The stable state PhD equations

Down in the hall we have a nice poster with faces of all faculty, staff members, postdocs, and grad students. It is not updated too frequently, but overall reflects the structure of the department. A great idea, by the way; each time I forget one of these strange English names people have in this country, I just go down and refresh it in my memory.

But seeing this poster made me ponder on the following: how does this distribution of roles in our department match the career plans of said grad students and postdocs? If our university were the only one in the Universe (or if all other universities followed about the same organizational structure), would this system be sustainable? Like in chemistry, you know, when you have a system of reactions, and you know the kinetic constants for each of them, you can calculate the concentrations, and vice versa. What's about the PhD pyramid?

So, we have about N professors, and about N postdocs working for them, and about 3/2*N aspiring grad students. Assuming (again) that one spends 5 years in grad school, then ~7 years as a postdoc, and ~30 years as a professor, what would be the probability of getting a TT position in a world like that?

Well, the formula is simple: it's just a ratio of the frequency at which new candidates are popping out, and a frequency at which old professors retire. So the total probability, from the grad student point of view, would be: p = N_TT/Time_TT/(N_grad/Time_grad) = 11% . Had the Universe be molded after our department, about half of the candidates would be fired at the grad-school-to-postdoc stage, and then about one fifth of the postdocs would make it from the postdochood to the TT. Which surprisingly perfectly matches my estimations for our field in general! It may be a nice coincidence, or a case of convergent evolution. Or maybe some clever people in the administration consciously try to keep the department about in the middle of the spread (which is usually a wise thing to do).

Still, it's kind of funny. 11% doesn't sound like much at all. That's a competitive field, huh?

Mayan vs Aztec

Google for "Mayan calendar" images. Get this:
https://www.google.com/search?q=mayan+calendar&tbm=isch

Now google for "Aztec calendar" images. See the same thing:
https://www.google.com/search?q=aztec+calendar&tbm=isch

In reality this famous thing is called an Aztec Sun Stone; it obviously is not Mayan at all, and, reportedly, is not even quite a calendar. Yet in the wake of impending apocalypse everybody screwed up their homework, and misguided each other. Straight it up people, before it is too late!..

Links 2012-12-21

A great summary: What advice would PhD people give to their former grad-student self.
More than a dozen people shared their thoughts. The result is both thought-provoking, and inspiring.

You are having a TT job interview, and they ask you if you have any questions. A nice list of questions to consider. And also - what to say if they ask you "tell us how you think you will fit here" (or rather how to prepare for questions like that, and what they really mean).

How reading random stuff, and not being too busy, are both so important for scientific success.

Guns and probability

Let's solve a simple (but unpleasant) probabilistic problem.

• You are in a room with 19 other people (so 20 in total). One of them turns to be a "freak".
• If a freak has a gun - they start shooting people until nobody is left.
• If a "normal person" has a gun, they shoot the freak, and save everybody.

What is the probability of dying in this situation, as a function of gun availability in the country?

Let's assume that the probability of having a gun is the same for everyone in the room, and equals p. Then the probability of the freak being the only armed person in the room is given by the formula d = p*((1-p)^(n-1)), where n=20. If everybody carry their guns openly, and the freak is rational enough; or if "normal people" manage to always kill the freak before the freak kills anybody, this formula will describe the probability of death in this situation. It will obviously go through a maximum, and then decline back to zero:

Let's assume however that "normal citizens" don't shoot the freak until they are 100% sure that this guy is actually a freak. So the freak always succeeds in killing one person, and only then they are stopped by a "militia" member. Then the curve would look slightly differently, because now the probability of death is 1 (for sure) if there's no other armed person in the room, but it is still 1/20 if there are militia members there: d = p*((1-p)^(n-1)*1 + (1-(1-p)^(n-1))*1/n). This is assuming that you are always a "good citizen", and never a freak.

