The peculiarity of the thought experiment is that. Logical structure of a thought experiment.doc - Logical structure of a thought experiment. The Infinite Monkey Theorem

PURPOSE: to teach students to use a thought experiment.

Tell about the thought experiments of G. Galileo.

1. A THOUGHT EXPERIMENT is an imaginary experience with ideal objects, thanks to which the foundations of some theoretical concept or its limits are set [22].

Thought experiment is based, generally speaking, on the evidence of this or that state of affairs. For example, it can be considered obvious that two equal weights will balance an equal-arm lever. That is, we can mentally imagine that the scales in this case will remain at rest.

An example of a more complex thought experiment is Galileo's famous mental experiment with a uniformly moving ship. Galileo was proud of the fact that while conducting thought experiments with falling bodies, etc., he established the facts of physical reality with great reliability “without having done a hundred tests, not even one” [22].

LET'S CONSIDER GALILEY'S FAMOUS EXPERIENCE WITH A SHIP.

Galileo says. Retire with one of your friends in a spacious room under the deck of a ship, stock up on butterflies, flies and other flying insects. Let you also have a large vessel with water and small fish swimming in it; hang a bucket at the top, from which water will fall drop by drop into another vessel with a narrow neck, placed at the bottom. While the ship is stationary, observe diligently how small flying insects move at the same speed in all directions of the room; the fish, as you will see, will swim indifferently in all directions; all falling drops will fall into the substituted vessel; and when throwing an object, you do not have to throw it in one direction with greater force than in the other, if the distances are the same; and, if you jump, pushing off with two legs at once, you will make a jump at the same distance in any direction. Observe all this diligently, although you have no doubt that as long as the ship is stationary, everything should happen in this way.

NOW MAKE THE SHIP MOVE WITH ANY SPEED UNIFORMALLY AND WITHOUT SUSPENSION - in all these phenomena you will not find the slightest change and by none of them you will not be able to determine whether the ship is moving or is stationary. When jumping, you will move on the floor the same distance as before, and you will not make large jumps towards the stern than towards the bow, on the basis that the ship is moving quickly, although during the time that you will be in the air, the floor below you will move in the opposite direction of your jump. Throwing some thing to a friend, you will not have to throw it with more force when he is on the bow and you are in the stern than when your relative position is reversed. The drops, as before, will fall into the lower vessel, and none will fall closer to the stern, although while the drop is in the air, the ship will travel a certain distance. Fish in water will not swim with great effort to the front than to the rear wall of the vessel; just as nimbly they will rush to food placed in any part of the vessel.

Finally, the butterflies will still fly in all directions, and it will never happen that they gather at the wall facing the stern, as if tired, following the rapid movement of the ship, from which they were completely isolated, holding for a long time in air.

If a little smoke is formed from a drop of lighted incense, then it will be seen how it rises up and keeps like a cloud, moving indifferently, in one direction no more than in the other. The reason for the COORDINATION OF ALL THESE PHENOMENA is that the movement of the ship is common to all objects on it, as well as to the air.

The thought experiment with the ship is unusual in its structure. And this affects the very style of presentation. Galileo does not invent anything here. He simply described phenomena that have been observed in the past countless times.

But, peering into the well-known, he sees something that was not known to anyone.

“Look, he says, here is a fact that everyone knows. But this fact, if you look at it "through the eyes of reason", irrefutably testifies to how the world is arranged in its foundations. "

THUS: GALILEUS'S LAW OF INERTIA IS OBTAINED BY A THINKING EXPERIMENT.

The law of inertia says BODIES SAVE VALUE AND DIRECTION OF SPEED WHEN NO FORCES ARE AFFECTING THEM / OR EQUALIZED FORCES ARE ACTING /.

Thought experiment can be widely used in school research. The use of this method in school is advisable to study such, for example, processes as:

The balance of bodies on inclined plane;

Fluid action in hydraulic machines;

Processes operating in the law of conservation of energy;

The use of a thought experiment in school helps to develop the thinking of students., The ability to carefully reason.

Solve the logic problem: you need to spill an 8-liter bucket of water in half using empty cans of 5 and 3 liters.

Explain the expression: “People know what is GOOD, but they do what is BAD” (Socrates).

Questions to consolidate the material.

1. What is the value of the thought experiment to the student?

2. What famous thought experiment did Galileo do?

3. What is specific used in the thought experiment?

State Educational Institution

Gymnasium №1505

abstract

"Thought experiment as a method scientific knowledge»

Completed: student of grade 9 "B"

Menshova Maria

Scientific adviser: Purysheva N.S.

