I posted the following in the Yahoo Adult Development forum and am cross-posting here. I'll keep you apprised of some key responses, provided I get any: 

Building on the post below* regarding Lakoff's embodied reason, he seems to call into question the type of abstract reasoning usually found at the formal operational level. This appears to be false reasoning based on the idea that reason is abstract, literal, conscious, can fit the world directly and works by logic (also see for example this article ). If formal reasoning is false wouldn't this call into question some of the assumptions of the MHC? That perhaps this "stage" is a dysfunction instead of a step toward post-formal reasoning? 

Now Lakoff has his own hierarchy of how embodied reason develops: image-schematic, propositional, metaphoric, metonymic, symbolic. (See for example "Metaphor, cognitive models and language" by Steve Howell.) So I'm wondering how the MHC takes into account Lakoff's work here and how it answers his charge of false reason? Terri Robinett noted in his Ph.D. dissertation (at the Dare Association site) that "work has already begun by Commons and Robinett (2006) on a hierarchically designed instrument to measure Lakoff’s (2002) theory of political worldview." So perhaps you can shed some light on this? 

* This is the referenced post: 

Since Michael brought up Lakoff as perhaps being "at right angles to the stage dimension" I read this by Lakoff this evening: "Why 'rational reason' doesn't work in contemporary politics." He distinguishes between real and false reason, the former being bodily based and the latter existing in some sort of objective, abstract realm. Very interesting indeed. Here are a few excerpts: 

"Real reason is embodied in two ways. It is physical, in our brain circuitry. And it is based on our bodies as the function in the everyday world, using thought that arises from embodied metaphors. And it is mostly unconscious. False reason sees reason as fully conscious, as  literal, disembodied, yet somehow fitting the world directly, and working not via frame-based, metaphorical, narrative and emotional logic, but via the logic of logicians alone."
 
"Real reason is inexplicably tied up with emotion; you cannot be rational without being emotional. False reason thinks that emotion is the enemy of reason, that it is unscrupulous to call on emotion. Yet people with brain damage who cannot feel emotion cannot make rational  decisions because they do not know what to want, since like and not like mean nothing. 'Rational' decisions are based on a long history of emotional responses by oneself and others. Real reason requires emotion."

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More from the Yahoo AD forum:

theurj: Is this recent physics discovery of any use here?

Barker: Yes. Great find! Fractal phase calculus (FPC) is aimed to be a universal formula for how humans represent entities and their actions. It is fractal, the core form is exactly the same at every iteration at every scale. It is phasic, it captures all degrees in the freedom of motion an entity can be or act within its inherent constraints. And it is calculus, functions of change but within functions of change within functions of change, horizontal and vertical directly adopted from Michael's model, but here adding diagonal.

In FPC the universal properties are static/dynamic, recursivity, n-dimension, indexing (mapping content into these), and axiomatization (rules/principles across systems).

In Arkani-Hamed and Trnka's model, static represents static particles (forces in equilibrium), dynamic represents force particles, recursivity is present in the iteration of processes which are required to hold the particles and interactions together, and n-dimension is the trajectories they measure on. The axiomatization is the rules that are present across their modeling.

Reread and look at the language they use: I would hypothesize the reason for the profound simplicity their model yields to accounting for the diversity of processes, is because they are basing it on universal properties intrinsic to the very foundation of constructing a representation. Here they demonstrate on the level of the behavior of composite particles (fermions, bosons, gluons, photons and gravitons), but this is just one tier/scale of the domain of materia (how people represent matter), which in the spectrum of human imagination is subatomic III or tier -11. Now consider if we could do this at any scale of matter, or even further with any human representation in any domain.

