Bill Harris writes:
I was re-reading your and Shalizi’s “Philosophy and the practice of Bayesian statistics” [see also the rejoinder] and noticed a statement near the end of section 6 about paradigm shifts coming in different magnitudes over different time spans. That reminded me of the almost-mystical ideas surrounding 1/f (f being frequency”) noise in some areas — the notion that almost everything exhibits that effect, and that effect extends to arbitrarily low f. (I sense the idea only gets mystical when f gets low enough so that the event that may happen stochastically is really big—say, you model the height of waves in the Atlantic as 1/f and discover that, at some low frequency, Bermuda becomes submerged. In other words, does the same mechanism that accounts for physical vibrations in the range of Hertz also account for the creation and destruction of islands that may occur in the range of reciprocal centuries?)
When I first encountered 1/f noise in the area of electronic noise measurement, I was intrigued, but I’ve not read seriously in that field for perhaps 25 years or more. Still, I thought you might find it of interest. Perhaps it could help smooth some of the challenges you point out in Kuhnian philosopy and contradict the so-called “law of the excluded middle,” in which (in Kuhnian terms) everything is either normal science or a paradigm shift, or so I presume.
Here are three links on 1/f noise:
– “1/f Noise.” Marvin S. Keshner. http://www.control.aau.dk/uav/reports/12gr1052/sources/articles/1_over_f_noise_Keshner.pdf
– Scholarpedia. http://www.scholarpedia.org/article/1/f_noise
– “1/f noise: a pedagogical review”. Edoardo Milotti. http://arxiv.org/pdf/physics/0204033
Does 1/f noise make any sense in the Kuhnian paradigm context?
My reply: I don’t know, but I think it’s safe to say that Cosma will have some strong opinions on the matter. I did take a look at the Scholarpedia article, which seems excellent.
I’m guessing Cosma will express skepticism about all this. Our article does have that bit about the fractal nature of scientific revolutions, but that’s something that I wrote that Cosma didn’t really like very much, he was just nice enough to let me keep it in. It’s one of my pet ideas (and, as a commenter noted, perhaps related to the fractal nature of scientific taxonomies) but I’ve never had any idea of how to study it formally.