Putnam

This has been my first year on the Putnam committee: the committee that selects the problems for the William Lowell Putnam undergraduate competition. The committee consists of 3 members appointed for a 3-year term each (each year, one person’s term ends and another one is appointed in his place) and a fourth person, Loren Larson, who is a “permanent” secretary of the committee. To start with, each committee member proposes some number of problems (normally, at least 10). The problem sets and solutions are then circulated and discussed, and eventually the committee meets in person to decide on the final selection. This is all done in strict confidence and well in advance of the actual competition.

I have never written the Putnam. I wrote the Math Olympiad back in the days and qualified for the International Math Olympiad in my last year of high school, but Putnam is not available in Europe. I’m not sure that I would have been interested anyway. I wanted to study the “serious” mathematics: the big theories, the heady generalizations, the grand visions. Olympiads and competitions faded into the distant background and pretty much stayed there until last year.

I did point out my Putnam virginity when I was approached about joining the committee, and was told that Putnam does try to engage from time to time people who are not normally on the circuit, if only to have a larger pool of potential ideas. Of course, the advantage of having people on the committee who are on the Putnam circuit is that they know what’s expected, what works and what doesn’t, what has already been used and shouldn’t be recycled, and so on. Last year’s other two committee members – Mark Krusemeyer and Bjorn Poonen – are Putnam veterans, and of course Bjorn is a four-time Putnam fellow. Mark’s term ends this year; I don’t know yet who will be joining us this January.

Well, you could call it a steep learning curve. Putnam problems are expected to be hard in a particular way: they should require ingenuity and insight, but not the knowledge of any advanced material beyond the first or occasionally second year of undergraduate studies, and there should be a short solution so that, in principle, an infinitely clever person could solve all 12 problems in the allotted 6 hours. (In reality, that doesn’t happen very often, and I’ve heard that it generates considerable attention when someone comes too close.) The problems are divided into two groups of six – A1-A6 for the morning session and B1-B6 for the afternoon session – and there is a gradation of the level of difficulty within each group. A1 is often the hardest to come up with – it should be the easiest of the bunch, but should still require some clever insight and have a certain kind of appeal. The difficulty (for the competitor, not for us) then increases with each group, with A6 and B6 the hardest problems on the exam. There are also various subtle differences between the A-problems and B-problems; this is something that I would not have been aware of if another committee member hadn’t pointed it out to me. For example, a B1 could involve some basic college-level material (e.g. derivatives or matrices), but this would not be acceptable in an A1, which should be completely elementary.

The competition is taking place in two weeks, so you’ll know soon enough what problems we ended up selecting. Meanwhile, it might entertain you to see a few of my duds: problems I proposed that were rejected for various reasons. They will not be appearing on the actual exam and I’m not likely to propose variants of them in the future. The solutions are under the cut, along with an explanation of why each problem is a dud.

1. A ball is shot out of a corner of a square-shaped billiard table at an angle to the edge . The ball travels in a straight line without losing speed; whenever it hits one of the walls of the table, it bounces off it so that the angle of reflection is equal to the angle of incidence. Find all values of such that the ball will hit one of the corners after bouncing off the walls exactly 2009 times.
2. Are there integer numbers such that ?
3. Given , determine the largest integer with the property that any points on a circle must determine at least obtuse angles .

Right back at ya

If you’re female and you’re reading this, stop whatever else you’re doing for a moment and go read these three posts at Women in Wetlands, now also on my blogroll. (Found in the comments here.) They offer sensible and practical advice on how to respond to situations such as this one:

Imagine you are in a meeting among colleagues, post-docs, support staff, and clients. You are part of a group who has received a $1.2 million grant from BP (British Petroleum) to do environmental impact assessments at some of their drill sites. You have just given an overview of your research project (to assess the effects of oil exploration activities on wetlands in Kookamoonga, BP’s newest drill site). When you finish and look to the group for some positive feedback, a senior male scientist (known for being loud and opinionated) states that:

“The research proposed by Mary involves a large amount of fieldwork in a VERY remote location, and in my opinion is too difficult for a woman to lead or conduct. I think it would be best assigned to Bob (his protege’) to head up; maybe Mary can be responsible for the sample processing and data analysis back here at BIU.”

What do you do?

I’ve been in some variant of every single one of these situations, including the one just described, and I wish I had been better prepared to deal with them.

It’s tempting to think of the Senior Male Scientist as some old guy that you don’t know well and never talk to anyway. In real life, though, it could be your friend or mentor, someone you trust, someone whose opinions you value. He might not say explicitly that a woman can’t lead – he’ll just suggest a male candidate to replace you – and, mind you, it’s not sexist at all, he just wants the best possible person to direct the project, and in any case this is a matter of professional judgement and you should not be so sensitive about it.

The beauty of the responses suggested in the WiW posts is that they’re civil enough to be used on a friend and that they let you make the statement you need to make without getting dragged into unnecessary discussions. There’s no point in analyzing the Senior Male Scientist’s possible intentions. You just need to respond to the words you’ve heard.