Their next logical step would be to do the same procedure one scale down at subatomic IV tier -12 with superstrings and resonance frequencies, or/and then one scale up at subatomic II, tier -10, with hadrons and the four forces, then coordinate the relationships across the scales. Note that the tiers of the building blocks of matter (-12, -11, -10) are on an n-dimension, a vertical one, and the different types of static and dynamic particles that exist at each tier can be horizontally indexed, and diagonal would in this case relate -12 directly to -10. A function (change in dynamic interaction between static particles) within a function (scalarity of matter), and they are accounting for all the permutations using a recursive function. Am I making sense? :)

Michael,
I agree with all, except that the relationship between linear and nonlinear is more philosophical than empirical or analytic. I think it can be all three, though in a mathematical sense it would be analytic, yes? Mathematically, the difference seems to be how many variables are effecting a change, which do not obey an overarching trajectory sequence (transivity) which frames it. Lets take order n+5. The main thing for me about nonlinearity is that the variables may not be from order n+4, but can come from n+3 or n+7. 
Your transivity axiom: if a > b and b > c, then a > c
 
My non-transivity axiom antithesis: if a > b and b > c, and c > a, then c a and b ≥ c
 
What's stopping this from also being true? For example, when someone behaves in a way where a lower order behavior has a top-down influence on a higher order behavior? 

In regards to mathematical development account, there gets to be too many moving parts; I completely agree with our previous conversation that it is hard to empirically get at them for a variety of reasons. The only way I can think to get a concise account of subtask and subsubtask is to simulate computationally, such as what Sofia's work may yield, or/and mine. That way the entire thing is captured in data sets and can be looked at.

theurj: Actually I'm just an idea guy and don't know much about math or science. So no, I don't understand a lot of the specific field jargon. I look for how general ideas in those fields though might apply to philosophy or worldview. My knowledge is more in the latter and politics.

MLC: Yes. The difference is that "experiental" knowledge is part of philosophical but mathematical is almost all analytic.

The actions to be coordinated have to come from the next adjacent lower order. The variable may come from any order when compounded but single variables are from the abstract order 10.

[Discussing non-transitivity from Barker's last post] This is true for many relationships like preference and friendship. But it is not true for orders of hierarchical complexity because transitivity is one of the axioms.

[On the difference between behavior and order] Behavior and order are different. How social systems are ordered is surely not based on stage. See Herb Koplowitz.

Barker: Herb, what is he referencing?

MLC: Who are the authors of Fractal phase calculus (FPC)?

Barker: Me.

MLC: Where do the goals with MHC differ?

Barker: FPC defines universal properties of entities and actions which are the same across domains and their scales/orders. MHC measures how complex behaviors are.

MLC: Is FPC a super or subset of MHC?

Barker: This is like a chicken or egg question to me. Sets can be contained by their members.

Following up on this earlier post, see "Dynamic Systems Theory in Cognitive Science: Major Elements,
Applications, and Debates Surrounding a Revolutionary Meta-Theory."

"Dynamic Systems Theory (DST) is a broad theoretical framework imported from the physical sciences and used in psychology and cognitive science in the past several decades that provides an alternative to the computational and information-processing approach that has governed main stream cognitive science since the dawn of the cognitive revolution in the mid-twentieth century (Beer, 2000; van Gelder & Port, 1995; van Gelder, 1998; Spivey, 2007). DST views all psychological processes and capacities as dynamic systems which are best described as complex, non-linear, self-organizing and emergent and whereby cognition develops over the life-course and occurs over real-time as a probable description of many possible alternatives instead of linear assembly of symbolic processes (Spivey, 2007; van Gelder & Port, 1995). Psychological capacities are viewed as emerging as more complex unique forms from prior simpler states, moving from chaotic to more stable trajectories in a theoretical state-space that culminate in the manifestation of a specific thought in real-time or a developmental phenomenon over ontogenesis (Spivey, 2006, Thelen & Smith, 1994; van Geert, 1998). There is a sensitivity to initial conditions and a determination by multiple causality, whereby psychological phenomena, be it a developmental capacity or cognition more generally, are softly-assembled (Thelen & Smith, 2003)." [...]

