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My coworkers are pursuing a generalization of one of my (recent) results. Is it wrong of me to frown a little on this? I would prefer it if they had an original idea of their own, or that if that they had to generalize a result, it would either be one of their own or one of someone they do not know.

The way I see it, a paper has a certain lifespan in terms of being read and cited. Once it has been generalized, that lifespan is in most cases over. If someone wanted to understand a theorem, they would probably look for the most general version. Of course, this does not always apply, for example if the work represents a milestone of some kind. One consequence of obsolescence is the stream of citations to my paper is short circuited. This will, in a sense, benefit them at my expense. Of course, I realize that my paper will eventually (hopefully) be generalized and become obsolete (i.e. no longer state-of-the-art). I just rather prefer that it wasn't my coworkers who are working towards that goal (they even started while I was still drafting my paper).

Please note: I do not mean for this to be read as a rant or a complaint. I do understand how science works by expanding on previous knowledge. I just want to know how others feel about the prospect of their research becoming obsolete, and how to approach that from the perspective of someone in the beginning (and at the same time, possibly the end) of their academic career. I imagine that for a professor such a thing would not be a big deal, for a number of different reasons.

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    Why aren't you cooperating with them on the generalization? It seems both natural and proper. – Buffy Oct 3 '18 at 17:39
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    Isn't this a fairly common and natural pattern in academic research? (I'm not an academic) – Jamie Clinton Oct 3 '18 at 18:43
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    Are you "frowning a little" because the fact is, you don't have any new ideas of your own to work on? In my view, if "the rest of my working life" is too short to follow up all my own research ideas, a few past projects going beyond their use-by date is no big deal - but YMMV of course. – alephzero Oct 3 '18 at 18:58
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    @aleph I added the note and emotional-responses tag hoping to avoid this type of comment. But to answer your question. I have ideas. But I will be evaluated on my ability to publish papers and get a number of citations that are above the average of the journals I publish in. The pipeline looks something like: write paper (6 months), get published (1-2 years), get cited (2+ years). The last two steps are mostly passive, but they create a large delay from idea to pay-off. If your early projects fail to take off, then you can't really compensate by doing new stuff within the required time frame. – Asdf Oct 3 '18 at 19:27
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    I do not understand this. Someone is reading your work and cares enough to actually try to extend it. So often you write papers and you feel like no one is reading them, and all the citations you get are meaningless, of the "oh here is some other related stuff" type. In your case, your results have been the basis of further research. I think this looks better for you than a paper that no one follows up on. Also, the notion that a paper stops being cited once it is generalized is very dubious. – Sasho Nikolov Oct 4 '18 at 4:35
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While I sympathize with you, I find it hard to answer your question.

On the one hand, as phrased you are asking whether an emotional response is valid. Well, it is not really for anyone other than you to determine the validity of your emotional responses, and in all of my experience, "That is not a valid emotional response" is rarely a useful piece of advice. On the other hand, your question is pitched in a certain level of generality, but understanding why you feel the way you do seems to require knowing more particulars of your situation than you have disclosed.

But let me say what I can and what might be helpful:

The way I see it, a paper has a certain lifespan in terms of being read and cited. Once it has been generalized, that lifespan is in most cases over. If someone wanted to understand a theorem, they would probably look for the most general version. Of course, this does not always apply, for example if the work represents a milestone of some kind. One consequence of obsolescence is the stream of citations to my paper is short circuited. This will, in a sense, benefit them at my expense. Of course, I realize that my paper will eventually (hopefully) be generalized and become obsolete (i.e. no longer state-of-the-art).

Since you speak of "theorems," I gather you are working in mathematics. (This is corroborated by one of your other questions, where you identify yourself as working in applied mathematics.) I am also a (pure) mathematician, and the way you describe "obsolescence" is neither the way I think about mathematical results nor how I have heard other mathematicians talking about them. Maybe it is quite different in applied mathematics, but in pure mathematics there is not any prescribed lifespan on papers being read and cited. To try to quantify this, I just looked back over my last 10 accepted papers, and for each one identified the earliest cited paper. Of these ten papers, the latest one was published in 1976. (Moreover the 1976 paper came from a five page note with only a few citations.) In other words, in all of my recent papers I have cited papers that are more than 40 years old, and in fact usually older than that. In my department I have many colleagues who are 10-20 years older than I but who have a similar number of publications to me (publication pressures have risen in recent years). Most of these colleagues have higher total citation numbers than I do -- I think because their papers from 10, 20, 30...years ago continue to be cited. My most highly cited works were published in 2013, 2005, 2006, 2010 and 2003, respectively.

[Moreover, in mathematics, citation numbers are not (yet!) the ultimate metric of academic worth. Papers written on finite graphs tend to get more citations than papers written on admissible representations of p-adic groups because there are more people working on the former and many more people who know what the former are. I think most mathematicians realize this.]

