THE MAN OF THE DESERT: symmetry and light by Evgeny Katz

Evgeny Katz

 

The desert is a cultural symbol and a scientific site. This is how Israeli professor Yevgeny 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.

 

DESERT AS A RESOURCE

 

Israel, as you know, is a small country, but its nature is incredibly diverse — as many as six climatic zones! True, for 60% of the territory, this diversity is irrelevant, since they are occupied by the Negev desert. On the scale of a tiny country, these are very large spaces to be so easily neglected.

Therefore, practically from the very beginning of its statehood, Israel considered the desert as a resource. As an object of science, it is actively pursued at the Ben-Gurion University of the Negev. Already from the name it is clear that our university is located in the Negev desert.

I work for a university department called the Desert Research Institutes. Its mission is to develop technologies that help people live and work fully in the desert. Essentially, these are three institutions. The first is the institute of water. Today, 70% of the fresh water consumed by the Israelis is obtained by desalting sea water.

And from year to year, the production of desalinated water continues to increase. In the Middle East, water has been a key and vital strategic resource since ancient times. This is as obvious today as it was 5,000 years ago. It is not surprising, therefore, that technologies for obtaining water in deserts are the pride of both our university and all of Israel.

The next technological direction logically follows from the first one — it is the development and implementation of highly efficient agricultural technologies that adapt to the conditions of the desert. This is a zone of scientific interest for specialists from the Institute of Agrobiology and Agrochemistry.

And finally, the third direction and the corresponding Institute for Energy and the Environment. I work in his Department of Solar Energy and Environmental Physics. Actually, from the name of the department it is clear what I am doing. Energy regulation is a very important component of the «desert economy», in which it is directly related to the management of desalinated water resources.

 

THE SUN HAS NO ALTERNATIVE

 

It is clear that as an employee of the Institute of the Desert and concurrently director of the National Center for Sun and Solar Energy, I am primarily focused on the problems of renewable energy, the main source of which, of course, is the energy of solar radiation. Today, humanity has learned how to effectively convert it into relatively cheap electricity.

The problems do not start in the field of production, but in the field of energy storage. If the cost of the converted electricity is included in the cost of storage devices (batteries), then it rises sharply. Nowadays, this is the most important factor that hinders the large-scale development of solar energy.

On the other hand, the scientific work that is being carried out in Israel today shows that by «crossing» the processes of desalination and photoelectric conversion of light, it is possible, firstly, to dramatically reduce the cost of desalination, and secondly, to solve the problem of energy storage. This function can be performed by the desalination process itself.

Energy strategy issues are coming to the fore all over the world today. The introduction of new technologies will inevitably increase consumption and demand for electricity. Consider trends such as electric vehicles, digital currencies, reducing the carbon footprint and tackling atmospheric emissions that negatively affect the planet’s climate … All of this requires more electricity.

There is now a consensus in the scientific community that the climate change we are observing is directly related to human activities. From this, some people conclude that we must curtail technological progress, and then the planet will return to climatic norm. This is a fundamentally wrong, dead-end path. A return to the Stone Age will not help us solve global problems.

We can change the situation only at a new stage of scientific and technological development. The latest technologies, including desalination technologies, require continuous growth in electricity production.

And today the only optimal and reasonable way to increase it is «solar» electricity. This fact is increasingly recognized by scientists around the world and humanity as a whole. The global society is now on the verge of the most powerful revolutionary changes associated with the use of photoelectricity.

 

 

PRICELESS LAND AND CHEAP SILICON

 

However, there are technological factors that are holding back the photovoltaic revolution. The main one in Israel — no matter how paradoxical it sounds — is the lack of territories where a solar power plant can be located. After all, the desert seems to be full of free space, build whatever you want. In fact, this is far from the case. Most of the Negev Desert is occupied by national reserves and parks, where the construction of industrial facilities is prohibited.

And solar stations, using thermal heating of water with concentrated sunlight to generate electricity, can only be installed on a flat surface.