There’s another reason to avoid protracted discussions of this sort: verbal sparring can only get you so far. I’ve seen enough situations where Dr. X was universally praised by colleagues for his excellent arguments and professional demeanor in the debate with Dr. Y, it was just so very unfortunate that the department would have to side with Dr. Y anyway. The debate would be a spectator sport, as opposed to something that could actually affect the outcome of the case. The lesson for you is that, instead of spending your time debating Senior Male Scientists with regard to their choice of wording, it could be more worthwhile to figure out why exactly the department sided with Dr. Y and how this might be applicable in your case. (That could be money, prestige, any number of things.) Making good headway in that direction is far more likely to convince Senior Male Scientists that they should take you seriously.

Which is not to say that you should not argue with Senior Male Scientists. You absolutely should, if only because having a good response will make you feel in control of the situation and that’s good for your morale, or because these things do make a difference in the long run. But short responses work better than long ones, and don’t give the Senior Male Scientist an opening to bring up the ever looming topic of your sensitivity if you can help it. That’s of course easier said than done. I haven’t always been good at it. I wish I had read posts such as these many years ago and taken some time to practice the responses in question. Then again – if you can’t come up with a good response, keep in mind that it’s only words…

Paint it red

I grew up in a socialist country.

I’m reminded of it every time I hear that public health care is socialist, or that financial regulation is socialist, or that regulating the auto industry is socialist, or that taxation is “spreading the wealth” and therefore socialist. I don’t get the impression that this refers to the “socialism” of the Scandinavian variety. More likely, it refers to the Soviet Union and its then-satellite countries – exactly where I was born.

I suppose I should recognize those various socialist things – oppose them, even – as marks of the failed system that I grew up with. But I don’t. Instead, I try to find a way to explain life under socialism to someone who doesn’t know it and I come up short every time. It’s not just explaining why apples are not like oranges. It’s explaining why apples are not like hockey and oranges are not like patio furniture.

Yes, we did have more political repression and government regulation. Yes, we had censorship, rationing and fewer consumer articles. People understand that. But then you mention to someone the high prevalence of tooth decay, and they respond, “sure, I bet you didn’t have fluoridated water”, and then you don’t know if you’ll be able to answer that without going on about it for half an hour, so you smile, say that it was actually a little bit more complicated, and change the subject.

Take for example taxation. Do you think it’s socialist? If so, you’ll be interested to know that neither my parents nor I had ever filed a personal tax return before I left Poland at the age of 23.

I won’t be breaking no rocks

Tom Verlaine and Jimmy Rip:

Therein lies madness

This got me a bit puzzled: why would a comment on this post link to a BBC documentary on Georg Cantor, Ludwig Boltzmann, Kurt Gödel and Alan Turing?

Given that I don’t know as much about the history of mathematics as I probably should, and that I was too tired late last night to do anything more intellectually challenging, I ended up clicking through and watching all 10 parts of the documentary.

The mathematics involved – Cantor’s hierarchy of different-sized infinities, Boltzmann’s statistical mechanics and entropy, Gödel’s incompleteness theorem – is described remarkably well. An expert might quibble about how some of the explanations are ambiguous and imprecise, especially where it concerns Gödel’s work, but that’s a relatively small price to pay for being able to communicate the excitement, audacity and impact of mathematical ideas to a lay audience. The images and animations are, for the most part, well done and helpful. Several mathematicians and scientists (including Roger Penrose) were interviewed for the documentary, and I am guessing that experts were consulted quite extensively about the mathematical content.

That’s only one part of it, though. The movie chooses to focus on Cantor, Boltzmann, Gödel and Turing not only for their groundbreaking contributions to mathematics, but also for the mental anguish and personal tragedy in their lives. Boltzmann and Turing committed suicide, Cantor and Gödel suffered from mental illness and were hospitalized for it, and Gödel ended up starving himself to death. Now, I understand that these are undisputed historical facts. I also understand that troubled characters make for a more interesting movie. But I’m tired of watching the media portray mathematicians as socially challenged and mentally unstable, not to mention poorly dressed. You’d never know that it is quite possible for a great mathematician to be a well adjusted and fully functional human being, to have a long, happy and accomplished life, or to face and overcome adversity without developing a mental illness.

Congratulations…

… to Willard S. Boyle, the Canadian physicist who shares this year’s Nobel prize in physics with George E. Smith and Charles C. Kao.

The Canadian inventor of technology that led to the birth of digital photography won a Nobel Prize Tuesday. But physicist Willard Boyle had to move to the United States to do his cutting-edge work.

Dr. Boyle, who won the award with former colleague George Smith, warned that managers need to give scientists leeway to come up with the kinds of transformative inventions that are too often stifled by paperwork and red tape.

What scientists face today is “almost disgraceful … The bureaucrats want to get a hold of the money and ask for business plans. Now do you think that George Smith and I ever wrote a business plan? Not at all,” Dr. Boyle, now 85 and retired, told a reporter Tuesday. “You don’t have time to do that kind of baloney.” [...]

