Possibilities of application of mathematical knowledge in everyday life. Lesson on the topic "the importance of mathematics in human life"

In society, there is a point of view according to which all people in matters of intellectual knowledge have a tendency either to the mathematical pole or to the humanitarian one. The child goes to school, gets an A in literature, but mathematics is not given to him in any way. “Nothing,” parents say, “he is a humanitarian with us.” The reverse situation is also often encountered.

But how fair is that? Is mathematics objectively more difficult to master than the humanities? Are human abilities inherent genetically or are they the result of upbringing?

During the study Mathematicians were smarter than the humanities it turned out that if a student does well in exams in the exact disciplines, in most cases he also successfully copes with the humanities. And students in liberal arts schools fail not only in mathematics, but also in languages.

Does this mean that mathematical disciplines more complex? No.

If a person does well in all exams, this speaks of his responsibility, and not of his abilities. Many people can easily operate with abstract concepts and learn languages, but mathematics is very difficult for them. In addition, other studies show that there is no connection between the development of mathematical and humanitarian disciplines at the level of brain activity. These are completely different cognitive abilities.

The physiological basis of intellectual abilities

Research Origins of the brain networks for advanced mathematics in expert mathematicians scientists recorded the brain activity of mathematicians and other people during the performance of various tasks. As a result, they came to the following conclusion.

While doing mathematical operations a person activates special areas of the brain that are not associated with language abilities.

It turns out that the difference between mathematical and humanitarian knowledge lies at the physiological level. There are zones responsible for mathematical thinking, and there are zones for linguistic thinking. It cannot be said that any of them is more perfect.

Nature and nurture

In the study mentioned above, scientists also concluded that the ability of children to perform simple algebraic operations is the key to further mathematical success. After all, at an early age, even before any education, parts of the brain develop differently in a person. Someone's mathematical zones are better developed, while someone's are worse.

Since both elementary and more complex tasks involve one neural network, you can predict the future talent of the child even before it manifests itself. The kid quickly understood why 1 + 1 = 2? Then in the future it will be relatively easy for him to get sines and cosines.

The same can be said about the humanities. The speed with which a child learns a language, the ability to capture the basic laws of grammar, allow us to assess how good he will be in comprehending the humanities, since early success in this area indicates the potential of the corresponding area of ​​\u200b\u200bthe brain.

It can be assumed, that physiological features predetermine our cognitive abilities. However, this is not the case, and here's why:

• Many other factors that influence the manifestation of talent are not taken into account. For example, a person may have the makings of a mathematician at the physiological level, but at the same time there is absolutely no interest in this discipline, because of which his natural talent will not be developed.
• What we speak of as a physiological tendency may in fact be the result of early parenting.

As the Swiss psychologist and philosopher Jean Piaget notes Cognition, the development of both linguistic and mathematical cognitive abilities occurs in the preoperative period (2–7 years). It is then that the physiological predisposition of the child to a certain activity can manifest itself.

This period in the development of the brain is the most important, since the creation of neural connections proceeds according to the principle of the frequency of their use. About the features of brain development from conception to adolescence. That is, after 2-3 years, those of its zones that are most often involved begin to actively develop.

At this stage, the development of the brain directly depends on the activity of a person and the repetition of any practices.

The study of twins also sheds light on the formation of human abilities. Their set of genes is approximately the same, and therefore differences in intellectual abilities are likely to be due to external factors.

Such studies conducted by Russian scientists in the 90s Where do smart kids come from?, showed that from the age of two, the intelligence of twins really becomes similar in relatively identical external conditions.

Approximately the same conclusion was made by scientists from the University of California at Santa Barbara. The high heritability of educational achievement reflects many genetically influenced traits, not just intelligence. The external environment matters and plays the role of a condition for the implementation of the biological basis.

conclusions

Whether a person becomes a humanist or a mathematician depends on the biological factor and heredity that determine the development of his brain. However, the manifestation of this factor is strongly influenced by activity in childhood. We are talking about the period when a person has not yet directly begun to study the disciplines themselves, but in the process of playing and communicating with parents somehow involves different areas of the brain, stimulating their development.

In practice, this means the following: parents should not impose on the child an activity for which he does not have a special attraction and in which he is not very successful. You need to try to find talent and contribute to its development.

Back forward

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Members: 7th grade students.

Goals:

• educational: the formation of a sustainable interest in mathematics;
• educational: the formation of such personality traits as cognitive activity.
• developing: development of creative abilities of students (imagination, observation, memory), monologue speech, the ability to identify cause-and-effect relationships, the development of logical thinking.

Tasks:

• study bibliographic sources on the topic;
• to introduce the history of the emergence and development of mathematics
• identify areas of application of mathematical knowledge.

Products: computer presentation.

Necessary equipment: projector, screen, computer.

Event progress

Introductory speech of the teacher:

1 slide Topic: "Mathematics in human life"

2 slide Fundamental question: Does a person need mathematics?

3 slide Problem questions:

• How and when did mathematics start?
• What professions need mathematics?
• What mathematicians do you know?
• Is knowledge of mathematics necessary for a modern person?

Student presentation:

To drive ships
To fly into the sky
There's a lot to know
And at the same time, and at the same time,
You notice,
Very important science
Maths!

Why ships
Don't run aground
And they're on course
Through fog and blizzard?
Because because,
You notice,
Helps captains
Maths!

So that a doctor, a sailor
Or become a pilot.
We must first of all
Know mathematics.
And there are no professions in the world
You notice,
Wherever you need
Maths!

4 slide How and when did mathematics start?

When it comes to something very simple, understandable, we often say: "The matter is clear, like two times two - four!".

But before you think of the fact that twice two is four, people had to study for many, many thousands of years.

Of course, this teaching did not go behind the desk. Man gradually learned to live: build dwellings, find a way on long trips, cultivate the land.

Because even in the most distant times, when people lived in caves and dressed in animal skins, they could not do without counting and measuring.

