Tanya Khovanova's Math Blog

The MIT Mystery Hunt starts on Friday. My old team—Manic Sages— fell apart after last years’ hunt. My new team—Death and Mayhem—started sending us daily practice puzzle to prepare for the hunt.

Today’s puzzle was written by Paul Hlebowitsh. As usual, the answer is a word or a phrase.

Puzzle 3: Humans

“After a long day taking care of the animals, it’s good to unwind by letting the taps flow.”

Tap 1: Sierra Nevada Pale Ale
Tap 2: Lagunitas Pale Ale
Tap 3: 21st Amendment “Brew Free! or Die IPA”
Tap 4: Wachusett Blueberry
Tap 5: Harpoon UFO

Alice, Bob, Carol, Danny, Erica, Fred, and Gregario, the seven children of Noah, went to a local bar before the flood to get drinks. Accounts of night vary, and no one remembers exactly what happened, but some facts have become clear:

1. Everyone had two drinks, in some order.
2. Danny liked his first drink so much he had it again. Everyone else had drinks from different breweries.
3. Erica was the only person to drink an IPA.
4. Four people had the Wachusett Blueberry as their first drink.
5. One person had the Sierra Nevada Pale Ale as their first drink.
6. Alice only drank beers with headquarters in California, in order to spite Bob and Danny.
7. Two Harpoon UFOs were ordered, as well as two Sierra Nevada Pale Ales. 8
8. Alice’s second drink was the same as Fred’s first drink.
9. Bob and Danny hate California and refuse to drink any beer from a company that’s headquartered there.
10. Alice and Erica had the same first drink.
11. Fred had a Harpoon UFO.

Who ordered which drinks and in what order?

I stopped losing weight. My Yellow Road plan stopped working. If you recall I draw a line on the weight/time plane which I call my target weight. If I’m more than one pound above my target weight, then I’m in the red zone and must restrict my evening food to apples. The hour at which the evening starts depends on how many pounds I’m above my target weight.

And now, back to my bump.

First I stopped following the plan exactly. I realized that I didn’t need to restrict myself to eating only apples in the evening when I am in the red zone. I can use salad or anything light.

One day I found myself in the red zone weighing two pounds over my target weight. I was invited to dinner that evening. I decided to accept the invitation and skip the plan for one day. At the party the food was so good I couldn’t resist it. The next day I was four pounds over my target weight.

My Yellow Road plan requires me in this situation to eat only apples from 2:00pm onward, but I knew that applying this restriction after 6:00pm worked for me. I decided not to torture myself and started to restrict my food only from 6:00pm. The weight didn’t go down. Even though I went to bed very hungry for two weeks, it didn’t work.

After these two weeks, I started to feel hungry all the time and even began dreaming about food. As a result, my food intake increased. Now I am seven pounds over my target weight. I’ve reached a plateau. For the last two months I’ve been stuck at 220 pounds.

There is some good news: I now have a partner on this journey. After I started my program, I received an email from Natalia Grinberg from Germany. She offered to join forces. We send each other weekly updates on our progress and cheer each other along. Natalia’s path wasn’t smooth from the start, so she tried to supplement her diet with Almased, which is very popular in Europe. Because Natalia likes it, I looked into it. While I am afraid of pills and chemical ingredients, Almased seems to be okay. It contains soy, yogurt, honey, and vitamins. I bought one can. It is expensive and tastes awful. I’ll experiment with cinnamon or pepper and see if that helps. Will Almased help me get over the Bump?

I collect geeky jokes. I think I’ve heard most of them. So I was surprised to stumble upon a website with many new ones: 50 People On ‘The Most Intellectual Joke I Know’. These are some of them:

* * *

Q: What does the “B” in Benoit B. Mandelbrot stand for?
A: Benoit B. Mandelbrot.

* * *

Entropy isn’t what it used to be.

* * *

There are two types of people in the world: those who can extrapolate from incomplete data sets

* * *

This sentence contains exactly threee erors.

* * *

There’s a band called 1023MB. They haven’t had any gigs yet.

