The Golden Ratio and its Consequences
JD: What was it for you to discover the new principles of the golden ratio?
JK: Confirmation that I am on some kind of a good track to sort out the world that fell apart in my youth. Because the world is interconnected - understanding even one small element improves our understanding of everything. For me, this came as an unusual surprise. Once I received the issue of the Japanese magazine "Forma" with my article, I was struck by a strange, unexpected, and consequently important thought for my life - even if I visited all the libraries of the world and read all the books, I would not find what I discovered. For the first time in my life, I felt a certain human dignity and reassurance. Maybe I'm not as helpless as I thought of myself. Maybe it's good to get in touch with your head alone sometimes? It was very shocking. Of course I remember the sentences of Blaise Pascal: "You want people to have a good opinion of you. Do not speak well of yourselves." So I say that I am an artist with mathematical and philosophical interests. Art - for me - is not an expression of what is known, but a tool for cognition. It is a specific medium allowing for the most personal experiments. It is in art that we recognize the authentic or artificial limits of our humanity, beauty and imagination. All my adult life I have been aware of the seriousness of imagination. Just as memory is responsible for the past, imagination is responsible for the future. It alone is capable of creating things that were not there before. All my adult life I have exercised my imagination.
JD: What is a discovery, anyway?
JK: At the openings of my exhibitions devoted to the K-drone (a new geometric shape I discovered in New York in 1985) - I often say that there are two people in me. One is an artist, the other is an explorer. And just like an artist, when he is reasonably intelligent, tries to talk to the cosmos - at the exhibition he should rather not say anything at the exhibition and show what he has achieved - in the case of an explorer - it is the Cosmos that talks to someone. The discovery is like a cosmic gift. Man then has an unusual sense of distinction. He feels responsible and his life changes dramatically. He understands the seriousness that has happened to him. And unlike an artist - he has to talk about his discovery for someone else to understand it. The same is true of the golden division.
JD: Let's try to talk about the golden ratio as we know it. We know that many of the everyday objects have been designed with the golden proportion in mind and are in an unknown way pleasing to our eye. So if one day we realized that the world would be devoid of mathematics, its numerical notation - what would this world be like?
JK: The world somehow came into existence. We have two perspectives; the first, that God created it out of nothing, and the second - scientific - that the world began with the Big Bang. As Hoimar von Ditfurth once said, "in the beginning there was hydrogen". We know how hydrogen turns into helium first, and then into over eighty other elements. I call this physical evolution. Elements were created that are components of the entire universe. As these elements began to dance and merge into dramatically different compounds and structures, the second stage began, which I called chemical evolution. No longer were there more and more elements. The development of the Cosmos has focused on creating endless chains and opportunities. At some point a miracle happened - these structures began to duplicate and multiply. Reproduce. And we already know this a little better thanks to Darwin - biological evolution has begun. The game with inorganic chemistry ceased - organic life began. The entire potential of the Cosmos has now focused on creating viruses and bacteria, slippers and ferns, flowers and fish, plants and animals. But at one point something completely unique happened, something that in no way resulted naturally from the earlier stages of the development of the physical world. One of the animals was banished from its natural paradise. Suddenly alone it faced Everything. It gained self-awareness. Biological evolution has ended. Mental evolution has begun. In my opinion - and this is the most important thing I want to say here - the evolution of the cosmos is happening with our heads. And yours. And mine. There are no more elements, compounds, plants and animals. Thoughts arrive. We want to understand this world. For myself and for the world. For the self-awareness of the world. When the atom was born, science says that time and space were born at the same time. It says it doesn't make sense to ask what was before. There was no time ahead of time? Which is Eternal? Let's leave this witting game to scientists, who are probably creatively busy and don't have time to think. But if I am already able to somehow understand and imagine the birth of time and space, then I ask the question - what about the square? A circle? A cube? A sphere? Are they too? Can a circle, a square, a cube or sphere be born from the fact that there is an explosion? Using recent mental evolution, that is, as a thinking animal, I want to emphatically say - before physical evolution there was never a geometric evolution. Geometry was, is, and always will be. Even if this world ends with the Great Failure. This longer statement was made to make your question whether the world can exist without mathematics provocative and absurd. It can't be at all! And not only because Pythagoras said - everything is a number.
