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the nature of fundamental scientific discoveries. XII. The nature of fundamental scientific discoveries Fundamental discoveries

Almost everyone who is interested in the history of the development of science, technology and technology - at least once in his life thought about how the development of mankind could go without knowledge of mathematics, or, for example, if we did not have such a necessary subject as a wheel, which became almost the basis of human development. However, often only key discoveries are considered and honored with attention, while discoveries that are less known and widespread are sometimes simply not mentioned, which, however, does not make them insignificant, because each new knowledge gives humanity the opportunity to climb a step higher in its development.

The XX century and its scientific discoveries turned into a real Rubicon, having crossed which, progress has accelerated its step several times, identifying itself with a sports car that is impossible to keep up with. In order to now stay on the crest of the scientific and technological wave, not hefty skills are required. Of course, you can read scientific journals, various articles and works of scientists who are struggling to solve a particular problem, but even in this case it will not be possible to keep up with progress, and therefore it remains to catch up and observe.

As you know, in order to look into the future, you need to know the past. Therefore, today we will focus on the 20th century, the century of discoveries that changed the way of life and the world around us. It should be noted right away that this will not be a list of the best discoveries of the century or any other top, it will be a brief survey of some of those discoveries that have changed, and possibly change the world.

In order to talk about discoveries, the concept itself should be characterized. Let's take the following definition as a basis:

Discovery is a new achievement made in the process scientific knowledge nature and society; the establishment of previously unknown, objectively existing laws, properties and phenomena of the material world.

Top 25 great scientific discoveries of the 20th century

1. Planck's quantum theory. He derived a formula that determines the shape of the spectral curve of radiation and a universal constant. He discovered the smallest particles - quanta and photons, with the help of which Einstein explained the nature of light. In the 1920s, Quantum theory developed into quantum mechanics.
2. Discovery of X-ray radiation - electromagnetic radiation with a wide range of wavelengths. The discovery of X-rays by Wilhelm Röntgen greatly influenced human life and today it is impossible to imagine modern medicine without them.
3. Einstein's theory of relativity. In 1915, Einstein introduced the concept of relativity and derived an important formula linking energy and mass. The theory of relativity explained the essence of gravity - it arises due to the curvature of four-dimensional space, and not as a result of the interaction of bodies in space.
4. The discovery of penicillin. Mold fungus Penicillium notatum, getting to the culture of bacteria, causes their complete death - this was proved by Alexander Flemming. In the 40s, a production facility was developed, which later began to be produced on an industrial scale.
5. De Broglie waves. In 1924, it was found that wave-particle duality is inherent in all particles, not just photons. Broglie presented their wave properties in a mathematical form. The theory made it possible to develop the concept of quantum mechanics, explained the diffraction of electrons and neutrons.
6. Discovery of the structure of a new DNA helix. In 1953, a new model of the structure of the molecule was obtained by combining the X-ray data of Rosalyn Franklin and Maurice Wilkins and the theoretical developments of Chargaff. She was brought out by Francis Crick and James Watson.
7. Rutherford's planetary model of the atom. He came up with a hypothesis about the structure of the atom and extracted energy from atomic nuclei. The model explains the basics of the laws governing charged particles.
8. Ziegler-Nat catalysts. In 1953, they carried out the polarization of ethylene and propylene.
9. Opening transistors. A device consisting of 2 p-n junctions that are directed towards each other. Thanks to his invention by Julius Lilienfeld, the technique began to decrease in size. The first working bipolar transistor was introduced in 1947 by John Bardeen, William Shockley and Walter Brattain.
10. Creation of a radiotelegraph. Alexander Popov's invention with the help of Morse code and radio signals saved the ship for the first time at the turn of the 19th and 20th centuries. But he was the first to patent a similar invention by Gulielmo Marcone.
11. Discovery of neutrons. These uncharged particles with a mass slightly greater than that of protons allowed them to penetrate into the nucleus without obstacles and destabilize it. Later it was proved that under the influence of these particles, nuclei fission, but even more neutrons are produced. So the artificial was discovered.
12. In vitro fertilization (IVF) technique. Edwards and Steptoe figured out how to extract an intact egg from a woman, created conditions in a test tube that were optimal for her life and growth, figured out how to fertilize her and at what time return it back to her mother's body.
13. The first manned flight into space. In 1961, it was Yuri Gagarin who was the first to realize this one, which became a real embodiment of the dream of stars. Humanity has learned that the space between the planets is surmountable, and bacteria, animals and even humans can safely be in space.
14. The discovery of fullerene. In 1985, scientists discovered a new type of carbon - fullerene. Now, due to its unique properties, it is used in many devices. Based on this technique, carbon nanotubes were created - twisted and cross-linked layers of graphite. They show a wide variety of properties, from metallic to semiconducting.
15. Cloning. In 1996, scientists managed to obtain the first clone of a sheep named Dolly. The egg was gutted, the nucleus of an adult sheep was inserted into it and planted in the uterus. Dolly became the first animal that managed to survive, the rest of the embryos of different animals died.
16. Discovery of black holes. In 1915, Karl Schwarzschild put forward a hypothesis of existence, the gravity of which is so great that even objects moving at the speed of light - black holes - cannot leave it.
17. Theory. This is a generally accepted cosmological model, which previously described the development of the Universe, which was in a singular state, characterized by an infinite temperature and density of matter. The beginning of the model was laid by Einstein in 1916.
18. The discovery of the relic radiation. This is the cosmic microwave background radiation that has been preserved since the beginning of the formation of the Universe and fills it evenly. In 1965, its existence was experimentally confirmed, and it serves as one of the main confirmations of the Big Bang theory.
19. Approaching the creation of artificial intelligence. It is a technology for creating intelligent machines, first defined in 1956 by John McCarthy. According to him, researchers to solve specific problems can use methods of understanding a person that biologically may not be observed in humans.
20. The invention of holography. This special photographic method was proposed in 1947 by Dennis Gabor, in which, using a laser, three-dimensional images of objects close to real ones are registered and restored.
21. The discovery of insulin. In 1922, a pancreatic hormone was obtained by Frederick Bunting, and diabetes ceased to be a fatal disease.
22. Blood groups. This discovery in 1900-1901 divided blood into 4 groups: O, A, B and AB. It became possible for a correct blood transfusion to a person, which would not end tragically.
23. Mathematical information theory. Claude Shannon's theory made it possible to determine the capacity of a communication channel.
24. The invention of Nylon. The chemist Wallace Carothers in 1935 discovered a method for producing this polymer material. He discovered some of its varieties with high viscosity even at high temperatures.
25. Discovery of stem cells. They are the progenitors of all existing cells in the human body and have the ability to self-renew. Their possibilities are great and are just beginning to be studied by science.

