House, design, renovation, decor.  Courtyard and garden.  With your own hands

House, design, renovation, decor. Courtyard and garden. With your own hands

» Sergey nikolaev: mathematical criteria for the beauty of a person's face. Criteria for the beauty of men Are there general criteria for beauty in art?

Sergey nikolaev: mathematical criteria for the beauty of a person's face. Criteria for the beauty of men Are there general criteria for beauty in art?

There are not only pragmatic but also aesthetic criteria for evaluating scientific theories ...

In other words, a scientific theory can be approached not only as a tool for explaining natural phenomena, but also as a work of art. This idea is unlikely to surprise any of the scientists - each of them during his work more than once came across such arguments, and sometimes he himself took part in them. On the other hand, the fact that scientists are not hopeless practitioners and rationalists as they are usually portrayed, but the same, like everyone else, connoisseurs of beauty and grace, may even shock the general public.

There are many examples of how this criterion works in science. Thus, the general theory of relativity, thanks to its elegance, was almost immediately accepted by scientists, although it took decades to experimentally confirm its predictions. This example shows - I want to emphasize this especially - that although beauty and grace can bend scientists in favor of one theory or another, they still cannot reverse experimental data. If the theory of relativity did not find experimental confirmation, it would be changed or rejected, despite all its beauty. Thus, the criterion of beauty can raise or lower the weight of a theory, but is not in itself a decisive factor in the acceptance of this theory.

However, the criterion of beauty is a rather vague and subjective thing. It is not as clearly defined as other concepts that we use in this book. For example, there is no clear interpretation of the word "beauty" in the context of scientific theories. Nevertheless, there are some generally accepted provisions. For example, the more universal a theory is, the more likely it is to be recognized as beautiful. The less random and hastily cobbled together data used to construct a theory, the less likely it is that it will be considered simply tailored to a specific set of facts, and the more elegant the theory will seem. And, of course, its simplicity plays an important role in the recognition of the theory as elegant (see Occam's razor). One must think that at least in relation to these three provisions, there is a certain unanimity among scientists.

Naturally, the question arises: is it possible to formulate a criterion of scientific beauty - more objective than the one that we use, say, in painting or in music? When I read other people's arguments about scientific beauty, I often find myself disagreeing with the author in his assessment of a particular scientific idea. For example, some find the idea of ​​a flat universe - where spacetime looks like a grid on a tabletop - beautiful. To me, this idea seems neither beautiful nor ugly. Others think that the universe in which the acceleration is caused by the cosmological constant is beautiful, but my friend Rocky Kolb, a renowned astrophysicist, finds such a universe "unspeakably ugly." In science, as in art, everyone has their own idea of ​​beauty.

There are not only pragmatic but also aesthetic criteria for evaluating scientific theories ...

In other words, a scientific theory can be approached not only as a tool for explaining natural phenomena, but also as a work of art. This idea is unlikely to surprise any of the scientists - each of them during his work more than once came across such arguments, and sometimes he himself took part in them. On the other hand, the fact that scientists are not hopeless practitioners and rationalists as they are usually portrayed, but the same, like everyone else, connoisseurs of beauty and grace, may even shock the general public.

There are many examples of how this criterion works in science. Thus, the general theory of relativity, thanks to its elegance, was almost immediately accepted by scientists, although it took decades to experimentally confirm its predictions. This example shows - I want to emphasize this especially - that although beauty and grace can bend scientists in favor of one theory or another, they still cannot reverse experimental data. If the theory of relativity did not find experimental confirmation, it would be changed or rejected, despite all its beauty. Thus, the criterion of beauty can raise or lower the weight of a theory, but is not in itself a decisive factor in the acceptance of this theory.

However, the criterion of beauty is a rather vague and subjective thing. It is not as clearly defined as other concepts that we use in this book. For example, there is no clear interpretation of the word "beauty" in the context of scientific theories. Nevertheless, there are some generally accepted provisions. For example, the more universal a theory is, the more likely it is to be recognized as beautiful. The less random and hastily cobbled together data used to construct a theory, the less likely it is that it will be considered simply tailored to a specific set of facts, and the more elegant the theory will seem. And, of course, its simplicity plays an important role in the recognition of the theory as elegant ( cm. Occam's razor). One must think that at least in relation to these three provisions, there is a certain unanimity among scientists.

Naturally, the question arises: is it possible to formulate a criterion of scientific beauty - more objective than the one that we use, say, in painting or in music? When I read other people's arguments about scientific beauty, I often find myself disagreeing with the author in his assessment of a particular scientific idea. For example, some find the idea of ​​a flat universe - where spacetime looks like a grid on the surface of a table - beautiful. To me, this idea seems neither beautiful nor ugly. Others think that a universe in which the cosmological constant causes acceleration is beautiful, but my friend Rocky Kolb, a renowned astrophysicist, finds such a universe "unspeakably ugly." In science, as in art, everyone has their own idea of ​​beauty.