"DST provides an account of cognitive phenomena that is dynamical, embodied, completely situated and ecologically-grounded and the ways that cognitive scientists go about conducting research and theory building is likely to be influenced by these fundamental aspects to this meta-theory."

Also review Section 5.2, Strange Mereology, of The Democracy of Objects starting on p. 208.

In several posts above I noted how image schema were in the middle of classical taxonomic hierarchies. That in itself changes said assumptions inherent to hierarchical complexity. So see this article by Kurt Fischer (also cited in several posts above) on dynamic skill theory wherein he uses dynamic systems theory. In particular, see the section on this starting at page 20. E.g., as related to the middle of things:

"People act in medias res – in the middle of things in the real world, not merely as logical agents acting on objects rationally and without emotion."

This statement is in the context of discussing developmental skill capacity, how it varies over a wide range depending on environmental support. I have though associated it with image schema, and how the latter change the very nature of hierarchical complexity.

And I'm reminded of Zak Stein's essay on mind as ecosystem, which first off acknowledges Lakoff et al. for how metaphors affect how we approach the world. The mind as computer metaphor has a host of working assumptions that delimit modeling, not the least of which is classical set theory based thereon. Stein studyed with Fischer at Harvard so took the latter's dynamic systems approach to development including this ecological tenet: "There is not one central 'unit' that can serve as an overall measure of the ecosystem." Hence the use of dynamic systems theory to account for these 'multifractal' interactions.

Some relevant posts from the fold thread:

This post:

Another way of approaching r/a terms is through basic categories and image schema. Recall that these prototypes are in the middle of classical categorical hierarchies, between the most general and the most particular. Basic categories are the most concrete way we have of relating to and operating within the environment. Thus both the more particular and more general categories are more abstract. And yet our usual way of thinking is that the more particular the category the more concrete or relative the object it represents is and vice versa.

Which is indeed related to the a-terms being asymmetrically dependent on the r-terms, if by r-terms we mean those concrete image schema which are the basis of more abstract derivations. It's easy to confuse them because our 'common sense' associates the more concrete objects of the world with the most particular objects on our constructed hierarchies; the same for the most abstract and emphemeral of thoughts, which do not seem physical or material. And yet these hierarchies are not constructed that way, instead being from the middle up and down via image schema and basic categories.

Such things are unconscious and not readily apparent. So of course we can 'reason' from both the bottom-up and top-down in such hierarchies if we associate the r-terms with the most particular and the a-terms with the most general or abstract. But we do so from the most concrete of image schema, the actual r-terms, while the top and bottom of the usual, classical hierarchy are the most abstract.

This post:

Following up on this recent post from Monday, I'm reminded of  this article from our FB thread. In discussing the r-terms as the basis of the a-terms he said: "As the concrete includes and exceeds the abstract." I.e, the concrete transcends and includes the abstract. This is an entirely different mereology than kennilingus where the more abstract transcends and includes the concrete. The most particular and the most general are the abstract a-terms while the basic categories are the most concrete and r-terms. Since basic categories are our most concrete connection with ourselves and our environments, and in the middle of such formal hierarchies, this turns such formal hierarchies inside out. I'm having a hard time picturing this and how it affects hierarchies (or holarchies), so will have to consult with Musique and report back.

The very next post after divining the six of pentacles:

This is the card chosen at random through which Musique hints. The first impression is of a wealthy man giving charity to the poor. But he holds a scale in the other hand, as if to measure how much generosity the poor deserve. It looks almost like crumbs he's doling out, sort of like trickle down economics.

But in relation to my question above, the scale has a fulcrum with two balancing dishes. As it's in his left hand this indicates it resides in our subconscious, as do the basic categories. Since we cannot directly access them we must infer them and this symbol provides such a conscious inference.

The fulcrum is the basic categories in the middle, the pans the abstract particular and general. The fulcrum is higher, the pans lower, thus consistent with the concrete transcending and including the abstract.

