A colleague recently complained to me about a postdoc of his who is still spending most of his/her time working on manuscripts related to Ph.D. research, even after being a postdoc for 2 years, and seems unable to do that and postdoctoral research.
I certainly spent postdoctoral time writing papers from my Ph.D. research, but I also worked on my new research projects and I enjoyed doing both. This fondness for having simultaneous projects at different stages of 'completion' has been a characteristic of my career, but I first discovered this during my postdoc.
For me, being a postdoc was an excellent time to do research and learn new things, without the time-consuming ancillary aspects of being a student (classes, exams) or the time-consuming administrative and teaching responsibilities of being a professor. (For this discussion, I am ignoring the harassment and discrimination I experienced as a postdoc; I enjoyed my work, but I did not like my work environment.)
I like having some research projects that are at the initial (crazy idea) stage, others that are just getting underway (with all the promise of discovering something interesting yet to come), others that are deep into the data/analysis stage (with all the intrigue and confusion of figuring things out), and others that are at various stages of being written up and coming together as manuscripts.
None of this is linear. Some projects go in unexpected directions. Some projects sprout one or more new projects. Others end up being kind of circular. Some terminate (after months, years, decades).
When I was a postdoc, I learned that I liked this, but I also started learning how to do this. Whether you end up balancing multiple research projects and teaching and administrative tasks, or some subset of research-teaching-service, being a postdoc is a good time to get more experience with multitasking of the sort required for your later career.
I don't believe that you have to work 24/7 to do this, but you do need to find a way of making progress on various projects simultaneously. The process is probably similar to the way that we figure out how to balance career and personal life.
As for my colleague, I told him to talk to his postdoc and make sure that his expectations are clear. They can probably work out various short- and long-range goals that will help them both. Most postdocs work on projects from previous positions -- Ph.D. research or a previous postdoc -- so this is an important issue that postdoc and supervisor should work out through discussion, ideally at the start of the postdoctoral appointment.
6 months ago