Undoubtedly, all these discoveries are only a small part of what the 20th century showed to society and it cannot be said that only these discoveries were significant, and all the rest became just a background, this is not at all the case.

It was the last century that showed us new boundaries of the Universe, saw the light, quasars (superpowerful sources of radiation in our Galaxy) were discovered, the first carbon nanotubes with unique superconductivity and strength were discovered and created.

All these discoveries, one way or another, are just the tip of the iceberg, which includes more than a hundred significant discoveries over the past century. Naturally, they all became a catalyst for changes in the world in which you and I now live, and the fact remains that the changes do not end there.

The 20th century can be safely called, if not a "golden", then certainly a "silver" age of discoveries, however, looking back and comparing new achievements with the past, it seems that in the future we will still have quite a few interesting great discoveries, in fact, the successor of the last century, the current XXI only confirms these views.

Among the various types of scientific discoveries, a special place is occupied by fundamental discoveries that change our ideas about reality as a whole, i.e. having an ideological character.

1. Two kinds of discoveries

A. Einstein once wrote that a theoretical physicist “as a foundation needs some general assumptions, the so-called principles, on the basis of which he can deduce consequences. His activity is thus divided into two stages. First, he needs to find these principles, and secondly. develop the consequences arising from these principles. For the second task, he is thoroughly armed from school. Consequently, if for a certain area and, accordingly, a set of relationships, the first problem is solved, then the consequences will not be long in coming. The first of these tasks is of a completely different kind, i.e. the establishment of principles that can serve as a basis for deduction. There is no method here that can be learned and systematically applied to achieve the goal. "

We will deal mainly with the discussion of problems associated with solving problems of the first kind, but first we will clarify our ideas about how problems of the second kind are solved.

Let's imagine the following problem. There is a circle through the center of which two mutually perpendicular diameters are drawn. Through point A, located at one of the diameters at a distance of 2/3 from the center of circle O, draw a straight line parallel to the other diameter, and from point B of the intersection of this line with the circle, we lower the perpendicular to the second diameter, denoting their intersection point by C. We need express the length of the segment AC in terms of a function of the radius.

How are we going to solve this school problem?

For this, let us turn to certain principles of geometry and restore the chain of theorems. In doing so, we try to use all the data we have. Note that since the diameters drawn are mutually non-perpendicular, the OAS triangle is right-angled. The value of ОА = 2 / Зr. Let us now try to find the length of the second leg, in order to then apply the Pythagorean theorem and determine the length of the hypotenuse AC. You can try using some other methods. But suddenly, after carefully looking at the drawing, we find that OABS is a rectangle, in which, as you know, the diagonals are equal, i.e. AC = OB. 0B is equal to the radius of the circle, therefore, without any calculations, it is clear that AC = r.

Here it is - a beautiful and psychologically interesting solution to the problem.

In this example, the following is important.

First, tasks of this kind usually relate to a well-defined subject area. Solving them, we clearly understand where, in fact, we need to look for a solution. In this case, we do not think about whether the foundations of Euclidean geometry are correct, whether it is not necessary to come up with some other geometry, some special principles to solve the problem. We immediately interpret it as referring to the field of Euclidean geometry.

Secondly, these tasks are not necessarily standard, algorithmic. In principle, their solution requires a deep understanding of the specifics of the objects under consideration, developed professional intuition. Here, therefore, some professional training is needed. In the process of solving problems of this kind, we are opening a new path. We notice "suddenly" that the object under study can be considered as a rectangle and it is not at all necessary to select a right-angled triangle as an elementary object to form the correct way to solve the problem.

Of course, the above task is very simple. It is needed only in order to outline the type of problems of the second kind in general. But among such problems there are immeasurably more complex ones, the solution of which is of great importance for the development of science.

Consider, for example, the discovery of the new planet Le Verrier and Adam-som. Of course, this discovery is a great event in science, especially if we take into account as it was done:

First, the trajectories of the planets were calculated;

Then it was discovered that they did not coincide with the observed ones; - then the assumption was made about the existence of a new planet;

Then they pointed the telescope at the appropriate point in space and ... found a planet there.

But why this great discovery can only be attributed to discoveries of the second kind?

The thing is that it was performed on the clear foundation of the already developed celestial mechanics.

While problems of the second kind can, of course, be subdivided into subclasses of varying complexity, Einstein was right in separating them from fundamental problems.

After all, the latter require the discovery of new fundamental principles that cannot be obtained by any deduction from existing principles.

Of course, there are intermediate instances between the tasks of the first and second kind, but we will not consider them here, but go straight to the tasks of the first kind.

In general, there were not so many such problems before mankind, but their solutions each time meant tremendous progress in the development of science and culture as a whole. They are associated with the creation of such fundamental scientific theories and concepts as the geometry of Euclid, the heliocentric theory of Copernicus, the classical mechanics of Newton, the geometry of Lobachevsky, Mendel's genetics, Darwin's theory of evolution, Einstein's theory of relativity, quantum mechanics, structural linguistics.

All of them are characterized by the fact that the intellectual basis on which they were created, in contrast to the field of discoveries of the second kind, was never strictly limited.

If we talk about the psychological context of the discoveries of different "" s ^^, then it is probably the same. - In its most superficial form, it can be characterized as direct vision, a discovery in the full sense of the word. A person, as Descartes believed, "suddenly" sees, that the problem should be viewed in this way and not otherwise.

Further, it should be noted that the discovery is never one-act, but is, so to speak, "shuttle" in nature. At first there is a sense of the idea; then it is clarified by deriving certain consequences from it, which, as a rule, clarify the idea; then new consequences are derived from the new modification, and so on.

But in epistemological terms, the discoveries of the first and second kinds differ radically.

The transition from one paradigm to another, according to Kuhn, is impossible through logic and references to experience.

In a sense, advocates of different paradigms live in different worlds... According to Kuhn, different paradigms are incommensurable. Therefore, the transition from one paradigm to another should be carried out abruptly, as a switch, and not gradually through logic.

Scientific revolutions usually affect the worldview and methodological foundations of science, often changing the very style of thinking. Therefore, in terms of their significance, they may go far beyond the specific area where they occurred. Therefore, we can talk about particular scientific and general scientific revolutions.