This motif is repeated with the rich man being the fulcrum above and between the two poor men. Thus the basic categories are 'rich' in the sense of being the concrete foundation of the 'poor' abstractions, who on their own are bereft without such a connection. Note that pentacles are the symbol not only for money but earth, the most concrete of elements and the fundament for the others.

Which of course reminds me of thoughts earlier in the thread, how differance is the foundation for the sensible and the intelligible, that dividing/connecting line at every boundary, like in/out or up/down. Which of course are concrete basic categories. They are the concrete boundary fulcrum between the abstract particular and general. And the scale is the image for how this hier(an)archy works.

A few posts later, after discussing objet a and differance:

So in terms of hier(an)archy, the object a as embodied image schema 'in the middle' is the networked interactions of the particular and the general. It appears as a hole or absence in such diagrams but it's not nothing. Like Emptiness it is the transcendental interrelations of dependent origination, not some outside or transcendent force and ground. This doesn't negate hierarchy per se, just contextualizes it with the middle ground as that which transcendentalizes the apparent transcendent and abstract top/bottom on a vertical ladder via formal, metaphysical reason. The top/bottom curve back on themselves, infolding back into the middle, while the middle curves out to enfold and relate the top/bottom. Hier(an)archy indeed.

Hi, t - mostly in order to keep some attention and some slight and auditorily chirpy traction on these topics that are engaged from this post in feb 2016, as you bring the Yahoo Commons conversation here, I post now.

What I can say at this moment is that the level of discussion is so far from my center of gravity of attentional potency, knowledge base, and maybe even reasoning ability, that I almost have to frame it as avant garde art. Foreign or alien language where I hear an identifiable word and phrase here and there. Or some other way of not suffering too much self-disappointment and some sense like drowning. Am I aligning myself with Eros-like dynamic when I think, I'll never get there, I'll never get it as much as some others do, I'll never, perhaps, get 'enough', but will continue to try or to shuffle across the infinite landscape in some fashion, until...? Whew :)

The initial theme of this thread, real, integrally embodied reason and understanding, distinct from false reason of high abstraction and without embodying integrations (if I have even this close enough for now), maybe helps me to re-locate myself as a humble human being, of some ongoing inherent value, por favor, who needn't be exercising with excessive stress my grasping for more. Something like that.

In some moments when I read the discussions of maybe you, Balder, LP, and these other folk. I have to find some framings, metaphors, and whatever mentations and sensations are available to me to not collapse in agogery. Perhaps, I remind myself that I'll never be able to stand on the lunar surface, dunk a basketball in regulation conditions, and much much much much much more. Dang. Damnation. Shit.

So where and what am I again?

Considerate and perhaps therapeutic suggestions may be possible to be entertained by me. Uhm, folks and friends and fellow-feeling kosmonauts?

theurj said:

Then I consulted with Commons' Yahoo adult development forum, like I did at the beginning of this thread. That conversation follows:

theurj: Just curious is anyone has explored the level of hierarchical complexity of multifractal mathematical analysis?

Michael F. Moscolo: Sara Nora Ross

theurj: I'm familiar with Sara's paper on how the MHC uses fractals in determining transitions, but I'm looking for the MHC level of multifractal analysis itself. And the MHC level of those that enact multifractal behavior on tasks, whether they understand multifractal analysis or not.

Michael Lamport Commons (MLC): I think Sara and possibly me have worked on. I would need more details. I have a paper on the fractal nature of subtasks within a stage. It is on the Dare Website, under special issues, I think vol 14 on stage transition. It be helpful if you would give more details of what you want.

theurj: I'm just curious 1) what MHC level is required to perform a multifractal (not monofractal) analysis, and 2) what level is someone who exemplifies multifractal task accomplishment.