Beauty criteria revealed

It was also found that children's proportions (the skin of adults did not change) add attractiveness. In the course of the experiment, photos of adult women were changed using computer graphics - children's features were added. In particular, the head was enlarged, most faces were taken away bulging forehead, the rest of the features were shifted somewhat downward, the nose was reduced and shortened, the cheeks were rounded, the eyes were made large and round. The majority of those surveyed preferred faces with childish traits ranging from 10 to 50 percent.

Psychologists believe that the attractiveness of a combination of childhood and maturity in a woman has a biological rationale: men, on a subconscious level, prefer young girls, since they are more capable of childbearing, stay longer in childbearing age, respectively, they can give birth to more children, to whom a man will pass on his genes further. At the same time, mature features signal to a man that a woman is no longer a child and can become a mother.

The second conclusion that scientists from the University of Regensburg were able to draw is that there is a stereotype of the perception of a beautiful person. At the final stage of the experiment, the subjects were asked to rate the character of people whose faces were found to be beautiful and, conversely, repulsive. The more spectacular the face was, the more successful, prosperous, pleasant, spiritual, intelligent, and diligent its owner was considered.

Beautiful people are credited with being very creative, touching, and able to positively influence those around them. The owners of less attractive or completely ugly faces are denied these positive qualities with only visual contact, they are classified as people who are dissatisfied, arrogant, stupid or tired of life.

Thus, the social consequences of physical attractiveness are enormous. Life is easier for beautiful people. They definitely have advantages in making contacts, looking for a job, in personal life, in everyday life, in general - everywhere.

Well, for those who are not lucky with natural attractiveness, plastic surgery will come to the rescue. Moreover, according to one of the researchers, Martin Grundl, the institutes of beauty and plastic surgery have already become interested in the results of the study.

Questions and tasks.

1. What is art in the wide and narrow sense of the word? If you have art albums at home, what understanding - broad or narrow - do they refer to?

Art in a broad sense is artistic creation as a whole: literature, architecture, sculpture, painting, graphics, arts and crafts, music, dance, theater, cinema and other types of human activity, united as artistic forms of mastering the world.

Art in the narrow sense is only fine art.

Album with paintings by Michelangelo Merisi da Caravaggio (Italian painter, 1571 - 1610) and his followers. This album will be related to art in a narrow sense, since it contains works of fine art. But it can also be attributed to art in a broad sense, since this album is related to painting.

2. * Why art should be brought closer together, but not completely identified with artistic culture. What are their similarities and distinctive features?

We will bring art closer, but not completely identify with artistic culture. They have similarities and differences. The similarity lies in the fact that art and artistic culture is a sphere of figurative and expressive attitude to the environment, a way of aesthetic expression of one's inner state, in which the moment of form even comes to the fore in comparison with the content of ideas and feelings. The main thing in art is the aesthetic expression of the surrounding world and its highly professional, masterful display in stone, theatrical production, on canvas, etc.

The difference is as follows. Art is just the pinnacle of artistic culture. The latter includes not only professional works of real artistic value, but also works of amateurs, amateurs, which are of value only for themselves. The main criterion for artistic culture is a figurative reflection of reality, feelings and thoughts of people. It can be perfect or imperfect. Art belongs only to that part of artistic culture, which is performed on high level and has artistic value to other people.

Thus, the criterion for distinguishing art culture is subject, and art is a qualification criterion. The artistic culture includes not only the results of the activities of professionals, but also the entire huge infrastructure that contributes to them (workshops of artists, halls and art galleries, conservatories and philharmonic societies, specialized magazines, newspapers, printed materials, television channels, publishing houses, departments and laboratories of universities, specialized schools and gymnasiums, lyceums, associations of artists, painters, writers and much more.).

Thus, the concept of artistic culture is broader than art. The latter includes only professional activity and trained people in the field. Art is only or predominantly an elite culture; artistic culture includes folk and elite culture.

3. What is the difference between fine arts and artistic creation? What is amateur art?

Fine arts - a section of the plastic arts that combines painting, sculpture and graphics. Visual arts reflect reality in visual, visually perceived images.

The concept of artistic creativity is broader. It includes literature, architecture, sculpture, painting, graphics, arts and crafts, music, dance, theater, cinema and other types of human activity, combined as artistic forms of mastering the world. Artistic creativity is synonymous with the concept of "artistic culture".

Their difference lies in the fact that fine art is a type of artistic creation.

