The fractal nature of scientific revolutions

With all this discussion of Kuhn and scientific revolutions, I’ve been thinking of the applicability of these ideas to my own research experiences.

At the risk of being trendy, I would characterize scientific progress as self-similar (that is, fractal). Each level of abstraction, from local problem solving to big-picture science, features progress of the “normal science” type, punctuated by occasional revolutions. The revolutions themselves have a fractal time scale, with small revolutions occurring fairly frequently (every few minutes for an exam-type problem, up to every few years or decades for a major scientific consensus).

For example . . .

At the largest level, human inquiry has perhaps moved from a magical to a scientific paradigm. Within science, the dominant paradigm has moved from Newtonian billiard balls, to Einsteinan physics, to biology and neuroscience and, I dunno, nanotechnology? Within, say, psychology, the paradigm has moved from behaviorism to cognitive psychology. In the comment on my earlier blog entry, Danielle Navarro gave an example of a paradigm shift within cognitive psychology. Although if you were to read this Regis College blog post on radical behaviorism, one might come to the conclusion that the paradigm has shifted back towards behaviorism, with new applications and studies.

But even on smaller scales, I see paradigm shifts. For example, in working on an applied research or consulting problem, I typically will start in a certain direction, then suddenly realize I was thinking about it wrong, then move forward, etc etc. In a consulting setting, this reevaluation can happen several times in a couple of hours. At a slightly longer time scale, I’ll commonly reassess my approach to an applied problem after a few months, realizing there was some key feature I was misunderstanding.

So, anyway, I see this normal-science and revolution pattern as fundamental. Which, I think, ties nicely into my Bayesian perspective of deductive Bayesian inference as normal science and model checking as potentially revolutionary.

(I guess that wasn’t so trendy—fractals are so ’80s, right?)

Summary

Scientific progress is fractal in size of problem and in time scale. Some further references are in the comments from our original post on this from 2005.

Further posts on the topic:

Kuhn, 1/f noise, and the fractal nature of scientific revolutions (from 2013)

Statistical Workflow and the Fractal Nature of Scientific Revolutions (from 2020)