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Re: Dynamical Hierarchies

Pretty impressive there, Tim!

I have a few comments to add. As Tim pointed out:
It appears to me that "dynamical hierarchies" is essentially an approach rooted in reductionism. The 'levels' of a dynamical hierarchy are structural and defined by the length scale. The authors give as one example monomers, polymers, and micelles as constituting three "levels", each at a larger length scale than the former.  The goal of the paper is to use this paradigm of dynamical hierarchies as a way to understand systems via understanding the interrelationships between various "levels".

Their goal of trying to understand the interrelationships between various levels is a worthy goal, but would probably not be well-served by this approach if they are trying to understand complex systems-- only simple ones. Substituting dynamical systems for complex systems will only take us so far before becoming counterproductive. That's because this would be a case of using dynamical systems as a model for complex systems and the entailment patterns are different. However, using dynamical systems to illustrate certain aspects of complex system behavior may be extremely useful. I'm thinking about experiments demonstrating things like: What happens if a static model of a dynamical system is used to create interactive plans for use with the actual dynamical system? The static model will leave out a lot of critical information and the interactive plans, when realized with the actual dynamical system, will create a plethora of side effects. This kind of experiment can show what happens when an oversimplified model is used to generate policy and here the analogy is that the static model represents "simple system" and the dynamical model represents "complex system" even though it's a simple system, itself. The reason it works is because the experiment itself is actually a model of a dysfunctional modeling relation and the entailment of the dysfunction is the same, so the model commutes.

The weather forecasting computer programs are examples of using dynamical systems as models of complex systems. Dynamical systems have the property of being computable, which complex systems don't have. However, as RR pointed out many times, in order for this to be useful, you have to keep switching from model to model, as it begins to digress (bifurcate) from the actual system's entailment patterns. It can only commute in a local/finite way (temporal aspects included) with the real system. He compared this sort of exercise to mapping a sphere using two-dimensional (flat) planes. It can be done and it can be extremely useful to do so, just as long as we are aware that there will be deformations in the resulting information (maps) and we don't use those maps to generate plans which rely on the aspects of the information which is suspect. Each mode of measurement will cause characteristic types of deformation of information like this, which can be seen when compared to the actual system. I wonder; is there a degree program teaching how to study the interactions of measurement modalities with various types of systems? It seems to me there should be!

In medicine, there is a branch which specializes in complications caused by therapies; Iatrogenic Medicine ("Doctor-caused" diseases/pathology). This is an example of precisely the kind of thing I'm referring to. It's a symptom of a dysfunctional relation between model and system.

TG: Rosen saw this a long time ago when discussing composition of equations of state in FM [sec. 7.12] and its negative consequences for reductionism [sec.7.13]. Rosen saw that, in general, compositions of equations of state of "elementary systems" will not lead to an equation of state for the composite system.

Yes. And what it illustrates, to my mind, is the causal power of relational interaction-- even when dealing entirely with simple systems. I used the example, in The Devil's Advocate, of molecular bonds (where sodium and chlorine can "become" sodium chloride/ table salt). Molecular structure is computable but that doesn't explain why the hell two toxic elements can, in the new organization, exhibit entirely different properties from either of the ingredients. That's because there are more than two ingredients in any single interaction between two entities: there is also the interaction itself, which represents "a relation"-- and that relational ingredient is further specified by all contextual relations which create IT, including temporal aspects. It is always going to be the case that any simple system we create, or are analyzing, exists in a complex universe and the entailments of relational interaction will always be a factor. That's what complexity means, really: that relational interactivity can change everything.

Automobiles rust. Automobiles in the U.S. rust far more quickly in the northern States than they do in the southern ones. The "environment" is blamed for this, as if the causal factors are simply rain, snow, road salt, abrasion.... over time. The real reason automobiles rust is because they exist in a perpetual relation with the rest of the universe and it's an interactive relational universe. Road salt is a contextual aspect of the northern States which doesn't exist in southern ones.

