Turning the tables – an interview with yours truly

Dear readers,

This week I had the pleasure of being interviewed by Holden Lee, the Vice-President of the MIT Undergraduate Mathematics Association. Excerpts from it are going to be published in the next edition of the upcoming Math Majors Magazine, but Holden was gracious enough to share the recording with me, and I’m happy to share it with all of you.

It was an interesting experience to be the one giving the interview, rather than the one conducting it, and I did end up asking Holden a few questions myself in the process (he recently won a prestigious scholarship and has done some work in mathematics education). We talked about my tortuous path in mathematics, what I learned from my mentors, the value of communicating mathematics to the non-specialists, this blog, mathematics education, and a few other things. Since Holden and I talked at a local coffeeshop, there is a certain amount of background noise, but it doesn’t seem to get in the way. Here is our conversation. Hope you enjoy it!

Mathematics and Theater – a Tale of Two Plays

Dear readers,

I recently wrote about mathematics and poetry, another art form that I appreciate a lot and engaged in seriously in the past. Today I’ll discuss mathematics and a different art form, theater. While I never went beyond acting in high school plays myself, I would certainly consider myself an avid theater-goer as I attend plays at least once or twice a month. Despite that, I’ve only ever seen two plays in my entire life that had mathematics as their main theme (though science plays would lengthen this list quite a lot).

About two years ago I went to see a really great one-woman play at the Central Square Theater called “Truth Values: One Girl’s Romp Through MIT’s Male Math Maze”. The actress, Gioia di Carli, had been a graduate student at MIT in the late 1980s, about 20 years before me. The play was both entertaining and thought-provoking. I saw it after I had already graduated, and some of it made me nostalgic. Mostly, though, I found myself thinking about how much MIT had changed in 20 years.

There were some universal themes in the play that I could relate to very well – the struggle of trying to solve a problem nobody had solved before you; the social interactions – or lack thereof – that you experience in graduate school; the communication issues you can have with your thesis advisor; and, most importantly, the burning desire to find something that motivates you enough to continue working on it for many years. In Gioia’s case, this turned out to be one of her hobbies, theater, rather than her graduate studies. But, along with many other audience members, I kept wondering if she might have been able to stay in mathematics if only she had had better mentors along the way. Nevertheless, mathematics’ loss was certainly theater’s gain, and the play kept my interest for the full 2 hours.

Interestingly, there were also some issues that I found very central to the play, but could not relate to easily on a personal level. Suffering from unwanted attention from your colleagues, having people place low expectations on your success, or being outright dismissed as not suited to do mathematics professionally, were not things I ever experienced, and I would love to hear about the experiences of other women in that respect. But I have definitely seen concerted efforts being directed at making the mathematics department, and MIT as a whole, a more welcoming place for everyone, regardless of their gender or background. I think that a play by someone who graduated in my cohort (which had 26 men and 11 women, compared to, apparently, only 2 women in Gioia’s cohort) would look very different, which is not necessarily to say it would not be as interesting.

The second mathematical play I’ve seen is David Auburn’s “Proof”, at the Merrimack Repertory Theater. My memories of it are quite vivid as I only saw it last night. It involves the family of a mathematician who just passed away – his younger daughter, who stayed home to take care of him in his last years, his older daughter, who left to live in another city with her fiance, and his “academic son”, a graduate student he advised.

Although this is a fictional story, it feels very real because of the intense emotions lived on stage by the actors. There are themes that people with no mathematical background can appreciate – jealousy, control, trust, self-doubt, attachment, betrayal, and more. I loved the flashbacks, the crisp dialogue and the sparse, but effective stage decorations. I was very surprised to learn from the playbill that the playwright, David Auburn, wrote the script in only three weeks!

The play starts with a conversation between father and daughter, only at the end of which do we find out that the father is, in fact, dead. The theme of mental illness in mathematicians (which I hope to address in a future post) is hinted at many times throughout the play. The former graduate student, who had been going through his advisor’s notebooks, then appears. A little bit later, the older sister arrives to attend the funeral. This is when all the conflicts between the characters surface.

Without spoiling the rest of either of the plays, I want to discuss some commonalities between them. Both use mathematics as the scaffolding for the story, but both are about more than just mathematics. They both illustrate the fragility of a mathematician’s ability to produce meaningful and interesting work, but also show the extreme satisfaction that this work can procure (even if one’s calling eventually turns out to be something else). Most importantly, unlike what movies usually do, they highlight the humanity of mathematicians instead of turning them into antisocial beings with mysterious talents.

In conclusion, I highly recommend you see both of these plays (“Proof” is in fact playing at the MRT until the end of this week, while “Truth Values” is touring different colleges in New England), and I would love to hear about any other mathematically-themed plays you know of; I feel we could use more of them!

Climate modeling – a non-expert’s thoughts

Dear readers,

I recently attended a panel on the role of science in society. A highlight of the evening was hearing one of the panelists, a biologist, talk about her experience of being asked for an interview about climate change by a TV channel because she was “not biased”. She, of course, responded that the channel would do best by asking an expert in climate modeling instead of her, since they would have the needed expertise. Her point was that just because you happen to be an expert in something doesn’t mean you’re necessarily biased (and that asking a non-expert showed a lack of understanding on the channel’s part).

