## Tuesday, February 5, 2013

### On the two body problem

 Figure 1: The two-body problem. Image taken from this blog

In academia there is something called the "two-body problem." The original two-body problem involves the gravitational interaction between two massive bodies, e.g. a planet orbiting a star. This is a problem in the mathematical sense, as in something interesting about the universe that we would like to figure out. This classical two-body problem has a solution, but interestingly it is in the form of a transcendental equation that can only be solved numerically. But when done so, it looks like this. Pretty nice, huh?

It turns out that there's an even more difficult two-body problem in science academia, but this one has to do with the attraction between two humans (cf Figure 1 above for a succinct description). The problem arises when one or both individuals are academics seeking post-graduate job positions. The problem, in a traditional sense of the word, is related to the fact that academia has been honed and perfected over the centuries to accommodate only a specific type of coupling. If you are an academic and in a relationship, there is a closed-form solution to the two-body problem if and only if the partner/spouse is not also an academic and has the ability/willingness to move every 2-3 years over the next six years while academic partner takes various postdocs and/or other job positions. Personally, I was fortunate to find this "solution." Most do not.

A further complication from the standpoint of young academic couples is that there is often only one or at most a few available/desirable job openings per institution per year. This means that it is highly unlikely that the coupled academics will find their ideal job position at the same institution. However, if they do solve the problem at the postdoc level, it is very unlikely that it'll happen again at the professor level. Think of multiplying two or more small probabilities; the result is a very small chance. On the other hand, if you have a traditional (read: 1950's-era) family, none of this is really a problem. One partner pursues their career, the other raises the family, and the solution is not only closed-form, but elegantly analytic.

However, in modern times there have arisen a whole host of complications. The primary one is that as more and more women enter graduate programs, more and more couplings are occurring within said grad programs---hot nerd-on-nerd action, if you will. In what follows, please allow me to apply a cold scientific analysis to an inherently human/emotional process (I'm already bracing myself or angry commenters noting that not all women date men in academia. Settle down nerds, I recognize and hereby acknowledge the difference between a simplifying assumption and reality, the difference between the mean and the dispersion of a distribution of human behavior.)

Since the male-female ratio in most grad astro programs is 2:1---which is very high among the sciences, but still far from parity---there will be more women with two-body problems than men, under the simplifying assumption that every woman couples to a man. For every 3 intradepartmental pairings, there are four men available (forced) onto online dating services, night clubs, etc. where they can meet a non-academic. As the male-female ratio increases, the frequency of two-body problems among women increases. This assumption is valid, in my opinion, given that astro grad students spend the majority of their waking hours in their offices doing problem sets, reading papers, and tracking down bugs in their data reduction and numerical integration codes, instead of hanging out where non-academic, single people congregate. And if one's soulmate is not in the same department, there's always Bio or Engineering across the street!

This hypothesis gives rise to a few predictions:
1. The majority of women in science will be in a relationship with another academic. Here's a test providing confirmation of this prediction.
2. The unequal male/female ratio will result in more women than men facing a two-body problem
3. Societal norms and/or other pressures will result in the woman giving up her career more frequently than the man giving up his. Anecdotally, but very obviously, I've noticed that the men in two-body situations tend to be 1-4 years older than their partner, which means they are more established when the tough decision-time comes. With a man in an established job further along in his career, it is often the woman who gives up rolling the dice on a future opportunity in favor of the sure-thing right now with her partner’s job offer.
4. There will be a higher attrition rate among women than among men in academia, causing the male-female ratio to increase from grad school, to postdoc, to professor.
5. The refusal of science programs to acknowledge and address this problem will exacerbate the gender disparity among their faculty.

Based on my personal observations during travels to various institutions, these predictions seem to hold up. The vast majority of my female friends/colleagues are in relationships with another academics, quite frequently with other astronomers. And far from being just a cute name given to a societal phenomenon, the two-body problem is a Problem with a capital P.

 Figure from Dual Career Academic Couples: What Universities Need to Know (PDF)
I can't imagine cutting my astronomy career short at this phase in my life, so I can only imagine how difficult it is for people to be forced to decide between their careers and their relationships. I've heard of women being told, "Your spouse has an excellent job opportunity here. Would it be so bad to give up your career?" I have to admit that I've entertained such thoughts in the past. But I find it doesn't work when I apply this reasoning to myself. When I think about my passion for astronomy, and how my research is what causes me to go to bed late and wake up early, there's just no way I could imagine giving up my career and still finding full satisfaction in life. I'm a trained slayer of hard problems, and I live to to drive big telescopes across the sky. I'm also passionate about undergraduate and grad education of the type that can only be implemented effectively as a professor. How could I just give that up? So, no, it's not at all an option to ask a coupled scientist to give up their careers.

When couples are able to hold onto their pursuits, long-distance relationships are very common, which puts strains not only on the individuals, but also on their science. Being away from one’s partner for extended periods of time leads to stress and anxiety, whcih negatively impacts day-to-day work. Excellent candidates pass up opportunities at top institutions (justifiably) to stay with their spouse. Top profs at leading institutions drop out at the peak of their games to find a solution to the two-body problem. Postdocs pass up fellowship offers to stay close to home. I really wish these weren't the choices that young scientists have to face. Our field would be much happier with a closed-form solution to the two-body problem.

