Tanya Khovanova's Math Blog

Hooray! My weight is down to two digits in kilograms: below 100. This is a big deal for me. I reached the desired number of digits. In pounds it means I weigh less than 220 and I’ve lost 25 pounds.

My friends have started to notice. The chubbier ones ask me to tell them about my Yellow Road. And I don’t actually know what to reply, because the Yellow Road is not a solution. I took many steps before I approached the Yellow Road. The Yellow Road is, I hope, the end of the road.

The idea of the Yellow Road is simple. If I weigh more than I want, I decrease food. All my skinny friends have always lived that way. The problem is that the rest of us do not know how exactly to reduce food intake and then how to sustain that reduction.

So today, I would like to explain to my friends and my readers what I really think helped me to lose weight.

1. I got desperate. I was ready to do whatever it takes. I was prepared not to ever eat again. If I had to extract my calories from the air, I was prepared to do that. I was ready to be hungry and restrain myself for the rest of my life. In short, I was totally motivated.

2. I fought my sugar addiction. I used to crave sugar. I used to think that sugar helps my brain. But once I looked into it, I realized that I might be wrong. I decided to experiment and cut off my carbohydrates intake significantly. That was the most painful thing I had to do. But after a week of withdrawal symptoms, I felt better and stopped craving foods and sugars as much.

3. I wrote my weight down everyday. Having numbers staring me in the face reminded me what I ate the day before. This moment of reflection allowed me to understand what causes the increase or decrease in my weight. Now I know that some foods provoke my appetite: carbohydrates, dairy, mayonnaise. I eat them in small portions, but I do not start my day with them. It’s better to have an increased appetite for a couple of hours in the evening, than for the whole day.

4. I had already changed some bad habits. I tried to build new healthy habits before I started my Yellow Road. These alone didn’t help me lose weight, but I think they contribute to my weight loss. I still do the following:

• I get organic fruits and vegetables delivered weekly from Boston Organics.
• I buy no more than one item of desert when I shop.
• At a restaurant, I divide my portion in half. I eat one half and wait for a minute. More often than not, I take the other half home.
• I talk to myself. Currently, I am persuading myself that at a party, I don’t have to try every dish: I can try half of them, hoping that the other half will be at the next party.

I feel that an internal switch was turned off. I don’t feel that hungry anymore. My son thinks that I’m in my hibernating state. I wonder if he is right and I will awake one day as hungry as ever.

My son, Alexey Radul, is gainfully unemployed. While looking for a new job he wrote several essays about his programming ideas. I am a proud and happy mother. While I can’t understand his code, I understand his cutting-edge essays. Below are links to the four essays he has posted so far. He is also a superb writer. You do not need to take my word for it. Each link is accompanied by the beginning of the essay.

• Digital FoxesThe successful fox must know more than the sum of what the hedgehogs know, for it must know the connections from one thing to another. This fact is key to the design of computer systems for solving certain kinds of problems. Read more
• Introduction to Automatic DifferentiationAutomatic differentiation may be one of the best scientific computing techniques you’ve never heard of. If you work with computers and real numbers at the same time, I think you stand to benefit from at least a basic understanding of AD, which I hope this article will provide; Read more
• On the Cleverness of CompilersThe “Sufficiently Clever Compiler” has become something of a trope in the Lisp community: the mythical beast that promises language and interface designers near-unlimited freedom, and leaves their output in a performance lurch by its non-appearance. A few years ago, I was young enough to join a research project to build one of these things. Neglecting a raft of asterisks, footnotes, and caveats, we ended up making something whose essence is pretty impressive: you pay for abstraction boundaries in compile-time resources, but they end up free at runtime. One prototype was just open-sourced recently, so that makes now a good time to talk about it. Read more
• Cleverness of Compilers 2: HowThe Cleverness of Compilers essay described the name of the hyperaggressive compilation game in broad, philosophical strokes. Here, I would like to walk through the Mandelbrot example in some detail, so that the interested reader may see one particular way to actually accomplish that level of optimization. Read more

I submitted four papers to the arXiv this Spring. Since then I wrote four more papers:

• (with Leigh Marie Braswell) Cookie Monster Devours Naccis. History and Overview arXiv: arXiv 1305.4305.

  In 2002, Cookie Monster appeared in The Inquisitive Problem Solver. The hungry monster wants to empty a set of jars filled with various numbers of cookies. On each of his moves, he may choose any subset of jars and take the same number of cookies from each of those jars. The Cookie Monster number is the minimum number of moves Cookie Monster must use to empty all of the jars. This number depends on the initial distribution of cookies in the jars. We discuss bounds of the Cookie Monster number and explicitly find the Cookie Monster number for Fibonacci, Tribonacci and other nacci sequences.

• A Line of Sages.
  • PDF.

  A new variation of an old hat puzzle, where sages are standing in line one behind the other.

• (Jesse Geneson and Jonathan Tidor) Convex geometric (k+2)-quasiplanar representations of semi-bar k-visibility graphs. Combinatorics arXiv: arXiv 1307.1169.

  We examine semi-bar visibility graphs in the plane and on a cylinder in which sightlines can pass through k objects. We show every semi-bar k-visibility graph has a (k+2)-quasiplanar representation in the plane with vertices drawn as points in convex position and edges drawn as segments. We also show that the graphs having cylindrical semi-bar k-visibility representations with semi-bars of different lengths are the same as the (2k+2)-degenerate graphs having edge-maximal (k+2)-quasiplanar representations in the plane with vertices drawn as points in convex position and edges drawn as segments.

• (with Leigh Marie Braswell) On the Cookie Monster Problem. History and Overview arXiv: arXiv 1309.5985.

  The Cookie Monster Problem supposes that the Cookie Monster wants to empty a set of jars filled with various numbers of cookies. On each of his moves, he may choose any subset of jars and take the same number of cookies from each of those jars. The Cookie Monster number of a set is the minimum number of moves the Cookie Monster must use to empty all of the jars. This number depends on the initial distribution of cookies in the jars. We discuss bounds of the Cookie Monster number and explicitly find the Cookie Monster number for jars containing cookies in the Fibonacci, Tribonacci, n-nacci, and Super-n-nacci sequences. We also construct sequences of k jars such that their Cookie Monster numbers are asymptotically rk, where r is any real number between 0 and 1 inclusive.