MLC: Multifractal is multivariate, there for systematic stage 12.

theurj: So then that would make monofractals less than stage 12? Sarah's paper noted above that the steps and stages display fractals because they are "recurring, self similar patterns" (366), which is monofractal. E.g. from this article [first article linked above]:

 "Fractals are self-similar mathematical objects: when we begin to expand one fragment or another, what eventually emerges is a structure that resembles the original object. Typical fractals, especially those widely known as the Sierpinski triangle and the Mandelbrot set, are monofractals, meaning that the pace of enlargement in any place of a fractal is the same, linear: if they at some point were rescaled x number of times to reveal a structure similar to the original, the same increase in another place would also reveal a similar structure.

"Multifractals are more highly advanced mathematical structures: fractals of fractals. They arise from fractals 'interwoven' with each other in an appropriate manner and in appropriate proportions. Multifractals are not simply the sum of fractals and cannot be divided to return back to their original components, because the way they weave is fractal in nature. The result is that in order to see a structure similar to the original, different portions of a multifractal need to expand at different rates. A multifractal is therefore non-linear in nature."

So if you're using a monofractal model for your steps and stages....

theurj: An article for your perusal, "Scaling in executive control reflects multiplicative multifractal c...." An excerpt:

"Self-organized criticality (SOC) purports to build multi-scaled structures out of local interactions. Evidence of scaling in various domains of biology may be more generally understood to reflect multiplicative interactions weaving together many disparate scales. The self-similarity of power-law scaling entails homogeneity: fluctuations distribute themselves similarly across many spatial and temporal scales. However, this apparent homogeneity can be misleading, especially as it spans more scales. Reducing biological processes to one power-law relationship [monofractal] neglects rich cascade dynamics. We review recent research into multifractality in executive-function cognitive tasks and propose that scaling reflects not criticality but instead interactions across multiple scales and among fluctuations of multiple sizes. [...]

"Executive control is a general phenomenon of biological systems whose explanation lies in generic principles of complexity, rather than specifically cognitive mechanisms (Van Orden, 2010). However, the evidence of scaling in executive control does not point simply to SOC-like dynamics. Like many other aspects of living systems (Ivanov et al.,2001; Plotnick and Sepkoski, 2001; Ihlen and Vereijken, 2010), executive control is better understood through multiplicative multifractal cascade dynamics."

Cory David Barker: I am working on bumping monofractal single-scale transitions to multifractal multiscalar transitions.

MHC and its fractal transitions do have limitations, one of which is that it only measures one scale of building blocks of an organism at a time across a developmental trajectory. The sub-tasks only measure on the given scale. I am trying to advance on this, and my potential solution to account for interaction across scalar processes is with an additional type of measurement I am calling diagonal complexity (in addition to Commons' vertical and horizontal).

Diagonal complexity hypothesis measures what is referred to in your citation as "rich cascade dynamics". Without it, there is no mathematical way to represent the cascading effects across different scale processes and development trajectories in MHC modeling. I first wrote about it in my masters thesis. I proposed some nonlinear axioms to compliment Commons (linear) axioms in my thesis which is aimed to allow for multiscalar measuring of such processes.

I am commenting on my comment (and hoping its very personal slant doesn't diverge too far from the theme of this thread.)

Sometimes (I suppose always) I write from a state of sorts. As with my prior posting, it can feel a bit stream of consciousness from a less censored aspect, a bit poetic, in this case sounding maybe hyperbolic, exploratory, multi-layered in how and where it might land, and plenty true, and not.

