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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Hi t - I like both of these quotes also. They say so clearly some of what I and we many have been thinking.

As for the polarization that seems to happen around Ken, I feel it and hear much of it as unfortunately charged and it is difficult for my personal aesthetics. And, of course, good to have critique, inquiry, and inner involvement with important themes.

Zak Stein seems like a mensch to me, in the various places I have heard and seen him. I sent this particular blog piece to my two daughters who have children and are looking at individuality and are concerned about their interfacing with the world. One daughter wrote back a wow - she really liked it and wanted more.

It turns out that I will be at ITC and though I'd like to hear him, I'll probably choose a seminar with continuing ed units for me. I have heard him before speaking critically about metrics, but it sounds from his abstract that he will be taking it further:


Thanks, mon.

I recently posted on this article at FB, correlating stream of consciousness literature with multifractals. Therein it is revealed that stream of consciousness literature was most representative of multifracticity (aka Multipli City). Multifracticity itself 'interweaves' other fractals, thereby displaying synius behavior. This appears to support my thesis stated many times in the Ning forum that its structure is more stream of consciousness than linearly structured academic writing. Hence the former is more an enactment of multifractivism. Interesting indeed.

LP seemed to suggest that is was the emergence of the green meme, which I questioned. One of my above points is that the sort of thinking and writing process involved, according to the article, is stream of consciousness. I don't find that at all in academic writing; it's very nature is antithetical to that sort of processing, very formal operations, i.e,, orange. It seems to me that is pretty much the same with so-called integral writing, except perhaps when Wilber, and some others wax poetic on occasion.

I foresee the rejoinder that integrality requires both the more logical, linear thinking and writing as well as the more streaming variety in some sort of balance. Of that I'm not so sure.

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.

Some more from the above conversation:

theurj: Since the MHC needs a 'bump' to multifractals, then I'm guessing you don't see that as systemic stage 12?

Barker: I think Michael is right, multifractal is systematic. But I would add that doing mappings of multifractal measurement onto a multiscalar system is metasystematic because one is coordinating systems in doing the mapping.

theurj: To clarify, MLC said in this thread that multifractals are stage 12 systematic. In the MHC stage 12 is metasystematic. So either he noted the wrong numerical stage or he meant metasystematic. So please clarify that MLC.

In either case, it brings up some questions. Since it is agreed by mathematicians that multifractals are at least an order more complex than monofractals, then how does using a monofractal system to justify transition and stage dynamics work? I would guess, maybe wrongly, that the MHC is itself a stage performance of what it purports, i.e., stage 15? So how does that work, a stage 15 performance using a stage 11 or 12 performance as justification for the very nature of steps and stages?

As you note, the one doing the coordinated mapping of multifractal measurement onto a multiscalar system might exhibit metasystematic task performance, which is what you're trying to do with the MHC. But it still leaves the above questions as to how this level of task performance could be done on the MHC itself, which I presume is a level 15 performance? If it isn't, then how can it measure performances beyond itself? Please explain, thanks.

Some more from the above conversation:

MLC: There is now an extra stage at near the bottom of the sequence. So metasystematic is now 13; http://www.dareassociation.org/bdev/bdb_archive/BDB%2019.3-A01.pdf. [As to the rest] I will think about this. Just got back from a 6 day grueling trip.

Barker: Commons & Jiang added a stage, automatic, as stage 1. This pushes the order numbers up one.

MHC is a paradigm for scoring how complex behaviors are. It consists of 1) metasystematic axiomatic principles which are the governing rules for how orders are measured, and 2) different measurement systems can be used, a) scoring interviews, b) micro development, c) Rasch, d) transition steps and substeps (which includes observation of fractal dimension and should be noted that the fractal observation is not disembodied from the transition steps and substeps). And as we've agreed, when a measurement system is used to map/measure another system, the task becomes a metasystematic one. There is more going on, but here are the two main metasystems at work.

I know what you might be wondering, how the transition steps can already be fractal, and fractal is formal, but above I say the transition steps and substeps are systematic. It is because the formal operations fractal component is at the same level as the other formal operation calculi behaviors of the transition system. By adding multiscalar dimensions, the formal operations fractal component will become a multifractal system in of itself, and will then be capable of being synthesized with the transition steps and substeps not as a part, but as an equally participating measurement at the same order of complexity. The horizontal complexity of elements coordinated at the metasystematic level will get longer as it broadens its ability to measure.

Barker's Master's Thesis is attached. He's now working on his Ph.D. at Mathematical Information Technology, University of Jyvaskyla.