* * *

A logician’s wife is having a baby. The doctor immediately hands the newborn to the dad. His wife asks impatiently, “So, is it a boy or a girl”? The logician replies, “Yes.”

* * *

The barman says, “We don’t serve time travelers in here.”
A time traveler walks into a bar.

* * *

The first rule of Tautology club, is the first rule of Tautology club.

* * *

A woman walks in on her husband, a string theorist, in bed with another woman. He shouts, “I can explain everything!”

* * *

What do you get when you cross a joke with a rhetorical question?

I used to love arXiv. I’ve long thought that it was one of the best things that happened to mathematics. arXiv makes mathematical research available for free and without delay. Moreover, it is highly respected among mathematicians. For example, Grigori Perelman never submitted his proof of the Poincaré conjecture to any journal: he just posted it on arXiv.

When I came back to mathematics, all my math friends explained to me that I should submit my paper to arXiv on the same day that I submit it to a journal. As my trust in arXiv grew, I started submitting to arXiv first, waiting one week for comments, and then submitting to a journal.

Now it seems that arXiv might not love its contributors as much as they used to. arXiv moderators seem to be getting harsher and harsher. Here is my story.

In June of 2013, I submitted my paper “A Line of Sages” to arXiv. This paper is about a new hat puzzle that appeared at the Tournaments of the Towns in March 2013. The puzzle was available online at the Tournaments of the Towns webpage in Russian. After some thought I decided that it is better to cite the Tournament itself inside the body of the paper, rather than to have a proper reference. Online references in general are not stable, and this particular one was in Russian. Very soon this competition will be translated into English and the puzzle will appear in all standard math competition archives.

arXiv rejected my paper. A moderator complained that I didn’t have a bibliography. So I created a bibliography with the link to the puzzle. My paper was rejected again saying that the link wasn’t stable. Duh. That’s the reason why I didn’t put it there from the start. I Goggled the puzzle and I still didn’t find any other links.

I argued with my moderator that the standards for papers in recreational mathematics are different from the standards for purely research papers. Short recreational notes do not require two pages of history and background, nor a long list of references. A recreational paper doesn’t need to have theorems and lemmas.

Meanwhile, the moderator complained that the paper was “not sufficiently motivated to be interesting to the readership.”

I got tired of exchanging emails with this moderator and submitted my paper to The Mathematical Intelligencer, where it was immediately accepted. So I dropped my submission to arXiv.

Now my paper is not available for free on arXiv. But anyone can freely buy it from Springer for $39.95.

I started my life wanting to be a mathematician. At some point I had to quit academia in order to feed my children. And so I went to work in industry for ten years. Now that my children have grown, I am trying to get back to academia. So I am the right person to compare the experience of working in the two sectors. Just remember:

• This is my personal experience.
• I am not a professor, so I never experienced the best part of academia.
• My academic experience was at Princeton and MIT: a very selective set.

Money. The pay is much better in industry. About twice as high as academia.

Time. I almost never had to work overtime while working in industry. That might not be true for programmers and testers. As a designer, I worked at the beginning of the project stage. Programmers and testers are closer to deadlines, so they have more pressure on them. The industrial job was more practical than conceptual, so I didn’t think about it at home. My evenings and weekends were free, so I could relax with my children. In academia I work 24/7. There are 20 mathematical papers that I have started and want to finish. This is a never-ending effort because I need those papers to find my next job. Plus, I want to be a creative teacher, so I spend a lot of time preparing for classes. I do not have time to breath.

Respect. When I was working in industry, some of my co-workers would tell me that I was the smartest person they ever met. In any case, I always felt that my intelligence and my skills were greatly appreciated. In academia, I am surrounded by first-class mathematicians who rarely express respect and mostly to those who supersede them in their own fields.

Social Life. Mathematics is a lonely endeavor. Everyone is engrossed in their own thoughts. There is no urge to chat at the coffee machine. In industry we were working in teams. I knew everyone in my group. I was closer to my co-workers when I worked in industry.