T your recent post on cognitive twisting on the states, stages, folds thread does seem to pertain to what I was saying, from a very quick glance. I hope to get to it, shuffling across an ideational landscape subjectively full of I know not whys and wherefores.

http://www.ncbi.nlm.nih.gov/pubmed/22253177

Top Cogn Sci. 2012 Jan;4(1):51-62. doi: 10.1111/j.1756-8765.2011.01162.x. Epub 2011 Oct 24.
Multifractal dynamics in the emergence of cognitive structure.
Dixon JA1, Holden JG, Mirman D, Stephen DG.
Author information

Abstract

The complex-systems approach to cognitive science seeks to move beyond the formalism of information exchange and to situate cognition within the broader formalism of energy flow. Changes in cognitive performance exhibit a fractal (i.e., power-law) relationship between size and time scale. These fractal fluctuations reflect the flow of energy at all scales governing cognition. Information transfer, as traditionally understood in the cognitive sciences, may be a subset of this multiscale energy flow. The cognitive system exhibits not just a single power-law relationship between fluctuation size and time scale but actually exhibits many power-law relationships, whether over time or space. This change in fractal scaling, that is, multifractality, provides new insights into changes in energy flow through the cognitive system. We survey recent findings demonstrating the role of multifractality in (a) understanding atypical developmental outcomes, and (b) predicting cognitive change. We propose that multifractality provides insights into energy flows driving the emergence of cognitive structure.
Copyright © 2011 Cognitive Science Society, Inc.

http://journal.frontiersin.org/article/10.3389/fphys.2015.00088/full
Front. Physiol., 19 March 2015
Demystifying cognitive science: explaining cognition through network-based modeling
Emma K. Soberano and Damian G. Kelty-Stephen, Grinnell College, Grinnell, IA, USA

Even more stunning has been the evidence that the sand/rice-pile model may not just be fractal but, in fact, multifractal: it may exhibit several power-law forms at once (Tebaldi et al., 1999; Cernak, 2006; Bonachela and Muñoz, 2009), making it more complex. This multifractal wrinkle in the self-organization narrative may be exactly what's needed to help cognitive science play by more ordinary scientific rules. Observation of multifractal fluctuations offers the possibility that fractal fluctuations might interweave and spread into one another (Halsey et al., 1986). Where we might once have envisioned anatomical parts each with their own mysterious capacities, there may be less rigidly defined regions engaging in ongoing exchange of fractal and multifractal fluctuations.

The sharing of multifractal fluctuations has empirical anchoring in behaviors extending beyond the brain. Network analyses such as vector autoregression (VAR; Sims, 1980) allow us to depict the flow of information across nodes in full-body network, even from measurements of living, breathing organisms. […] The sharing of multifractal fluctuations may underwrite body-wide coordinations in ways that only network analyses have revealed.

Exciting as simulations may be, we see more promise in this latter attempt to draw from fractal statistics and matrix algebra to help us probe the full-body network. Distributing cognition across the body is still not repaying the loans of intelligence, but it may diminish the borrowed principal. Network modeling thus allows us to envision behavior—real, observed behavior—as the time-varying mixture of an extended field of multifractal fluctuations. Through this lens, behavior begins to require much less faith and much more like generic physical processes. Cognitive science need not ask to play by different rules or to start with different assumptions. On the contrary, network science might allow cognitive science operate on the same playing field as other sciences, whether sciences of living systems or otherwise.

http://journal.frontiersin.org/article/10.3389/fphys.2012.00102/full
Front. Physiol., 19 April 2012

Scaling in executive control reflects multiplicative multifractal cascade dynamics
Damian G. Stephen1*, Jason R. Anastas2 and James A. Dixon2,3,4

Self-organized criticality (SOC) purports to build multi-scaled structures out of local interactions.

Evidence of scaling in various domains of biology may be more generally understood to reflect multiplicative interactions weaving together many disparate scales. The self-similarity of power-law scaling entails homogeneity: fluctuations distribute themselves similarly across many spatial and temporal scales. However, this apparent homogeneity can be misleading, especially as it spans more scales. Reducing biological processes to one power-law relationship [monofractal] neglects rich cascade dynamics. We review recent research into multifractality in executive-function cognitive tasks and propose that scaling reflects not criticality but instead interactions across multiple scales and among fluctuations of multiple sizes. [...]