Many rules from school textbooks of arithmetic and geometry were known to the ancient Greeks more than two thousand years ago.

Other ancient peoples - Egyptians, Babylonians, Chinese, peoples of India - in the third millennium before our era had knowledge of geometry and arithmetic, which some students of the fifth or sixth grade lack.

With every decade, mathematics has become more and more people need.

5 slide Pythagoras

The great scientist Pythagoras was born around 570 BC. on the island of Samos. Pythagoras' father was Mnesarchus, a gem-carver.

Pythagorean theorem- one of the fundamental theorems of Euclidean geometry, establishing the relationship between the sides of a right triangle. It is believed that it was proved by the Greek mathematician Pythagoras, after whom it is named.

The theorem goes like this: AT right triangle the square of the hypotenuse is equal to the sum of the squares of the legs .

6 slide

In the late nineteenth century, various suggestions were made about the existence of human-like inhabitants of Mars. Jokingly, though not entirely unreasonably, it was decided to send a signal to the inhabitants of Mars in the form of the Pythagorean theorem. It is not known how to do this; but it is obvious to everyone that the mathematical fact expressed by the Pythagorean theorem takes place everywhere and therefore inhabitants of another world similar to us must understand such a signal.

7 slide

Sofia Kovalevskaya

A girl from a noble family loved mathematics and even at night hid a difficult problem book under her pillow (her parents did not approve of her hobbies).

At that time, it was not customary for women to go to college, but she went against the will of her parents to Germany, to the university, and came to a famous professor. He did not want to take her and, in order to get rid of it, he gave several problems that he himself had compiled, saying that if she decides, she will take her to her.

These problems could not be solved even by professors. The girl decided in twenty minutes.

Sofia Kovalevskaya graduated from the university and became a world-famous mathematician

8 slide

What can mathematics do?

• It helps the astronomer determine the paths of distant stars.
• An engineer uses mathematics to design a jet plane, a ship, or a new power plant.
• To a physicist, mathematics reveals the laws of the atomic nucleus, and to a sailor it shows the path of a ship in the ocean.
• In a word, mathematics can do everything or almost everything where you need to calculate something.

But everything starts with mathematics.

• The child has just been born, and the first figures in his life are already being heard: height, weight.
• The kid grows up, cannot pronounce the word "mathematics", but is already engaged in it, solves small problems of counting toys, cubes.
• And parents do not forget about mathematics and tasks. When preparing food for a child, weighing him, they have to use mathematics.
• After all, you need to solve elementary tasks: how much food you need to cook for the baby, given his weight.

9 slide

1 example

You stand at the checkout and pay for the goods. You bought food for 432 rubles, and you have 500 rubles in banknotes of 100 rubles. And they give you change of 40 rubles, although they should give you 68 rubles. So you were shortchanged by 28 rubles !!!

10 slide

2 example

I need to be at the dacha at 15.40. I spend 1.40 hours on the road. Today I have to go to the store. When should I leave? How much time can I spend in the store?

11 slide

12 slide

Solve the problem.

How to get 100 with one action and five units?

13 slide

• 111 - 11 = 100

14 slide

Where can you do without mathematics?

• The builders are building a house. It is necessary to calculate how much cement, how many bricks. Height, width. Compose the project.
• Here the dressmaker is going to sew a dress. Measures a person, makes a pattern. Does she need math? Maybe…
• The store considers the received goods, revenue.
• The bank counts money, dealing with huge amounts, with interest.
• Even in music, in poetry, you have to count - rhythm, size, eighths, quarters, iambs, choreas.
• What can we say about such complex sciences as space (rockets, satellites), computer technology, television, radio! Of course, none of this would have been invented without calculations, without mathematics.
• That is, mathematics is our whole life?

15 slide

The task of applying the sign of equality of triangles to measure the distance between two inaccessible objects .

Condition: The road-laying team has to make a tunnel, but the distance to be cut through the mountain is not known. What should the team do to find out this distance, if the distance from A to C and from B to C is known (Fig. 1)?

Picture 1

Solution: The brigade cannot make a road around the mountain. Therefore they took little trick: a person was placed at the entrance to the not yet cut tunnel - (A) and at the exit point too - (B), a third person was placed on the side of the mountain - (C), a triangle ABC was formed. Person A draws a straight line through point C, and person B also draws a straight line through point C. After drawing straight lines and placing two more people on them at a certain distance - (D,e) so CD=AC, a SW = EU.Corner ACB=ECD by the property of vertical angles, so the triangle DEC equal to triangle ABC. Now the brigade connects points D and E with a segment on the ground. It remains for the workers to measure the distance from E to D, which will be equal to the desired distance from A to B.

16 slide

Is knowledge of mathematics necessary for a modern person?

The world and life itself is rapidly changing. It includes new technologies. Only mathematics and problem solving in the traditional sense do not change themselves. Mathematical laws have been verified and systematized, so a person in important points can rely on her to solve any problem. Math won't let you down.

But every year we have more and more wonderful machines: complex machine tools, various automatic machines. In order to work well on such machines, you need a lot of knowledge. Now mathematics is needed not only by a scientist or engineer, but also by a foreman and a factory worker.

However, even a few decades ago, there were many such problems that were almost impossible to solve, although mathematicians knew how to solve them. It happened that dozens of people worked for several years to solve a single problem. The calculations were slow. The main "tools" of a mathematician were the same as in the days of the ancient Greeks - his own head and a blank sheet of paper with a pencil.

And now mathematics has a new powerful assistant, which is called an electronic computer. Existing high-speed computers operate hundreds of thousands of times faster than humans.

Mathematics has never been so comprehensive and such a science needed by people as it is today. It is difficult to talk about what mathematics will be like tomorrow. It is developing so rapidly now, new discoveries are made in it so often that it is probably useless to guess what will be. One thing is certain: tomorrow mathematics will become even more powerful, even more important and more needed by people than today.