The emergence of quantum mechanics is a vivid example of a general scientific revolution, since its significance goes far beyond the bounds of physics. Quantum-mechanical representations at the level of analogies or metaphors have penetrated into humanitarian thinking. These ideas encroach on our intuition, common sense, and affect our perception of the world.

The Darwinian revolution in its significance went far beyond the boundaries of biology. She radically changed our ideas about the place of man in Nature. It had a powerful methodological impact, turning the thinking of scientists towards evolutionism.

New research methods can lead to far-reaching consequences: to a change of problems, to a change of standards. scientific work, to the emergence of new areas of knowledge. In this case, their implementation means a scientific revolution.

So, the appearance of the microscope in biology meant a scientific revolution. The entire history of biology can be broken down into two stages, separated by the emergence and introduction of the microscope. Entire fundamental branches of biology - microbiology, cytology, histology - owe their development to the introduction of the microscope.

The advent of the radio telescope marked a revolution in astronomy. Academician Ginsburg writes about it this way: “Astronomy after the Second World War entered a period of especially brilliant development, in the period second astronomical revolution"(The first such revolution is associated with the name of Galileo, who began to use telescopes) ... The content of the second astronomical revolution can be seen in the process of transformation of astronomy from optical to all-wave."

Sometimes a new area of ​​the unknown opens up before the researcher, the world of new objects and phenomena. This can cause revolutionary changes in the course of scientific knowledge, as happened, for example, with the discovery of such new worlds as the world of microorganisms and viruses, the world of atoms and molecules, the world of electromagnetic phenomena, the world of elementary particles, when the phenomenon of gravity, other galaxies, the world of crystals , radioactivity phenomena, etc.

Thus, the scientific revolution may be based on the discovery of some previously unknown spheres or aspects of reality.

Many major discoveries in science are made on a well-defined theoretical basis. Example: the discovery of the planet Neptune by Le Verrier and Adams by studying disturbances in the motion of the planet Uranus on the basis of celestial mechanics.

Fundamental scientific discoveries differ from others in that they are not associated with deduction from existing principles, but with the development of new fundamental principles.

In the history of science, fundamental scientific discoveries are highlighted related to the creation of such fundamental scientific theories and concepts as Euclidean geometry, Copernicus' heliocentric system, classical Newtonian mechanics, Lobachevsky geometry, Mendelian genetics, Darwin's theory of evolution, Einstein's theory of relativity, quantum mechanics. These discoveries changed the idea of ​​reality as a whole, that is, they were of a world outlook.

There are many facts in the history of science when a fundamental scientific discovery was made independently by several scientists at almost the same time. For example, non-Euclidean geometry was constructed almost simultaneously by Lobachevsky, Gauss, Bolyai; Darwin published his ideas about evolution at about the same time as Wallace; special theory of relativity was developed simultaneously by Einstein and Poincaré.

From the fact that fundamental discoveries are made almost simultaneously by different scientists, it follows that they are historically conditioned.

Fundamental discoveries always arise as a result of solving fundamental problems, that is, problems that have a deep, ideological, and not private nature.

So, Copernicus saw that two fundamental worldview principles of his time - the principle of the movement of celestial bodies in circles and the principle of the simplicity of nature - are not realized in astronomy; the solution to this fundamental problem led him to a great discovery.

Non-Euclidean geometry was built when the problem of the fifth postulate of Euclidean geometry ceased to be a particular problem of geometry and turned into a fundamental problem of mathematics, its foundations.

In accordance with the classical concepts of science, it should not contain “ no admixture of delusions". Now truth is not considered as a necessary attribute of all cognitive results that claim to be scientific. It is the central regulator of scientific and cognitive activity.

Classical ideas about science are characterized by a constant search for “ started learning», « reliable foundation"On which the entire system could rely scientific knowledge.

However, in the modern methodology of science, the idea of ​​the hypothetical nature of scientific knowledge is developing, when experience is no longer the foundation of knowledge, but mainly performs a critical function.

In place of fundamentalist validity as the leading value in classical concepts of scientific knowledge, the value of efficiency in problem solving is increasingly being promoted.

Various areas of scientific knowledge have been used as standards throughout the development of science.

« Beginnings»Euclid for a long time were an attractive standard in literally all areas of knowledge: in philosophy, physics, astronomy, medicine, etc.

However, the boundaries of the significance of mathematics as a standard of scientificity are now well understood, which, for example, are formulated as follows: “In the strict sense, proofs are possible only in mathematics, and not because mathematicians are smarter than others, but because they themselves create the universe for their experiments, nevertheless the rest are forced to experiment with a universe that was not created by them. "

The triumph of mechanics in the 17th-19th centuries led to the fact that it began to be regarded as an ideal, an example of scientificity.

Eddington said that when a physicist tried to explain something, “his ear struggled to pick up the noise of the machine. A person who could construct gravity from cogwheels would be a Victorian hero. "

Since the modern era, physics has been established as a reference science. If at first mechanics acted as a standard, then later - the whole complex of physical knowledge. The orientation towards the physical ideal in chemistry was clearly expressed, for example, by P. Berthelot, in biology - by M. Schleiden. G. Helmholtz asserted that “ final goal"Of all natural science -" dissolve in mechanics". Attempts to build social mechanics», « social physics”Etc. were numerous.

The physical ideal of scientific knowledge has certainly proved its heuristic, but today it is clear that the realization of this ideal often hinders the development of other sciences - mathematics, biology, social sciences and others. As noted by N.K. Mikhailovsky, the absolutization of the physical ideal of scientific character leads to such a formulation of social issues when “ which natural science gives Judah the kiss of sociology", Leading to pseudo-objectivity.

The humanities are sometimes offered as a model of scientific knowledge. In this case, the focus is on the subject's active role in the cognitive process.

V.I. Kuptsov

XII. THE NATURE OF FUNDAMENTAL SCIENTIFIC DISCOVERIES

Among the diverse types of scientific discoveries, a special place is occupied by fundamental discoveries that change our ideas about reality as a whole, i.e. having an ideological character.

1. TWO KINDS OF DISCOVERY

A. Einstein once wrote that a theoretical physicist “needs some general assumptions, the so-called principles, on the basis of which he can deduce consequences. His activity is thus divided into two stages. First, he needs to find these principles, and second, to develop the consequences arising from these principles. For the second task, he is thoroughly armed from school. Consequently, if for a certain area and, accordingly, for a set of interrelationships, the first problem is solved, then the consequences will not be long in coming. The first of these tasks is of a completely different kind, i.e. the establishment of principles that can serve as a basis for deduction. There is no method here that can be learned and systematically applied to achieve the goal. "

We will deal mainly with the discussion of problems associated with solving problems of the first kind, but first we will clarify our ideas about how problems of the second kind are solved.