As we in astronomy begin to embrace diversity as a key ingredient for excellence, we must find a robust solution to the two-body problem. To keep the conversation moving forward, here are some solutions I have heard suggested or come up with on my own:

1. Make postdoctoral fellowships last 4-5 years, rather than 2-3. The extra years relieve pressure and stress on couples to immediately begin searching for the next job and reduces the number of times a postdoc must move before (hopefully) settling into a more permanent professorship.
2. Restructure job searches to allow for two-body hires. I've heard it argued that this is undesirable because it would require sacrifices in "excellence" to hire a spouse that isn't as "excellent" as the primary hire. But what good is hiring an excellent individual when they will be looking for a more accommodating position from day-one after starting at your university? How much excellence can be traded for an unhappy, loosely-bound workforce? On the flip side, think about how much more loyal your employees will be if hired together. You better believe they'll work harder than anyone else in your dept, and be far less likely to be enticed by competive offers later (immunity to poaching is valuable, no?). Also, think of the message you send to your entire workforce when you demonstrate the value of family security in your workforce.
3. Coordinate among departments to make mixed-academic hires. One department might have to make a bit of a sacrifice along the (percieved) excellence dimension this time, but think of what can be gained the next time around when their top applicant is coupled to another academic. Astronomy is not the only field facing the problem.
4. Recognize the considerable uncertainty in judging excellence in the traditional sense. How many previously-identified excellent hires didn't attain tenure at your institution and other top universities in the past 20 years? If hiring committees can miss that badly in one direction, why not hire the person who is deemed an 8/10 on your scale in order to retain the 10/10 in your dept now, with the recognition that that 8.0 is really 8 +/- 1

What have I missed? Discuss!

Anonymous said...

Thank you for this insightful, thoughtful post. My relationship is a result of one of these grad school nerd-on-nerd actions. I can't imagine a better partner for me for life. We've been lucky to find postdocs at the same institution, but there has been A LOT of stress involved in thinking about the next step in our careers. I do think it helps alleviate some of the problems that we're at the same stage -- one is not leading the other. We've been given a lot of advice whether to bring up our partner in faculty interviews, and in the end, we've decided the best advice is not to.

With all that said, I much prefer to refer to this as the Two Body Bonus, not the Two Body Problem. That's how hiring institutions should be thinking about it.

L. Trouille said...

Northwestern University's CIERA (Center for Interdisciplinary Exploration and Research in Astrophysics) took advantage of the fact that they were able to hire a half dozen or so postdocs in one year and strategically hired 2 couples (my husband and me & another couple). They got quality and stability as a result. If your department/institution is in a similar position, I highly recommend being proactive in soliciting applicants that you know are in a 2-body *bonus*, and recruit them as a unit.

Eilat said...

Thank you for saying all of this out loud. Speaking up is a major step!

Your second suggestion, I think, nails it. And makes the best argument I have heard so far for two-body hires. The difficulty in implementing this change is that it needs to be accepted at two levels: the departments must accept your argument *and* the institutional higher-ups must also see the light. But it is definitely worth pursuing, especially if we can once and for all remove the need to hide one's spousal status during an interview.

I also want to point out (as someone who does not have a 2-body problem, having found a "solution" as you have) that there is the N-body problem that arises when the 2-body system procreates. And in those instances, a long distance solution is basically impossible.

But, I think in fairness to the largeness of this problem, we should try to tackle the 2-body problem first ;-)

John Asher Johnson said...

I'm happy to speak up. The way I see it, we're scientists. We're trained to solve problems. This one is clearly not going to solve itself, so let's throw some thought at the problem until it goes away.

I truly hope that this sparks a wide-ranging discussion up and down the chains of command at various institutions. We have allies in powerful positions, some of them right here at this blog. The problem isn't trivial, but unsolved problems rarely are. Besides, as a scientist, I wouldn't want my problems any other way. There's no fun in solving easy problems!

Anonymous said...

To say nothing of queer two-body problems in science! Do you know any out professors?

John Asher Johnson said...

Anonymous: Yes, I actually know of many out astronomers, and I thoroughly enjoyed my time at the WGGLE reception at the AAS meeting last month. These individuals face a number of challenges, some similar and many different from women and racial minorities in astronomy. Perhaps that's a subject for a future post on my personal blog. Thanks for your feedback.

Nicolle Zellner said...
This comment has been removed by the author.
Nicolle Zellner said...

At my college, we have two married couples (one in chemistry, one in geology) who share one position in their respective departments. This means they earn one salary, but each has their own benefits coverage. Additionally, when they go up for tenure, promotion, etc. they are treated like one person, i.e., their CVs are evalauted *together*. They have been able to supplement the one income by taking on extra responsibilities, such as Honors Director; the other one then, just take a heavier teaching load. It works for them.

Anonymous said...

Thank you for posting this. The odd mix of dreamer and intellectual realist that describes many astronomers struggles mightily with this problem. While just about everyone knows about the problem, I don't think many fully appreciate the stress it engenders. Unfortunately, that includes a lot of the people directly involved in it. Be open, put yourself in your partner's position and be honest in your evaluation of how it would feel, and work together.