It is known that mathematics is never alone, it is always applied to something! This suggests that no other science can exist without mathematics. Therefore, if humanity had not created the world of mathematics, it would never have been able to possess SCIENCE! Let's take technological progress as an example. In order for some new apparatus to be born, many scientists and developers are needed. Among them there will definitely be a mathematician, because there is undoubtedly a need for this! Hence follows the important role of mathematics in the development of the world around us and humanity in general.

The development of methods of computational mathematics and the increase in the power of computers make it possible today to perform accurate calculations in the field of dynamics of the most complex living and non-living systems in order to predict their behavior. Real success along this path depends on the readiness of mathematicians and programmers to work with data obtained in traditional ways in the natural and human sciences: observation, description, survey, experiment.

Position of mathematics in modern world far from what it was a hundred or even only forty years ago. Mathematics has become a daily tool of research in physics, astronomy, biology, engineering, production organization and many other areas of theoretical and applied activity. Many eminent physicians, economists, and social scientists believe that the further progress of their disciplines is closely related to a wider and fuller use of mathematical methods than has been hitherto. No wonder the Greek scientists said that mathematics is the key to all sciences.

Of course, the above once again proves how important mathematics is not just in itself, but how other sciences need it, rely on mathematical facts and, thereby, help humanity develop further and further! Mathematics has always been an integral and essential part of human culture, it is the key to understanding the world around us, the basis of scientific and technological progress and an important component of personality development.

Mathematics contains features of volitional activity, speculative reasoning and striving for aesthetic perfection. Its main and mutually opposite elements are logic and intuition, analysis and construction, generality and concreteness.

We have already considered many reasons why mathematics is considered not even one of, but the most important science. Let us now try to give a number of facts proving this. They are simple, they are faced by any person, and every day.

1. Mathematics is found and used in Everyday life, therefore, certain mathematical skills are needed for every person.

Isn't it true that we have to count in life (for example, money), we constantly use (often without noticing it) knowledge about the quantities that characterize the length, area, volume, time intervals, speeds and much more. All this came to us in the lessons of arithmetic and geometry and came in handy for orientation in the world around us.

Mathematics is needed for children to form a spiritual image, develop the necessary character traits (patience, diligence). A girl can take into account the fact that mathematics will help her to be a good mother (to help her children, to conduct developmental work with them). For some, doing this science gives self-confidence, someone is glad that he learns about interesting people (for example, about Archimedes). To some, mathematics is pleasant as a science, the majority is aware of its need for future profession.

Mathematical knowledge and skills are required in almost all professions. First of all, of course, in those related to natural sciences, technology and economics. Mathematics is the language of natural science and technology, and therefore the profession of a natural scientist and engineer requires a serious mastery of many professional information based on mathematics. Galileo said it very well: “Philosophy (we are talking about natural philosophy, in our modern language - about physics) is written in a majestic book that is constantly open to your gaze, but only one who first learns to understand its language and interpret it can understand it. signs with which it is written. It is written in the language of mathematics. But now there is an undoubted need to apply mathematical knowledge and mathematical thinking to a doctor, linguist, historian, and it is difficult to cut off this list, it is so important mathematical education for professional activities in our time. Therefore, mathematics and mathematical education are needed to prepare for a future profession. This requires knowledge of algebra, mathematical analysis, probability theory and statistics.

One more the main reason The need of mankind in mathematics is the education in a person of the ability to understand the meaning of the task assigned to him, the ability to correctly, logically reason, to learn the skills of algorithmic thinking. Everyone needs to learn how to analyze, distinguish a hypothesis from a fact, criticize, understand the meaning of the task, schematize, clearly express their thoughts, etc., and on the other hand, develop imagination and intuition (spatial representation, the ability to foresee the result and predict the solution path and etc.). In other words, mathematics is necessary for the intellectual development of the individual. In 1267 the famous English philosopher Roger Bacon said: ``He who does not know mathematics cannot know any other science and cannot even show his ignorance.''

The military security, economic and technological independence of the country depend on the mathematical literacy of its citizens, and the bulk, and not the elite group. It is difficult to overestimate the importance of mathematics, mathematical education and mathematical culture in the modern world. All modern science permeated mathematical methods and mathematical ideas.

Poor mathematical education violates the basic rights of a citizen, in particular the right to free choice of profession. People who do not know what mathematical proof, mathematical reasoning are, are easily manipulated by shameless politicians, as well as financial tycoons and crime bosses through the media they control. Mathematically uneducated people are ready to dutifully follow any false prophet, they listen with delight to demon-possessed clairvoyants and illiterate astrologers. Mathematically illiterate leaders of states, large industrial and financial corporations, surrounded by insufficiently mathematically educated advisers and consultants, today pose a huge danger to humanity. They are not able to think systematically, they cannot even calculate the immediate consequences of their actions, which more and more often lead to military conflicts, economic crises, financial shocks, environmental and humanitarian disasters, which are very quickly losing their local character.

Mathematical modeling should become an obligatory stage preceding the adoption of any responsible decision. Achievements of the Soviet-Russian mathematical science and mathematical education are well known and generally recognized. It was they who became the basis of many real successes of Russia. Soviet period. The Russian mathematical school had a serious impact on the development of world science and education in the second half of the 20th century. Her students can be found in all major scientific centers of the planet. But today we are bitterly witnessing a significant decline in the mathematical education of our society, the fall of its mathematical culture. Numerous so-called innovations are destroying the traditions of Russian education, offering the worst Western examples as benchmarks. The economic ruin, which has become the main sign of the reforms taking place in our country, has pushed the problems of education to the last place. In the education system itself, it was mathematics that found itself in the most difficult position, as a subject that does not correspond well to market ideology. Recently, there has been a constant reduction in hours for mathematical subjects, reduction and simplification of programs. Practically no modern scientific literature on mathematics is published, without which it is impossible to educate highly qualified specialists. The ongoing emigration and semi-emigration of leading scientists and teachers, and now of the best students, is greatly accelerating this process of decay.