So I have to wonder about the specific situation you are describing. In a different question, you mention a colleague of yours who worked on the same problem as you and came up with a result that was in some but not all ways more general, and then you published at least two papers together. I don't understand why this would "short circuit" your citations. Now you describe a situation in which your colleagues are working on generalizing one of your results, apparently without any new ideas. In this latter situation especially, I would expect that if they publish an improvement of your results using ideas essentially due to you, then that should augment your results in every way (including citations), not detract from it. (You are aware that senior mathematicians do this all the time, and the work of their students is usually viewed as an extension of their own work, I trust?)

Then you say:

I just rather prefer that it wasn't my coworkers who are working towards that goal (they even started while I was still drafting my paper).

If it gets to the point of an independently published generalization of your work, then I don't see how it makes any difference whatsoever if your coworkers were involved. However, before that happens the fact that it is your coworkers puts you in a much better situation: namely, in the worst case you have much more advance knowledge of what they are working on and can plan accordingly. In the best case you can pursue a collaboration with them in whatever way seems best to you.

If I may take a guess -- are you perhaps most upset by the fact that your coworkers have chosen to pursue these generalizations of your work without your involvement, so that they seem to be competing with you right under your nose? I could understand why that would be upsetting. If you feel that way, I think you should be much more proactive about collaborating with them.

  • Sorry Pete, but your bibliometrics are extremely dubious, and subject to all sorts of bias. The concept of a citation half-life is a rather standard concept in bibliometrics. You can argue that it's not a factor in mathematics or that the half-life is too long to matter or make a solid bibliometric case that it doesn't exist, but the anecdotal hand-waving in this answer is not too far from arguments that climate change doesn't exist because it was cold last week. – E.P. Oct 3 '18 at 20:51
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    @E.P., I'd strongly agree with Pete that, in the parts of "pure" mathematics I follow, in many cases citations peak surprisingly-later, like 20 or 30 years later. Some of my (better!) papers got close-to-zero citations for many years, but/and did "finally" get quite a few. Yes, sometimes "the original paper" gets superceded to the extent it's no longer cited at all, though I must say that I myself try to preserve that record in my bibliographies. – paul garrett Oct 3 '18 at 23:04
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    @paulgarrett And then results get so famous that one doesn't bother to cite them, but we still give names, e.g., "By Wedderburn's theorem, ..." (and you don't even know which Wedderburn's theorem I mean yet!) – Kimball Oct 4 '18 at 3:31
  • @E.P.: In responding to "obsolescence" I spoke of the citation life rather than the half-life. People in some other STEM fields would I think be very interested to hear that it is common to cite work that is more than 40 years old. I don't see much resemblance to arguments about climate change, but sure, one could ask for a more systematic, quantitative analysis. See e.g. researchgate.net/publication/…. – Pete L. Clark Oct 4 '18 at 12:33
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    @PeteL.Clark The core point is that your sampling is backwards. If you want to make the point that a substantial fraction of old papers have long citation lives, then you need to sample old papers and see whether their citations stay up over the years, not sample new papers, which are subject to e.g. congregating their old-paper citations on a small subset of the old-papers population. The situation is similar to the old 'paradox' that allows "most children live in large families" and "most parents have small families" to describe the same population. – E.P. Oct 4 '18 at 12:48
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Short answer, two possible approaches:

  • collaborate with your coworkers. From what you write, it sounds like they may have already suggested and you may have been hesitant because you wanted unique ownership. Science is collaborative and you will both benefit from this collaboration

  • keep being original, create new streams of research. Some academics enjoy new challenges, then get quickly bored and prefer breadth (variety of research areas one contributes to) to depth (being leading expert in a very specific subfield). There is nothing wrong with enjoying breadth in research areas.

My feeling is that you are stuck in the middle. Just pick one of two routes and you will be happy again in no time 🙂

  • Actually, I want to do something new or different. The lack of such ambition on their part is one of the things that frustrate me in this situation. I am in a new project now, so I would like to focus on that. However, I feel that they are pulling me back into the old project. I just have to commit to the new project and ignore what they are doing :) – Asdf Oct 3 '18 at 18:21
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    @Asdf: If your coworkers' project is beneath you, how does it diminish your work? How are they going to make your work obsolete without any new ideas? I confess I don't really get it. – Pete L. Clark Oct 3 '18 at 18:25
  • They prove the same theorem in a more general setting. The theorem is about the convergence of dynamical systems. It is interesting because it was unexpected. Now they attempt to show that the theorem applies under some weaker assumptions. This is not interesting to me, because if this type of theorem holds under the strong assumption, then someone always makes an extension under the weaker assumptions. Doing it can be hard, but the idea of doing it is super obvious. However, because this is applied math, the weaker assumptions are important for 'applications' (i.e. for motivations). – Asdf Oct 3 '18 at 18:40
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    @Asdf: Thanks for your response. I can see why you might not be interested in this kind of generalization (and also I can see why your colleagues would be interested!). But to have other people work on technical strengthenings of your unexpected theorem is just about the most positive outcome I can think of. Of course I have to go back to a point in my answer: you are entitled to feel the way you feel about it, and my telling you to feel differently is probably not going to be so helpful. – Pete L. Clark Oct 4 '18 at 18:21
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Ask yourself what goal you want to achieve. Do you want your colleagues to publicly apologize to you? Postpone their publications until yours gets enough citations? Abandon their work on the topic altogether? Include you in their paper as a co-author?