And this formula suddenly makes some sense. It is possible to decrease the probability of shooting sprees by increasing gun ownership. But at some point the shootings will become that frequent, that even if each of them is stopped almost immediately, they will still take a toll. Because in each of them at least one innocent person will be killed. You change the assumptions, and the parameters, and the curve will move around, but the idea will stay the same.

- "Well", - the right-wing person would say, - "but people never turn freaks right in the room; they usually turn mad while at home, and take their time to prepare. What if a freak is 5 times more likely to find a gun than a "normal person", because a freak is actively looking for one?" In this case, indeed, the only way to stop the freaks is to give everybody a gun, because d = (1-(1-p)^5)*((1-p)^(n-1)*1 + (1-(1-p)^(n-1))*1/n).

In reality however all freaks are different, and while there are some who will sale their belongings and prepare for years, most of them will probably kill other people only if given an opportunity. The harder it is to get a gun, the fewer freaks capable of doing so you will find. For example, if on top of "purely opportunistic freaks", as described above, you'll also find 1/2 as many freaks that are twice more persistent in getting a gun, 1/4 as many freaks that are three times as persistent, etc., you'll end up with this curve:

And here basically, in essense, we return to the curve #2. If everybody has a gun - people die all the time. If you reduce gun ownership, rate of murders go down. At some point however you may feel helpless, because if 10% of people walk around with a gun in their pocket, sprees will still happen regularly, and they'll be already quite deadly. That is essentially the situation in any school, or any mall, where the majority of public obey the "gun free zone" laws. However, once you drop the average gun ownership rate below a certain point, gun control becomes the only efficient way to further reduce the casualties.

Unaccessible citations

Science is important, but if I have two citations on hand, and one of them is easily accessible, while the other one is not, I'm going to cite the accessible one.

I feel a bit sorry for the author (maybe they did not have any choice). I also realize that most probably I'm not "punishing" the publisher at all, because they simply don't care (especially in case of old publications, when citations do not affect the impact factor anymore). But still there's an emotional component to it. You're not giving me this 1975 paper, even though you clearly have a PDF version of it, and our university has access to your jornal? Fine! I'll just cite the latest review!

At the same time I wonder if there's any incentive at all for the publishers to put their old papers online. Right now I can not think of any, and it is kind of sad. Without references to old papers new publications become kind of boring: too mechanistic, arrogant, and shallow. It's like a case of anterograde amnesia, when a person kind of keeps the discussion going, but does not remember anything about the global picture anymore. Also in behavioral sciences even papers from 1960s may be directly relevant to your current research, because animals were the same back then as they are now, and the descriptions of their behavior are probably still quite valid.

So, while for new papers the invisible hand of the market can, in principle, encourage authors to publish in open-access journals, old papers are simply left behind.

Ideal number of PhDs: is it better to die early, or not to be born?

Job market is like weather: not that it changes as frequently, but as weather it makes a nice and safe discussion topic. You met another postdoc, and don't know what to talk about? Just whine together about the bleakness of job opportunities. You'll both get depressed, as a side effect, but at least you'll avoid the awkward silence.

When talking to people, I like asking them about what would they do to improve the academia, if they had the power to do so. Here are the axioms (the rules of the game):

1. The funding is fixed (increasing funding is an entirely separate topic)
2. Number of people willing to do science is fixed (it's not actually, but again, for the sake of simplicity)
3. You want to increase the scientific output (or at least keep it at the current level)
4. ...while increasing the "average happiness" (whatever it means)

So, what would you do?

Surprisingly, there's no common theme among the answers I receive. The only pattern I could spot is that people generally call for making the bottleneck they have just crossed a bit tighter, while loosing the one they are facing. Thus grad students call for decreasing grad school enrollment, while making graduation more "guaranteed"; postdocs think that "we need fewer PhDs", to reduce competition for the TT positions, and so on. I also follow this pattern by the way.