Concern about the state of mathematical education in Russia is expressed today by many foreign scientists. Russian mathematical education has been and still remains a model for the whole world, and its destruction can be the beginning of the destruction of the mathematical education of all civilized mankind.

Mathematics is a phenomenon of global culture, it reflects the history of the development of human thought. Destroying mathematics, mathematical education, we are destroying human culture, destroying the history of mankind. Universal computerization not only did not reduce the importance of mathematical education, but, on the contrary, set new tasks for it. A decrease in the level of mathematical education and mathematical culture of society can turn a person from the owner of a computer into his servant and even slave.

In the process of cognition of reality, mathematics plays an ever-increasing role. Today there is no such field of knowledge where mathematical concepts and methods would not be used to one degree or another. Problems that were previously considered impossible to solve are successfully solved through the use of mathematics, thereby expanding the possibilities scientific knowledge. Modern mathematics combines very different areas of knowledge in single system. This process of synthesis of sciences, carried out in the bosom of mathematization, is also reflected in the dynamics conceptual apparatus. In order for humanity to develop, and develop fruitfully, we need not only “ the best minds", but also fresh ideas. And this requires creative people with unusual thinking, a broad outlook, a flexible mind. For all this to be in a person, it is necessary that he perfect himself. Mathematics makes us think, analyze. In the process of searching for information for the message I prepared, I found one interesting site. On it, people of different ages, education, worldviews shared their opinions about mathematics, namely: they left their votes for and against mathematics, for love or hatred in relation to it. Here is what one of the participants in the discussion wrote: “There are no lies in mathematics. All formulas and theorems have a rigorous proof. Mathematics develops the ability to think logically, which allows a person to live interestingly and never be bored. I read a lot of textbooks on higher mathematics. Thanks to the study of higher mathematics, a philosophical analytical mind and the ability to think independently are acquired. The conclusion from this can be drawn as follows: the development of human intellect is necessary for the development of civilization. This is possible thanks to the "philosophical analytical mind and the ability to think independently", which is achieved as a result of "brain warm-up".

Mathematics in human life

Have you ever heard such an expression: mathematics is a country without borders? This phrase about mathematics has a very good reason. Mathematics in human life takes special place. We are so close to it that we simply do not notice it.

But our life begins with mathematics. The child has just been born, and the first figures in his life are already being heard: height, weight. The kid grows up, cannot pronounce the word "mathematics", but is already doing it, solving small problems of counting toys, cubes. And parents do not forget about the tasks. When preparing food for a child, weighing him, they have to use mathematics. After all, you need to solve an elementary problem: how much food you need to cook for the baby, given its weight.

At school math problems there are many and their complexity grows every year. They do not just teach the child certain actions. Mathematical tasks develop thinking, logic, a set of skills: the ability to group objects, reveal patterns, determine relationships between phenomena, make decisions. Mathematics, solving mathematical problems develops the personality, makes it more purposeful, active, independent.

And after school, mathematics is very useful. While studying at the university, at work and at home, you need to constantly solve problems related to mathematics. What is the probability successful delivery exam? How much money do you need to earn to buy an apartment? What is the surface area of ​​the walls of your house, and how much brick should you buy to insulate your house? How to calculate correctly so that a girl or a boy is born? And this is where math comes in. It follows a person everywhere, helps him solve practical problems, makes his life much more convenient.

The world and life itself is rapidly changing. It includes new technologies. Only mathematics and problem solving in the traditional sense do not change themselves. Mathematical laws have been verified and systematized, so a person can rely on it at important moments, solve any problem. Math won't let you down.

National action plan for 2012-2016 for the development of functional literacy of schoolchildrenpays special attention to such basic competencies as literacy in reading, mathematics, and science.

What is the purpose of mathematics education?

University preparation.

Preparation for the future profession.

Intellectual development.

Formation of the worldview.

Orientation in the environment.

Physical education of the brain.

Here are some motivations regarding the importance of mathematical education for the individual.

Mathematics is found and used in everyday life , therefore, certain mathematical skills are needed for every person. We have to count, for example, money in life. We constantly use, often without noticing it, knowledge about the quantities that characterize the extent, area, volume, time intervals, speeds, and much more. All this came to us in the lessons of arithmetic and geometry and came in handy for orientation in the world around us.

Mathematical knowledge and skills are necessary in almost all professions, first of all, of course, in those related to the natural sciences, technology and economics. But there is no doubt the need to apply mathematical knowledge and mathematical thinking to a doctor, linguist, historian, and it is difficult to cut off this list, mathematical education is so important for professional activity in our time. Consequently,mathematics and mathematical education are needed to prepare for a future profession . This requires knowledge of algebra, mathematical analysis, probability theory and statistics.

Philosophical comprehension of the world, its general patterns and basic scientific concepts is also not possible without mathematics. And that's whymathematics is necessary for the formation of a worldview .

Mathematics should contribute to the development of the ethical principles of human society. Its study is designed to educate in a person intellectual honesty, objectivity, the desire to comprehend the truth,it also brings up the ability to aesthetic perception of the world, the beauty of intellectual achievements .

“Mathematics already then needs to be taught, that it puts the mind in order,” - M.V. Lomonosov. Not only arms, legs, body require training, but alsothe human brain needs exercise . Solving problems, puzzles, mathematical puzzles develops logical thinking, speed reaction. No wonder they say that mathematics is the gymnastics of the mind.

Mathematics teacher of KSU "Kokpekty secondary school" Germash E.A.