News of the prize comes as scholars in Canada and around the world are becoming increasingly concerned about the tendency of governments to wade into research by putting strings on funding. In Canada, moves by the federal government to fund projects directly rather than through arms-length granting councils have come under fire by the academic community, as have restrictions on some money given to the councils.

For recent examples of that, see here or here:

Each Strategic Research Network will receive $5 million over five years through NSERC. They were selected through a peer-reviewed competition and support the research priorities areas identified in the Government of Canada’s Science and Technology (S&T) Strategy.

Click through the first link above if you want to see what the nine networks are. I’m more interested in the list of priority areas:

For the 2009 competition, preliminary applications will only be accepted in three target areas (Advanced Communications and Management of Information, Healthy Environment and Ecosystems, and Sustainable Energy Systems), which have an increased competition budget due to additional earmarked funds received by NSERC.

Would Dr. Boyle and Dr. Smith have qualified? Well, they could fall under “Advanced Communications and Management of Information”, if they were doing their work today. But they did it 40 years ago. That’s right. Digital photography may be relatively new, but Boyle and Smith first came up with their idea back in 1969, almost 20 years before I saw a Commodore 64 for the first time. Boyle retired in 1979. Would it have been a “priority area” back then? At Bell Labs, it didn’t have to be. That’s the point.

I’m sure that the strategic networks are doing excellent work. But what the rest of us need is, in Dr. Boyle’s words, “a chance to do the things [we] want to do.”

Thank you, Dr. Boyle, for speaking for us.

Oy-oy-oy

Rep. Steve King (R-IA) on gay marriage: “Not only is it a radical social idea, it is a purely socialist concept in the final analysis.”

I’m on ur payroll, sipping ur sherry

An offensive and uninformed rant from The Globe And Mail:

“My colleagues do everything they can to get out of teaching,” says Rod Clifton, who works in the faculty of education at the University of Manitoba. “They’d rather not have the students around, because they’d rather do research and stand around and sip sherry.”

Canadian universities now have about 800,000 undergraduates. But as enrolment soared, teaching loads – with the help of strong faculty unions – went down. In Mr. Clifton’s department, for example, the teaching load is six hours a week for one semester of 13 weeks, and nine hours a week for another 13 weeks. That adds up to 195 hours spread over just 26 weeks a year – less, if someone has administrative duties. Of course there’s prep time and marking and so on. But it’s still not much.

Let’s start with the teaching workload. In my department at UBC, we are expected to spend 40% of our time on research, 40% on teaching, and 20% on administrative work. That would translate to 2 full working days out of a 5-day business week spent on teaching. Our normal teaching load is 3 courses per year. They’re generally not distributed uniformly throughout the year, but if they were, we’d teach 1 course in each of the three 4-month semesters. Each course has 3 lecture hours per week, plus the required 3 office hours per week, more if students ask for additional appointments. Ms. Wente dismisses the “prep time and marking and so on” as “not much”, but I would say that for each lecture hour there are at least 3-4 additional hours spent on class preparation, selection of homework assignments, preparation of midterms, providing instruction to the TA’s, marking, answering email from students, maintaining a course web page, and other such. That adds up to 16-20 hours per week – somewhat more than the two 8-hour days.

Gender dependent

That’s what I thought when I read the articles linked below, even though gender is never mentioned explicitly. Instead, there seems to be an implicit assumption that everyone involved is male. (Presumably white, too – but that would be a story for someone else to write.)

First, there’s this stunning book review by Scott McLemee, linked also at Crooked Timber:

The most powerful figures in this system [Italian academic promotions], says Gambetta, tend to be the least intellectually distinguished. They do little research, publish rarely, and at best are derivative of “some foreign author on whose fame they hope to ride…. Also, and this is what is the most intriguing, they do not try to hide their weakness. One has the impression that they almost flaunt it in personal contacts.”

[...] Gambetta argues that the cheerful incompetence of the baroni is akin to the mafioso’s way of signaling that he can be “trusted” within his narrowly predatory limits.

“Being incompetent and displaying it,” he writes, “conveys the message I will not run away, for I have no strong legs to run anywhere else. In a corrupt academic market, being good at and interested in one’s own research, by contrast, signal a potential for a career independent of corrupt reciprocity…. In the Italian academic world, the kakistrocrats are those who best assure others by displaying, through lack of competence and lack of interest in research, that they will comply with the pacts.”

Also, this from the comments at CT:

I experienced this in a past position, and reached the same analysis as Gambetta. My attempts to signal that I would leave if I didn’t get better treatment were exactly the wrong ones to send. The people who won the battles were those signalling “I can never go anywhere else, so I will fight to the death to get my way here”.

I’d be interested to know how many of those incompetent-and-proud-of-it academics are female. Because, at least over here on this side of the Atlantic, somehow I don’t see a lot of female professors (or lawyers, or businesswomen) showing off their weaknesses on purpose.

In case you were interested…

Yes, I did enjoy my vacation.