But the deserts of Israel are very mountainous, it will not work to level them all on an industrial scale. To date, Israel has built a fairly large land-based solar power plant of this type. Fortunately, the Israeli bureaucracy and lawmakers have come to understand that the land is «not rubber».

Therefore, in the very near future the law on the so-called «second application» will come into force. That is, if you want to build a solar power plant on the roof, then photovoltaics must be connected to something else. For example, power generation on a rooftop can be combined with a greenhouse facility that is located under that roof. It is planned that in this way the deficit of production space will be overcome.

The key difference between solar energy and thermal or nuclear energy is that it is not compact. The energy density is very low here, and it has to be collected from large areas. And mankind has less and less free and at the same time suitable spaces for this. That is, the land, the territory becomes the resource that humanity will begin to save very much in the very near future.

It is not surprising, therefore, that solar energy production is transforming into a global multibillion-dollar business closely related to geopolitics and geoeconomics. So far, China is the clear leader in the «solar» race. It produces the vast majority of solar panels in the world. Most of these batteries are based on crystalline silicon.

This technology is not new, it has been improving for decades. Today, the cost of silicon-based solar cells is quite low. However, their efficiency has already approached its theoretical limit. To move forward, fundamental scientific breakthroughs are needed.

The solution came when a family of new semiconductors, metal halide perovskites, was discovered. Solar cells based on them are much cheaper than silicon ones, since they can be produced from solutions, for example, printed on a printer.

In addition, the prospect of obtaining a «tandem solar cell» opens before us. If metal halide peroxide is applied on top of silicon, the efficiency of the solar battery increases from 26% to 35–40%. And this is very important.

The only thing that hinders the development of this technology is its low stability; materials quickly degrade in the light. The area of ​​my current scientific interest lies precisely in the search for solutions that will help to increase the service life of perovskite and tandem solar cells.

 

THE PERFECT LIGHT OF THE NEGEV DESERT

 

The place where we conduct our experiments doesn’t just have a lot of sunny days a year. Our sunlight is very high quality. On a cloudless day, its intensity is close to the laboratory standard of the natural solar spectrum accepted throughout the world — AM 1.5. Sunlight is known to consist of direct and diffuse radiation scattered in the atmosphere. Thanks to it, we, for example, can see objects in the shade of the sun.

Since the time of Archimedes, we have been able to concentrate direct light using the so-called geometric optics — lenses or mirrors of a certain shape. And diffusely scattered light cannot be concentrated like that. So, the peculiarity of the Negev desert is that here almost all the light is direct. This means that we can work effectively with a very high concentration of it.

Solar power standard — 1 sun — 100 mW per square centimeter. In real operating conditions of solar power plants, this power is significantly less. We have learned to concentrate natural sunlight up to 10,000 suns!

The concentration of natural light begins outside the laboratory. Then, with the help of optical waveguides and other devices, the light is transported to the laboratory in an ultra-concentrated form.

We use this for a variety of experiments: we synthesize new materials, accelerate their degradation and study its mechanisms, conduct an accelerated stability test. This is what we are doing to develop stable perovskite devices. Our research is interdisciplinary, it is at the junction of several sciences: physics, chemistry and a kind of «solar engineering».

 

THE PLACE WHERE FREEDOM

 

As a scientist, I am an atheistic person, or rather an agnostic. Nevertheless, I sense a certain continuity between the archaic human interest in the desert and modern scientific interest. The part of the Negev Desert where I work is described in the biblical Book of Exodus as the «Qing Desert». For man, the desert has always been a symbol of freedom, a place to receive revelation, a breakthrough of the human spirit to some previously unseen heights.
These insights may well be both religious and quite scientific in nature. Thanks to the desert, generations of ascetics feel some kind of spiritual continuity, a connection with God. With scientists, sometimes something similar happens in a mystical way. I got to the Negev «not on my own» and «for a reason».