The meaning of life - mathematical models. Part 1

1. Introduction.

Around 1998, I tried, on the basis of the elements of management theory and system analysis known to me, to formulate some limitations of life strategy in mathematical formulas. Even earlier, in 1991-1994. I gave a course of lectures at the Institute of Instrumentation on Control in Biological and Medical Systems and introduced into these lectures some mathematical descriptions of control algorithms and life strategies. Elements of these lectures I have also introduced into this essay. Naturally, I did not pretend to give recipes for a life strategy - for this there are professional philosophers, founders of philosophical and religious teachings, prophets, mystics, etc. My goal was much more modest - to see how these problems look from the mathematical side. Accordingly, the result is quite modest - one should not look for a direct correspondence between mathematical formulas and life categories - mathematics is not well adapted for the correct description of these categories. I added here a number of literary digressions, some of which I used in my time for the entertainment of students.

2. Preliminary agreements and restrictions.

The concept of "Meaning of life" is ambiguous - it includes explanations of its biological and social mechanisms (how?), its causal relationships (why?), its goals (why?). Most often, when asking this question, it is associated with the latter (why?), i.e. the concepts of "meaning" and "goal" become synonymous in the everyday sense (although this is not at all the case in the mathematical sense). The main part of the further presentation will be devoted to the last understanding - "The Meaning of Life" as "The Purpose of Life".

Literary digression 1.

<<Ситуация очень схожа со сценой из «Фауста» Гете - при попытке перевода Библии на немецкий язык Фауст с первых же строк сталкивается с затруднением: «В начале было Слово». Дело в том, что в древнееврейском и древнегреческом (повидимому, Библию Фауст переводил с одного из этих классических языков, т.е. с подлинника или «Септуагинты») эта строка читается по-разному и в нее вкладывается многозначный смысл.

In ancient Greek, this is "Logos" - the concept includes the cosmic mind of the Universe, the Main Idea and much more. This concept is closest to the translation "Creative Thought". The most clear presentation of the concept is in Plato. The Supreme Being is conceived as the chief architect of the universe.

In Hebrew, this is in one of the variants of "Kabbalah" - for a sage-Kabbalist, the ability to literally create worlds with the "Word" is an absolute truth - you just need to pronounce it correctly, with all the aspirations and rituals. In contrast to the ancient Greek, here the “Word” is given the mystical meaning of direct creation (by the way, historically this precedes the concept of “Logos”). The Supreme Being is conceived as the main master - the demiurge, who creates the Universe.

When trying to find a German analogue of this concept, Faust sorts through the concepts of "Word", "Thought", "Deed" (in Russian translation, and in German also "Will" - a very important addition).

It is quite obvious that in the concept of "The Meaning of Life" there are all these options - and the main idea, and the main thought, and the main thing, as well as the main goal and the will to achieve it, and in addition, for esotericists (initiates) - also mystical understanding.>>

From the foregoing, it is clear that “words correspond to concepts” (also from “Faust”), and if we want to put our research on a scientific basis, then for each quite obvious (in the everyday sense) word, we need to define the concept that we have in mind, of the many possible concepts corresponding to given word. Wittgenstein defines the process of association between a word and a concept as a "language game”: “The whole process of using words in a language can also be represented as one of those games with the help of which children master their native language. I will call these games"language games" and sometimes speak of some primitive language as language game».

The correspondence between a word and a concept can be done most simply, although not very clearly, at the mathematical level - at the level of models. Abstract mathematical models, of course, will be homeomorphic in relation to the described phenomena of life, but not isomorphic, i.e. the model is the likeness of life, but life is not the likeness of the model. Since we are studying the concept of “Goal”, then in the model for us its predictive value will be the main thing - if the forecast made according to the model allows us to correctly plan the trajectory of movement, strategy and tactics of behavior, then this model will be considered satisfactory. Therefore, the most common objection is mathematics, but in life everything is not so - it turns out to be untenable - the model does not claim to be a complete description, but only serves to predict.

Descriptions of phenomena in terms and categories of culture and morality are, in essence, a list of restrictions imposed on behavior patterns that can also be described mathematically, but are more concise, although less formally accurate. The degree of correspondence of these descriptions to real life phenomena in the prognostic sense is approximately the same as that of purely mathematical models, that is, these descriptions are quite pragmatic.

Another significant limitation: in order not to multiply entities beyond the necessary (Pluralitas non est ponenda sine necessitate - Occam's razor), we will not involve the Creator, aliens, the fourth dimension, the aura, midi-chlorian and the Force when describing the mathematical models (from " star wars") etc. (the list can be continued indefinitely).

A remark about the list of references - the list of sources is too long for the traditional list of printed publications (from Herodotus and Hegel to the Strugatskys and Spinoza); it focuses on Internet sources inon- line- a query in any search engine by the name of the author gives links to dozens of sites.

3. Formation of a hierarchy of goals at the individual level.

In cybernetics, the main feature of a living organism is the property of homeostasis, i.e. retention within the specified limits of the basic parameters of life due to adaptive behavior.

The electromechanical model of the homeostatic system is Walter's famous turtles, held on the edge of the table, the mathematical model is given, in particular, by Ashby:

Since the step functions change in jumps, the analytical integration of these differential equations is impossible, but nevertheless, these equations uniquely determine the behavior of the system if the initial conditions (the state of the system) are given, and the solution can be found with any degree of accuracy using numerical methods.

Living systems, determined by the equations of homeostasis, correspond to organisms that fully implement adaptation due to unconditioned reflexes. The adaptation program is fully recorded at the genetic level (in the DNA structure). The amount of information an organism can pass on to its offspring is entirely determined by the size of its genome.

Literary digression 2.

