Day 7 - Math and Art

13 October 2006 – 12:01 – Chaiyapum

Today is my last day in Chaiyapum and this is probably the last post to my blog during my Thailand visit. I will be in Bangkok tomorrow morning to see a few more friends, to buy a few more books and to visit a few more places. I was planning to write on Orhan Pamuk, Nobel Prize and Armenian Genocide but a question, which has been posted on Math World (Matematik Dunyasi) e-mail group caused a swift change in my mind. It will also be better for me to read and think more before writing on controversial issues like genocide or Nobel Prize.

The question was about the relationship between Art and Mathematics. In recent years, it is a raising issue in young people’s minds and it is very easy to find plenty of information on Internet if one only tries to search. Once you click on search button, you will definitely find thousands of web pages devoted to Fibonacci Numbers, Escher’s paintings, Golden Ratio, Functions with Complex Variables and Fractals etc… It is very common in modern world to connect everything with everything without knowing the real source of the connection. To appreciate the beauty is always considered one of the main responses to an art object. This is why when we stand in front of an art piece, we appreciate both the art and the artist. I believe that almost all mathematicians have a desire to show to the whole world that Math itself is beautiful and it does not need any other supplementary factor to make it look more beautiful. Actually, I know that this is one of the main principles of the Matematik Dunyasi. Unfortunately, it is impossible not to indulge the mathematicians with external beauties.

Firstly, I would like to say that I am sick to death of the articles on finding Fibonacci Numbers and Golden Ratio in nature, drawing fractals on computer with admiring sounds, figuring out how mathematically perfect bodies we have etc… The writers of these articles usually have two main purposes. They would like to gain attention of mathematically-blind – This is a new word. It might mean the people who do not spend much time Mathematical concepts more than daily needs like addition, multiplication etc… - people by surprising them so that the article –or the book where the article is located- will be sold more. The other reason is unrelated with Math but more related with religion. The writer wants to say that our minds and the nature both have been created by the same omnipotent/omniscient God. Therefore, we are here to find it out and appreciate His beautiful design and art. It can also be interpreted as our minds, our bodies and our thought are all coming from the nature in the evolutionary perspective but the writers usually skip this alternative because it is totally against the message they want to give. I am against to both of these approaches. Let me explain why!

Firstly, there is nothing more usual than finding the Golden Ratio in nature. We can find it in the nature because the ratio itself is natural. When I say it is natural, I don’t mean the golden ratio itself is a natural number. It is well-known that the number is irrational. What I am trying to say is the ratio comes as a result of a natural sequence. At the end, Fibonacci numbers can be found in nature wherever we have reproduction process. It is a sequence of all zeros (babies) become one (adult who is ready to give birth) and all ones give birth to a zero while keeping itself alive at each step of reproduction. We start with a 0, then it second ste, it becomes 1, then 1 becomes 10 (itself and the baby) and 1 again becomes 10 and 0 become 1, so we have 101, then 10110, 10110101, 1011010110110, 101101011011010110101 etc… As you easily see, the number of digits sums up to Fibonacci Numbers. Once you divide consecutive terms, the limit will approach to 1.618033988… ,which is known as golden ratio. This kind of reproduction can be seen in sunflowers, seashells and the leaves of trees. In the famous “kitch” novel “Da Vinci Code” , the writer gives Fibonacci sequence as a password of a bank account. Then the novel goes with other secrets of Mona Lisa… We all get surprised when we read the paragraphs with mathematical concepts since it sounds exciting. But why do we get excited when we see these numbers in an artwork or in the columns of a temple! Isn’t it normal?