Let's imagine the following problem. There is a circle through the center of which two mutually perpendicular diameters are drawn. Through point A, located at one of the diameters at a distance of 2/3 from the center of circle O, draw a straight line parallel to the other diameter, and from point B, the intersection of this line with the circle, we lower the perpendicular to the second diameter, denoting their intersection point by K. it is necessary to express the length of the segment AK in terms of a function of the radius.

How are we going to solve this school problem?

Turning for this to certain principles of geometry, we restore the chain of theorems. In doing so, we try to use all the data we have. Note that since the diameters drawn are mutually perpendicular, the UAC triangle is rectangular. The value of ОА = 2 / 3r. Let us now try to find the length of the second leg, in order to then apply the Pythagorean theorem and determine the length of the hypotenuse AK. You can try using some other methods as well. But suddenly, having carefully looked at the drawing, we find that OABK is a rectangle, which, as you know, has equal diagonals, i.e. AK = OB. OB is equal to the radius of the circle, therefore, without any calculations, it is clear that AK = r.

Here it is - a beautiful and psychologically interesting solution to the problem.

In this example, the following is important.

First, tasks of this kind usually relate to a well-defined subject area. Solving them, we clearly understand where, in fact, we need to look for a solution. In this case, we do not think about whether the foundations of Euclidean geometry are correct, whether it is not necessary to come up with some other geometry, some special principles to solve the problem. We immediately interpret it as referring to the field of Euclidean geometry.

Secondly, these tasks are not necessarily standard, algorithmic. In principle, their solution requires a deep understanding of the specifics of the objects under consideration, developed professional intuition. Here, therefore, some professional training is needed. In the process of solving problems of this kind, we are opening a new path. We notice "suddenly" that the object under study can be considered as a rectangle and it is not at all necessary to select a right-angled triangle as an elementary object to form the correct way to solve the problem.

Of course, the above task is very simple. It is needed only in order to outline the type of problems of the second kind in general. But among such problems there are immeasurably more complex ones, the solution of which is of great importance for the development of science.

Consider, for example, the discovery of a new planet by W. Leverrier and J. Adams. Of course, this discovery is a big event in science, all the more considering how it was made:

First, the trajectories of the planets were calculated;

Then it was discovered that they did not coincide with the observed ones;

Then it was suggested that a new planet existed;

Then they pointed the telescope at the appropriate point in space and ... found a planet there.

But why this great discovery can only be attributed to discoveries of the second kind?

The thing is that it was performed on the clear foundation of the already developed celestial mechanics.

Although problems of the second kind, of course, can be subdivided into subclasses of varying complexity, A. Einstein was right in separating them from fundamental problems.

After all, the latter require the discovery of new fundamental principles that cannot be obtained by any deduction from existing principles.

Of course, there are intermediate instances between the tasks of the first and second kind, but we will not consider them here, but go straight to the tasks of the first kind.

In general, there were not so many such problems before mankind, but their solutions each time meant tremendous progress in the development of science and culture as a whole. They are associated with the creation of such fundamental scientific theories and concepts as

Euclidean geometry?

Copernicus heliocentric theory,

classical Newtonian mechanics,

Lobachevsky geometry,

Mendel's genetics,

Darwin's theory of evolution,

Einstein's theory of relativity,

quantum mechanics,

structural linguistics.

All of them are characterized by the fact that the intellectual basis on which they were created, in contrast to the field of discoveries of the second kind, was never strictly limited.

If we talk about the psychological context of the discoveries of different classes, then it is probably the same.

In its most superficial form, it can be characterized as direct vision, a discovery in the full sense of the word. A person, as R. Descartes believed, "suddenly" sees that the problem should be considered exactly this way, and not otherwise.

Further, it should be noted that the discovery is never one-act, but is, so to speak, "shuttle" in nature. At first there is a sense of the idea; then it is clarified by deriving certain consequences from it, which, as a rule, clarify the idea; then new consequences are derived from the new modification, and so on.

But in epistemological terms, the discoveries of the first and second kinds differ radically.

2. HISTORICAL CONDITIONALITY OF FUNDAMENTAL DISCOVERIES

Let's try to imagine a solution to problems of the first kind.

The advancement of new fundamental principles has always been associated with the activities of geniuses, with illumination, with some secret characteristics of the human psyche.

An excellent confirmation of this perception of this kind of discoveries is the struggle of scientists for priority. how many

was in the history of the most acute situations in the relationship between scientists associated with their confidence that no one else could get the results they achieved.

For example, the well-known utopian socialist Charles Fourier claimed to have revealed the nature of man, discovered how to organize society so that there were no social conflicts in it. He was convinced that if he was born before his time, he would help people solve all their problems without wars and ideological confrontation. In this sense, he linked his discovery with his individual abilities.

How do fundamental discoveries come about? To what extent is their implementation connected with the birth of a genius, the manifestation of his unique talent?

Turning to the history of science, we see that such discoveries are really carried out by outstanding people. At the same time, attention is drawn to the fact that many of them were made independently by several scientists at almost the same time.

N.I. Lobachevsky, F. Gauss, J. Bolyai, not to mention the mathematicians who developed the foundations of such geometry with less success, i.e. a whole group of scientists, almost simultaneously came to the same fundamental results.

For two thousand years people have been struggling with this problem of the fifth postulate of Euclid's geometry, and “suddenly”, within literally 10 years, a dozen people solve it at once.

Charles Darwin first announced his ideas about the evolution of species in a report read in 1858 at a meeting of the Linnaean Society in London. At the same meeting, Wallace also spoke with a presentation of the research results, which, in essence, coincided with Darwinian ones.

The special theory of relativity is known to be named after A. Einstein, who outlined its principles in 1905. But in the same 1905, similar results were published by A. Poincaré.

Absolutely surprising is the rediscovery of Mendelian genetics in 1900 simultaneously and independently of each other by E. Cermak, K. Correns and H. de Vries.

A huge number of similar situations can be found in the history of science.

And as long as it is the case that fundamental discoveries are made almost simultaneously by different scientists, then, consequently, there is their historical conditioning.

What is it in this case?

Trying to answer this question, let us formulate the following general position.

Fundamental discoveries always result from solving fundamental problems.

First of all, let us pay attention to the fact that when we talk about fundamental problems, we mean such questions that relate to our general ideas about reality, its cognition, about the value system that guides our behavior.

Fundamental discoveries are often interpreted as solutions to particular problems and are not associated with any fundamental problems.