<< Рассмотрение организма как машины имеет очень давнюю традицию, хотя принято связывать эту аналогию с 18-м веком (веком Просвещения). Любопытно, что уже в то время делались небезуспешные попытки ввести для простейших организмов - машин понятия нравственности. У Потоцкого в «Рукописи, найденной в Сарагосе» один из героев (математик) рассуждает, имеет ли моллюск в раковине понятие о добре и зле. Первичная дихотомия добра и зла у него отождествляется с дихотомией «съедобно - несъедобно»: моллюск открывает свою раковину и поглощает съедобную частицу или закрывает раковину и отвергает несъедобную. Рост сложности системы (и, соответственно, усложнение нравственности) достигается за счет увеличения числа возможных выборов поведения. Таким образом, по Потоцкому, моллюск оперирует 2 понятиями, а гений на уровне Исаака Ньютона - 10 000 понятий - вот пример чистой математической индукции, без учета качественного изменения системы.>>

The next stage of more perfect adaptive behavior is associated with the introduction of the concept of a conditioned reflex. Modeling of the conditioned reflex was also carried out for Walter's turtles, but the most popular mathematical model of systems with conditioned reflex is Rosenblatt's perceptron. The main idea of ​​the perceptron is the ability to change the coefficients feedback and distribution of step functions from homeostasis equations in the learning process. Learning outcomes (positive or negative) serve to reinforce or weaken the feedback of individual blocks of the system. Then the process in the homeostatic system is determined not only by its initial state, but also by the process of its learning, i.e. the structure of the system adapts to the environment in the learning process. The amount of information that is transmitted to descendants, in this case, significantly exceeds the volume of the genome.

The main drawback of control at these 2 stages is the delay of control - control uses only information about the current state of the environment, when the environmental parameters change, there is a time lag between obtaining new information and forming a new control, which reduces the organism's chances of survival.

The next step in improving adaptive behavior is the construction by the bodymodels environment, predicting the future state of the environment using the model and planning their behavior using this model. Here we first encounter the conceptgoals because planning involves solving some problem. The question of understanding this task is key here, since without setting this task there is no concept of a goal. Whether the concept of purpose is inherent only to man, or to other higher animals, is a debatable question and is of no fundamental importance for our study.

The mathematical model of purposeful systems is described in general theory systems (Mesarovic and Takahara) as follows:

and the pair (x, y) belongs Sif and only ifyis a solution to the decision problem given by the element X . Multiple inputsXis called the set of solutions, the setY- a set of output quantities that can be obtained in response to input actions X. Complication mathematical model goal-oriented systems leads to the concepts of the task of satisfaction, the model of the control object and the decision-making system. To describe and analyze these models, a deeper knowledge of set theory is required. Moreover, any system that converts inputs into outputs can be described as a decision-making system. The phenomenological and purposeful approaches here depend on what the researcher's interest is aimed at. We will naturally take a targeted approach.

If we introduce a set of restrictions into the equations of the systemNassociated with moral and cultural taboos, the equations will take the form:

With the advent of the concept goals associated with the introduction of the objective function, the search for the extremum of which is a control problem. Note that with adaptive control, reaching the extremum of the objective function is not necessary. The target function represents a functional of type

t- time, T - the time interval over which the integration is performed (for example, the duration of life). The search for the extremum of the objective function is performed on the space of input variablesxn. The solution with any degree of accuracy to achieve the extremum of the objective function is found by numerical methods.

F value corresponds to the degree of satisfaction of the totality of some human needs - both material and emotional.

Here, two types of tasks are traditionally distinguished: target planning tasks and operational control tasks (although at the modern level of computer technology, the line between these two types of tasks is blurred, since the solution of target planning problems can be carried out in real time with a sufficiently large computing power).

For target planning tasks, depending on the type of objective function, the following are used:

linear programming (Kantorovich) - it is required to find the maximum of the function

2. dynamic programming (Bellman) - typical task solved by this method is the traveling salesman problem: there isn+1 cities A 0 , A 1 ,… Anwith given distances between themdij; it is required to choose such a route of movementA 0 , Ai 1 , Ai 2 ,… Ain, A 0 , at which the total path is minimal;

3. heuristic programming (Newell, Shaw, Minsky) - at the same time, information about the control object is incomplete and, in particular, expert decision-making systems are used;

4. game methods applied to conflict situations and stochastic control objects - this group of methods, in particular, includes the so-called "business games".

For operational management tasks, apply various methods real-time automatic control:

1. For deterministic systems, extremum search methods: Gauss-Seidel method, steepest descent method (according to the gradient maximum);

2. For stochastic systems - correlation-extreme method (Miller, Tarasenko, Melik-Shakhnazarov, Markatun) - while determining the optimal location coordinates or their derivatives is carried out by finding the extremum of the correlation functionRijor its varieties.

Of course, the above lists of methods for solving problems of target planning and operational management are far from complete and include only the most traditional and well-mastered methods.

We summarize the above: the goal of life in the traditional interpretation is modeled as finding the maximum of the objective function F (happiness) during life T (note that T - inconstant and depends on the search strategy). Here, for the first time, we introduced the concept of happiness into our study. It (continuing the language game again according to Wittgenstein) is very complex and, strictly speaking, cannot be fully disclosed. However, in order to be able to move on, let us assume in our language game that in the formula for F can be taken into account with certain weighting factors, both material and emotional incentives to satisfy the individual. Mathematization of the concepts of morality and emotions will be considered in Sections 8 and 9 of this study.

Since in the objective function F must be taken into account with the sign “-“ the misfortunes and sufferings of life, then the result F may be negative. With a pessimistic approach (if the weights of suffering are taken higher than the weights of pleasure), the most profitable strategy is the complete absence of control (action) so as not to increase the amount of suffering (the ideal is nirvana). It is easy to understand that with such a strategy, the existence of both the individual and society is impossible. Therefore, in what follows we will not consider such a strategy, since the result is trivial.

Literary digression 3.

<<Религиозные мыслители рассматривают T , as a value tending to infinity (taking into account the existence beyond the grave). Then the objective function search strategy takes on a completely different form. Here is Pascal's proof of the existence of God, based on the theory of probability:

Atheist strategy - T1 = T - the time of earthly life, the final value, F1 - the amount of goods acquired by a person in earthly life, the possible gain - F1 - does not depend on the probability of the existence of God r b .

