Good to have an agreement on ubiquity of 1/f scaling, I also am of the opinion experimental control is essential (see Hasselman, 2013). I would add that direct confrontation of theoretical predictions is crucial as well:
"In order to advance scientific knowledge about scaling phenomena in living systems a program of strong inference that aims to produce closed theories of principles is needed. In order to reach this goal, empirical inquiries need to go beyond describing scaling phenomena in different populations in the context of impaired performance or pathology (e.g., Goldberger et al., 2002; Gilden and Hancock, 2007; West, 2010; Wijnants et al., 2012a). Several recent studies reveal scaling phenomena can be brought under experimental control, which is essential for a program of strong inference (e.g., Kello et al., 2007; Wijnants et al., 2009; Van Orden et al., 2010; Correll, 2011; Holden et al., 2011; Kuznetsov et al., 2011; Stephen et al., 2012). The diverging theoretical predictions examined in most studies reveal that the observed waveforms are more likely to originate from interaction-dominant complexity than from component-dominant mechanics (also see Turvey, 2007; Kello et al., 2010; Diniz et al., 2011)."
From: http://journal.frontiersin.org/article/10.3389/fphys.2013.00075/full
At least these articles revealing experimental control over scaling exponents should have been discussed:
- Wijnants et al., 2009 (Practice motor learning http://fredhasselman.com/main/wp-content/papercite-data/pdf/wijnants2009.pdf)
- Wijnants et al., 2012 (Speed-Accuracy TradeOff http://dx.doi.org/10.3389/fphys.2012.00116 )
- Correll, 2008; 2011 (Correll, 2008 was replicated, manipulation failed, but all subjects showed 1/f noise)
- Kuznetsov et al., 2011; (instruction manipulation)
Then, there are many more studies that make risky predictions or directly confront two or more competing predictions (in fact, all predictions in 1/f studies are more risky than mainstream, because they concern interval predictions and not merely > 0). In any case, they do much more than 'just' show another case of 1/f noise in some population.
- Van Orden (2005) Tested presence of a low-frequency plateau predicted by AR models by recording a timeseries of several hours.
- Den Hartig et al. (Rowing proficiency https://www.researchgate.net/publication/274318392_Pink_Noise_in_Rowing_Ergometer_Performance_and_the_Role_of_Skill_Level )
- Wijnants et al. 2012 (correlations between scaling and reading in dyslexic readers, but not in average readers http://dx.doi.org/10.1007/s11881-012-0067-3 )
- Lowie et al. 2014 (multilingual speech production: http://www.tandfonline.com/doi/abs/10.1080/10407413.2014.929479 )
All the best,
Fred
http://journal.frontiersin.org/article/10.3389/fphys.2013.00075/full
Article Experimental control of scaling behavior: what is not fractal?
Article Pink Noise in Rowing Ergometer Performance and the Role of Skill Level
This is a very interesting and important question. Correct me if I am wrong, but I believe a paraphrase of the first part of your question is... is a signal fractal because some measure of scale invariance falls within a certain range of values, or can we only claim that a signal is more or less fractal than that of a control condition?
The latter approach seems to suit basic science research, since it seeks to determine the causal efficacy of fractality for a given phenomenon. The former might be best for applied research in which scaling norms might be very useful!
This is a very interesting and important question. Correct me if I am wrong, but I believe a paraphrase of the first part of your question is... is a signal fractal because some measure of scale invariance falls within a certain range of values, or can we only claim that a signal is more or less fractal than that of a control condition?
The latter approach seems to suit basic science research, since it seeks to determine the causal efficacy of fractality for a given phenomenon. The former might be best for applied research in which scaling norms might be very useful!
Hi Brandon, thanks for your answer.
My questions were triggered by the article: "Experimental control of scaling behavior: what is not fractal?" by Aaron D Likens, Justin M Fine, Eric L Amazeen, Polemnia G Amazeen
I agree with the message of the article: Experimental control is crucial, but I claim that this has already been displayed in several previous studies of which I wonder why they were not discussed. For some reason these studies are also completely ignored by critics like Wagenmakers et al. (2012) http://www.ejwagenmakers.com/2012/WagenmakersEtAl2012Topics.pdf
To return to your question, yes I believe that in addition to experimental control, the predictions about scaling behavior based on a principled, complex system approach, are much more risky and therefore should not be considered irrelevant, because of the frequency with which scaling is encountered: Theoretical considerations yield interval estimates of measurement outcomes. Not many theories about cognitive phenomena can do such a thing.
Moreover, if systematic absence or presence of associations (by correlation) between scaling exponents and more traditional performance measures is theoretically predicted for different populations, then this would go beyond 'merely' evidencing
Dear Fred,
I am interested in the question you pose and your work and although I am not currently studying self-similarity, I see that 1/f scaling is hypothesised as some kind of overarching principle underpinning cognition. While important issues can certainly be addressed by studying fractal-like dynamics of cognitive (but especially motor and physiological) processes, 1/f noise is observed in a number of non-living processes too (e.g. tides, electronic systems, volcano eruptions etc.). To progress towards a program of strong inference, should one not first establish how cognitive/motor/physiological 1/f dynamic is substantively different from its non-living analogues? Otherwise, there would be little point in treating 1/f as a "signature" of human cognition. I couldn't find a discussion of this issue in the paper you cite.
Further, in the paper, an example of across-scale coupling is given using parts of speech. 1/f scaling appears to emerge as a phenomenon that connects syllables to words to sentences (other examples could have been given). But sentences are not formed by concatenating syllables etc. Sentences are the primary wholes that are deliberately decomposed on several scales in order to study their elements. Is it then surprising that the resulting "building blocks" of speech show complex dependencies on the whole from which they were isolated in the first place? Is this not potentially circular? Could it be that these fractal signatures are byproducts of attempting to reconstruct a complex system from its elements? Such systems are not likely to show a white noise (too complex and consequently uninteresting) or a brown noise profile (too simple to afford extended study).
I think studying fractal-like processes in cognition is an interesting and possibly rewarding venture. I also apologise if I've missed answers to above points in previous work.
All the best,
Alex
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