For example, to the question of how Copernicus' theory was created, they answer that the studies showed a discrepancy between observations and those predictions that were made on the basis of the Ptolemaic geocentric system, and therefore a conflict arose between the new data and the old theory.

To the question of how non-Euclidean geometry was created, the following answer is given: as a result of solving the problem of proving the fifth postulate of Euclidean geometry, which they could not prove in any way.

3. KOPERNIK'S HELIOCENTRIC SYSTEM

Let us look from these positions at the features of the process of fundamental discoveries, starting our analysis by studying the history of the creation of the heliocentric system of the world.

The representation of the Copernican system of the universe as arising from the discrepancy between astronomical observations and Ptolemy's geocentric model of the world does not correspond to historical facts.

First, Copernicus' system did not at all describe the observed data better than the Ptolemaic system. By the way, that is why it was rejected by the philosopher F. Bacon and the astronomer T. Brahe.

Secondly, even if we assume that the Ptolemaic model had some discrepancies with observations, one cannot reject its ability to cope with these discrepancies.

After all, the behavior of the planets was represented in this model using a carefully designed system of epicycles, which could describe any complex mechanical movement... In other words, no problem of matching the motion of the planets according to the Ptolemaic system with empirical data simply did not exist.

But how, then, could the Copernican system arise and even more so assert itself?

To understand the answer to this question, you need to understand the essence of the worldview innovations that she carried with her.

In the time of N. Copernicus, the theologized Aristotelian view of the world prevailed. Its essence was as follows.

The world was created by God especially for man. The Earth was also created for man as his habitat, placed in the center of the universe. The firmament moves around the Earth, on which all the stars, planets, and also spheres associated with the movement of the Sun and Moon are located. The entire heavenly world is designed to serve the earthly life of people.

In accordance with this setting, the whole world is divided into sublunar (earthly) and supra-lunar (heavenly)

The sublunary world is a mortal world in which every single mortal person lives.

The heavenly world is a world for humanity in general, an eternal world in which its own laws, which are different from the earthly ones, operate.

In the earthly world, the laws of Aristotelian physics are valid, according to which all movements are carried out as a result of the direct action of some forces.

In the heavenly world, all movements are carried out in circular orbits (system of epicycles) without the influence of any forces.

N. Copernicus radically changed this generally accepted picture of the world.

He not only changed the places of the Earth and the Sun in the astronomical scheme, but changed the place of a person in the world, placing him on one of the planets, confusing the earthly and celestial worlds.

The destructive nature of Copernicus' ideas was clear to everyone. The Protestant leader M. Luther, who had nothing to do with astronomy, spoke in 1539 about Copernicus's teachings as follows: “The fool wants to turn the whole art of astronomy upside down. But, as the Scripture points out, Joshua ordered the Sun to stop, not the Earth. "

Could some insignificant reason have prompted such radical new ideas?

What does a person do when a splinter hits his finger? He, of course, is trying to pull out the splinter, to heal the finger. Now, if gangrene has begun, then he will not regret a whole hand.

The problems of accurately describing the observed trajectories of the planets, as already mentioned, could not be the basis for such bold and decisive actions.

On the other hand, it should be borne in mind that the astronomy of that time also contained considerable opportunities for rather significant innovations. So, Tycho Brahe, solving astronomical problems associated with the improvement of the calculations of the trajectories of the planets, proposed, in full accordance with the traditional worldview, a new system in which the Sun revolved around the Earth, and all other planets around the Sun.

Why did N. Copernicus need to put forward his ideas?

Apparently, he was solving some fundamental problem of his own.

What was the problem?

And Ptolemy, and Aristotle, and Copernicus proceeded from the fact that in the heavenly world all movements occur in circles.

At the same time, even in antiquity, a deep thought was expressed that nature is in principle simple. This thought eventually became one of the fundamental principles of cognition of reality.

At the same time, observational astronomy had discovered by that time the following. Although the Ptolemaic model of the world had the ability to describe any trajectory as accurately as desired, for this it was necessary to constantly change the number of epicycles (today - one number, tomorrow - another). But in this case, it turned out that the planets did not move along the epicycles at all. It turns out that epicycles do not reflect the real motions of the planets, but are simply a mathematical device for describing this movement.

In addition, according to Ptolemy's system, it turned out that to describe the trajectory of one planet, a huge number of epicycles had to be introduced. Complicated astronomy performed poorly in its practical functions. In particular, it was very difficult to calculate the dates of religious holidays. This difficulty was so clearly realized at that time that even the Pope himself considered it necessary to carry out reforms in astronomy.

N. Copernicus saw that two fundamental ideological principles of his time - the principle of the movement of celestial bodies in circles and the principle of the simplicity of nature - are clearly not realized in astronomy.

The solution to this fundamental problem led him to a great discovery.

4. GEOMETRY OF LOBACHEVSKY

Let's move on to the analysis of another discovery - the discovery of non-Euclidean geometry. Let us try to show that here, too, the discussion dealt with a fundamental problem. Considering this example, we will find out a number of other important points interpretation of fundamental discoveries.

The creation of non-Euclidean geometry is usually presented as a solution to the well-known problem of the fifth postulate of Euclidean geometry.

This problem was as follows.

The basis of all geometry, as it followed from the Euclidean system, was represented by the following five postulates:

1) a straight line can be drawn through two points, and, moreover, only one;

2) any segment can be continued in any direction to infinity;

3) a circle of any radius can be drawn from any point as from the center;

4) all right angles are equal;

5) two straight lines intersected by the third will intersect on the side where the sum of the inner one-sided angles is less than 2d.

Already at the time of Euclid, it became clear that the fifth postulate is too complicated in comparison with other initial positions of his geometry. Other points seemed obvious. Precisely because of their obviousness, they were considered as postulates, i.e. as what is accepted without evidence.

At the same time, even Thales proved the equality of the angles at the base isosceles triangle, i.e. a position much simpler than the fifth postulate. Hence it is clear why this postulate has always been viewed with suspicion and tried to present it as a theorem. And in Euclid himself, geometry was constructed in such a way that at first those propositions were proved that do not rely on the fifth postulate, and then this postulate was used to develop the content of geometry.

It is interesting that the fifth postulate of Euclid's geometry tried to prove as a theorem, while maintaining the conviction of its truth, literally all major mathematicians, up to N.I. Lobachevsky, F. Gauss and J. Bolyai, who eventually solved the problem. Their solution consists of the following points:

The fifth postulate of Euclid's geometry is indeed a postulate, not a theorem;

It is possible to construct a new geometry, accepting all Euclidean postulates, except for the fifth, which is replaced by its negation, i.e. for example, the statement that through a point lying outside a straight line, you can draw an infinite number of straight lines parallel to a given one;

As a result of such a replacement, a non-Euclidean geometry was constructed.