Of relevance from the Thesis:

"Through the lens of MHC [model of hierarchical complexity], those other meta-notation systems [meta-semiotic, meta-logic, meta-mathematical notion] tend to score at only the metasystematic order of coordinating systems. By contrast, FPC [fractal phase calculus] needs to coordinate information from a much higher order of abstraction and thus a much greater order of complexity. This is because FPC was posed to describe the underpinning qualia of all orders and transitions between them, scaling all the way up and down the hierarchy, across and for all domains in the recursive architectonic task" (40).

theurj: The following from Cory's thesis is getting at some of my point. [Then I quote the above paragraph.]

I've long suspected that the formal math of fractals limited the very structure of the MHC. I've also long suggested that at each stage beyond the formal there must be a corresponding math to model it. If the  self-recurring patterns of formal fractals is used as the 'universal' to ground each transition and stage construction then it seems to be just horizontally extended that formal logic to each stage. Hence Cory has come up with a diagonal math to accommodate this limitation.

With multifractals, different fractals interact with each other to form rich cascade dynamics. It is similar to Derrida's notion of iteration, in that there is certainly something of the same retained from each predecessor, and yet something different and novel has to emerge with each iteration. Same difference, aka differance. This was the poststructural break from formal structuralism and provided a new, multifractal 'universal.'

So what I've long intuited is that every stage, and perhaps even the very structure of transition steps, there must be a multifractal iteration that changes, if only slightly, those very structural dynamics. And that goes for the math to model it. Still the same, but somehow also different.

Barker: I conjecture that FPC is paradigmatic because it is the coordination of universal principles of measurement that underpin different sets of principles of measurement.

MHC is largely a linear model with linear math. Sara Ross brought some nonlinearity into it when she identified the fractal dimension. They both used the phrase "downward assimilation" to describe how the content coordinated by one order can be coordinated then by a lower order. And the subtask concept was nonlinear also, but I never saw a fully worked out math to account for it and include the other kinds of multiscalar interactions not just content but also with orders themselves. Michael has some calculus maths but no demonstrating proofs, though it was in my opinion logically sound. So my idea for diagonal complexity came out of that, that there was a missing dimension they were talking around, but not explicitly working out.

I'm convinced human representation of reality is fractal, and reality it represents therefore is probably also fractal. My spectrum of human imagination model is like an ultimate multifractal. It is ontological, architectural. So it fits what we are talking about, the multifractal-multiscalar content-architecture of the multifractal multiscalarity of complexity-processes.

I am trying to figure this out! [A new math to fit the model.]

ekk1959: Cory, what do you mean by ontological?

Barker: I mean it in a generic sense. Study of being - things and their relations. But here I mean what humans imagine to exist, not what is in reality, because people don't agree on what is real, and ideas change. SHIM ontology is recursive for this reason, it iterates when people or myself find inconsistencies, built in as a function. Currently in the 84th version and now mostly stable.

Commons: The data and math for stage is that it is equally spaced ordinals, a power function = 2 to the nth power where n is stage, 2N.  Power functions are non-linear. Development of stage is also a power function, where stage = log to the base 2 of age.

What is left out is stage is only one of at least 4 things going on in development. 2. is periods (such as found in Erikson). It seems to have a sociological and cultural compent to it. I do not know of any models for that. 3d. is maturation.  It is usully thought to be an log function of age. 4th is skill and information. I know of no models of them either.

My own guess, is that the non-linearity versus linearity arguement is more philosophical than empircal or analytic. There are just no clear models or tests of them, just proposals.

Jan Boom has the only data on stage transition based on subtasks. For example, during primary order, one first has counting, then addition, and finally multiplication. With only 3 points, it is not possible to see a clear metric because regression eats up 2 degrees of freedom.

Scoring of substeps or substages ares not understood in terms of shape because so far they are just ordinal. We are just in the beginning of a mathematical developmental account. But think of how to test the models when proposing them.

We recently published an article on stage acquition. http://www.dareassociation.org/bdev/bdb_archive/BDB%2019.4-A01.pdf

What is FPC? please do not use abreviations. They make the average reader feel stupid when they do not know them.

Also, fractal is used because the first 3 definition or order of hierarchical complexity generates an infinite chain of fractals. The higher or task actions is defined and non-arbitrary orders two or more the adjacent lower order actions. This is what generate the power function 2N where N is order because these hold for every order.  There is nothing else to it.

Also see this post and several following posts on that and the next page of another thread.

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