The believer's strategy T2 -> “infinity”( afterlife duration), F1 -> 0 - zero amount of benefits received by a believer in earthly life with righteous behavior, F2 -> “infinity” (an infinite amount of benefits received by a believer in the afterlife, i.e. eternal bliss), a possible gain - F2 * r b .

Comparing the possible payoffs, we find that the believer's strategy gives a larger payoff for an arbitrarily small r b . Note that if we try to define r b according to the principle of a scientific experiment, then this probability should be defined as the ratio of the number of successful (confirming the existence of God) experiments to the total number of experiments. The whole problem is that the scientific validity of successful experiments is unprovable because of the fundamentally different interpretation of their results by an atheist observer and a religious observer. >>

Search for the maximum F is considered as a strategic task of long-term planning, or a tactical task of operational management, and there is a logical paradox - the type of the objective function is determined by the subject himself, implementing the search strategy, while the objectivity of the choice is lost - the correctness can only be assessed by an outside observer (or a group of observers representing society ). Which of the types of happiness is objectively optimal - health and longevity, wealth, power, social prestige, wisdom, self-satisfaction from drugs, alcohol and debauchery - cannot be determined at the level of the individual.

Literary digression 4.

<< Одно из древнейших доказательств субъективности определения счастья мы находим в рассказе о Солоне и Крезе (Геродот, Плутарх, Ксенофонт). Лидийский царь Крез, накопивший несметные богатства, показал их афинскому мудрецу Солону и спросил, кто, по его мнению, является счастливейшим человеком на земле. Солон привел в пример афинских граждан - одни пали смертью героев на войне за отечество, другие после праведной жизни умерли в святилище богини. Крез с возмущением спросил его - не знает ли он счастливых среди живущих, на что Солон сказал, что объявлять счастливым того, кто еще живет - то же, что объявлять победителем в беге того, кто еще не закончил дистанцию. Через некоторое время царство Креза было разорено завоевателями, а сам он приговорен к смерти на костре и на себе ощутил справедливость суждения Солона. Здесь в основе понимания счастья две системы ценностей: у Креза - материальные блага; у Солона - авторитет в обществе на основе высокого уровня Платоновского «тимоса». «Тимос» понимается как врожденное чувство справедливости, порождающее жажду общественного признания (Фукуяма).>>

Literary digression 5.

<<Насколько далеко мы ушли от понимания счастья во времена Солона и Креза, покажем на следующем отрывке из Кристофера Лога (цитируется по сказке Стругацких):

"You're asking:

What do I think

Am I the highest happiness on earth?

Two things:

Change the state of mind in the same way,

How would I exchange a penny for a shilling,

young girl

Hear the singing

Out of my way, but following

How did you find out the way for me?

Perhaps, paradoxically, this passage is closest to the modern understanding of happiness.

It remains to add the following quotation from the Strugatskys:

“Are such things algorithmized?!”

But the Strugatskys are not Holy Scripture, and we will continue this hopeless cause.>>

The source of the paradox when choosing the objective function is the construction of a hierarchy of goals using the method of mathematical induction: to solve a small tactical problem (for example, conducting a commercial operation), the tactical goal of the lowest level is determined (obtaining a certain amount of money), the tactical task of the next level (achieving wealth) is determined by the method of induction next target (full financial well-being), the next level (the conquest of power in society on this basis) puts forward the next tactical goal. There is an illusion that the method of induction is applicable to human life in general. However, Gödel's theorem comes into force here: those tasks that were formulated within individual segments of human life cannot be formulated by an individual for human life as a whole. For an objective statement of the task of optimizing the objective function, it is necessary to move to the next system level - to consider not an individual, but society.

4. Formation of goals at the level of society .

Unlike the previous section, the system for which the tasks of survival, adaptation and optimization of the objective function are solved is not a single individual, but a society or part of it. At different stages of development, the part of the society that set and solved these tasks for itself was the clan (family), tribe, people (ethnos), humanity as a whole (the latter is still only in the future).

The choice of the objective function here is also quite arbitrary, but the correctness of this choice is determined over the observable historical periods according to the state of this part of the society. A management strategy for society is, on the one hand, a certain set of restrictions that set the rules for the social behavior of individuals (morality, religion, morality, cultural taboos, jurisdiction, etc.), on the other hand, an idea that unites part of society, in particular, a national idea ( world domination, freedom and unlimited possibilities the development of the personality of individuals, guaranteed bliss in the afterlife, the improvement of the race and the creation of a superman, a high level of well-being for everyone, etc.).

The correctness of the choice of strategy can be judged from a historical perspective, on the basis of an analysis of what is the stability of the society with the chosen strategy, what is the amount of happiness and unhappiness received by members of the society. Note that when analyzing the correctness of a strategy, we must again go beyond the analyzed system and consider a system that includes as constituent parts society and environment(the planet, and in the future the whole space).

Retrospective (historical) analysis of the correctness of the society's strategy on individual historical stages It also has the limitation that the attitude of individuals at different stages of civilization is not comparable, and therefore, the definition of happiness and unhappiness of a member of society is impossible. For us, the worldview of the ancient Hellenes, the Chinese of the era of Confucius, the Aztecs and the Mayans is incomprehensible. Attempts to reconstruct this attitude have literary, but not objective, value.

Therefore, when developing a national idea or a code of morality and morality, one can only be guided by clearly negative examples (the short-lived existence of the Third Reich, an unsuccessful attempt to build a communist society in Russia, etc.).

The maximum that an individual in society can do when planning his personal strategy:

understand the target function of your part of society and bring your personal strategy in line with it (changing part of your personality) - Confucian approach,

to find for oneself a part of the society, the target function of which is more consistent with the personal strategy, to become a member of this part of the society (and endure all the inconveniences and additional efforts necessary to change the environment) - an individualistic approach,

change the target function of your part of society, bringing it into line with your personal target function (transformation of society with minimal chances of success) - a revolutionary approach.

Self-regulating systems .