Let us now pose the following questions.

Why for two millennia no one even thought about the possibility of constructing non-Euclidean geometry?

To answer these questions, let us turn to the history of science.

Before NI Lobachevsky, F. Gauss, J. Bolyai, Euclidean geometry was regarded as the ideal of scientific knowledge.

This ideal was worshiped by literally all thinkers of the past, who believed that geometric knowledge as presented by Euclid is perfect. It was presented as a model of organization and evidence of knowledge.

I. Kant, for example, the idea of ​​the uniqueness of geometry was an organic part of his philosophical system. He believed that the Euclidean perception of reality is a priori. It is a property of our consciousness, and therefore we cannot perceive reality otherwise.

The question of the uniqueness of geometry was not just a mathematical question.

He bore an ideological character, was included in the culture.

It was geometry that was used to judge the capabilities of mathematics, the features of its objects, the thinking style of mathematicians, and even the ability of a person to have accurate, evidence-based knowledge in general.

Where, then, did the very idea of ​​the possibility of different geometries come from?

Why N.I. Lobachevsky and other scientists were able to come to a solution to the problem of the fifth postulate?

Let us pay attention to the fact that the time of the creation of non-Euclidean geometries was critical from the point of view of solving the problem of the fifth postulate of Euclid. Although mathematicians have been dealing with this problem for two millennia, they have not had any stressful situations about the fact that it has not been solved for so long. They thought, apparently, like this:

Euclid's geometry is a superbly constructed building;

True, there is some ambiguity in it associated with the fifth postulate, but in the end it will be eliminated.

However, tens, hundreds, thousands of years passed, and the ambiguity was not eliminated, but this did not particularly bother anyone. Apparently, the logic here could be as follows: in the end, there is only one truth, and there are as many false paths as you like. The correct solution to the problem has not yet been found, but it will undoubtedly be found. The statement contained in the fifth postulate will be proved and will become one of the theorems of geometry.

But what happened in early XIX in.?

The attitude to the problem of proving the fifth postulate changes significantly. We see a number of direct statements about a very unfavorable situation in mathematics due to the fact that it is in no way possible to prove such an unfortunate postulate.

The most interesting and striking evidence of this is the letter of F. Bolyai to his son J. Bolyai, who became one of the founders of non-Euclidean geometry.

“I beg you,” my father wrote, “just don't try to overcome the theory of parallel lines; you will spend all the time on it, and you will not prove it all together. Do not try to overcome the theory of parallel lines in the way that you tell me, or in any other way. I have studied all the paths to the end; I have not come across a single idea that I have not developed. I went through all the gloomy darkness of that night, and I buried every light, every joy of life in it. For God's sake, I pray you, leave this matter, fear it no less than sensual hobbies, because it can deprive you of all your time, health, peace, all the happiness of your life. Thousands of Newtonian towers could be sunk by this gloomy darkness. It will never become clear on earth, and the unfortunate human race will never own anything perfect, even in geometry. "

Why does such a reaction occur only at the beginning of the 19th century?

First of all, because at this time the problem of the fifth postulate has ceased to be a particular one, which can not be solved. In the eyes of F. Bolyai, she appeared as a whole fan of fundamental questions.

How should mathematics be structured in general?

Can it be built on really solid foundations?

Is it valid knowledge?

Is it logically sound knowledge at all?

This formulation of the question was due not only to the history of the development of research related to the proof of the fifth postulate. It was determined by the development of mathematics in general, including its use in various spheres of culture.

Until the 17th century. mathematics was in its infancy. The most developed was geometry, the beginnings of algebra and trigonometry were known. But then, starting from the 17th century, mathematics began to develop rapidly by the beginning of the 19th century. it represented a rather complex and developed system of knowledge.

First of all, under the influence of the needs of mechanics, differential and integral calculus were created.

Algebra has undergone significant development. The concept of a function organically entered mathematics (a large number of different functions were actively used in many branches of physics).

The theory of probability has developed into a fairly integral system.

The theory of series was formed.

Thus, mathematical knowledge has grown not only quantitatively, but also qualitatively. At the same time, a large number of concepts appeared that mathematicians did not know how to interpret.

For example, algebra carried with it a certain concept of number. Positive, negative, and imaginary values ​​were equally her objects. But no one knew what negative or imaginary numbers are until the beginning of the 19th century.

There was no clear answer to a more general question - what is a number in general?

And what are infinitesimal quantities?

How can one justify the operations of differentiation, integration, summation of series?

What is probability?

At the beginning of the XIX century. nobody could answer these questions.

In short, in mathematics by the beginning of the 19th century. a generally difficult situation has developed.

On the one hand, this area of ​​science has developed intensively and found valuable applications,

On the other hand, it rested on very unclear grounds.

In such a situation, the problem of the fifth postulate of Euclid's geometry was perceived differently.

The difficulties in interpreting new concepts could be understood as follows: what is unclear today will become clear tomorrow, when the corresponding field of research is sufficiently developed, when enough intellectual efforts are concentrated to solve the problem.

The problem of the fifth postulate, however, has existed for two millennia. And she still has no solution.

Maybe this problem sets some standard for interpretation state of the art mathematics and understanding what mathematics is in general?

Maybe then mathematics is not exact knowledge at all?

In the light of such questions, the problem of the fifth postulate has ceased to be a particular problem of geometry.

It has become a fundamental problem in mathematics.

This analysis provides us with further confirmation of the idea that fundamental discoveries are solutions to fundamental problems.

He also shows that problems become fundamental within the framework of culture, in other words, fundamentality is historically conditioned.

But within the framework of culture, not only fundamental problems are formed, in them, as a rule, many components of their solution are prepared. From this it becomes clear why such problems are solved precisely in this moment, and not at any other time.

Consider again in this connection the process of creating non-Euclidean geometry. Let's pay attention to the following interesting fragments of the history of research in this area.

The proofs of the fifth postulate of Euclid were carried out for two millennia, but at the same time they were considered a problem of the second kind, i.e. the postulate was represented by a theorem of Euclidean geometry. It was a task with a clearly fixed foundation for its solution.

However, in the second half of the 18th century. studies appear in which the idea of ​​the insolubility of this problem is expressed. In 1762, Klugel, publishing a review of studies of this problem, comes to the conclusion that Euclid was, apparently, right, considering the fifth postulate as a postulate.