Moscow 2011

Introduction ................................................. .................................................. ................... 3

Chapter 1. The role and significance of a thought experiment in physics .............................. 5

Chapter 2. Thought experiment in classical physics .................................... 9

Chapter 3. Thought experiment in the Theory of Relativity ............................. 22

Conclusion ................................................. .................................................. ............... 33

List of used literature ............................................... .......................... 34

INTRODUCTION

Thought experiment as a method of scientific cognition consists in obtaining new or verifying existing knowledge by creating objects and managing them in artificially given situations.

Thought experiment is quite often used to prove or disprove the most significant ideas from the point of view of science, such as: free fall of bodies, proof daily rotation Earth. Even the very creation of the theory of relativity and quantum mechanics would be impossible without the use of thought experiments. Modern philosophy and all sciences would be greatly impoverished without thought experiments.

The history of the development of physics shows that in ancient times and the Middle Ages in the conditions of development experimental science At that time, the thought experiment was the main research method. Today we can say with confidence that the founder of the application this method was Aristotle. Although this great philosopher did not formulate the definition of the method itself, he understood that scientific knowledge is impossible without it. Almost all famous scientists who lived after him also paid some attention to this method.

To understand the features of a thought experiment, let's look at an example that clearly illustrates them. We visualize a certain situation; we perform some mental activity using our imagination; we mentally observe what is happening and draw a conclusion.

The most striking thought experiment, in our opinion, is the proof of Titus Lucretius Cara about the infinity of space. We will assume that there is a "wall" around the perimeter of the universe. Accordingly, we can throw a spear into this wall. If the spear flies through it, then we can safely say that there is no wall. If the spear is reflected and comes back, then this will mean that something is outside the edge of space. To get the latter, the wall must really exist. Either way, there is no wall; space is infinite.

Currently given scientific method is used in economics, demography and sociology, experiments that use mathematical models of economic, demographic and social processes and which are carried out with the help of computers (electronic computers), allowing you to work simultaneously with various complexes of factors interacting or related to each other. A special type of thought experiment is scenario development of the possible development of the course of events.

In the course of school physics, a thought experiment, unfortunately, is rarely used. It is believed that it often interferes with giving basic knowledge about real objects and about the nature of physical phenomena, and therefore is more often additional material to the main course. This situation seems to be incorrect, because does not allow to present with sufficient completeness the methods of scientific knowledge.

This paper shows the importance of a thought experiment as a method of scientific cognition, based on an analysis of the literature on this topic.

The purpose of this work is to substantiate the importance of a thought experiment in the development of physical science and a description of thought experiments in classical physics and the theory of Relativity.

The main tasks of this work are: analysis of the concept of "thought experiment", the study of thought experiments in various branches of physics, generalization of the ideas of scientists and philosophers different eras about the nature that they expressed in their thought experiments, their points of view; and the presentation of this information in the form of an abstract.

This abstract is divided into three parts. First chapter- the role and significance of a thought experiment in physics - a concept, a review of the literature on this topic. Chapter two- thought experiment in classical physics - thought experiments of Galileo Galilei, Rene Descartes. Chapter Three- a thought experiment in the theory of relativity by Albert Einstein.

Chapter 1

ROLE AND SIGNIFICANCE OF A THOUGHT EXPERIMENT IN PHYSICS

"What would be observed in experience, if not with the eyes in the forehead, then with the eyes of the mind?"

Galileo Galilei

Thought experiments appeared in the ancient period, more than one and a half thousand years ago. He made huge contribution into science and helped philosophers and scientists of different eras to discover new laws and theories.

A thought experiment is a cognitive process that has the structure of a real physical experiment, with an ideal physical model created on the basis of visual images, the functioning of which obeys the laws of physics and the rules of logic. At the same time, a thought experiment combines the power of formal logical inference and experimental reliability.

Physics studies nature with the help of abstract ideal models, which are described using a mathematical apparatus. Thought experiment allows teaching the transition from reality to abstract ideal models, as a result of actions with which to obtain results applicable to real objects.