Freedom. In both industry and academia there are bosses who tell you what to do. But while building my university career, a big part of my life is devoted to writing papers. It is not a formal part of my job, but it is a part of the academic life style. And in my papers I have my freedom.

Motivation. In academia, one must be self-motivated.

Rejection. The output of an academic job is published papers. Most journals have high rejection rates. For me, it’s not a big problem because from time to time I get fantastic reviews and I usually have multiple papers awaiting review. I have enough self-confidence that if my paper is rejected, I don’t blink. I revise it and send it to a different journal. But this is a huge problem for my high school students who submit their first paper and get rejected. It is very discouraging.

Perfectionism. In industry I was working on deadlines. The goal was to deliver by the deadline a project that more or less worked. Time was more important than quality. My inner perfectionist suffered. When I write papers, I decide myself when they are ready for publication.

Impact. When I was working at Telcordia I felt that I was doing something useful. For example, we were building a local number portability feature, the mechanism allowing people to take their phone numbers with them when they moved. I wish Verizon had bought our product. Just a couple of months ago I had to change my phone number when I moved five blocks from Belmont to Watertown. Bad Verizon. But I digress. When I was working at Alphatech/BAE Systems, I was designing proofs of concepts for future combat systems. I oppose war and the implementation was sub-standard. I felt I was wasting my time. Now that I am teaching and writing papers, I feel that I am building a better world. My goal is to help people structure their minds and make better decisions.

Fame. All the documents I wrote in industry were secret. The world would never know about them. Plus, industry owns the copyright and takes all the credit. There is no trace of what I have done; there is no way to show off. People in academia are much more visible and famous.

Happiness. I am much happier now. I do what I love.

I gave the following puzzle from Raymond Smullyan’s book What is the Name of this Book? to my AMSA students.

What happens if an irresistible cannonball hits an immovable post?

This puzzle is known as the Irresistible Force Paradox. The standard answer is that the given conditions are contradictory and the two objects cannot exist at the same time.

My AMSA student gave me a much cuter answer: The post falls in love with the cannonball as it is so irresistible.

It has been a while since I wrote my last essay and my readers have started to worry. Sorry for being out of touch, but let me tell you what is going on in my life.

In September I received an offer from MIT that changes my status there. In exchange for a slight increase in pay, I am now conducting recitations (supplemental seminars) in linear algebra In addition to my previous responsibilities.

My readers will know that just a slight increase in money in exchange for significant demands on my time would not appeal to me. But this offer comes with perks. First, my position at MIT changes from an affiliate to a lecturer, which looks so much better on my CV. Second, it includes benefits, the most important of which is medical insurance.

I lived without insurance for three years. On the bright side, lack of insurance made me conscious of my health. I developed many healthy habits. I read a lot about the treatments for colds and other minor problems that I had. On the other hand, it is a bit scary to be without insurance.

Many people are surprised to hear that I didn’t have any insurance: Doesn’t Massachusetts require medical insurance for everyone?

The Commonwealth levies a fine on those who do not have insurance. But I was in this middle bracket in which my income was too high for a subsidized plan, and too low to be fined. You see, the fine is dependent on one’s income and is pro-rated. So I didn’t have to pay it at all.

I got my insurance from MIT in October, but ironically my doctor’s waiting list is so long, that my first check-up will not be until January.

Anyway, I sort of have four jobs now. I am coaching students for math competitions at the AMSA charter school six hours a week. I am the head mentor at the RSI summer program where I supervise the math research projects of a dozen high school students. I do the same thing for the PRIMES program, in which I have the additional responsibility of mentoring my own students. And as I mentioned, I am also teaching two recitation groups in linear algebra at MIT.

Teaching linear algebra turned out to be more difficult than I expected. I love linear algebra, but I had to learn the parts of it that are related to applications and engineering. Plus, I didn’t know linear algebra in English. And my personality as a perfectionist didn’t help because to teach linear algebra up to my standards would have taken more time than I really had.

This semester I barely had time to breathe, and I certainly couldn’t concentrate on essay pieces. Now that this semester is almost over, my as yet unwritten essays are popping up in my head. It’s nice to be back.

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.