Unless you can define a specific goal which you deem achievable and are ethically OK with, the best advice I can give is to get yourself comforted by close friends over a beer, then get over it and move on.

If you feel that including you as a co-author could make sense, think about what you could contribute to colleagues' research (other than the paper you've already published), then speak with them about this possible collaboration as soon as possible.

  • Actually, I just want some peace of mind to be able to better focus on another project. I mainly wrote this post to process my feelings and get through the emotional labor of the whole thing. Co-authorship would of course be nice, but it is not something I feel I must or should have. – Asdf Oct 4 '18 at 22:46
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One consequence of obsolescence is the stream of citations to my paper is short circuited. This will, in a sense, benefit them at my expense.

Possibly the opposite. Citations, IMO, tend to quote the base paper as well as the generalization.

This will, in a sense, benefit them at my expense. Of course, I realize that my paper will eventually (hopefully) be generalized and become obsolete (i.e. no longer state-of-the-art). I just rather prefer that it wasn't my coworkers who are working towards that goal (they even started while I was still drafting my paper).

You should look upon it as having been granted the privilege of having found some knowledge to humanity and having your work rewarded by inspiring others to extend it.

The vast majority of people will never experience discovering something like this and all too many people never have the luck to inspire others by their labors.

Historically (centuries past) it was not uncommon for scientists to deliberately keep discoveries to themselves to profit from them in some way. For example the dispute between Cardano and Tartaglia over the solution of a type of cubic equation. These days are (hopefully) gone and it's now a slightly better system of publishing as fast as possible and chasing citations (as they are a kind of bizarre currency). However ultimately you should try and look at the personal reward of discovery and sharing as your only rewards. Those are the only rewards you can be reasonably certain to get.

You have a small (?) place in the written history of the world. Be happy, most do not through no fault of their own.

You don't want to be part of the new project (I'd at least keep in touch with them if possible), so there's no gain in thinking about it.

Let this go and move on.

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    I agree that the original paper is often quoted together with the generalisation. So this should not affect you on citation side either. Typically citations drop to zero when new findings invalidate the assumptions of your paper. – famargar Oct 3 '18 at 19:55
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    I'm not an academic, but this is similar to my thinking. He should be proud that they found his work worthy of expanding on, not annoyed that they're replacing it. – Barmar Oct 4 '18 at 1:55
  • @Barmar I had the similar reaction to user Asdf when I finished my first paper and somebody picked it up - They are taking my baby! The annoyance ended only after my second like of research started to be fruitful. Only then I appreciated that others picking up where I left my work was a compliment! – famargar Oct 4 '18 at 13:20
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    @Asdf you will. Early success is a good predictor of having the right skill set. Now all you need is the right mindset. And recognising the problem (the emotional response) means you are already close to the solution (letting it go and start being creative again). Best of luck! – famargar Oct 5 '18 at 7:28
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    In case it wasn’t clear, having a paper that is interesting enough for your collaborators in your institution to inspire further research, at an early stage of your career, is the early success I was referring to – famargar Oct 5 '18 at 15:13
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One consequence of obsolescence is the stream of citations to my paper is short circuited. This will, in a sense, benefit them at my expense.

Increasing the amount of knowledge not only benefits them but also the scientific community and humankind as a whole. This is very positive effect of obsolescence of scientific results.

Of course, I realize that my paper will eventually (hopefully) be generalized and become obsolete (i.e. no longer state-of-the-art). I just rather prefer that it wasn't my coworkers who are working towards that goal (they even started while I was still drafting my paper).

This sounds a bit like a missed chance for more cooperation between you and your coworkers and because of that possibly some waste of resources. Did they contact you and ask you for your further plans, maybe suggesting a further cooperation? Were they open about what they are working on? If not, your coworkers might simply have decided to leave you out of future developments. You could then try to compete with them and be faster or leave this particular field to them and do something else.

I did not experience direct competition from coworkers, but in cases of competition from other groups I always tried to be as fast as possible.

One lesson for the future could be that collaborations have a social dimension and that trust about future arrangements matters. Collaborations can be very long term and fruitful. It's probably a good idea to stick with those that worked well for you.

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