Ernst Mach is famous for the fact that it was he who first introduced into physics, and then into other sciences, the term "thought experiment" (Gedankenexsperiment). In his book The Science of Mechanics, Mach said that we possess a large store of "instinctive" knowledge, obtained from personal experience. Such knowledge is not always clearly formulated, but in a suitable situation it will find its application in practice. A child, for example, not knowing anything about the forces of action and reaction, from own experience has the idea that if you hit the table hard with your hand, it will hurt for a long time. The child does not even realize that the table applied the same force to him as the child applied to the table. It turns out that in his imagination, each person can mentally create this or that situation, having performed certain mental actions, get a result that will correspond to the result in real life.

Thought experiment originated in ancient times. Modern science came from ancient philosophy, therefore, it is important to consider the significance of the thought experiment in ancient philosophy.

Ancient science was distinguished by the fact that it did not imply real experiments as a method of cognizing the surrounding world. It was believed that theoretical conclusions and thought experiments are the only correct methods of cognition, they were speculative and could not be associated with observation and measurement.

In ancient times, such philosophers as Thales of Miletus, Anaximenes, Heraclitus, Empedocles, Anaximander, Anaxagoras, were interested in the question of the structure of matter. They tried to understand what can be considered elementary, indivisible. Soon after Anaximander and Anaxagoras came to the concept of atoms, the school of atomists appeared. The founders of this school, the philosophers Leucippus and Democritus, suggested that all substances are composed of the same type of primary matter. Moreover, the existing differences in the properties of these bodies arise due to the difference in the shape and size of the simplest particles. A well-known line from the teachings of Democritus-Epicurus: "Bodies il things represent the beginning, il they consist of a confluence of particles of the original" [cit. on 2, p.19].

Heron of Alexandria is famous for his treatise "Pneumatics". It describes various pneumatic devices that operate with compressed or heated air and steam. The book describes many mechanisms based on hydraulics and pneumatics: a water clock, a siphon, a water organ, an eolipil (a ball rotating by the force of steam - the prototype of the current steam turbine). It is striking that Heron did not create in practice any of his devices or mechanisms. The ancient philosopher used theories and thought experiment. Most likely, Heron understood that it was impossible to realize these inventions at the level of technology he was using today.

The greatest philosopher of antiquity, Aristotle (384 BC) paid great attention to the issues of movement. He reasoned that there are two types of movement: natural and artificial. Natural movement is inherent in ideal objects located in the superlunar world, and artificial - in bodies in the sublunary world. Natural movement is completely and does not require the application of force, such as the movement of a body in a circle, the movement of planets. Artificial or violent movement of bodies appears as a result of the action of various forces on them.

Aristotle called his law "vis impressa". It boils down to the fact that a moving body will sooner or later stop if the force that sets it in motion ceases to act.

The purpose of thought experiments is to study physical phenomena. Quite often, carrying out a real physical experiment is impossible due to its complexity for technological, practical or economic reasons. Sometimes the conduct of a real experiment is limited by the level of development of knowledge, technology and technology, and sometimes it cannot be carried out due to the frequent idealization of situations in thought experiments.

a way of thinking in which the researcher tries to mentally imagine the possible results of those operations that can actually be undertaken in a certain situation.

EXPERIMENT, THINKING

A type of non-experimental thinking in which the researcher considers the possible outcomes of the operations that might be done. In general, such thought experiments are useful heuristics for examining the meaning of certain theoretical models or for thinking about the meaning of accumulated facts. Also called Gedanken experiments, from the German word for thought.

THOUGHT EXPERIMENT

view cognitive activities, built on the type of a real experiment and having its structure, but developing entirely in an ideal plan. It is in this fundamental position that the activity of the imagination is manifested here, which gives reason to call this structure an imaginary experiment. To M. e. even Aristotle addressed, proving the impossibility of emptiness in nature. The widespread use of M. e. begins with Galileo, who was the first to give a sufficient methodological indication of M. e. as a special cognitive education, qualifying it as an imaginary experiment. M. e. does not reduce to operating with concepts, but is a cognitive education that arises on the basis of imagination in the process rational knowledge... M. e.- an activity carried out in an ideal plan, contributing to the emergence of a cognizing subject of new heuristic possibilities both in the logical-conceptual and in the sensory-figurative reflection of reality. M. e. replacing the real in some way, it serves as its continuation and development. The subject can make, for example, an indirect verification of the truth of knowledge, without resorting to real experimentation where it is difficult or impossible. In addition, M. e. allows you to explore situations that are not realizable in practice, although fundamentally possible. Since M. e. proceeds in an ideal plan, the correctness of the forms of mental activity plays a special role in ensuring the real significance of its results. At the same time, it is obvious that mental experimentation obeys logical laws... Violation of logic in the operation of images in M. e. leads to its destruction. In M. e. activity unfolds in an ideal plan, and the specific bases of objectivity in this case are the logical correctness of operating with images, on the one hand, and the activity of imagination, on the other. Moreover, the decisive role, as it should be in an experiment, belongs here to the "sensory" side, ie, to the imagination. Thus, M. e. differs from a real experiment, on the one hand, in its ideality, and on the other hand, the presence in it of elements of imagination as the basis for evaluating ideal constructions (L.D. Stolyarenko).