Before me, Professor Mark Mikhailovich Koltun, one of the leaders in the development of solar cells in the USSR, moved to Israel to live and work. They were then actively used in space technologies, including being «participants» in the space race of the Soviet Union and the United States.

Mark Mikhailovich was a creative, versatile gifted person. He was widely known not only as a serious, prominent scientist, but also as the author of such brilliant popular science books as «The World of Physics», «The World of Chemistry» and others. We collaborated professionally.

The thing is, I’ve been doing solar cells for almost forty years. My diploma at the Department of Materials Science of Semiconductors at the Moscow Institute of Steel and Alloys (1982) and then my Ph.D. thesis (1990) were devoted to the study of polycrystalline silicon and solar cells based on it.

In addition, my acquaintance with Mark Mikhailovich, apparently, pushed me to popular science writing. Having moved to Israel, Professor Koltun invited me to work with him. Unfortunately, he died tragically almost immediately after my arrival. He drowned in the Mediterranean.

As I went through the papers left in his office, a quote from Rockwell Kent on the wall caught my eye: «Why do people love wild places? For the mountains? They may not exist. For forests, lakes and rivers? But this may be a desert, and people will still love it. The desert, the monotonous ocean, the untouched snowy plains of the north, all the deserted expanses, no matter how dull, are the only places on earth where freedom dwells».

 

«AND THE SKY IS LIKE BLUE GLASS»

 

Since then, for me, the desert and freedom of spirit, which is necessary for a person, including for scientific discoveries, are synonymous words. Finding yourself alone in a deserted and desolated place, you begin to experience some very strong existential experiences. The very first meeting with the Negev surprised me a lot.

In the Soviet Union, I have developed a kind of stereotypical idea of ​​the desert — it is a flat area with a lot of sand. In the mountainous and rocky Negev, there was neither one nor the other. This desert was so beautiful that I fell in love with it at first sight.

Several years ago in China, I was in the Gobi Desert and saw there hundred-meter dunes of insane beauty, which seemed to have come down from the paintings of Matisse or Modigliani. However, the beauty is completely different.

By the way, more about our desert sunlight. Many have heard the stunning lines from Vertinsky’s song Palestinian Tango:

 

And the people there are shy and wise

And the sky is like blue glass there.

And to me, tired of lies and powder,

I was quiet and light with them

 

Vertinsky wrote this song after a visit to the Holy Land (where, among other things, he gave concerts and was very warmly received). It was not by chance that the poet’s eyes noticed this detail of the Israeli desert — «the sky there is like blue glass” — the standard of solar radiation. The Negev is truly bathed in the ideal sun spectrum.

 

 

FULLER MOLECULE

 

The Israeli desert revealed to me not only its beauty, but also the amazing harmony and symmetry of the macrocosm and microcosm. My arrival in Israel coincided with the discovery of a molecule of 60 carbon atoms (C60) called Buckminsterfullerene, after Richard Buckminster Fuller, an engineer, designer and architect. He was an amazing, encyclopedically educated person.

He created an alternative to the globe «cartographic projection of the world», discovered the multifaceted «geodesic sphere» and developed on its basis the concept of air dwellings. Fuller was a fierce advocate and advocate for renewable energy. The shape of the molecule named after him — a truncated icosahedron — resembles a modern soccer ball, consisting of 12 pentagons and 20 hexagons.

The story had a continuation: people who received the Nobel Prize in chemistry for the discovery of buckminsterfullerene continued their research and discovered a whole family of similar molecules — fullerenes.

After the discovery of C60, I became involved in the development and research of a new type of solar cells based on fullerenes and conducting polymers, the so-called organic photovoltaics (OPV).

OPV devices have not been used for large-scale solar electricity generation today, but the knowledge gained from the development of these devices and materials has spurred the unprecedented success of the perovskite technology I mentioned above.

