Balancing Fact and Formula in the Science of Complex Systems: The example of 1/f spectra.

Abstract:

More than 100 years ago, Thomson and Tait's classic "Treatise on Natural Philosophy" 
cautioned its readers against "considering the formula and not the fact as physical
reality". Deciding what the facts actually *were*, then as now, was left as an exercise
for the student! Complex systems, of which space plasmas are a very rich example, show
many cases [1] of what Thomson & Tait were talking about. I will discuss one such case
today-the "1/f" spectral shape seen in many areas of physics. As Mandelbrot pointed out in
several papers in the mid 1960s [2] this could be explained by long range dependence (LRD)
in a stationary model, or various forms of nonstationarity. He was at pains to urge us to
use our eyes as well as formalism, and I will discuss several results inspired by this
approach, including new Bayesian methods for choosing between LRD models [3], and work on
a dynamical origin for the Hurst effect [4].

[1] Watkins, Bunched Black Swans, Invited GRL Frontiers Review, 2013

[2] Graves et al, A Brief History of Long Memory, Submitted 2014

[3] Graves et al, Efficient Bayesian inference for long memory processes, Submitted 2014

[4] Watkins and Franzke, Hurst Without Joseph, In prep.