Thought experiment

One of the most obvious forms of manifestation of the imagination in science is a thought experiment. Even Aristotle turned to a thought experiment, proving the impossibility of emptiness in nature, i.e. using a thought experiment to reject the existence of certain phenomena. The widespread use of the thought experiment begins, apparently, with Galileo. In any case, E. Mach in his Mechanics believes that it was Galileo who was the first to give sufficient methodological indication of the thought experiment as a special cognitive formation, qualifying it as an imaginary experiment. A thought experiment is not reduced to operating with concepts, but is a cognitive formation that arises on the basis of imagination in the process of rational cognition.A thought experiment is a type of cognitive activity that is built like a real experiment and takes on the structure of the latter, but develops entirely in an ideal plan. It is at this fundamental point that the activity of the imagination manifests itself, which gives reason to call this procedure an imaginary experiment. Thought experiment is an activity carried out in an ideal plan, contributing to the emergence of new heuristic possibilities in the cognizing subject, both in the logical-conceptual and in the sensory-figurative reflection of reality. A thought experiment, replacing in some way a material experiment, serves as its continuation and development. The subject can make, for example, an indirect verification of the truth of knowledge, without resorting to real experimentation where it is difficult or impossible. In addition, a thought experiment allows one to study situations that are not realizable in practice, although they are fundamentally possible. Since the thought experiment proceeds in an ideal plan, the correctness of the forms of mental activity plays a special role in ensuring the real significance of its results. At the same time, it is obvious that mental experimentation obeys logical laws. Violation of logic in operating with images in a thought experiment leads to its destruction. In a thought experiment, activity unfolds in an ideal plan, and the specific grounds for objectivity in this case are the logical correctness of operating with images, on the one hand, and the activity of imagination, on the other. Moreover, the decisive role, as it should be in an experiment, belongs here to the "sensory" side, ie. imagination. A thought experiment, therefore, differs from a real experiment, on the one hand, in its, so to speak, ideality, and on the other hand, in the presence of elements of the imagination in it as the basis for evaluating ideal constructions. So with the help of the imagination, rather rigidly guided by logic, Galileo presents a situation in which the reasons that hinder the free movement of the body are completely eliminated. Thus, he oversteps the line of what is really possible, but on the other hand, with all possible evidence demonstrates the feasibility of inertial motion - the body will maintain its motion for an infinitely long time. The productive power of the imagination presented here a situation that was impossible from the point of view of Aristotelian physics. And Galileo was aware of the fact that Aristotelian physics is opposed by the imaginary result of a thought experiment - a body that continues to move in the absence of its driving forces is something impossible from the point of view of physics. Thus, it is the logical opposition of competing theories that forms the context in which unacceptable (from any of the competing positions) assumptions and "crazy" hypotheses are quite admissible. In short, imagination is permissible in every sense of the word.

Imagination and thought experiment

The history of the development of science testifies to the brilliant results of the application of a thought experiment, and modern trends in the development of knowledge turn it into one of the most important procedures of cognition. The thought experiment was used by Galileo and Newton; A. Einstein, N. Bohr, G. Heisenberg constantly turned to it. However, there is no uniform terminology for the thought experiment. It is called mental idealized, imaginary, theoretical.

Thought experiment and creative imagination

Thought experiment is a cognitive activity where important place takes the scientific imagination. D.P. Gorsky calls a mental experiment a method "that allows resorting to distractions, as a result of which an idealized object (abstraction, idealization) is created". Thought experiment is defined here as one of the forms of mental activity of the cognizing subject. On the other hand, a mental (imaginary) experiment is characterized as a mental process that is built like a real experiment and accepts its structure. This is a kind of theoretical reasoning that implements one of the main human functions search for new knowledge. Thought experiment is a form of human mental activity that is widespread in science as a heuristic research tool.