Regardless of how Klugel regarded his conclusion, his conclusion was very serious, since it provoked the following question: if the fifth postulate of Euclid's geometry is indeed a postulate, and not a theorem, then what is a postulate? After all, the postulate was considered an obvious position, and therefore does not require proof.

But such a question was no longer a question of the second kind.

He already represented a meta-question, i.e. brought thought to the philosophical and methodological level.

So, the problem of the fifth postulate of Euclid's geometry began to generate a very special kind of thinking.

The translation of this problem to the metalevel gave it a worldview sound.

It is no longer a problem of the second kind.

Another historical moment. The studies carried out in the second half of the 18th century seem to be very curious. I. Lambert and J. Saccheri. I. Kant knew about these studies, and it was not by chance that he spoke about the hypothetical status of geometric positions. If things-in-themselves are characterized geometrically, then why should they not obey any other geometry, different from Euclidean, according to I. Kant?

I. Kant's line of reasoning was inspired by the ideas of the abstract possibility of non-Euclidean geometries, which were expressed by I. Lambert and J. Saccheri.

J. Saccheri, trying to prove the fifth postulate of Euclid's geometry as a theorem, i.e. looking at it as an ordinary problem, he used a method of proof called "proof by contradiction."

J. Saccheri's line of reasoning was probably as follows. If we accept the opposite assertion instead of the fifth postulate, combine it with all other assertions of Euclidean geometry and, deriving consequences from such a system of initial positions, arrive at a contradiction, then we will thereby prove the truth of the fifth postulate.

The outline of this reasoning is very simple. It can be either A or not-A, and if all other postulates are true and we admit not-A, but we get a lie, then it is A.

Using this standard method of proof, J. Saccheri began to develop a system of consequences from his assumptions, seeking to discover their inconsistency. Thus, he deduced about 40 theorems of non-Euclidean geometry, but found no contradictions.

How did he assess the current situation? Considering the fifth postulate of Euclid's geometry a theorem (that is, a problem of the second kind), he simply concluded that in his case the "proof by contradiction" method does not work. So, looking at this problem as a problem of the second kind, he, having a new geometry in his hands, could not correctly interpret the situation.

Two conclusions follow from this.

First, in a certain sense, the new geometry appeared in culture even before non-Euclidean geometry was discovered.

Secondly, it is precisely the correct assessment of the problem of the fifth postulate, i.e. its interpretation as a problem of the first, not of the second kind, allowed N.I. Lobachevsky, F. Gauss and J. Bolyai to come to a solution to the problem and create a non-Euclidean geometry. It was necessary to understand the very possibility of creating such geometries.

J. Saccheri admitted such a possibility only as a logical one, having made a constructive step in solving the problem of the Euclidean postulate in the traditional style. But he did not at all consider it seriously, believing that non-Euclidean geometries are impossible, although logically admissible.

Thus, history not only prepares the problem, but also largely determines the direction and possibility of its solution.

Consider the Copernican Revolution from this perspective.

As is well known, it was not N. Copernicus who discovered the heliocentric system. It was created by Aristarchus in antiquity. Perhaps N. Kopernik did not know about this? Nothing of the kind! He knew and referred to Aristarchus.

But then why are they talking about Copernican?

The fact is that N. Kopernik transferred the already known model to a completely new cultural environment, realizing that with its help a number of problems could be solved. This was precisely the essence of his revolution, and not at all in the creation of a heliocentric system.

5. OPENING OF MENDEL

Let us now consider the question of the cultural preparation of discoveries on the example of the discovery of G. Mendel.

This discovery contains not only the so-called Mendel's laws, representing the empirical laws that are usually talked about, but also a system of very important theoretical propositions, which, in fact, determines the significance of Mendel's discovery.

Moreover, the empirical laws, the establishment of which is attributed to G. Mendel, were not at all established by him. They were known even before him and were studied by O. Sagre, T. Knight, S. Noden. G. Mendel, in fact, only specified them.

It is also significant that his discovery had methodological significance. For biology, it provided not only a new theoretical model, but also a system of new methodological principles, with the help of which it was possible to study very complex phenomena of life.

G. Mendel suggested the presence of some elementary carriers of heredity, which can be freely combined during cell fusion during fertilization. It is this combination of the rudiments of heredity, which is carried out at the cellular level, that gives various types of hereditary structures.

This theoretical model includes a number of very important ideas.

First, it is the release of elementary carriers at the cell level.

Justifying such a selection, G. Mendel relied, obviously, on the theory cellular structure living matter. She was very important to him. G. Mendel got acquainted with its main provisions in the course of F. Unger's lectures at the University of Vienna. Unger was one of the innovators in the use of physicochemical methods in the study of living things. At the same time, he believed that these studies should reach the level of the cell. - Secondly, G. Mendel believed that the laws governing the carriers of heredity are as definite as the laws governing physical phenomena.

Obviously, here G. Mendel proceeded from a general worldview, which was deeply rooted in the culture of that time, i.e. attitudes about the laws of nature, which extended to the phenomena of heredity.

Thirdly, G. Mendel realized in his research the general ideal of physical knowledge of the world, according to which one should identify an elementary object, find the laws governing its behavior and then, relying on this knowledge, construct more complex processes, describing and explaining their features.

Fourth, G. Mendel suggested that the laws governing its elementary carriers are probabilistic laws. For 1865, in which he published his discovery, this was a very new idea. Indeed, it was at that time that probabilistic concepts began to be introduced into physics. A little earlier - in the 30s - the probabilistic description of the phenomena of reality entered culture, thanks to the works of G. Quetelet on social statistics... G. Mendel borrowed the ideas of probabilistic description precisely from social statistics.

In addition, G. Mendel assumed that his theory would explain heredity only if it is confirmed by experience. This was very important, especially since in the science of that time, the phenomena of life, like many other phenomena, were explained in a speculative way.

But how could this theory be compared with experience in biology?

For G. Mendel, a new problem arose here. It was to be carried out on the basis of statistical processing of elementary data. It was the inability to process statistical material, according to G. Mendel, that did not allow, for example, S. Noden to establish the correct quantitative ratios in the splitting of signs.

Finally, it should be noted that Mendelian experimental approach to biology was planned for a very long time. G. Mendel himself conducted experiments for about ten years, implementing a pre-planned research program.

