Which might be helpful to some.

]]>That’s a pretty unappealing way to think about dynamical systems imo!

]]>I have some experience with chaos/fractals in ecology and epidemiology (measles epidemics, lynx/hare cycles, etc.) and more recently with neurological (EEG) data (an undergraduate student did a review of linear and nonlinear metrics for characterizing EEGs).

While it’s reasonable to hope that nonlinear metrics (such as fractal dimension, Lyapunov exponent, various entropies) would be a powerful way for capturing differences in time series driven by strongly nonlinear processes, in practice this is (1) harder than you think (a lot of the estimation methods do badly in very noisy systems, or where the noise is anything other than Gaussian/white) and (2) IMO, typically a dead end relative to pursuing mechanistic models. The *combination* of plausible mechanistic models with nonlinear metrics as probes is great, but trying to use nonlinear metrics by themselves, or nonlinear metrics accompanied by armwaving about the dynamics, doesn’t seem to have been very fruitful.

]]>All this talk of “non-Euclidean geometry” makes me feel like I’m in a H.P. Lovecraft story though…

]]>This sure sounds like gobbledygook (or word salad?) to me.

]]>Said Chesterton, approximately.

]]>That being said, I’m not sure how to parse this:

A classical view is that motor learning has distinguishable early, intermediate, and late phases. A recent view is that motor learning is the acquisition of an abstract equation of motion that specifies the time evolution of a pattern of coordination. The pattern is expressed by a collective variable that enslaves or orders component subsystems that, in turn, act on and generate the collective variable. In these latter terms, early learning resolves the collective variable and its motion equation, intermediate learning stabilizes and standardizes the subsystems or active degrees of freedom (DFs) producing the collective variable’s dynamics. The preceding ideas, and the phase-space reconstruction methods required to determine active DFs, are developed in tutorial fashion in the context of an experimental investigation of learning a bimanual rhythmic coordination. Results show that intermediate learning reduces the dimensionality of the learned coordination’s dynamics and renders those dynamics more deterministic. The tutorial development relates the preceding concepts, results and methods of analyses to (a) the contrast between Poincaréan and Newtonian dynamics, (b) contemporary interpretations of random processes, (c) definitions of DFs in respect to Bernstein’s problem, (d) the potential contribution of chaos to the adaptability of a learned coordination, and (e) possible links between active (dynamical) DFs and the control variables r, c, and μ identified by the λ hypothesis.

Mitra, S., Amazeen, P. G., & Turvey, M. T. (1998). Intermediate motor learning as decreasing active (dynamical) degrees of freedom. Human Movement Science, 17(1), 17-65.

]]>Sapoval et al., “Self-stabilised fractality of sea-coasts through damped erosion,” arXiv:cond-mat/0311509

]]>Subtle is the weasel word for swamped by other, more powerful, effects.

]]>Working out what is happening is someone’s head is hard, but sometimes those counterintuitive processes produce beautiful things.

Therefore, our psychological processes must be determined by quantum physics, nonlinear dynamics, and the mathematics of fractals. QED.

]]>“Obviously, this [fractal geometry] is in opposition to the ancient, conventional vision based on Euclidean geometry and widely adopted concepts, such as homeostasis, linearity, smoothness, and thermodynamic reversibility, which stems from a more intuitive—but artificially ideal—view of reality.”

I don’t know what to call that. Given the recent discussion on this blog, I’m getting more careful with words like “disingenous” and “dishonest”. It certainly seems designed to play to the kind of postmodern attitude that dismisses classical techniques just because they’re classical, without discussing how well they work. After all, Hausdorff dimension is a generalization, not a rejection, of Lebesgue measure, which was developed in order to deal with the stuffy, linear topic of Fourier series. Those in turn were developed to deal with the (equally classical, linear, and smooth) heat equation, which is intimately bound up with Brownian motion, one of the central examples of roughness and self-similarity. I don’t have the expertise to comment on the quality of Forsythe’s work or Brown’s criticism, but I think the term “fractal zealot” gets at something real.

]]>You’re talking about Objects of the class “Pauline Kael”, which also includes Alice Waters, Mata Hari, Agatha Christie, and Helen Keller. Also good cases can be made for Queen Elizabeth 1, Margaret Mead, Oprah Winfrey, Rachel Carson, Mary “Mother” Jones, Temple Grandin, Marie Curie, Margaret Thatcher, Mary Baker Eddy, and Ellen Willis. I wouldn’t put Susan Sontag in this class.

]]>The most influential baseball stadium designer of the last three decades has been Janet Marie Smith, who invented the “retro look” at Baltimore’s Camden Yard in the 1990s:

http://www.sportsbusinessdaily.com/Journal/Issues/2017/03/20/Champions/Janet-Marie-Smith.aspx

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