But this made me think about the "best theoretical solution" to this "bottlenecks distribution" problem. Does it exist at all? If you follow a reductionist approach, and, for the sake of simplicity, concentrate on the "selection process" for future TT faculty, what would be the best "extinction process" to use? If you were the King of NIH, when would you get rid of them lazy bastards, people who will never become PIs? Of all those who foolishly dream of becoming TT faculty, how many would you push out of the system at each respective year of their evolution?

According to my estimations, the current actual "Extinciton chart" for Neuroscience looks somewhat like that:

About 50% of applicants get accepted to grad schools (I assume acceptance rates within each school of ~10%, and each person applying to ~5 schools). 5 years in grad school (I should have assumed more actually); 50% graduate with PhD; then 7 years of post-doc, 20% of postdocs get a TT position.

Is it optimal? Obviously, the answer depends on your definition of "optimal". If you try to increase scientific output (without restructuring job descriptions), you would have to keep them all till the last moment, and then suddenly fire. If you want to decrease spending, you'd have to admit to the grad school only ~5% of applicants, thus making the tenure track more or less guaranteed. If you want "productivity" in terms of "Impact-factor-per-buck", you'll have a complex interplay of different factors, and lots of assumptions about salaries, talent distributions, education investments, etc.

But this dichotomy is obvious. What I find much more interesting is another type of an inherent contradiction here: that between Happiness and Fairness.

The "average happiness among the young folks in academia" would obviously decrease, as you increase the competition at the later stages. If you keep everybody in the system for 15 years, and then perform one giant massacre, people will be extremely unhappy about that. You may think of unhappiness being generated when people are forced to leave academia: the more of their life-time they invested into this thing, the more they sacrificed for it, the more unhappy they will be. Or you may think of it as of frustration that is linearly generated over time, in view of the decimation bottleneck to come. The math is the same in both cases: the earlier you fire people, the less they lose. Thus the system in which only 5% of applicants are accepted into grad schools would produce the most "happy" (in terms of being relaxed) academia.

But this system would also be the least fair one! Because 5% admission at the level of grad school would mean that the admissions would be quite arbitrary. What would you base your decisions on? GPA? Undergraduate education? Scholarships and early publications? All these points would essentially translate into one: "pure luck of being born in a wealthy family with good connections". Older applicants, women with kids, foreigners, lower-class applicants would all be judged against, just because they would be perceived as "more risky" investments.

It is kind of similar to the heritability of IQ issue: the later in life you measure the IQ, the more heritable it becomes. In elementary school kids IQ is almost entirely explained by the environment that is "forced" upon them (bad school, good teacher, etc.), but as we move on, to older subject, IQ gradually starts to become more and more "heritable", with up to ~75% heritability in adults. The common interpretation of this fact is that as you move on, more and more aspects of your life become a result of your personal choice. We all gradually become self-made people, in both good and bad. Granted enough time, we settle kinda where we deserve to be. At the age of 50 your pre-school experiences are largely irrelevant for your success.

And that's why the later you decimate the postdocs - the more fair the system becomes. If a person doesn't have a Nature paper by their 3d postdoc position, it's not just "pure luck" anymore. They had a chance to choose a  grad school; a PI there; and then, say, 3 different labs. They had a chance to either upscale, or downshift. The luck is still important, but while having 1 failed project is quite normal, having 10 of 10 projects failed over a course of 10 years would probably reveal some kind of a pattern.

This being said, if you think that the grad-school-to-postdoc environment is unhappy and depressing, please, do realize that it means that it is at least decently fair. Trying to make everybody in the system "more happy" at the expense of decreasing the in-flow is likely to make the system less fair, less productive, and more frustrating for those worthy people who would be left behind due to their suboptimal early life experiences. Your gambling on your future, and your uncertain career perspectives right now, are a reflection of the fact that you have the liberty, the chance to take a risk. In a no-risk environment, you probably would not had a chance to try.

