Tanya Khovanova's Math Blog

Samuel Hansen has an unusual profession: he is a mathematics podcaster. He interviewed me for his Relatively Prime podcast titled 0,1,2,3,…, where we discussed my Number Gossip project. The podcast also includes interviews with Neil Sloane, Michael Shamos, and Alex Bellos.

My previous interview with Samuel is at acmescience.com. There I discuss both math education and gender in math issues.

When I listened to myself, I found it strange that I seemed to have a British accent on top of my Russian accent. Did you notice that too?

I am Russian; I know how to play chess. My father taught me when I was three or four. We played a lot and he would always win. I got frustrated with that and one day, when I was five, I didn’t announce my check. On the next move, I grabbed his king and claimed my victory.

He was so angry that he turned red and almost hit me. This frightened me so much that I lost my drive for chess that very moment.

I still understand its beauty and solve a chess problem about once a decade. Look for a cute chess puzzle in my next post.

I would like to report on my weight loss progress. Last time I added two new habits, walking my toy dog every day, and drinking more water from the enticing cute bottles I bought.

I named my stuffed dog Liza and I walk with her every day. I didn’t expect immediate weight loss due to this new regime, because my first goal was to get out of the house every day, even if only for two seconds. The next step will be to increase walking time to ten minutes.

Drinking a lot of water doesn’t work well. I spend too much time looking for bathrooms and panicking that I will not make it. I like the idea of drinking a lot of water, but I am not sure I can hold to it, if you understand what I mean.

Since taking on this challenge, I’ve gained two habits, but I haven’t lost a pound.

Now I’m upping my game. Below is my analysis of why I eat. When I eat, I believe that I am hungry. But looking at this more objectively I think this is not always the case: sometimes there are other reasons. I am listing these other reasons so I can fight them face-to-face. Here we go:

• I eat to finish what is on my plate. My mom lived through World War II in Moscow, and instilled in me a terrible guilt when I throw away food.
• I eat extra when I do not know when my next meal is. I experienced extreme hunger in my childhood, so I try to prevent ever having that terrible feeling again.
• I can’t resist free food. I do not feel comfortable with my financial situation, so saving money gives me an extra push to eat even when I’m not hungry.
• I procrastinate by eating. When I am facing a chore I don’t really want to do, I delay it by eating.
• I crave sugar. It used to be worse.
• I have a problem with delicious food. I think that deep inside I feel that life was unfair to me and this piece of tiramisu will be a small bright spot in my usually rainy life. Therefore I need to grab it and gobble it down before it disappears.

Hmm. That was painful to write. My psychoanalyst taught me that pain means I am on the right track.

Thank you to everyone who helped me to find a host for my Number Gossip website. Some readers and friends even offered me free hosting on their servers. I decided to pay for hosting because I have many specific requirements and that might be a burden on my friends.

On the basis of my readers’ recommendations, I chose Dreamhost as my new webhosting provider. I apologize for the interruption in the flow of the gossip. I know that many people use Number Gossip for birthday gift ideas. I can tell you that on my previous birthday, you could have congratulated me on becoming prime and evil.

I’m trying to lose weight. Many books explain that dieting doesn’t work, that people need to make permanent changes in their lives. This is what I have been doing for several years: changing my habits towards a healthier lifestyle.

This isn’t easy. I am a bad cook; I hate shopping; and I never have time. Those are strong limitations on developing new habits. But I’ve been a good girl and have made some real changes. Unfortunately, my aging metabolism is changing faster than I can adopt new habits. Despite my new and improved lifestyle, I am still gaining weight.

But I believe in my system. I believe that one day I will be over the tipping point and will start losing weight, and it will be permanent. Meanwhile I would like to share with you the great ideas that will work someday.

• Declare some food non-food:
  • I used to keep a kosher kitchen. It was so easy to shop. I didn’t need to go to every aisle in the store because the kosher dietary laws excluded so many foods. Now I’m not kosher anymore, but I like the idea of restricting bad foods, so I created Tanya’s own kashrut rules:
    • Soda is not drinkable.
    • Only dark chocolate deserves to be eaten.
    • Corn syrup, artificial colors and sweeteners are poison.
• Make healthy foods easily accessible:
  • I have Boston Organics fruits and vegetables delivered to me every other week. Initially they all rotted and I had to throw them out, but I am stubborn. Now I’ve learned how to make a turnip salad and how to enjoy an apple. I will soon switch to a weekly delivery.
  • When I’m in a restaurant, I have a rule that I must order vegetables. I do not have to eat them, I just have to order them. But since I do not like things wasted, I end up eating at least some of them. Now I’ve grown to like eggplants and bell peppers.
• Make unhealthy foods less accessible:
  • I buy precut frozen cakes. When I am craving sugar, I defrost one piece. A while ago I would have finished the whole cake the day I bought it, but now, after one piece, I am usually too lazy to defrost another.
  • I buy fewer sweets now. Actually I buy exactly one desert item, as opposed to the half a shopping cart I used to buy. I used to rationalize that I need deserts to serve potential guests. Then I would eat all the sweets myself. Now I’ve decided that my friends will forgive me if I don’t serve desert.
• Engage my friends:
  • Three of my girlfriends and I signed up for the gym together. Without them, I would have dropped the gym a long time ago. Natasha’s call inviting me to yoga often is the extra push that I need. Now, several years later, the habit is formed and when necessary I go alone.
  • Introduce other good habits:
    • I have a separate computer for games. I put it on top of my bookcase, so I have to stand while playing. This way I can’t play for too long, and burn extra calories at the same time.