 

 

PEDIGREE OF FORMS AND IDEAS

 

I was so fascinated by new fullerene-based nanomaterials that I started writing the popular science book Fullerenes, Carbon Nanotubes and Nanoclusters: A Genealogy of Forms and Ideas. Perhaps this is how my midlife crisis manifested, when I want something more, and you strive to finally understand yourself and the world …

The search for harmony in my own life in some amazing way coincided with the fact that I plunged headlong into the geometry of molecules, the study of the properties that follow from it. Investigating the genealogy of scientific ideas in this area, I inevitably came to the need to study the history of the geometry of polyhedra.

The shape of the C60 molecule — a truncated icosahedron — belongs to the class of so-called Archimedean polyhedra or Archimedean solids. As you may have guessed, their discovery is attributed to Archimedes. Unfortunately, his manuscripts have not survived.

It is believed that they were irretrievably lost as a result of the fire in the Library of Alexandria. But in some ways we were still lucky — the Greek mathematician Papp made verbal descriptions of these drawings, we can read them and reconstruct some of the Archimedean ideas.

When I say «we», I mean the Europeans, because the mathematicians of the Islamic world did not lose this knowledge, the continuity with ancient Greek scientific thought in the Middle Ages. Today we know of 13 Archimedean polyhedra.

They are characterized as semi-regular, because each face of such a body is a regular polygon and each vertex is absolutely symmetric. But unlike the regular — Platonic solids — the Archimedean faces of different types are possible (for example, in the truncated icosahedron — C60 — pentagonal and hexagonal faces).

 

ABOUT PLATOUS AND ARCHIMEDIAN BODIES AND A LITTLE ABOUT THE «NATURE OF THINGS»

 

There are only five Platonic polyhedrons — cube, octahedron, tetrahedron, icosahedron and dodecahedron. They are identical in everything to semi-regular bodies, except for one thing: their faces are of the same type. For Plato’s philosophy, these polyhedrons were of tremendous importance, because they were associated with the five elements that make up everything. Four is fire, water, air, earth, and the fifth is «quintessence», what can be otherwise called the cosmic environment, «ether» or simply «space».

I would say that our ideas about physics have not changed much since the time of Plato, we just switched to a different language of description. Earth is the «name» of the solid state of matter, water — liquid, air — gaseous, fire — plasma. Well, space has remained space.

And yet it seems to me that a different interpretation of the Platonic concept of primary elements is more consistent with the modern scientific paradigm: the four elements are time, space, matter and energy.

But the fifth element, «quintessence», is light (the same light that we convert into electrical energy in the Negev desert). Radiated by matter, it brings us energy. And he also unites space and time. After all, when we look at the stars, we see the light emitted sometime in the past and came to us from the depths of the galaxy.

These ideas dominated the minds of generations of thinkers, starting with the Pythagoreans, who creatively developed their doctrine of the Platonists, and ending with Kepler. Scientists and philosophers seriously believed that the five elements are not only the basis of existence, but are directly related to the five correct bodies.

Before deriving his famous laws, Kepler spent a huge amount of time on geometric constructions. He inscribed one correct body in another an infinite number of times and in the end was forced to abandon this fruitless research.

Platonic solids have been known in Europe for a long time. But the «Archimedean» was only partially discovered in the Renaissance. This was done by great artists, who were also the greatest mathematicians of their time: Piero della Francesca, Leonardo da Vinci, Durer.

Piero’s pupil, the mathematician and monk Luca Pacioli, was not an artist; he persuaded his friend Leonardo to illustrate the book «Divine Proportion». Each of these mathematicians rediscovered Archimedean polytopes one by one. The last of the thirteen bodies was described by Kepler in the book «World Harmony».

 

 

ANY TECHNOLOGY IS HISTORY AND CULTURE

 

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.

 

A BRIDGE BETWEEN SCIENCE AND ART

 

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.

 

SYMMETRY IS A PROPERTY OF OUR WORLD AND A PHENOMENON OF CULTURE

 

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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