Rachel said...

My two-body problem eventually resulted in my husband leaving research (in another scientific field). The tremendous stress involved in joint job searches and in decisions about who was going to get the shaft (because one of us had to) was not good for us or for our children. He is happy in his current position, but it was very hard for us to get to this point.

Like Eilat, I am concerned about not just 2-body problems but N-body (in my case, N=5).

I think there must be a better system than what we have now.

Sarah Tuttle said...

I think the most telling is the very end of your article, and speaks not just to the two body bonus, as it were, but to hiring in general. Maybe it is worth discussing if our hiring criteria turn out to be such great indicators of future success...It might help inspire a little more flexibility. That 8/10 today might be an 11/10 in 5 or 10 years in terms of what your dept needs. I don't think we're great at estimating that.

Anonymous said...

Maybe young graduate students should be told very frankly how the two-body problem could affect their future career, and gently encouraged to meet people outside their field. The two-body problem seems somewhat more tractable when one member of the couple is in a different academic area, particularly one that has industry job options for PhDs. I can understand that fellow astronomers might bond over shared interests (or homework :)), but is there such a big difference between that and an astronomer+chemist or astronomer+aerospace engineer pair? Besides, casting a wide social circle and engaging in non-astronomy recreational activities outside one's department is probably a very healthy thing!

Aki Roberge said...

In response to the last comment, when I arrived at grad school, a senior professor did in fact tell all us female grad students not to marry other astronomers. He said we'd never solve the two-body problem and even if we did, the male would always be more senior and our careers would take a back-seat. I'll admit that this does happen; I think the two-body problem is probably the #1 problem for woman scientists today (as John nicely discusses). But I still think the advice was bull-crap. It assumed a level of crippling sexism in the field and that it would never change.

I ended up ignoring this advice and married another male astronomer slightly more senior than I am. It was one of the best things I ever did for my career (and pretty damn excellent for my life in general too). We've solved the two-body problem with equally good permanent positions at the same institution (a very large one). And we help each other's careers in a million ways, through discussing our work and by being understanding of each other's career demands.

John Asher Johnson said...

Thanks, Aki, for sharing your experience!

Anonymous: I can see the appeal of your proposed solution--its easier than fixing the structure of our field's hiring practices. And I agree that student should maintain broad social circles outside of astronomy. But personally, I think professors should minimize their involvement in their students' love lives.

First, it's hard enough to guide a student's research focus without tackling the tougher problem of advising them on who to date. Second, while a student might see our logic and follow our advice on something like the ordering of an author list or the choice of a calibration, they aren't likely to be in complete control over when and with whom they fall in love. As I'm sure you know, love does not follow logic. So I don't think that gentle nudging would do much good, as Aki can attest.

But even *if* it did work, it would only be a stopgap kludge for one of the biggest issues facing a diverse astronomical (scientific) workforce. Let's focus our brainpower on finding that closed-form solution.

Peter said...

The 2-body penalty is much like the marriage penalty in US federal income taxation. Both manifest from (at least) two ideals in conflict. In both cases, one of the conflicting ideals is that couples be treated as a unit. Respectively, the conflicting ideals are A) employment should be considered on an individual basis, or B) progressive taxation. Both share a common heritage in that policies have developed over generations in a society markedly different from the current one. "Policies lag change" which often makes sense, generally speaking. The stakes for the marriage penalty are high (US "individual" income tax revenues being 1.4 million million USD in FY 2104) but still the "problem" persists. Such is evidence that problems that manifest from two desirable ideals in conflict cannot be "solved." If we did, then it will have morphed to a perceived unfairness to those individuals with non-academic spouses (e.g. J. J.). Some might say that already happens at times. http://taxpolicycenter.org/publications/url.cfm?ID=900952

Thronson (1991) and Metcalfe (2008) model the production of astronomers. (ADS lists fewer than 5 citations to each.) I think any such model should try to include the friction of dual-careers.

One policy that has developed over generations is tenure, which reduces liquidity in the already niche academic job market. Reduced liquidity could exacerbate finding two academic jobs in the same geographic area within a similar time frame.

A related issue is the insidious incentive for employers to get two for the price of one, either explicitly or implicitly. This is another "ideals in conflict" problem. 1) one person's salary should be enough to raise a family, 2) each person's salary should be neutral with respect to his/her personal life. One interpretation of the conflict is that in a macro-economic sense, two-career couples are paid too much. I think the "solution" our society is adapting to (has adapted to?) is to raise consumer-lifestyle expectations and to lower salaries until raising a family "requires" more than one salary.

Small reality check here: to zeroth order, astronomers in the 21st century all live like or better than kings and queens. For much of human history and still in much of the world, you could die for lack of a dollar's worth of antibiotics. And only recently could you communicate face-to-face with nearly anyone anywhere anytime.

Isn't there a typo in the original post? If the male:female ratio is 2:1, then wouldn't there be three (not four) males on Match.com for every three academic couples? M(MF)+M(MF)+M(MF)?