  I have many other ideas that for different reasons haven’t yet become habits. So I am thinking about tricks to turn them into habits.

  • Start every meal with water.

  I keep forgetting to start my meals with water. Besides, I do not like plastic bottles. So now I’ve bought glass bottles with protective sleeves to carry in my car and my bag conveniently. They look so cool that I enjoy sipping from them.

  • Exercise every day.

  I never exercise in the mornings, because I want this time for mathematics. But in the evenings I am often too tired and skip my scheduled gym sessions and dance classes. I often spend the whole day inside in my pajamas. So to help me to exercise daily, my friend crocheted a small toy dog for me. Now I pretend that it’s a real dog that needs to be walked every day.

  I have many more ideas, but I gotta run now. I need to walk my dog.

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.

There is an array containing all the integers from 1 to n in some order, except that one integer is missing. Suggest an efficient algorithm for finding the missing number.

A friend gave me the problem above as I was driving him from the airport. He had just been at a job interview where they gave him two problems. This one can be solved in linear time and constant space.

But my friend was really excited by the next one:

There is an array containing all the integers from 1 to n in some order, except that one integer is missing and another is duplicated. Suggest an efficient algorithm for finding both numbers.

My friend found an algorithm that also works in linear time and constant space. However, the interviewer didn’t know that solution. The interviewer expected an algorithm that works in n log n time.

The company claims that they are looking for the smartest people in the world, and my friend had presented them with an impressive solution to the problem. Despite his excitement, I predicted that they would not hire him. Guess who was right?

I reacted like this because of my own story. Many years ago I was interviewing for a company that also wanted the smartest people in the world. At the interview, the guy gave me a list of problems, but said that he didn’t expect me to solve all of them — just a few. The problems were so difficult that he wanted to sit with me and read them together to make sure that I understood them.

The problems were Olympiad style, which is my forte. While we were reading them, I solved half of them. During the next hour I solved the rest. The interviewer was stunned. He told me of an additional problem that he and his colleagues had been trying to solve for a long time and couldn’t. He asked me to try. I solved that one as well. Guess what? I wasn’t hired. Hence, my reaction to my friend’s interview.

The good news: I still remember the problem they couldn’t solve:

A car is on a circular road that has several gas stations. The gas stations are running low on gas and the total amount of gas available at the stations and in the car is exactly enough for the car to drive around the road once. Is it true that there is a place on the road where the car can start driving, stopping to refuel at each station, so that the car completes a full circle without running out of gas? Assume that the car’s tank is large enough not to present a limitation.

Imagine a slice of buttered white bread with a heap of sugar on top. That was my favorite lunch when I was a kid. My mom was working very hard, I was the oldest sister, and this was what I would make for myself almost every day.

Later someone told me that sugar is brain food. I believed that sugar and chocolate helped me do mathematics, so my love for sugar got theoretical support. I finally figured out the source of this love when my first son was born. To teach my son to stop requesting milk at night, my mother pushed me to give him sugar-water instead. At that moment, I realized that I developed my love of sugar with my mother’s milk. Or, more precisely, instead of my mother’s milk.

Now there is more and more evidence that the love of my life is a mistake. See for example Is Sugar Toxic?. Will I ever be able to break my oldest bad habit, the one I developed before I can remember myself doing it?

Several years ago my son Sergei started a new movement: Sergeism. Followers of this philosophy seek to maximize Sergei’s happiness. Since Sergei’s happiness involves everyone being happy, becoming happy is a consequential goal of his followers.

Let me explain why this might be a perfect religion for many people, not the least myself. My parents didn’t teach me to love myself. They taught me to sacrifice myself and put other peoples’ interests ahead of my own. After reading tons of books and spending hours in therapy, I’ve learned to love myself — well, somewhat. But the truth is, I still feel guilty when I pamper myself. Sergeism eliminates this guilt. I can freely invest in my happiness as a committed member of this movement.

I became a Sergeist when I lost all hope of losing weight. I realized that my own health wasn’t a strong enough motivation. But I’m always glad to skip a cookie in tribute to Sergeism. If, like me, you put others ahead of yourself and never find the time to exercise or the will to refuse deserts, join me. Become a Sergeist and lose weight for Sergei.

My webpage and my blog generate a lot of emails. I love receiving most of the emails, but if I reply to them, I won’t have time to work on my blog. My favorite type of message is one that is full of compliments, with a note that the writer doesn’t expect a reply.

I am grateful to people who send me things I requested, like pictures of Russian plates, or some interesting number properties. I apologize that it takes me so long to reply.

The emails that I don’t enjoy reading contain amazing elementary proofs of Fermat’s last theorem, or any other theorem on the Millennium list, for that matter. I also do not like when my readers ask me for help with their homework.

Like most people, I’m already dealing with spammers who want to enlarge the body parts I do not have or to slim the ones I do have. However, if you do need to send me millions of dollars that I won in your lottery, there is no reason to waste time on email exchanges: you can process them through my “donate” button.

You are welcome to contact me, but ….