Well, in today’s post I’m going to try to do what she refused to do, in other words, provide my thoughts on climate modeling without having any expertise in it. The reason why I feel it is reasonable for me to do so is because of my expertise with mathematical modeling in general. However, in order to ground myself in the subject matter at hand I’ll frame this post as a discussion of this article in The Economist.

The first point the article makes is that there is a mismatch between the predictions of climate models and the temperature trends observed over the past decade, namely, that “surface temperatures since 2005 are already at the low end of the range of projections derived from 20 climate models”. This is used as a way of bringing the models’ validity into question. I disagree with this statement. Although agreement with observational data is frequently used as a litmus test for the validity of a mathematical model, such agreement is neither necessary nor sufficient for a model to be useful. A model’s main task is to provide new insights into the behavior of a system, not to mimic it exactly. In fact, when a model fits the (historic) data too closely, this may be a warning sign that it is being “overfitted”, which means that the model’s parameters are selected to produce trends too similar to the input data. This may be a problem if the model is going to be used beyond its original context (see, for example, the Titus-Bode law which appears to be simply a nice coincidence). At the same time, a model that can predict critical features such as the periodic nature of climate trends without having them “built in” may be providing valuable insights without necessarily producing perfect agreement with data. Finally, agreement with data needs to be evaluated on a longer timescale; being off for one decade is not a model’s death knell…

The second, related, point the article makes is that there are two different kinds of models used to represent climate, namely, bottom-up models known as “general circulation models”, and top-down models known as “energy balance models”. The former are essentially mechanistic models, detailing the processes by which different factors influence climate, including various feedback loops. According to the article, “Their disadvantage is that they do not respond to new temperature readings.” The latter are less complex, and “do not try to describe the complexities of the climate”, but they do “explicitly use temperature data to estimate the sensitivity of the climate system”. Thankfully, the article does not make any conclusions about which type of model is “better”. Indeed, it shouldn’t. Different types of models have different ranges of applicability. While I don’t claim to understand the complexities of the distinctions between the two types of climate models I can draw a parallel with biochemical system models, with which I have extensive experience from my PhD days. There are also two main classes of models there: the more complex kinetic models, and the simpler flux-balance models. Kinetic models are detailed and describe exactly the rates at which each reaction happens and how the concentrations of the various molecules change over time. Their drawback is that they require a lot of prior knowledge which is often difficult to obtain experimentally, such as kinetic constants. Flux-balance models, on the other hand, require a lot less detail, and simply assume that the concentrations of all the molecules have reached a steady state and derive conclusions from there. Neither class of models is “perfect”. The main point, however, is that both types of models provide valuable information and insights about the biochemical system being analyzed, even though they do answer somewhat different questions about it.

The third point is that there is disagreement about the actual value of “equilibrium climate sensitivity”, the long-term amount of temperature increase due to a doubling of atmospheric CO2 levels. Curiously, the article cites estimates by Julia Hargreaves published in 2012, that a cursory search of her website’s publications page has failed to turn up (let me know if you have better luck), as well as “Nic Lewis, an independent climate scientist”, who turns out to be a semiretired financier with a background in math and physics with only one published paper on the subject. It is disappointing that The Economist uses a less-than-credible source like Nic Lewis on par with actual climate scientists. Granted, there may well be disagreement about the actual value, as there should be, but evidence needs to be properly weighted. Call me elitist, but I don’t see how giving equal weight to an amateur scientist with one publication and an expert in the field makes sense. Another source that is mentioned as providing evidence for a lower climate sensitivity is an “unpublished report by the Research Council of Norway, a government-funded body”. If there is one thing that I don’t think should belong to an article about science, it is unpublished reports (that being said there is a recent article by the team behind this research that’s freely accessible). My point here is that not all sources are made equal, and even if peer review does not always guarantee sensible publications, The Economist appears to exhibit a surprising bias in favor of dubious sources.

Another point that I want to make based on my own recent experience with epidemiological models of infectious diseases in Sub-Saharan Africa is that reconciling the predictions of multiple models (or even understanding the sources of the discrepancies between them) is extremely challenging albeit necessary to inform policy decisions (see this article examining the impact of antiretroviral therapy on HIV in South Africa predicted by 12 different models). Nevertheless, if a large fraction of the models predict a particular range of results, the laws of probability suggest that the correct answer is within that range even when several new models appear to give predictions outside that range. Of course, the really hard decision that needs to be made is on the policy level, which in the case of climate change largely falls into the buckets of “mitigation”, meaning a significant reduction in CO2 emissions, and “adaptation”, meaning adjustment to the change in climate, which would make sense if that change were less severe. If I know little about climate science, I know even less about policy, but in this case I tend to agree with William Nordhaus of Yale University, quoted in this article as supporting drastic interventions as a sort of disaster insurance protecting humanity against fairly unlikely events with catastrophic consequences.

In conclusion, The Economist does an excellent job of describing the scientific challenges of modeling climate in simple terms, but appears to overestimate or overstate the disagreement between different models, partly based on its use of less-than-credible sources. It also highlights the difficulty of taking a scientific conclusion and translating it into policy. But it seems to be missing some fundamental points about models by evaluating them purely based on their agreement with observations. Furthermore, it is misleading in suggesting that newer models may be more accurate than older ones, when they actually seem to be based on a less detailed, rather than more detailed, representation of the system in question. I hope that, by educating the general public about the development and use of mathematical models, as well as the conclusions that can and cannot be drawn from their results, we mathematicians and scientists may one day help it reach a level of understanding that will make such articles superfluous.