A Management Tool every PI should Know and Use

Let's face it: every PI is a manager. PIs have people working for them: people for whom they are somewhat responsible; people who can screw up in innumerable ways, who can suffer, despair, get lost, or make the lab a toxic environment. PIs are managers, even if sometimes they don't want to admit it.

And this is a nice thing, really, because it means that every PIs has access to all these techniques, tools and methods that managers in business were developing for years. All these "management tools" that work, and that are used every day by hordes of tie-wearing "managers" in cubicles and offices all over the world. These tools are effective, simple, well described, and "ready to be served": even if their names and some of the descriptions may sound cheesy to an average academic (especially to a "hard science" one). For a PI to reject these managements tools just because they originate from a different subculture is exactly as irrational as for a business manager to get engaged in some uninformed self-medication. When you need to treat a medical condition, you find a doctor. When you need to manage people, you read a book on managing people. It's a good and worthy thing to do.

Anyway, let me give you a practical example. If I were to pick a single most important management technique that every PI should learn and use, it would be the "One on one meetings". Now, even if you mentally roll your eyes, and think "Gosh it is so boring...", don't close the page yet, but rather read. It is important.

Consider this obvious statement: people who are easy to manage, don't actually need to be managed. They are doing just fine: they catch most hints, they usually keep their promises, and they can always come to you with questions, when they have any. You don't need a special technique to interact with them! But surely there are some people in your lab that need guidance, support, or control. People who tend to generate problems of some sort. And you know what? It's hard to manage them, and thus it is unpleasant, and that's why you don't like it, and are avoiding it at all costs. Maybe you dread talking to them about their progress, because they get so defensive that your head aches. Or maybe they are easily offended; or lie to you; or find hundreds of excuses every time you ask them a question. But in any case, by now you may be habitually evading any serious conversations with them. You tried to use jokes to send them a hint, but they don't get hints, and the situation is slowly getting worse. Most probably they also don't come to you with questions about their progress, because these discussions are unpleasant for them as well. So here's the point: those people who need your management the most, are the ones that will never get it. Unless you consciously do something about it.

And here's a good news: many of them can be salvaged through a simple, but structured management process. Actually almost everybody can be salvaged, just at some point you will hit the cost / benefit ceiling of a sort, when the effort won't justify the outcomes. Still it's good to give it a try. Everybody are born clueless, but most people pick it up, and require much less care as time goes on. Try to put it on a right track from the very beginning, and most probably it will only become easier.

- So, what do you want me to do?
- Establish a sequence of regular one-on-one meetings. Put them in the calendar. For those in your team who are "doing fine", do them every quarter. For newcomers and people who may be slightly lost, do it monthly. In most immature / critical cases do it once every two weeks. Reduce the frequency as the situation improves.

- Why would I make them formal? I hate everything formal! What good is it? They can come to me any time, I'm not hiding from them!
- First, they won't come, because they either don't know they need to, or they are scared. Call them. Second, make it formal, and book some time for the meeting, like 30 minutes or so. The benefit here is that surprisingly it will make your discussions much, much easier. Talking to a person about their progress is always awkward. Some people hate saying bad things; some people have hard time saying good things, because it just sounds stupid! Why would you suddenly, in some random hour of some random Wednesday, start praising, or criticizing anybody? And here's where a scheduled meeting helps: you sit together, and you have to talk good things. And you have to talk bad things. You have scheduled the time, came to the room, closed the door, it was all really awkward, and thus the quota of awkwardness is already met. Now, as you have to talk about the person's progress, you'll be able to do that. Because you've staged it all correctly.

- But what the heck will we be talking about? It's all clear, and I never make my opinions secret! I always share them in some form or another! How would one more repetition help?
- Again, most probably you did not really share your feedback "openly", even if you think you did. You made some comments here and there, but you never combined them all into one picture for the person to see. And there were other people around, and you might have adjusted your words a bit, or at least it sounded that way. The person may have not heard you. They may have thought it's a joke, or an understatement, or an exaggeration. It's surprising how effective the words could be if they are said openly and simply, behind closed doors, one on one. You look them in the eyes (or you don't - I hate looking people in the eyes actually), but for the matter: you say them what you need to say. "This is good. And I mean it. This is bad. And I also mean it. Now that's what we do next." People need that. Most people need that.

