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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See this thread discussion of Murray's article in IR, highly relevant to this thread.

Sara Ross said of the Model of Hierarchical Complexity (MHC):

"To possess 'universal, scale-free' properties means the MHC’s orders of hierarchical complexity are fractal. Fractal means the repetition of self-similar patterns at different scales. Behavioral scales from the micro-biological to large social systems evidence the orders of hierarchical complexity (see Commons & Ross, 2008). The fractal transition theory is proposed as a universal, scale-free general model as well (Ross, 2008)."

This recent study in Nature Communications takes issue with scale-free models:

"Here, we organize different definitions of scale-free networks and construct a severe test of their empirical prevalence using state-of-the-art statistical tools applied to nearly 1000 social, biological, technological, transportation, and information networks. Across these networks, we find robust evidence that strongly scale-free structure is empirically rare, while for most networks, log-normal distributions fit the data as well or better than power laws."

The following from the same issue of Nature Communications, akin to the tenets of the MHC, which are at question. I've said much the same in this thread, but not in these scientific terms.

"The appeal of scale-free networks came from
complexity science—an umbrella term for many research directions trying to find hidden laws in the complex world around us, and simple rules to explain them. One such idea is emergence—the phenomenon that a multitude of interacting units can as a group behave in ways not predictable from the behavior of the units alone. […] Sometimes emergent patterns can be scale free, meaning roughly that they are organized similarly at different (e.g., spatial) scales [...with] power-law degree distributions. […] A final concept of complexity science that is important for understanding the success of scale-free networks is universality. Emergent patterns are often consequences of basic symmetries and behavioral rules of the constituents. […] This means that rather different systems can share emergent properties […] that the scale-freeness of networks is such a universal phenomenon."

"In the Platonic realm of simple mechanistic models, extrapolated to infinite system size, the concepts of emergence, universality and scale-freeness are well-defined and clear. However, in the real world, where systems are finite and many forces affect them, they become blurry. If you meditate in front of a broccoli, you will notice that even though the same principles of organization occur at different scales, there are also differences—you can guess how zoomed-in a picture of a broccoli is. This blurring makes complexity concepts less applicable to the real world. […] Critics made the point that although the degree distribution is scale free, the actual networks are not. They pointed out that power-law degree distributions and the preferential attachment mechanism were already discovered. Even more polarizing, however, was the claim that degree distributions rarely follow power laws."

From the first Nature article:

"These results indicate that genuinely scale-free networks are far less common than suggested by the literature, and that scale-free structure is not an empirically universal pattern. […] These results demonstrate that scale-free networks are not a ubiquitous phenomenon, and suggest that their use as a starting point for modeling and analyzing the structure of real networks is not empirically well grounded. […] The variation of evidence across social, biological, and technological domains is consistent with a general conclusion that no single universal mechanism explains the wide diversity of degree structures found in real-world networks."

See Sara's further response below. The articles directly question modeling actual complex networks using universal, scale-free models. And most real world networks don't display that tenet. I don't see how that can be missed as directly related to the MHC, which claims those tenets for everything.

"I realize and appreciate that you’re in an earnest search for understanding.

All I have time to do is iterate my original point about using MHC in comparisons. It’s a general theory about how behaviors of a living actor that can increase in complexity do so in a consistent pattern of increasing hierarchical complexity step by step, stage by stage. This is a general theory for developmental behavioral analysis and measurement.

As the complexity science literature displays, countless phenomena of countless types have been determined to be or not be scale-free. “Scale-free” means they display fractal patterns. Such patterns can be abstract and descriptive (like definitions of networks studied in the article you cited), or concrete/static, or economic, and on and on. MHC doesn’t have any “grip” on what other things may or may not be scale-free. It’s irrelevant.

If you find a study that delves into analyzing the behaviorial development of social networks ( because, yet, such networks can/do develop!), then MHC could be used to help with analysis.

That’s all I’ve got!

Cheers
Sara"l I have time to do is iterate my original point about using MHC in comparisons. It’s a general theory about how behaviors of a living actor that can increase in complexity do so in a consistent pattern of increasing hierarchical complexity step by step, stage by stage. This is a general theory for developmental behavioral analysis and measurement.  

As the complexity science literature displays, countless phenomena of countless types have been determined to be or not be scale-free.  “Scale-free” means they display fractal patterns. Such patterns can be abstract and descriptive (like definitions of networks studied in the article you cited), or concrete/static, or economic, and on and on.  MHC doesn’t have any “grip” on what other things may or may not be scale-free. It’s irrelevant.