JD: It's very Platonic thinking ...
JK: That's exactly right.
JD: But for us the world of ideas is inaccessible ...
JK Well it turns out not to be inaccessible, because as you can see it is available. It is we who have forgotten it, as Plato said. There was a shape in the world of ideas that I discovered. But we associate the word discovery with Columbus. Why did Columbus discover America? Because it was there. I had an intuition that this shape was somewhere. But where? It took me 8 years to find where the K-drone is in space. But - and this is the most important thing I want to say - if I did, like those who do not believe in Platonic concepts, I would have to ask myself - why think about something that is not there? And I believed it was. After 8 years, I discovered the dual nature of the cube. Two k-drones form a cube, but it is a different cube than we have known so far. I presented this at mathematics conferences where there were mathematicians such as John Conway and Roger Penrose. I want to say that it was only this belief in the earlier existence of the K-drone that made me discover it in the Cosmos. If I hadn't thought so, I wouldn't have found it there.
Coincidence is the ultimate possibility of Providence to make things happen. Geometry is the sacred idea from which the world takes its existence.
JD: The same mystery is the golden ratio. It has already been handed down to us by antiquity that the golden proportion, also called later the divine proportion, is in a completely extraordinary way present in what man perceives as harmony in the world, what man perceives as harmony in nature and art, but also in himself. Can we equate harmony with beauty?
JK: What is harmony? Uniformity in diversity. If something is harmonious, it means that it interacts pleasantly with itself. It gives us pleasure. Someone has to feel this harmony. Two accidental sounds will make one's ears prick up in horror. So it is a natural - harmonious - relationship of various elements. I stress again - every human being has a nose, eyes and mouth. But not everyone is beautiful because of this. Because beauty lies not in the presence of all these elements, but in the distances between, which we call proportion. You can read a fuller account of the seriousness of proportion in my essay on the golden ratio.
JD: Is it possible to measure beauty with measurement?
JK Yes - and this is the axis of my meditations related to my discovery of the new principles of the golden ratio. The golden ratio appeared as a special division of a segment in Euclid's Elements. Kepler discovered in the Fibonacci sequence that the ratio of the next word to the previous word tends toward the golden ratio. This was a shocker. He said two such sentences that caught my attention. The first, that geometry has two gifts from the Greeks - one is Pythagoras' theorem, the other is the golden ratio. The second: understanding the golden ratio is a direct insight into the mind of the Lord God. I am the third man in history to have something fundamental to say about the golden ratio. Little, without my discovery it is hard to understand why my predecessors were so fascinated by it. I was able to find the kind of structure that enforces the golden ratio, and this means, in my opinion, that the golden ratio is much more important than we have thought so far.
JD: On the grounds of psychology and statistics, the 19th century confirmed the existence of an internal harmony of the golden ratio. So what is beauty then? Is this a category that needs no proof? And can any particular harmony be identified with beauty?
JK: As I said, harmony is sensed, harmony is felt. Harmony is our human definition of some favourable situation. If we feel that something is harmonious, it certainly gives us pleasure. And it is in this sense that we say that the golden division is harmonious. In the research you mentioned, there were 8 thousand people who were shown rectangles of different proportions. And what did they find? 85 percent of the people pointed to the rectangle with the most perfect proportions, the golden rectangle. The golden rectangle is formed from the golden division of a segment - the shorter part is its one side, the longer part - the other. When we cut off a square in it, the part that remains after cutting off is again a golden rectangle. So, we in this rectangle subconsciously sense its inner harmony and, consequently, its beauty.
JD: But what are we getting at? To such axiomatic thinking.... We are, as humans, capable of receiving mathematical values. There is a certain relationality that comes from mathematics. We recognize this relationality. You say that beauty can be described by them. What is it in your opinion?
JK: We said to ourselves that beauty is proportion, harmony of uniformity in diversity. The coherence of things, a certain order and symmetry. Harmony, especially in music but also in architecture, is the harmony of partial elements in a multithreaded whole.
