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

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




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”.




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.




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.


THE MAN OF THE DESERT: symmetry and light by Evgeny Katz (Part II)
Evgeny Katz with a model of the C60 molecule




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).




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.


THE MAN OF THE DESERT: symmetry and light by Evgeny Katz (Part II)
A photovoltaic installation can also have icosahedral symmetry


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”.

Photo from the personal archive of Evgeny Katz


Read Part III

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