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THE MAN OF THE DESERT: symmetry and light by Evgeny Katz (Part III)

THE MAN OF THE DESERT: symmetry and light by Evgeny Katz (Part I)
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The desert is a cultural symbol and a scientific site. This is how Israeli professor Evgeny Katz sees it. His research interests are technologies for converting solar energy into electricity.

But work on breakthrough technologies at the Institute of the Desert pushed him to something more… Today Professor Katz shares his thoughts on this topic with the readers of our almanac.


Read Part I

Read Part II



When I started to deal with this problem, lecture and write on this topic, I ended up at an interesting scientific conference that was devoted to the relationship between science and art. There I met the president of the SIS – short for International Society for the Interdisciplinary Study of Symmetry – Hungarian mathematics historian Denes Nagy.

He also invited me to the SIS congress, which unites people who consider the phenomenon of symmetry as an object of science and a phenomenon of culture at the same time. Since that time, I have become an active member of the community, which includes writers, poets, musicians, architects, physicists, chemists, engineers. It coincided with my scientific interests and ideas about the world and the role of science in society.

Now I am a member of the SIS International Executive Committee, which organizes congresses three times a year in different countries of the world. They gather like-minded people who believe (like me) that science is a part of culture, and not just a base for new technologies.

Of course, the creation of such a base is an important function of modern science but not the only one. Broadly speaking, science is an integral part of culture. Therefore, it is associated with all the variety of aspects and options for understanding the world.

Imagine that at the very beginning of the 20th century, doctors and physicists would be asked: “What scientific discovery in the near future will have the most significant impact on the development of medicine?” None of them would then have answered “Investigation of electrical discharges in gases.” But it was precisely this direction that led to the discovery of X-rays and revolutionized medicine.

There is a legend according to which the following dialogue took place between Michael Faraday and the British Prime Minister. After demonstrating to scientists the newly created electromagnetic machine, the prime minister asked the question: “Will there be any practical benefit from this?” Faraday replied: “I don’t know for sure, but someday you will take taxes from this”. It is impossible to predict the influence of fundamental science on the development of society, its role is the study of the world.

My associates at SIS and I believe that the study of symmetry as a cultural phenomenon can become a universal basis for combining two separate cultures – science and art, for understanding the world in the entire set of interrelationships existing in it. Our task is to show people how you can look at the world in a different way.




Now I am working on the creation of a new interdisciplinary course “A bridge between mathematics, exact sciences, architecture and art: symmetry, polyhedra, fullerenes”, which should be open to undergraduate students from all departments of our university. Perhaps not everyone is able to cross this bridge, but they can admire it, walk along it, stand on the other side and then return back to their usual shore…

In any case, such a journey should be culturally and intellectually enriching. My task is to show that around a person there is an endless and boundless world, not divided, like universities, into departments. It is no coincidence that I focus on the history of science, because history belongs to the humanitarian sphere, in the center of which, one way or another, but always there is a person.

Why did Renaissance artists suddenly become concerned with the geometry of polyhedra? Where did it come from and why did such an incredible interest of the geniuses of the Renaissance in geometry arise? It is not easy to give an unequivocal answer, and perhaps we will be captivated by conjectures for a long time. The cultural historian may ask one more question.

Why did the Renaissance happen in Western Europe, in a very small area of ​​the globe? The answer will require fundamental knowledge from us from various fields. And here the first difficulties already arise. When I was giving a pilot seminar for my future interdisciplinary course, I failed.

The fact is that for my experiment I chose teachers from the Department of Theory and History of Art at our university. I informed the listeners that knowledge of mathematics at the basic school level is enough to participate in the seminar. We were initially guided by it. However, it turned out that even at this level it is incredibly difficult for the humanities to perceive mathematical logic.

Therefore, in the future, I plan to implement the idea of ​​a seminar at the natural science departments with the possibility of attendance by humanities students. Although I am aware that I can face here with a complexity of a different order: the problems of the humanities – history, painting – may well be beyond the interest of this audience.

Nevertheless, I am rather optimistic and hope that ultimately the interdisciplinary course will find its “special”, interdisciplinary listener. Look at the world’s greatest scientists.