I used to believe that Mathematics is queen of all knowledge because it is not empirical like Physics, Chemistry or Biology which are usually called natural sciences because they are based on observation and experiment. It is party true that mathematical knowledge is based on deductive reasoning much more than any other source of knowledge like experiment or observation. Mathematicians, throughout the centuries, believed that Math is a pure product of our mind, it is irrefutable, undeniable and permanent. Since the time of Plato, philosophers had this definition for Math and kept it as a last castle to be occupied by the skeptics. However, the recent developments in Physics and Mathematics changed people’s paradigm. We have found that even in Math there can be more than on truth at the same time relative to where you stand. Euclidian and Riemanian spaces do not form a consistent unique Math. Conversely, they create different Maths. This can bring a big question to our mind! Is mathematics really pure product of human mind? I doubt it! I might define Mathematics as a generalization of the natural objects. I admit that there is no circle in nature, so we have defined it in the world of Mathematics. We don’t have Euclidian space but we could have been imagined a perfectly smooth surface and had perfect lines, points, rays, triangles etc… on it. Once we have lines and squares, we can have the concept of area. Then, we can prove Pythagorean Theorem, then we can prove many other theorems. Proving processes do not need observations since the mathematical objects are perfectly defined and isolated from effects of worldly troubles. It does not matter whether North Korea tries another Nuclear Bomb or President Bush picks his nose while trying to clear another microphone gaff for the fact of 28 is a perfect number. 28 is a perfect number because it satisfies all the conditions of being a perfect number. However, the concept of number or the concept of adding is not something we discovered from out of nowhere. Basically, Math was never somewhere in our brain faculties. Slowly and patiently, human civilization built it on the basis of observation and generalization. I don’t believe the flying man – a man who is lack of his five senses- of Ibn-I Sina can understand the Mathematical concepts as we can. For more information about the nature of mathematical knowledge, I got most of these opinions from David Deutch’s famous book which I have read years ago: The Fabric of Reality: http://www.qubit.org/people/david/FabricOfReality/FoR.html He basically claims a similar thing that I tried to explain in above paragraphs briefly.

If we can accept that Mathematics was born from basic observations of daily life and developed as a generalizations and evolution of these observations, we can now start to talk about art. In classical term, art is defined as imitation of reality. From Plato to Renaissance, there was not much change. Art object was not supposed to show the incompleteness of reality because eventually reality itself is an imitation of ideal world. A certain person might have messed up his life, might have an unusual body or might have cheated on his wife but the perfect man in the realm of ideas is very different. He is more or less similar to statue of Alexander the Great or David. The main target of the artist is to depict the idea, not the reality. This concept of art naturally modified to today’s modern art with the advent of developments in Science and Technology. Stendhal defines novel as “take a mirror in your hand and walk through the streets of Paris”. How many of us can define man’s body better than Michalengelo’s David or a woman’s body better than Boticelli’s Venus? However, in literature, Flaubert’s Madame Bovary symbolizes the end of the era because Emma Bovary was not a perfect woman. Neither was Anna Karenina or Sonya! Actually, the concept of perfect man or woman also varies in different times and different societies but this is another issue. Today’s artists express art in different ways. An artist can depict the problems in the poor countries of Africa and it is obvious that the realm of perfect ideas will not be enough to reach this target. Renaissance art imitated reality in a way, which is supposed to be more perfect than the reality itself. This makes sense for the ones who try to find a connection between Mona Lisa and Golden Ratio or the columns of Parathion and golden rectangle.

As a conclusion, Mathematics and Art can be considered as related and there is nothing extraordinary about it because they are both coming from the same source. They both imitate reality to some extent and take their own methods to reach their targets. Math itself is beautiful with simple proofs of complicated theorems, with the way of thinking straight, with the methodology of using mind correctly. This should be enough to appreciate Mathematics, as it is itself an art piece created by accumulated efforts of all humanity. Of course, there is no point in hanging the frame of a printed version of Euler Equation in your living room. That is why we appreciate the works of Escher and Bach. Both of these artists have strong mathematical background in their art. We can see the mathematical complexity in Escher’s paintings as well as the harmony in Bach’s music. The beauty in math is not something visible. It is more like mental beauty and can be revealed by the interpretation of either artist or the mathematician. I am sure, those who enjoy doing math can understand me better. As a Math teacher I used to tell my students “Math is beautiful” and they always blamed me for this optimism toward Math. However, I had the privilege of having some smart and caring students who understood my words after working hard to learn Math. At the end, As Mevlana says, if you want to know how it feels to be burnt alive, you must enter our dergah (community of dervishes).