Tanya Khovanova's Math Blog

Two girls. One is older and more experienced. The other is younger and more naive. Which of these two girls will the unnamed male narrator choose? What a great plot for a math book.

I am talking about Hiroshi Yuki’s book Math Girls. The plot allows the author to discuss math on different levels. Miruka’s math is more advanced and mysterious. Tetra’s math is simpler and more transparent.

The book starts discussing sequences and patterns. Can you guess the pattern behind the sequence: 1, 2, 3, 4, 6, 9, 8, 12, 18, 27, …? Can you explain how the beginning of this sequence might be very deceptive?

For the answer, you can read the book, which also discusses tons of fun topics: prime numbers, sum of divisors, absolute values, rotations and oscillations, De Moivre’s formula, generating functions, arithmetic and geometric means, differential and difference operators, Catalan numbers, infinite series, harmonic numbers, zeta function, Taylor series, partitions, and more.

I usually do not like math fiction, but this is more math than fiction. It’s quite superior to most other math books I’ve read, for it shows the unity of mathematics. It allows the readers to discover connections among different parts of mathematics, and it accomplishes this in a very thrilling way. Frankly, more thrilling than the romantic sections.

The fictional element brings an additional value to the book. The author uses dialogue to discuss points that are usually skipped in regular text books. The two girls give the narrator an opportunity to explore math on different levels: to talk about heavy stuff with Miruka and to provide explanations with Tetra.

I expected to be more interested in the sections dealing with advanced math. But the book is so well-written that the simpler things were a lot of fun, too. For example, I never before noticed that the column notation for n choose k is exactly the same as for a 2d vector with coordinates n and k. And I will never ever shout “zero” because the exclamation makes it “one”.

I have a problem with my binocular vision. The muscles that are responsible for moving my eyes outwards are very weak, much weaker than the muscles that move my eyes inwards. When I am very tired, I can’t focus on people or things that are far away. I start seeing doubled monsters with extra eyes and noses.

Luckily, instead of looking scary, the monsters look familiar. In fact, they look exactly like Picasso’s portraits. I bet Picasso had problems with his eye muscles.

More than ten years ago I went through a process of psychotherapy which, although very painful, was extremely successful. When I tell my friends about this, they are interested in knowing what can be gained through psychotherapy, so here’s my story.

I was living in Princeton, NJ, and I was very tired all the time. My primary care doctor told me that I was depressed and needed to do psychotherapy. A friend of mine recommended Dr. Ella Friedman. During my first visit Ella told me that I block my negative emotions. I protested. All my life I truly tried to be honest with myself. She insisted. I had nothing to lose because I had to solve the problem of my constant exhaustion and I had no other potential solutions. Besides, I liked her very much. So I decided to play along and started my search looking for negative emotions.

For some time I tried to convince Ella that if my best friend broke my favorite mug I wouldn’t get angry with her. Ella tried to convince me otherwise. She pushed me back in time to the source of my beliefs and feelings. After several months of therapy, I discovered that I had a strong underlying belief that for my mother to love me, I must be a good girl who is always fair. Since my friend who broke the mug didn’t do it on purpose, I wasn’t allowed to be angry with her. I repressed all my angry feelings.

It took a lot of time for Dr. Friedman to rewire me and persuade me that my negative emotions do not mean that I am a bad girl. My actions define my goodness, not my emotions. I resisted. She had already convinced me that I might have negative emotions, but I didn’t want to look at them. The power forcing me to block my emotions was the threat that my mother would withdraw her love if I wasn’t a good girl. Dr. Friedman converted me. I started to believe her and continued more vigorously searching for my hidden emotions. Finally one day I collapsed in the shower. I actually felt my blocked emotions flooding me.

Negative emotions protect us. If someone treats you badly you need to be able to recognize it and get away from the danger. Because I didn’t see my emotions I stayed in situations, like toxic relationships, that caused me great pain, without realizing it.

My psychotherapy didn’t stop then. We started working on how to understand my emotions and how to process them. Now when someone is talking to me, I listen not only with my ears, but also with my gut. Suppose someone tells me, “I am so glad to see you,” but I feel a strange tightness in my stomach. I start wondering what the tightness is about, and usually can figure it out. For the first time I was able to hear my gut and it was more illuminating than what I was hearing with my ears. All my life I processed information as text. Now the sentence “I am so glad to see you” has many different meanings.

The therapy changed my life. It feels as if I added a new sense to my palette  of senses. I feel as if I was color blind for many years and at last I can see every color. Now that I’ve learned to recognize my pain, I can do something about it. I am so much happier today than I ever was before. While my friends may not have consciously recognized the big change in me, they have stopped calling me clueless and now often come to me for advice.

Did this solve my problem of tiredness? When Ella Friedman told me that I was no longer depressed, I still felt tired. I started investigating it further. It turns out that the depression was a result of the tiredness, not the other way around. It seems that I have a sleeping disorder and an iron problem.

SEAHOP created a practice puzzle, called “Making Connections,” that includes me. It seems I am making connections.