Amateur art is one of the forms of folk art. It includes, among other things, the creation and performance of works of art by the efforts of amateur performers individually (singers, readers, musicians, dancers, acrobats) or collectively (circles, studios, folk theaters).

4. Explain what art culture is and what is involved in it. Where does literature, music, theater go?

Artistic culture is the totality of all types of artistic activity - verbal, musical, theatrical, visual, etc., including the product and process of this activity: creation, storage, distribution, perception, evaluation, study of works of art, as well as the education of artists, upbringing critics, art critics, the public.

Literature, music, theater are elements of artistic culture.

5. Describe the main subjects of artistic culture.

Subjects of artistic culture are divided into those who:

Creates new works and ideas;

Extends new works and ideas to non commercial basis;

Finances new works and ideas;

Introduces new works and ideas;

Teaches new works and ideas;

Engaged in mass replication of new works and ideas;

Sells new works and ideas on a commercial basis and thus makes a profit;

Evaluates and examines new works and ideas;

Exercises state control and management over the creation and dissemination of new works and ideas;

Reads, looks and listens to new works and ideas;

Becomes a fan, a supporter of new works and ideas.

6. * What role do Beauty, Goodness, Truth play in culture?

Truth, Beauty, Goodness are three pillars on which the spiritual sphere of society rests. Whatever we take from this sphere - a scientific theory, a pedagogical method or a religious teaching - they will necessarily correspond to one degree or another to the three main principles of the spiritual. In scientific theory, Truth comes to the fore, in religious teaching - Good, in the field of education - a little bit of both. In works of art, Beauty comes to the fore.

7. Can painting, sculpture and architecture be classified as fine arts? What is your example of the fine arts?

Yes, painting, sculpture and architecture can be classified as fine arts because they meet the criteria of Truth, Goodness, Beauty.

Literature, theater, dance are examples of the fine arts.

?Problem. Think about the problem - are there general criteria for beauty?

Beauty is an aesthetic (non-utilitarian, non-practical) category denoting perfection, harmonious combination aspects of the object, in which the latter causes aesthetic pleasure for the observer.

There are no general criteria for beauty. In different periods of time, beauty was understood in different ways: “In the variety of changes, beauty remains eternally new” (Dionysius of Halicarnassus). Even within the same era, ideas about beauty differed from person to person. Criteria for beauty were more or less general in individual societies.

For example, in Ancient Greece there was a cult of athletic physique; among the Maya Indians, a body painted with tattoos was considered beautiful. In ancient China, the fragility and diminutiveness of a woman was valued. At the age of five, the girl's legs were tightly bandaged, and they stopped growing. According to the canons of beauty, women whitened their faces, extended eyelashes, and painted thin lines instead of shaved eyebrows. V Ancient egypt gracefulness was valued in women. The woman had to be slim. The owner of narrow hips and small breasts was considered beautiful. Of all the colors, the Egyptians preferred emerald. The most beautiful girl was considered in green eye. Arrows in front of our eyes were drawn with green paint. Exactly the same beauty today in African countries, India, Japan, the United States will be different.

We should not forget about the beauty of the soul. The beauty of the flesh has a limit; spiritual beauty is infinite.

You can hear about the beauty of music, the beauty of the building, the beauty of the city, the beauty of the park, the beauty of the painting, the beauty of the vase. In the East, in the 11th century, at the court of some rulers, it was popular to sing the beauty of ordinary things in poetry. It could be cutlery, weapons, shoes, clothes, or whatever.

However, the concept of beauty in different people will depend on their preferences, formed in them in the process of socialization. What is beautiful for one may be ugly for another.

Workshop. Explain why only works of elite visual culture can be classified as art.

Elite, or high, culture is created by a privileged part of society or by its order by professional creators. Her motto is "art for art." In any community, only a trained minority had a deep understanding of art. High culture, for example, the painting of the Spanish artist P. Picasso or the music of the Austrian composer A. Schoenberg, is difficult for an unprepared person to understand (for example, in contrast to graffiti). As a rule, it is decades ahead of the level of perception of an average educated person.

MATHEMATICAL CRITERIA FOR BEAUTY
HUMAN FACES

Sergey NIKOLAEV

The beauty of a human face is usually considered a rather subjective thing, but, as you know, there is no subjectivity in the world that can change the real state of affairs. I have long been fascinated by the idea of ​​calculating mathematically the correct proportions of a face using the example of a person regarding whom it would be difficult to find the opposite opinion.

And so, having decided to write about the mathematical criteria of beauty, I began to shovel a collection of photographs in search of examples. And I ran into unforeseen difficulties - I simply do not have photographs strictly full-face, and if this happens, the photographed person, in addition, begins to show a wide smile, which in this case only interferes. The situation is similar with photographs of Hollywood stars, models and other already washed-out beauties. When I was already in a state of permanent despair, Yulcha helped me out, as always. :)

Of all the photos, I chose two:


With all the variety of shapes, four main types of faces can be distinguished - round, triangular, square and oval. To study the necessary proportionality of facial features, we will draw the following reference lines.