- Still I don't know how it can be useful at all, because what would happen is that we'll have the same conversation again and again. It will not work, because adults can not be changed.
- You're not trying to change them, you're trying to change their behavior. And that's a much easier thing to do. There are two tricks that will ensure you don't have the same discussion happening again in every meeting. First: you'll introduce some measures, and some deadlines (or target dates). You'll be quantitative. And second: you'll write down your agreements, and you'll share them after the meeting, by e-mail. This way:

1. In the beginning of each meeting you'll check your notes from the previous one, and compare the actual situation with the one you planned / agreed on. You'll start with the facts. How many experiments were done? Where's the paper? How is the figure doing? Rig construction? Training? Certification? And don't get lost if your initial estimations were wrong. You'll correct them if necessary, but at least you'll have a starting point for a discussion, and a seemingly objective one. It's OK to make mistakes and miscalculate everything, especially in science, where experiments routinely take 10 times longer than they were supposed to. But it's much easier to disregard the numbers when you have them than to invent the numbers on the spot.
2. Your trainee's words will become a promise, and they will have to provide explanations if the "actuals" don't match the "projection". They will become more accountable. If they disagree - they should ideally disagree in the meeting. Once they promised to do something, they are supposed to keep the promise. If something changes, you either discuss it at the next meeting, or they try to find you in between, but at least they won't be able to say that "they thought it's OK", or "they forgot", or "they did not actually mean it". No, guys, if you agreed with something, do it. If you disagree, say it now. Don't assume: ask. Get certain about what you both mean, and clarify the misunderstandings upfront.
3. The opposite is also true! If you said something, you become accountable for your words. And that's a good thing, as your trainees won't have a chance anymore to say that you promised something and did not do it, or that you changed the scope of the project without telling them explicitly, or that you never told them they are doing it wrong. It's on paper now. 
4. If worse comes to worst, and your trainee doesn't perform, these papers will help you to part with them without feeling bad and cruel (as you'll have their performance documented), and without looking cruel in the eyes of the broader community (again, because you have it documented). I'm not even going into the lawsuits topic here, but you can extrapolate if you wish.
5. If worst comes to even worst, and you get insane, and really start changing projects in your mind without telling anybody, your trainees will have the documents on hand that will prove their performance. So at least their future won't be screwed. You see: it's your mutual protection! It's good!

To sum up: Regular, scheduled meetings, with target dates, numerical measures, and after-meeting recaps make your interactions with trainees transparent and clear; make both of you accountable; give you an opportunity to address any issues early (including the sensitive ones that nobody would share in the "lab meetings"), and also protect both of you in case of a conflict.

References: here's a really nice set of podcasts about management techniques. Note the topics (and names) of 2 first podcasts ever recorded (in year 2005!).  It's indicative.
http://www.manager-tools.com/podcasts/manager-tools?page=17


PS. If you, my beloved reader, are not a PI, but a postdoc, graduate, or an undergraduate student, all that was said here still applies to you, only in reverse. If your PI doesn't have a process like that on hand - for God's sake - force them, or trick them into it. Meet with them regularly (even if they don't realize you're having one-on-ones). Send them notes of your discussions (even if they don't read them). Update them on your status, and demand a feedback from them (whether you meet the expectations, or exceed them, or do not meet them - in which case do immediately learn why, and how you're supposed to meet them). If your boss is overly delusional, you'll know it now, not 4 years into the grad school. If your boss is mistaken, you'll clear the misunderstanding now, while it is still small, and neither of you had built an immune response against the other. Do it, it's useful!

(image source)