An experiment carried out in practice is a type of material activity that has as its purpose the study of an object, verification of the knowledge gained, and so on. Any material experiment presupposes the choice of a certain object of research and a certain method of influencing it. The exposure is carried out under strictly reproducible conditions, which ensures the reproducibility of the experimental result.

Thought experiment, in turn, develops from a material experiment. At some stages of the development of the experiment, the subject does not separate the understanding of its course from the objective course of the experimental process. Later, the ability to perform the experiment appears, as it were, in the mind, without materially influencing the very course of the experiment. Characteristic feature conscious human life is the fact that before performing directly, the subject mentally solves various practical and theoretical problems, performs complex and varied mental operations that anticipate immediate action.

The peculiarity of a thought experiment is associated with the fact that it is a type of cognitive activity in which the structure of a real experiment is reproduced in the imagination. This means that there is a certain analogy between thought and material experiment. This analogy is an essential feature of mental experiment. “Not only can we create images more or less arbitrarily, we can also modify them and then find out what changes can result as a result of certain features. We can carry out an imaginary experiment by introducing transformations into images and then noting what further content can be imaged in terms of these changes. This procedure is much like a physical experiment; images can be manipulated in the same way as physical objects. " "A person in his mind operates with spatial images, mentally puts this or that object in different positions and mentally selects such" experimental "situations, writes A.P. Chernov, in which, as in ordinary experience, more important or for some reason interesting features of a given object. "The researcher mentally introduces the object under study into more and more new interactions, puts it in various conditions, constantly taking into account the emerging cause-effect relationships, space-time and other changes that must occur in the object, and correlating them with the initial conditions and connections. The phenomenon under study is repeated many times in a different composition and order, and new, previously unknown properties and aspects are revealed in it.

Creative imagination makes it possible to anticipate many actions. Mentally, a person can create a variety of connections and immediately slow down them if they do not give the desired effect. He mentally tests many variants of preliminary hypotheses before putting them into the basis of the experiment. Depending on the success or failure of certain trial actions, it becomes possible to exclude some areas of search, to significantly limit its probable area.

source unknown

Thought experiment is not reducible to operating with concepts, but is a cognitive formation that arises on the basis of imagination in the process of rational cognition.

Thought experiment is a type of cognitive activity, built on the type of a real experiment and accepting the structure of the latter, but developing entirely in an ideal plan... It is at this fundamental point that the activity of the imagination manifests itself, which gives reason to call this procedure an imaginary experiment.

A thought experiment is an activity carried out in an ideal plan, contributing to the emergence of new heuristic possibilities in the cognizing subject, both in the logical-conceptual and in the sensory-like reflection of reality. A thought experiment, replacing in some way a material experiment, serves as its continuation and development. The subject can make, for example, an indirect verification of the truth of knowledge, without resorting to real experimentation where it is difficult or impossible. In addition, a thought experiment allows one to explore situations that cannot be realized in practice, although in principle possible.

Since the thought experiment proceeds in an ideal plan, the correctness of the forms of mental activity plays a special role in ensuring the real significance of its results. At the same time, it is obvious that mental experimentation obeys logical laws. Violation of logic in operating with images in a thought experiment leads to its destruction. In a thought experiment, activity unfolds in an ideal plan, and the specific grounds for objectivity in this case are the logical correctness of operating with images, on the one hand, and the activity of imagination, on the other. Moreover, the decisive role, as it should be in an experiment, belongs here to the "sensory" side, ie, to the imagination.

Thought experiment thus differs from a real experiment, on the one hand, in its, so to speak, ideality, and on the other, in the presence of elements of imagination in it as a basis for evaluating ideal structures.

So with the help of imagination, rather rigidly guided by logic, Galileo imagines a situation in which the reasons that hinder the free movement of the body are completely eliminated. Thus, he oversteps the line of what is really possible, but on the other hand demonstrates with all possible evidence the feasibility of inertial motion - the body will maintain its motion for an infinitely long time.

The productive power of the imagination presented here a situation that was impossible from the point of view of Aristotelian physics. And Galileo was aware of the fact that Aristotelian physics is opposed by the imaginary result of a thought experiment - a body that continues to move in the absence of its driving forces is something impossible from the point of view of physics.

Thus, it is the logical opposition of competing theories that forms the context in which unacceptable (from any of the competing positions) assumptions and crazy hypotheses. In short, imagination is permissible in every sense of the word.