The history of science tells us that many of them were polymaths and reached the pinnacle of skill in various fields. The Americans even conducted a statistical study on this topic. One set of questions asked to respondents was about their hobbies.

Three groups of people were interviewed: the average citizens, people with an academic education, and eminent scientists, among whom were Nobel laureates, members of American academies, etc. The first two groups were not statistically different from each other. But in the third, the statistical majority showed more hobbies than in the first two.




Pushkin called “harmonic accuracy”, “a sense of proportionality and conformity” as the main criteria for artistry. This innate feeling is inseparable from human nature, it was familiar to man long before Pythagoras described the phenomenon of symmetry, although he did not use the term itself. Symmetry in the understanding of the ancient Greeks is precisely the embodiment of the principle of proportionality and conformity.

Starting with Kepler, crystallography began to emerge as a separate branch of knowledge. It was from the depths of crystallography that the mathematical science of symmetry emerged. In the era of the Renaissance, which was obsessed with the search for ideal proportions in everything, the emphasis began to be placed not so much on mathematics as on aesthetics.

According to the Renaissance understanding of the laws of beauty, we like a person’s face when it is perfectly symmetrical. Such a face is considered beautiful. However, modern research has shown that it is not the case. We really don’t like asymmetrical people.

But dissymetry – a slight deviation from symmetry – we tend to consider it extremely beautiful and would rather give preference to it than to a perfectly symmetrical face. The geniuses of the Renaissance, although they were convinced symmetrists, consciously or unconsciously followed the “truth of life.”

Take Michelangelo’s famous Medici Tomb in Florence, for example. It seems to you that it is absolutely symmetrical, but, looking closely, you can notice a lot of subtle “deviations”. It was in them that the genius of Michelangelo manifested itself, striving for the maximum likeness of life. He realized that in the pursuit of perfect symmetry, living is very easy to turn into dead.

Symmetry is God’s territory: in some world cultures, mortal and sinful man cannot and should not claim it. When certain cultures created something symmetrical, they often imperceptibly used secret signs that symbolized the “imperfection” of the object and, accordingly, humility before God.

For example, there is such a secret asymmetry in the Taj Mahal. In Islamic culture, the artist, who created the most complex ornament, always left an imperceptible “mark” that broke the ideal symmetry.

Strikingly, fifth-order symmetry and the Penrose lattice were found in the ornaments of Iranian mosques. But modern crystallography has approached these concepts quite recently. The point is that “classical” crystallography forbids fifth-order symmetry. If the body is rotated 180 degrees, and at the same time it transforms into itself – this is a second order symmetry.

Having done a similar operation with an isosceles triangle, square and other figures, we get the symmetry of the first, second, third, fourth and … sixth orders. And where did the fifth disappear, you ask? The fact is that until 1995, crystallographers were convinced that the fifth order in the world of crystals does not exist – it is simply impossible to fill a plane without gaps with regular pentagons.

Until the Israeli chemist and materials scientist Dan Shechtman proved otherwise. He discovered a quasicrystal, discovering that alloys with fifth-order symmetry do exist. Prior to this, crystals were considered a kind of solid body, which has some kind of elementary cell. For example, if you take a cube and broadcast it in three directions, you will receive a cube crystal. Shechtman quasicrystals are crystals without such translations.

We see that the idea of ​​symmetry and the attitude towards it changed depending on the era, the type of civilization and cultural attitudes. Since the 20th century, modern physics has come to the realization of the multivariance of the laws of physics. In our today’s understanding, symmetry is any mathematical operation that is capable of transforming a body or physical law into themselves.

And the point in the study of symmetry is still far from being put … Its existence reminds us that a person is called to a holistic perception of the world and its creative transformation according to the laws of harmony and beauty.

This understanding comes with all clarity in the Negev desert, where we experiment with the fifth element of the universe – light. Behind every modern technology there is also culture, linking together our scientific knowledge, time and existence. And I must admit: the feeling that you are a part of this grandiose world plot is really inspiring.


Photo from the personal archive of Evgeny Katz

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