If you find a study that delves into analyzing the behaviorial development of social networks ( because, yet, such networks can/do develop!), then MHC could be used to help with analysis.

That’s all I’ve got!

Cheers
Sara"

Further discussion at the Yahoo Adult Development group. My last comment follows:

Both Sara and Cory note that the MHC and the actual networks measured are two different things, apples and oranges. And yet the first reference is clear, in that the
model doing the measuring must be consistent with the networks it measures.

"These results demonstrate that scale-free networks are not a ubiquitous phenomenon, and suggest that their use as a starting point for modeling and analyzing the structure of real networks is not empirically well grounded."

The second reference also notes that while scale-free modeling might be internally consistent mathematically, it is nonetheless an ideal, Platonic model not consistent with the networks it models. I'm reminded of Michael noting that the MHC "is a mathematical theory of the ideal," whereas the performance is only a "representation of the ideal," perhaps analogous to the ideal model and the real world network? Perhaps it is the difference between a worldview that sees the relationship between the ideal and real as dichotomous and one that sees them as mutually entailing?

Santa Fe Institute (SFI) has a recent, several part online course on fractals and scaling, summarized in the video below. Some real world objects indeed display fractal-like scaling but are limited within real world constraints, unlike abstract, mathematical fractals ad infinitum (2:00). Other real world applications do not exhibit fractal scaling, so other models are better suited to measure them (10:00). Here Clauset et al's earlier work was cited, Clauset's later empirical work (cited previously) on about 1000 networks confirming that scale-free networks are indeed rare so thus different models are needed to evaluate them. Hence questions arise if one wants to make a model of everything based on fractal scaling as first principles (11:25). Summing up the themes, the video notes that objects can be more or less fractal like (as Clauset's recent study attests) and are not in an either/or category. And that fractal scaling, where it is seen in objects, "does not necessarily reveal its essence" (17:40). I'd add that it in no way reveals its essence, as that is a topic well investigated in postmetaphysics in the current issue of Integral Review.

After I posted the above in the Yahoo Adult Development forum, this is Commons' reply, which completely ignores the data and analysis provided and just reinforces MHC data:

"We have hundreds of studies that show that Rasch measured difficulty of items is predicted with an r of over .9 by the Order of Hierarchical Complexity of the item. This is true over 10 different instrument from numerous domains.
My Best,

Michael Lamport Commons, Ph.D.
Assistant Professor"

From this article. Good luck with getting the power law religion, like any religion, to change. It too, like most religion, has to have a 'universal' to rule them all. Proponents even admit it is idealized, that the real world doesn't fit it. It's just barely warmed over, metaphysically dichotomous Gnosticism hiding under the rubric of science and math.

“These results undermine the universality of scale-free networks and reveal that real-world networks exhibit a rich structural diversity that will likely require new ideas and mechanisms to explain."

"Supporters of the scale-free viewpoint, many of whom came to network science by way of physics, argue that scale-freeness is intended as an idealized model, not something that precisely captures the behavior of real-world networks."

"Steven Strogatz, a mathematician at Cornell University (and a member of Quanta’s advisory board) […] said, there’s a 'power law religion.'”

"Clauset sees his work with Broido not as an attack but as a call to action to network scientists, to examine a more diverse set of possible mechanisms and degree distributions than they have been doing. 'Perhaps we should consider new ideas, as opposed to trying to force old ideas to fit,' he said."

Pace layering: How complex systems learn and keep learning. I appreciate this different take on hierarchy, as

"the relationship between components in a system that have different change-rates and different scales of size. […] Consider the differently paced components to be layers. Each layer is functionally different from the others and operates somewhat independently, but each layer influences and responds to the layers closest to it in a way that makes the whole system resilient."

This is much more like the dynamic systems and autopoietic approaches that operate via structural coupling versus the hierarchical complexity approach, where the latter sees each layer being subsumed into the higher via the same scale-free, fractal dynamic.  I call the former approaches hier(an)archical synplexity to differentiate them.

"It's not objectively out there in the world." And two versions of set theories can come up with opposite results. Why? Watch the video. The cognitive and neural foundations of math:

All of this is not to deny that the MHC is useful. All math is useful depending on the context in which it is used. Where the MHC is wrong is that it assumes its premises are ontological and thereby makes claims to reality as such. All of the above points to a multiplicity of useful and consistent maths and metaphors, often contradictory, where none of them owns the exclusive claim to reality as such. Which is, btw, a more accurate tenet of postmetaphysics.

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