A beautiful face should be symmetrical. Vertical line A is the axis of symmetry and crosses the line 3 ; their intersection point is at the tip of the nose. At the point of intersection, draw a circle, the radius of which is equal to the distance between the tip of the nose and the tip of the chin, which is on the line 5 - the lower border of the face. Having drawn it, we understand that with the reference symmetry of Yulch's face, the photograph is not an ideal frontal view: the face is slightly turned to the right. :)

The top of the circle touches the brow line 1 ... Approximately one third of the radius, equal to the segment between the tip of the nose and the tip of the chin, passes middle line mouth 4 ... Eye line 2 located at a distance of approximately 1 / 3-1 / 4 from the eyebrow line. Lines B are drawn perpendicular to the line of the eyes through the centers of the pupils, and the segment between the lines B Is the center-to-center distance. It will be useful to us in the future.

Direct WITH touch the circumference, the line of the temples D pass close to the lines WITH, and the outlines of the chin are inside the circle, which makes it possible to classify Yulchin's face as a triangular type.


Now, in the same photo, we determine the vertical proportions. To do this, draw four lines along the corners of the eyes - on a beautiful face of distance A,V and WITH between these lines must be equal. The borders of the nose should not protrude beyond the inner borders of the eyes, and the width of the mouth, highlighted with white lines, should be approximately one and a half times the width of the nose.

For owners of an oval face, vertical lines drawn through the pupils should also pass through the corners of the mouth, i.e. the width of the mouth should be approximately equal to the center-to-center distance. For a triangular face, such a mouth will be overly wide, so the lines Z drawn parallel to the lines K drawn through the midpoint of the temple and the right corner of the jaw. In general, the mouth should not be more than half the width of the face. The opposite can be easily seen in any Julia Roberts movie.


Now let's pay attention to Yulchin's profile photo. These dimensions should have been shown in the previous photo, but it was cut off at the top, alas.

The ideal length of the nose is equal to the height of the forehead and the distance from the nose to the chin. A=B=C... This, as well as the correct vertical proportions, were calculated by Leonardo da Vinci in an attempt to find the ideal ratio of parts of a woman's face. Now this rule is used by plastic surgeons and artists all over the world.


Let's move on to the next one. The shape of the nose also forms the ideal female profile. Injection S, which I drew a little incorrectly (but not critically), and was too lazy to redraw, is called nasolabial. For women, it is preferable that the nasolabial angle is greater than 90 degrees. More precisely, in the region of 100-105, like Yulchi's, because too large angles already cause snub-nosedness. Which, in principle, is also not critical. :)


Let's go further. Injection F, indicated below, is drawn by the line of the nose and the line of the forehead and lips. V ideal option it is between 30 and 40 degrees. Too large an angle outlines an excessively high nasal bridge, too small an angle low, the face visually becomes flat and unpleasant.


Continuing the nose theme, there are a few more things to note. Speaker 2 , or, in other words, columella is a bridge between the nostrils. It is considered beautiful when the column is lowered just below the level of the wings of the nose.

Perhaps everyone knows that the nasal bridge should be straight. No humps, shark fins, or brick attack victims. A slight bend is possible in the profile line of the nose 3 inside, which gives the female profile a little more charm. I had to draw a circle with a huge radius to repeat this bend.


The arch of the eyebrows should follow the line formed by the wings and bridge of the nose. We know from geometry that a kink is where the concavity changes to convexity. So - no kinks: the simpler, smoother and more organic the line, the better. One more important detail should be noted. The eyebrow should start at the point indicated by the line that goes through the edge of the wing of the nose and inner corner eyes, and end, respectively, on a line drawn through the edge of the nose and the top outer corner... The shape of the eyebrows, selected for a particular owner by a professional beautician, always fulfills this simple rule.

There are no special rules regarding the thickness of the lips. My personal opinion is that the lips should be of medium thickness. Hypertrophied thick lips do not give the appearance of sexuality, but they evoke a feeling of silicone and vicious character of their owner. Very thin lips, especially in combination with a thin aristocratic nose, make the appearance of a rat.

In conclusion, anticipating objections on the topic of individuality, it must be said that the voiced foundations of beauty are not an absolute, and we are not talking about a standard, which, by definition, can be only one and must lie in the Paris Chamber of Weights and Measures. On the contrary, these criteria are very flexible, i.e. people with such face proportions can be very different due to the variability of little things, but not a single cute mole and not a single unusual spread of eyebrows will save a face that does not fit too much into the above framework.