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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, Dan Navarro gave an example of a paradigm shift within cognitive psychology.

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?)


Scientific progress is fractal in size of problem and in time scale. (As always, any references to related work in the history or philosophy of science would be appreciated.)


  1. roby says:

    a reference from sociology: Chaos of disciplines

  2. Cosma says:

    Donovan, Laudan and Laudan (eds.), Scrutinizing Science, is a collection of empirical case-studies on scientific change, and how well the cases conform to the Kuhnian description. If I recall correctly, nothing looks exactly like what Kuhn says a paradigm-shift should look like, and some are really very different indeed.

    One of the contributors to that volume, Deborah Mayo, has a very good book of her own, Error and the Growth of Experimental Knowledge, on Kuhn, Popper, Bayes, model testing and the philosophy of statistics.

  3. Andrew says:

    Roby and Cosma,

    Thanks for the references. I've never been convinced by anything of Kuhn, but I realized that the "scientific revolution" idea fit with my research progress at all levels.

    Just today, I had a meeting with two collaborators (we are studying models for serial dilution assays for lab measurements of allergens) and I realized an error in my whole conception of part of the problem (an extension of our model to contaminated samples).

    And the way we realized this was by carefully following the implications of our (wrong) idea until we realized its contradiction. So I definitely see the similarity between micro-level and macro-level "revolutions."

  4. Cosma:

    Thanks for the pointer to Deborah Mayo–much of her work is available online through JSTOR–you've just doubled my reading backlog!

  5. Uri says:

    For the record, Andrew Abbot suggested the principle of fractal internal divisions of science back in "the system of professions" (1988, pp 316-18), and explicated it to the social sciences in "The Chaos of Disciplines" (2001) which has a nice fractal on the cover. Maybe not SO '80s.