Have you seen “population pyramids“? They’re diagrams that show snapshots of a population, how many people there are of each age. They can give you an intuition for how a population is changing, and where the biggest hurdles are to survival.
I wonder what population pyramids would look like for academia. In each field and subfield, how many people are PhD students, postdocs, and faculty?
If every PhD student was guaranteed to become faculty, and the number of faculty stayed fixed, you could roughly estimate what this pyramid would have to look like. An estimate for the US might take an average 7-year PhD, two postdoc positions at 3 years each, followed by a 30-year career as faculty, and estimate the proportions of each stage based on proportions of each scholar’s life. So you’d have roughly one PhD student per four faculty, and one postdoc per five. In Europe, with three-year PhDs, the proportion of PhD students decreases further, and in a world where people are still doing at least two postdocs you expect significantly more postdocs than PhDs.
Of course, the world doesn’t look like that at all, because the assumptions are wrong.
The number of faculty doesn’t stay fixed, for one. When population is growing in the wider world, new universities open in new population centers, and existing universities find ways to expand. When population falls, enrollments shrink, and universities cut back.
But this is a minor perturbation compared to the much more obvious difference: most PhD students do not stay in academia. A single professor may mentor many PhDs at the same time, and potentially several postdocs. Most of those people aren’t staying.
You can imagine someone trying to fix this by fiat, setting down a fixed ratio between PhD students, postdocs, and faculty. I’ve seen partial attempts at this. When I applied for grants at the University of Copenhagen, I was told I had to budget at least half of my hires as PhD students, not postdocs, which makes me wonder if they were trying to force careers to default to one postdoc position, rather than two. More likely, they hadn’t thought about it.
Zero attrition doesn’t really make sense, anyway. Some people are genuinely better off leaving: they made a mistake when they started, or they changed over time. Sometimes new professions arise, and the best way in is from an unexpected direction. I’ve talked to people who started data science work in the early days, before there really were degrees in it, who felt a physics PhD had been the best route possible to that world. Similarly, some move into policy, or academic administration, or found a startup. And if we think there are actually criteria to choose better or worse academics (which I’m a bit skeptical of), then presumably some people are simply not good enough, and trying to filter them out earlier is irresponsible when they still don’t have enough of a track record to really judge.
How much attrition should be there is the big question, and one I don’t have an answer for. In academia, when so much of these decisions are made by just a few organizations, it seems like a question that someone should have a well-considered answer to. But so far, it’s unclear to me that anyone does.
It also makes me think, a bit, about how these population pyramids work in industry. There there is no overall control. Instead, there’s a web of incentives, many of them decades-delayed from the behavior they’re meant to influence, leaving each individual to try to predict as well as they can. If companies only hire senior engineers, no-one gets a chance to start a career, and the population of senior engineers dries up. Eventually, those companies have to settle for junior engineers. (Or, I guess, ex-academics.) It sounds like it should lead to the kind of behavior biologists model in predators and prey, wild swings in population modeled by a differential equation. But maybe there’s something that tamps down those wild swings.
4 gravitons 
It seems to me that having an attrition rate very much above zero is a misallocation of resources. If the ultimate outcome is that a physics Ph.D become a data scientist, or a quantitative trader, or whatever the most recent fad is, surely it would be better to determine that as early as possible and not waste time training them to do something largely unrelated. A Ph.D. in physics is not optimized to train people for any job other than that of an academic researcher (nor should it be). I am somewhat skeptical of claims that it has been the best possible path into some newly emerging career, but if this occurs it must be accidental (and thus likely rare) and very brief. It is surely more effective to just train people directly to do the job they will end up with.
The current situation reminds me a bit of people who sell learning Latin on the basis that it will help with learning romance languages, when if your goal was to learn e.g. French you’d get there much more quickly, and with less effort, if you just studied French (even if it’s true that French is easier for one who knows both English and Latin than for one who only knows English etc).
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I’m not even sure what “zero attrition” even means. Lots of high school students apply to University intending to become physics majors. Many end up not doing that. Of those who do, many apply to graduate school, with the intent of getting PhDs. Many end up not doing that. Of those who do get PhDs, many apply for postdocs. Etc …
If you want zero attrition between stages n and (n+1), then the attrition needs to take place somewhere between stage 1 and stage n. It’s not zero; it’s just taking place somewhere else in the chain.
What’s the best place to do that? Do we want to select which students are going to eventually become physics faculty while they are still in primary school? That would be madness.
Better to accommodate as many people at each stage, who have the interest and aptitude for that stage, as you have the resources to accommodate.
There are lots of other things that people end up doing with their lives , for which a background in physics is useful. And if physics is fun (at least I think it is), why deprive them of that pleasure prematurely, through some unnecessary act of social engineering designed to (what?) save them some future disappointment?
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One thing I think I agree with you on: it makes zero sense for individual scientists to be trying to implement this kind of thing, or for universities to unilaterally impose ratios like the university of Copenhagen one I mentioned. I can unreservedly call that a dumb policy.
But I don’t think you can avoid someone doing social engineering here. The reason why is hidden in your comment: “as you have the resources to accommodate”. The distribution of those resources, between funding for PhD positions, postdoc positions, and faculty positions, is a result of policies of different organizations, and many of them have the goal of maintaining a certain academic population, even if they don’t math out that goal in detail. For example, the EU’s MSCA postdoc fellowship grants are explicitly training-focused, the choice of how many of those to fund in each field is fundamentally a social engineering choice about what the EU wants EU academia to look like. Similarly, when research-focused universities make decisions about departmental funding and departments make the decisions they can make after that, people are making decisions about what they want their corner of academia to look like. I suspect very few of these decisionmakers are thinking about it in those terms, but it’s really the only terms by which you can assess those decisions. We can’t track the benefits of most individual scientific results, just the overall effect of maintaining a population of scientists of a certain size and composition.
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>Better to accommodate as many people at each stage, who have the interest and aptitude for that stage, as you have the resources to accommodate.
This logic seem to pre-suppose that each level is independent (in terms of resource availability). However, this is surely not completely true, especially at the Ph.D. level and up. If the levels compete for resources to some extent (and from the point of view at the highest organizational level they must, since money is fungible, and non-fungibility must come from legal or administrative constraints), then it makes sense to ask what is the ideal ratio between e.g. postdocs and Ph.D. students, or between faculty and postdocs, even if that implies taking fewer people than you could at a given level (in order to take more at another level).
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