The golden division is a law that we sense. Like gravity. Take nature, specifically the human body. When we put two hands together - as I show in the photo of my hands - the golden division shows up exactly between the thumb and index finger.
I call this the "carpenter's golden point" because this is where he puts the nail he wants to hammer into anything. The navel - in a man slightly higher, in a woman slightly lower - also roughly divides the body in the golden ratio (see Leonardo da Vinci's "Vitruvian Man"). Nature does not repeat anything - oak leaves are oak leaves, and each one is different, and has its own unique record. In this sense, I want to talk about the beauty of the golden division. It is like an oak leaf - each one is different, none is repeated, and each one is the same.
JD: It is therefore an ordering value ...
JK: Exactly so. It is an archetype.
JD: And that would mean that as humans we have some kind of internal code by which we read beauty. We know very well that one thing will be beautiful to the inhabitants of Polynesia, another to the Africans and another to the Europeans. Therefore, can we speak of the properties of beauty as being the same or different for the whole of humanity?
JK: As I said a moment ago, harmony or beauty revealed in the golden ratio is an archetype that - since Carl Jung - has been understood as "structural elements of the collective unconscious shared by all people in the world". That is, Polynesians, Africans, and Europeans. It is the proportions that unite us. The eyes, nose and mouth are always different. If this code you mentioned is born again in every leaf and in every tree and in another tree and in another leaf - similarly we can talk about beauty. The man of the east or the man of the west is subject to the same gravity. Also the same proportion. It is obvious that a bonsai tree from Japan, a sequoia from America or a willow tree from Poland are different. But every tree has its own proportions. It is beautiful in a different way. Since it is a cosmic value, it does not belong only to European man.
JD: Is the canon of beauty a relational category? How does beauty relate to other values?
JK: Not to oversimplify. We experience beauty in the same way, it is a cosmic value. It is archetypal. When someone says there is no beauty, if he has a beautiful wife, let him give her to a friend and let him take care of the ugly one. In ordering the world, recognizing and acknowledging its hierarchy, Beauty is a key value. Next to Goodness and Truth. The holy trinity of everything. God is viewed from three different sides. We can say: Good - is the true face of God, Beauty - the wise, Truth - the good face of God. I once wrote - "beauty is the part of the Universe in which the Creator failed to hide". About beauty, good, truth and you can not talk to someone who does not understand the meaning of words. Language is both good and safe. If I see a falling stone and yell for you to move to the left - and you do - I can save your life. But if you start questioning the word "left" - I leave you in the place you have chosen for yourself. Beauty should be discussed with people who respect our common struggle for meaning, for whom beauty is not ugliness, good is not evil, and truth is not falsehood. The word "one" means - one, and the word "two" means two. And truth does not lie in the middle. Truth is one, lies infinitely many.
JD: The Renaissance attempted to integrate the concept of anatomical representation of the human body with something, something that is probably "body art" - that is, derived from geometry, attempts to seek a representation of the ideal body, some kind of anthropometry-a canon of principles that captured the configuration of body parts in a relationship of absolute harmony. But the anthropometric idea was discredited on the grounds of racial studies in the 20th century. Is there now a place in art for such research or, as we can observe, has it moved completely into the realm of pop culture, aesthetic medicine and genetics?
JK: It didn't start in the Renaissance, because it was an object of inquiry in ancient art. There was the Egyptian canon. There were a lot of canons created in Greece - Lysippus, Polycletus, Phidias. Venus de Milo has its navel in the golden division. Aware of this uniqueness, the uniqueness of the golden division, they used it because it harmonized with their sense of beauty. The study of proportion is just a tool, the same as a knife with which one can slice bread but also kill another human being. With the minor remark that the knife was created first to kill. It was the same with atomic energy - first there was Hiroshima, then the nuclear power plant..
JD: Would it mean that the paths of beauty and art have diverged definitely?
