; otherwise, he doesn't need God anymore."[8-9]
Stephen Gokroger wrote in Descartes' Biography, "He has a deep religious belief as a Catholic, and has kept it until the day of his death, with a firm and enthusiastic desire to explore the truth."[10]
Died in DescartesSwedenAfter,Chrisina von Schweden Abandoned her throne and converted to Roman Catholicism (Swedish law requires the ruler to beprotestantismBelievers).The only Catholic she has ever contacted is Descartes, who was once her personalprivate tutor。[11]
Descartes' main mathematical achievements are concentrated in his "geometry".At that time, algebra was still a new science, and the thinking of geometry still occupied a dominant position in the minds of mathematicians.
Before Descartes, geometry and algebra were two different research fields in mathematics.Descartes stands on methodologynatural philosophyThe Greek geometry was too dependent on figures, which constrained people's imagination.For the popular algebra at that time, he felt that it was completely subordinate to the rules and formulas and could not become a science to improve intelligence.Therefore, he proposed that we must combine the advantages of geometry and algebra to establish a "real mathematics".
The core idea of Descartes is to reduce geometric problems to algebraic problems, and use algebraic methods to calculate and prove, so as to achieveFinal settlementThe purpose of geometric problems.According to this idea, he founded "analytic geometry".
In 1637, Descartes published Geometry and foundedRectangular coordinate system 。He uses the distance from a point on the plane to two fixed lines to determine the position of the point, and uses coordinates to describe the point in space.He further founded analytic geometry, which changed the trend of separation of algebra and geometry since ancient Greece, unifying the opposite "number" and "shape", and combining geometric curves with algebraic equations.Descartes' ingenuity is moreCalculusThe foundation was laid by the establishment of, thus opening up a wide range of variable mathematics.The most valuable thing is that Descartes, from the point of view of motion, regards a curve as the trajectory of the motion of a point, not only establishes the corresponding relationship between a point and a real number, but also unifies the two opposite objects of shape (including points, lines, and surfaces) and "number", and establishes the corresponding relationship between a curve and an equation.The establishment of this correspondence not only marks the germination of the concept of function, but also marks the entry of variables into mathematics, making a great turning point in mathematical thinking methods - from constant mathematics to variable mathematics.Dialectics has entered mathematics, with variables,Differential and integralIt is immediately necessary.These achievements of DescartesNewton、LeibnizThe discovery of calculus opened the way for a large number of mathematicians to make new discoveries.[21-22]
Anecdotes of characters
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Descartes died in the tombGrave robberExcavated, its skull has changed hands several times and is now in Paris, FranceSummer Palace(Palais de Chaillot) Muse é e de l'Homme.
Descartes firmly denied that he and GermanyRose Cross SocietyThere are many coincidences in the relevant documents left by him. He does not admit that it may be because of the church at that time.
Descartes shared with Beckman his earlier research on integrated geometry and algebra, and said: "Ifhave a chance toWhen you don't mind using my research or ideas, you can say that it is your idea. "This is just his too polite and modest attitude, but Beckman really takes it as his own credit.Descartes was insulted, so he condemned Beckman's "stupidity and ignorance".
Social evaluation
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Descartes is one of the founders of modern European philosophy,HegelHe is called "the father of modern philosophy".He formed his own system, meltingMaterialismAndidealismYu Yilu had a profound impact on the history of philosophy.
Descartes' methodology had an important impact on the development of physics later.Based on the ancient deductive method, he created a mathematical based deductive method:RationalismSelf explanatoryAxiom of intuitionStart, use mathematical logic deduction, and deduce the conclusion.This method andBaconExperiments advocatedInductionCombinedHuygensandNewtonThe comprehensive application of human beings, especiallyTheoretical physicsImportant methods.As one of the most successful examples of his general method, Descartes used the method of algebra to solve geometric problems, and established the foundation of coordinate geometry, namely analytic geometry.
There are two points worth noting in Descartes' methodology.
First, he is good at using intuitive "models" to explainphysical phenomenon。For example, use the "tennis ball" model to explainRefraction of light；The "walking stick of the blind" is used as a metaphor for the instantaneous transmission of light information along matter;useWaterAnd successfully explained the rainbow phenomenon.
Second, he advocated the use of assumptions and hypothesis methods, such asVortex theory。In addition, he proposed the principle of "universal suspicion".Under the historical conditions at that time, this principle played a great role in opposing church rule, advocating authority, promoting rationality, and advocating science.
Descartes can be called one of the most influential masters in European philosophy and science in the 17th century and later, and is known as the "ancestor of modern science".
