Critical mass for academic research

The current issue of the magazine "Mathematics Today" (vol 47, no 3, dated June 2011) includes an article Critical Masses of Research Groups in the Mathematical Sciences
in which the authors (Ralph Kenna and Bertrand Berche) have analysed the research ratings of academic groups in the United Kingdom, as recorded in the Research Assessment Exercise of 2008 (RAE2008). It is based on more extensive work that they have published (Critical mass and the dependency of research quality on group size).

In summary, the authors plotted the outcome of RAE2008 (measured as a quality between 0 and 100) against the size of the research group that reported to RAE2008. This yielded scatter diagrams, which can be interpreted as being piecewise linear, with no, one or two "knees" or breakpoints where the slope changes. Small groups get small scores, and the score increases rapidly as the group size increases. At a critical size, the slope is reduced, and the score increases more slowly. A second "knee" means that the slope is reduced still further, almost to flatness.

The interpretation of the "knees" is that they represent critical sizes for research groups. The lower one is the smallest viable size; less than this, and the quality of the research falls sharply. The upper one represents an upper limit, beyond which adding extra researchers will not add to the quality of the output.

Having said that, the authors report that in pure mathematics, the lower critical mass is at most 2, and the upper one is at most 4. For applied maths, the figures are 6 and 13.

But for statistics and O.R., the critical sizes are 9 and 18. In other words, to produce good academic output, O.R. scientists and statisticians need to be in a large group. Our work makes us gregarious; we work well with other people around us. Since I read the article, I have wondered why this should be, and concluded that it is in the nature of academics in these disciplines that they work together well, they have complementary skills, and those skills are heterogeneous, and they like to collaborate in teams. It chimed with my experience and observations. At various times I have been in groups of between 9 and 18, where we worked well together, and the interplay of ideas flowed. I have also been in a smaller group, and then there was much less academic stimulation. One might think that this would also be true of applied mathematicians, but I suspect that they are more homogeneous in academic expertise than those in stats/O.R.. And the pure mathematics area is much more dependent on individuals with their ideas and theories than those who work with mathematical models and statistical data. (Pure mathematicians -- I love you a lot! -- but you will probably admit to flying solo much of the time.)

Many years ago, I found a spoof paper which was written by M.V.Wilkes under the pseudonym H.W.O.Petard on the optimum size of an establishment. It argues that time gets wasted by people reporting to one another ....