The success of his experiments was primarily due to the choice of material. Mendelian laws of heredity are very simple, but they appear in fact on a small number of biological objects. One of these objects is peas, for which, moreover, it was necessary to choose clean lines. G. Mendel was engaged in this selection for two years. He clearly imagined, following the physical ideal, that the object he chooses should be simple, completely controllable in all its changes. Only then can precise laws be established. Of course, G. Mendel did not represent for sure all the details that he will receive in the future.

But there is no doubt that all his studies were clearly planned and based on a system of theoretical views on the laws of inheritance.

In principle, he could not take even one step along this path if he did not have enough theoretical ideas developed in advance.

Thus, the discovery of G. Mendel includes not just the discovery of a set of empirical laws that were not so much discovered by him as refined.

The main thing is that G. Mendel was the first to build a theoretical model of the phenomena of heredity, which was based on the selection of its elementary carriers, obeying probabilistic laws.

Particularly noteworthy is the very system of ideas of a methodological nature related to the assessment of the role of statistics, probability and planning of empirical research in science.

G. Mendel's discovery was not accidental.

It, like other fundamental discoveries, is due to the peculiarities of the culture of his time, both European and national.

But why this outstanding discovery was made precisely by G. Mendel, a monk, and why exactly in Moravia, essentially the periphery Austrian Empire?

Let's try to answer these questions.

G. Mendel was a monk of the Augustinian monastery in Brno, which concentrated many thinking and educated people within its walls. Thus, the abbot of the monastery F.C. Napp is considered an outstanding figure of the Moravian culture. He actively promoted the development of education in his region, was interested in natural science and dealt, in particular, with the problems of selection.

Among the monks of this monastery was T. Bratranek, who later became the rector of the University of Krakow. T. Bratranek was attracted by the natural philosophical ideas of F. Goethe, and he wrote works in which he compared the evolutionary ideas of Charles Darwin and the great German poet.

Another monk of this monastery - M. Clatsel - was passionately fond of G. Hegel's teaching on development. He was interested in the laws governing the formation of plant hybrids, and conducted experiments with peas. It was from him that G. Mendel inherited the site for his experiments. For his liberal views, M. Clatzel was expelled from the monastery and went to America.

P. Krzhizkovsky, a reformer of church music, who later became the teacher of the famous Czech composer L. Janacek, also lived in the monastery.

G. Mendel from childhood showed great ability in the study of sciences. The desire to get a good education and get rid of heavy material worries led him in 1843 to the monastery. Here, while studying theology, he at the same time showed an interest in agriculture, horticulture, viticulture. In an effort to gain systematic knowledge in this area, he attended lectures on these subjects at the School of Philosophy in the city of Brno. As a very young man, G. Mendel taught Latin, Greek and German languages and a course in mathematics and geometry at the Znojmo gymnasium. From 1851 to 1853 G. Mendel studied natural Sciences at the University of Vienna, and from 1854, for 14 years, taught physics and natural science at the school.

In his letters, he often referred to himself as a physicist, showing great affection for this science. Until the end of his life, he retained an interest in various physical phenomena. But he was especially interested in the problems of meteorology. When he was elected abbot of the monastery, he no longer had time to conduct his biological experiments, and, moreover, his eyesight deteriorated. But until his death he was engaged in meteorological research, and at the same time was especially fond of their statistical processing.

Already these facts from the life of G. Mendel give us an idea of ​​why G. Mendel, a monk, was able to make a scientific discovery. But why did this discovery take place precisely in Moravia, and not, say, in England or France, which were at that time the undoubted leaders in the development of science?

During the life of G. Mendel, Moravia was part of the Austrian Empire. Its indigenous population was severely oppressed, and the Habsburg monarchs were not interested in the development of the Moravian culture. But Moravia was an extremely favorable country for development. Agriculture... Therefore, in the 70s of the XVIII century. Habsburg ruler Maria Theresa, carrying out economic reforms, ordered the organization of agricultural societies in Moravia. In order to collect more produce from the land, everyone who runs the farm was even ordered to take exams in the basics of agricultural sciences.

As a result, agricultural schools began to be created in Moravia, and the development of agricultural sciences began. In Moravia, a very significant concentration of agricultural societies has developed. There were perhaps more of them than in England. It was in Moravia that they first started talking about the science of breeding, which was introduced into practice. Already in the 20s of the XIX century. in Moravia, local breeders are actively using the hybridization method to develop new animal breeds, and especially new plant varieties. The problems of breeding science became colossally aggravated just at the turn of the 18th and 19th centuries, since the rapid growth of industry and the urban population required an intensification of agricultural production.

In this situation, the disclosure of the laws of heredity was of great practical importance. This problem was also acute in theoretical biology. Scientists of the XIX century. they knew quite a lot about the morphology and physiology of living things. Thanks to Charles Darwin's theory of natural selection, it was possible to understand the essence of the process of evolution of life on Earth. However, the laws of heredity remained unknown.

In other words, a clearly expressed problematic situation of a fundamental nature has been created.

Remarkable and even in many ways surprising results obtained by G. Mendel were also rooted in the culture of that time.

In this sense, the idea of ​​the probabilistic nature of the laws of heredity is especially indicative. It was borrowed by G. Mendel from social statistics, which, thanks primarily to the works of A. Quetelet, attracted general attention at that time. The expanding practice of statistical processing of empirical material in both social statistics and physics at that time undoubtedly contributed to its spread to the field of life phenomena.

At the same time, the desire to single out the elementary units of inheritance and, on the basis of their interaction, explain the features of the inheritance process as a whole was an obvious adherence to the physical methodology of cognition.

This ideal was clearly formulated already at the beginning of the 19th century. And he actively penetrated into all sciences. By the way, it was following him that physicochemical methods began to be used more and more widely in biology. In psychology, I. Herbart conducted research directly guided by this ideal. O. Comte was guided by it, substantiating the need for creating a sociology. G. Mendel followed the same path in the study of the phenomena of heredity.

The idea to build a scientific theory of inheritance at the cell level could have arisen only in the middle of the 19th century.

Finally, if we talk about such details as the choice of the object of research itself - peas - the properties of splitting, the dominance of this object were discovered at the end of the 18th - beginning of the 19th centuries. There are a number of works describing these properties, which attracted Mendel's attention.

In short, here, as in other examples, we see that fundamental discoveries are the solution to a fundamental problem.

They are always historically prepared.

Not only the problem itself is prepared, but also the components of its solution.

But this should not create the illusion that geniuses are not needed at all for such discoveries. Awareness of a fundamental problem, finding real ways to solve it requires tremendous intelligence, wide education, and commitment, which allow the scientist to feel the breath of time better than others.