Executive control is a general phenomenon of biological systems whose explanation lies in generic principles of complexity, rather than specifically cognitive mechanisms (Van Orden, 2010). However, the evidence of scaling in executive control does not point simply to SOC-like dynamics. Like many other aspects of living systems (Ivanov et al.,2001; Plotnick and Sepkoski, 2001; Ihlen and Vereijken, 2010), executive control is better understood through multiplicative multifractal cascade dynamics.

Original Research ARTICLE
Front. Syst. Neurosci., 17 September 2015 | http://dx.doi.org/10.3389/fnsys.2015.00130
Distinguishing cognitive state with multifractal complexity of hippocampal interspike interval sequences
Dustin Fetterhoff1,2*, Robert A. Kraft3, Roman A. Sandler4, Ioan Opris2, Cheryl A. Sexton3, Vasilis Z. Marmarelis4, Robert E. Hampson2 and Sam A. Deadwyler2

Fractality, represented as self-similar repeating patterns, is ubiquitous in nature and the brain. Dynamic patterns of hippocampal spike trains are known to exhibit multifractal properties during working memory processing; however, it is unclear whether the multifractal properties inherent to hippocampal spike trains reflect active cognitive processing. To examine this possibility, hippocampal neuronal ensembles were recorded from rats before, during and after a spatial working memory task following administration of tetrahydrocannabinol (THC), a memory-impairing component of cannabis. Multifractal detrended fluctuation analysis was performed on hippocampal interspike interval sequences to determine characteristics of monofractal long-range temporal correlations (LRTCs), quantified by the Hurst exponent, and the degree/magnitude of multifractal complexity, quantified by the width of the singularity spectrum. Our results demonstrate that multifractal firing patterns of hippocampal spike trains are a marker of functional memory processing, as they are more complex during the working memory task and significantly reduced following administration of memory impairing THC doses. Conversely, LRTCs are largest during resting state recordings, therefore reflecting different information compared to multifractality. In order to deepen conceptual understanding of multifractal complexity and LRTCs, these measures were compared to classical methods using hippocampal frequency content and firing variability measures. These results showed that LRTCs, multifractality, and theta rhythm represent independent processes, while delta rhythm correlated with multifractality. Taken together, these results provide a novel perspective on memory function by demonstrating that the multifractal nature of spike trains reflects hippocampal microcircuit activity that can be used to detect and quantify cognitive, physiological, and pathological states.

http://psycnet.apa.org/psycinfo/2010-15559-004

Interaction-dominant dynamics in human cognition: Beyond 1/ƒα fluctuation.
Ihlen, Espen A. F.; Vereijken, Beatrix
Journal of Experimental Psychology: General, Vol 139(3), Aug 2010, 436-463. http://dx.doi.org/10.1037/a0019098

It has been suggested that human behavior in general and cognitive performance in particular emerge from coordination between multiple temporal scales. In this article, we provide quantitative support for such a theory of interaction-dominant dynamics in human cognition by using wavelet-based multifractal analysis and accompanying multiplicative cascading process on the response series of 4 different cognitive tasks: simple response, word naming, choice decision, and interval estimation. Results indicated that the major portion of these response series had multiplicative interactions between temporal scales, visible as intermittent periods of large and irregular fluctuations (i.e., a multifractal structure). Comparing 2 component-dominant models of 1/fα fluctuations in cognitive performance with the multiplicative cascading process indicated that the multifractal structure could not be replicated by these component-dominant models. Furthermore, a similar multifractal structure was shown to be present in a model of self-organized criticality in the human nervous system, similar to a spatial extension of the multiplicative cascading process. These results illustrate that a wavelet-based multifractal analysis and the multiplicative cascading process form an appropriate framework to characterize interaction-dominant dynamics in human cognition. This new framework goes beyond the identification of 1/fα power laws and non-Gaussian distributions in response series as used in previous studies. The present article provides quantitative support for a paradigm shift toward interaction-dominant dynamics in human cognition. (PsycINFO Database Record (c) 2012 APA, all rights reserved)

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