There is an illusion that it is enough to establish the rules of the game and, given enough good rules the system itself will develop in a "good" direction and lead society to a prosperous state. In our time, the most indicative here is the idea of ​​a market economy, which itself will regulate everything and improve the economic performance of society. This can be compared to the effect of evolution on animal world planets. Evolution is indeed effective in weeding out less fit organisms, it remains to be seen whether dinosaurs and Neanderthals would have been satisfied with its results. By the way, the Neanderthal brain was larger in brain volume modern man, so perhaps the extinction of the Neanderthals closed the way for humanity to a more intelligent society.

5. Information management model.

Another remark concerns the ability of the individual to develop the right tactics and management strategy. The control information model developed by Wiener defines the optimal control condition as:

H(X)>= H(Y) (5),

The above ratio is known as the law of necessary diversity and, translated into ordinary language, means that the information capabilities of the controlling individual must be no less than the information wealth of the controlled object, i.e. optimal control with incomplete information about the object is impossible.

Therefore, when developing a life strategy, it is necessary to take into account:

The fundamental incompleteness of information that an individual can collect during his life.

The need to take into account the total information accumulated in society.

The importance of information filters for assimilation of useful information for management and elimination of harmful information.

The choice is up to the individual. The objectivity of the choice increases with understanding of various aspects of the problem - personal capabilities, lifestyle in certain parts of society, prospects for the development of oneself and society, voluntary acceptance of the restrictions that apply in society (rules of the game). Obviously, a scientific understanding of the problem of building a life strategy sharply narrows the possibility of a personal free choice of life alternatives.

Note that the value of information wealth for management was practically the basis for the selection of officials in ancient China - to be appointed to a post, an official had to pass exams in classical philosophy (according to Confucius), in literature, mathematics (including geometry). The result of the skilled work of officials was success in construction (the Great Chinese Wall), irrigation, the creation of a giant fleet and other industries where Ancient China was far ahead of the surrounding countries.

Literary digression 6.

<<Информационная модель Винера имеет достаточно простой житейский аналог, который по-латыни формулируется так:

Ubi nil vales, ibi nil velis.

Where you can do nothing, there you should not want anything - that is. if your information wealth is significantly less than the information wealth of an object, you cannot manage that object. Submit and do not make plans.

Seneca, from letters to Lucilius:

“Ducunt fata volentem, nolentem trahunt.”

“Fate leads the humble, drags the recalcitrant.”>>

The Stoic philosopher's approach is formulated for a static model, when the functionsH(X) and H(Y) are constant during the solution process. However, in practice, a dynamic approach is more often used - when the managing individual conducts a study of the structure of the managed object. At the same time, the information wealth of the controlling individual increases.H(X) and becomes possible execution condition of successful control (5).

True, another option is also possible - when the managing individual, instead of increasing his information wealthH(X) reduces the information richness of the objectH(Y), i.e. remakes the controlled object in order to eliminate obstacles to control (for example, destroys the political opposition) - a dictatorial approach.

Only it will no longer be the same object and not the same controlling subject, and control turns into suppression.

The management information model leads to the task of selecting governing subjects, i.e., to the choice between classical democracy of the “one person - one vote” type and meritocracy (the rule of the worthy, i.e., in our case, the most qualified experts in the art of management). Partially, such a system of two-stage elections is implemented in the United States. In the transition to two-stage elections inevitably arises eternal question: "who guards the guards" or "Quis custodiet ipsos custodes?». Selection system experts is a key issue, but not a hopeless one. The community of academic scientists and managers is quite capable of forming a competent expert group.

6. The dependence of the strategy on the age of the ethnic group and the individual

In the previous sections, it was tacitly assumed that the individual's personal strategy is adopted by him somewhere at the beginning of life and then does not change throughout life, i.e. the individual accepts the “rules of the game” and follows them (the type of functionalF(x 1 , x 2 ,… xn) does not change throughout life T ). For strategy 1 (the Confucian approach), this is possible only if the individual is brought up in the “correct” spirit, which is typical for relatively young ethnic groups. Examples: ancient Sparta, ancient China, samurai in Japan, chivalry in medieval Europe. The knight's motto is "without fear and reproach" (chevalierSanspeuretSansreproche) - "do what you must, and let it be what will be." Even in the conditions of one closed type of civilization, this type of strategy was rarely fully maintained during the life of an individual. For example, Socrates was raised as a warrior, in his youth he was an exemplary warrior, then he became a philosopher. Social dynamics (social “elevators”) made kings out of ordinary knights, shoguns out of ordinary samurai; at the same time, the strategy of behavior changed radically from strategy (1) (the Confucian approach) to strategy (2) (the individualistic approach). Freelancers appeared instead of knights “without fear and reproach” (freelancers) - free spearmen who were looking for their happiness, choosing for a short time the next overlord. Currently, freelancers (albeit in a completely different sense) are one of the main groups of the active population, especially in creative, creative professions - programmers, designers, etc. At the same time, large group are clerks who are true to the “corporate” spirit, i.e. following Confucian ethics. Such is the general dynamics of groups characteristic of post-industrial society.

On the other hand, such dynamics is also characteristic of the development of an individual. At the beginning life path the individual is basically brought up and accepts the ideology of life “according to the rules”; as you grow up and assimilate an increasing amount of information about your capabilities (self-knowledge) and about external environment(knowledge of life) (see Wiener's management model in the previous section) individualistic or revolutionary traits are amplified; at the end of his life, when his strength dries up, he goes back to the Confucian way of life.

Taking into account the change in the chosen strategy during the lifetime, the formula for the objective function takes the form:

Where k+1 - the number of strategies used by the individual during life;

Fi- functional determined by the type of strategyi.

Literary digression 7 (and last).

<<” SiJeunessesavait, sivieillessepouvait”(Etienne, 1594) -“If youth knew, if old age could.” >>

Still, there are quite accurate analogies between mathematical formulas and worldly wisdom, you just need to dig.

culture art society science meaning of life, target planning, information model