# This is Not an Essay About Golden Ratio

## How many numbers are there between 0 and 1?

| Ekim 2018

I love mathematics. Both of my parents are mathematicians. Yet I promise you, my love for mathematics has nothing to do with my parents’ occupation. I am not brainwashed into liking it.

The reason why I love mathematics is that it is beyond anything. And as painful it is to admit, I think that it is even beyond art. Before you get angry with me… I very deliberately used the word “beyond” and not “better” as such a comparison would be unfair to both of the fields.

Mathematics is not an emotionless monster that makes you fail calculus every semester. If you really think about it, mathematics is the most generous concept in our lives to offer us order and solution in a world of chaos. The problem of mathematics is the way we are introduced to it. We learn to quantify mathematics with the numbers and never to actually appreciate it for what it is. Our system of education teaches us to use derivation to calculate the slope and integration to area. But the part we miss is that mathematics is not about finding a number. It is about using the number to find what could not be expressed before you made that calculation. It is about making incomprehensible comprehendible. And the surprising truth is, I truly liked mathematics after I learned about the theory of art. Art taught me the value of abstraction and developing a keen understanding of an abstract composition.

Before my education in the department of architecture, I learned mathematics only because it was a requirement. I remember reading through some of my father’s analytical geometry books. It frustrated me to see no more numbers in those books. There were only letters as a means of expression. And today, I can actually understand how valuable it is to create such perfectly abstracted expressions. It is where mathematics gets one step further. It is where mathematics is freed of its form and finally finds its spirit. And it is funny how art helped me to understand mathematics, and now mathematics is helping me to understand art. Art is like a function. The domain you can put is limited really. Depending on the branch of art, you can use colours, notes, words, forms and so on. But it is not the domain that makes art so interesting. It is the output, the range. With such limited input, you can receive indescribable amount of emotions, reactions, atmospheres, expressions etc. Every artist defines a different function. With the same domain, they define different ranges. Given the same set of canvases and paints, do you think that Picasso and Dali would create the same artwork? Definitely not. They define different functions and they project onto different ranges however the similar their domains may be. The visible world is limited. Art searches the invisible using the tools of the perceptible realm. So does math.

How many numbers are there between 0 and 1?

How many numbers are there between 0 and 100?

The answer is: equally many, infinite. Can an infinity be more infinite than the other?

I remember how it astonished me as a child to discover that there were as many numbers between 0 and 1 as 0 and 100. That day I found out that mathematics was not black and white. It had the weird ironical sense of humour that originated from the irrational rationality and the illogical logic. As I gave it some thought, I came to realize that it was not the answer that made mathematics so interesting, but the question. The question stimulates us into creating a methodology and a systematics that will take us to the answer. And the process of constructing this methodology we go through changes us, not the answer. By asking us “what” questions, mathematics actually encourages us to consider the “HOW” of the problem. And every question in this world that I think counts, begins with “HOW”. So yes, I love mathematics. Because it gives me the super power of seeing the invisible. Because it makes me understand art. And because it helps me ask the questions that are worthy of pursuing.

Visuals: İrem Küçük

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