JK: Aristotle said that a small mistake made at the beginning grows into a very big one at the end. You don't have to be very intelligent to see that the world has reached a very big mistake and it has crumbled before our eyes. Two conflicting pieces of information about the same fact, having the same right to exist, cause us to lose our measure and honest view of the world. There is a mistake somewhere that we haven't noticed. It behooves me to take a fresh look at the world. This is where a small mistake at the beginning was unfortunately unavoidable. The paths of art and beauty have not diverged. Our understanding of them has momentarily diverged.
JD: But do we still need the category of beauty?
JK: In a pragmatic sense I have already explained it; give up your beautiful wife and take an ugly one. You can see that it is nonsense to think about it. When we withdraw from understanding what beauty is, then we start to ask the question: can we live without it? Well, we can't! We experience beauty and we want to experience it constantly. Art is about beauty. But it is also about Good and Truth. If we do not rebuild the order and hierarchy of principles - chaos will arise. The point is that someone who exercises in "beauty" should not lose to one who exercises in "unbeauty." The eye should be developed as well as the mind, because the eye is the same as wisdom. The wise, when he meets the foolish, knows that he has met the foolish, but the foolish does not know that he has met the wise.
JD: Let's stop a little bit at this subjectivization. There is a current of thought in contemporary culture called anti-culture...
JK: Culture - Culture - as the name implies - is a space, allowing for the utterance of any opinion, even the opinion that let there be no culture. You have the right to say whatever you want - the first place the amendments to the U.S. Constitution in 1789 were precisely to protect free speech. For people - seemingly cultured people - to say that culture has no meaning is absurd in itself. It is a statement that can, admittedly, be treated with culture and discussed, but only if culture is still in power. The problem with anti-culture is that it eliminates this space of freedom. Goodness allows both good and evil to exist. It is good. Destructive evil not only denies good, but by its very nature, even itself. It cannot, after all, want good. Not even for itself. It is evil. To the anti-culturalists I would say: if in the name of denying culture you buy land and they make an anti-culture paradise for yourselves, that's ok, but if we culturally give you money to fight culture, that's probably not right? In other words: what you say, what you claim - experience it yourself. Make your dreams come true, but at your own expense and on your own responsibility.
JD: But there is a lack of measure in this, a human hubris. The kind that accompanied us metaphorically before the Tower of Babel. Now we speak a multitude of languages, not to be agreed upon.
JK: A bit like that. Everything is possible, we accept everything because this is what political and social correctness wants. Once in Gazeta Wyborcza I gave an interview for a Proust poll. The question was: what is my present state of mind? I answered that I suspected that no man is wrong. Surprisingly, even after years, this confession is still somehow close to me. But when you utter such a statement, you must therefore assume, and your right, that you too are not wrong. What follows from this? First of all - responsibility. But it also follows that perhaps there is some higher meta-view and from that point of view it is possible that no one is wrong.
JD: But the map you draw here is a map of bubbles. Everyone lives and has the right to express themselves within their own. Sometimes maybe just a critical look into your neighbor's bubble....
JK: But notice that these bubbles are attracted to each other. They get into a reaction. By themselves, they don't have rights themselves. They have to defend themselves and thus become aggressive.
Truth does not require a witness. And they need a witness for the truth to exist.
JD: Have we broken the contract with the past?
JK: If you break and you don't know what you're breaking, then your gesture doesn't make sense. Besides, let's not exaggerate - not everyone has broken up. And besides, those who have been indifferent so far are somehow becoming radicalized, too. Because they see that it threatens not only the one who is talking such foolishness, but also all of us. When everyone turns out to be wise, it is the really wise people who suffer the most.
JD: What is the mission before art then?
JK: The same as always. Beauty is one of the three foundations of the world and cannot cease to exist. It has its territory not only in eternity, but also in the now. This "now" we call contemporary art. But the Cosmos has only such artists as we are. In the hierarchy of human needs proposed by the American psychologist Abraham Maslow, higher needs - among them art - are in last place. After eating, sleeping, excreting, or reproducing. The problem is that all animals need to provide for themselves. Except for the last one. It is the only one that sets us apart and gives us dignity and meaning to existence. As long as humans aspire to humanity art will always be their garden of meaning. We once called this garden paradise.
Drawing: Ignacy Czwartos