Logistic functions are everywhere – hockey sticks always break eventually.
Geneticist Casey Bergman writes, about the state of science:
On a regular basis I see how the current system negatively affects the lives of talented students, post-docs and early-stage faculty. I have for some time wanted to write about my point of view on this issue since I see these trends as indicators of bigger changes in the growth of science than individuals may be aware of. I’ve finally been inspired to do so by a recent piece by Euan Ritchie and Joern Fischer published in The Conversation entitled “Cracks in the ivory tower: is academia’s culture sustainable?“, which I think hits the nail on head about the primary source of the current problems in academics: the deeply flawed philosophy that “more is always better”.
He asserts that the era of exponential growth in academic research is over, and attributes this conclusion “almost entirely derived from a book written by Derek de Solla Price entitled Little Science, Big Science“, a book which may be hard to track down. (It’s just the sort of thing that Amazon someone ought to scan and post. Is there some way to put in a request?) Anyway, Bergman writes
Price pointed out that the doubling time of the number of scientists is much shorter than the doubling time of the overall human population (~50 years). Thus, the proportion of scientists relative to the total human population has been increasing for decades, if not centuries. Price makes the startling but obvious outcomes of this observation very clear: either everyone on earth will be a scientist one day, or the growth rate of science must decrease from its previous long-term trends. He then goes on to argue that the most likely outcome is the latter, and that scientific growth rates will change from exponential to logistic growth and reach saturation sometime within 100 years from the publication of his book in 1963
Much more at Bergman’s blog entry. Very similar to arguments about post-growth economics.