TG: in my view, it is not profitable to pursue a general program of system analysis by using a paradigm of dynamical hierarchies , since the paradigm applies unproblematically only in trivial cases of S, yet the authors readily agree that emergent properties do occur. To begin with a paradigm which from the outset cannot handle the general case seems a poor choice. In particular, in the case of biological organisms, which seem to be rife with emergent properties, this paradigm appears to have little to offer. 

I would encourage caution here. It's more of a wording caution, really, because I totally agree with you. However, the way it's worded can make it seem that you are saying that dynamical hierarchies would not be useful for any program of system analysis. I don't think that's what you actually said. My ultimate interpretation of what you wrote is: While it's true that dynamical systems are too limited to be the sole source of analysis or mode of representation in a complex universe, that doesn't mean that "system analysis by using ... dynamical hierarchies" would be "unprofitable". It's just not profitable to base a paradigm on it and create a general program of system analysis based on that paradigm. The word "paradigm"-- which you DID use in your original sentence-- needs to be stressed because it tends to slip past (I missed it the first couple times I read it, myself). It's a really important point though.

Bravo.

Judith


Web address: http://www.rosen-enterprises.com
BioTheory: An electronic journal of general science based on the Relational (Rosennean) Complexity Paradigm
On Oct 9, 2005, at 9:25 PM, Tim Gwinn wrote:

I found an earlier paper by Rasmussen et al entitled "Ansatz for Dynamical Hierarchies", in Artificial Life, 2001, vol 7, issue 4. This is downloadable from MITPress for free:
http://mitpress.mit.edu/catalog/item/default.asp?ttype=5&tid=1067
 
It appears to me that "dynamical hierarchies" is essentially an approach rooted in reductionism. The 'levels' of a dynamical hierarchy are structural and defined by the length scale. The authors give as one example monomers, polymers, and micelles as constituting three "levels", each at a larger length scale than the former.  The goal of the paper is to use this paradigm of dynamical hierarchies as a way to understand systems via understanding the interrelationships between various "levels".
 
In particular, the authors note that emergent properties occur in such hierarchical descriptions.  (Where emergent means: "A property that applies at a given level is emergent if it does not apply at any lower level. That is, the property applies to a composite entity but not to any of its components.")
 
The authors also note that it is somewhat arbitrary at what "level" one begins - that is, at what "level" one calls first-order. Since they are primarily interested in the interrelationships between levels, this is understandable, although it raises in my mind the question of what is supposed to guide the choice what constitutes a "level": is there some objective criteria for choosing length scales which then dictates the constituent matter to be considered as part of that "level", or do these length scale choices simply follow as a consequence after choosing constituent matter which seems subjectively to belong to a something that looks like a "level"?
 
In any case, the notion is to take a system S, and to create a set of analyses of S, where each analysis is of a different structural "level" of S. Using the language of FM and Life Itself, each analysis is a distinct equivalence relation on S, such that we end up with a set of analyses {S/R<x-tad-smaller>a</x-tad-smaller>, S/R<x-tad-smaller>b</x-tad-smaller>, S/R<x-tad-smaller>c </x-tad-smaller>,...}, where the length scale of R<x-tad-smaller>a</x-tad-smaller> is less than that of R<x-tad-smaller>b</x-tad-smaller> is less than R<x-tad-smaller>c</x-tad-smaller> and so on.
 
Such a set constitutes a description of a dynamical hierarchy of S. The authors call a trivial example of an Nth-order structure as one which possesses no emergent properties which are not possessed by the (N-1)th-order structure. Thus, if we are to consider the utility of this paradigm, we must consider that it is only in the entirely trivial case where the description of every higher "level" is entailed by the descriptions at correspondingly lower "levels". That is,
S/R<x-tad-smaller>a</x-tad-smaller> entails S/R<x-tad-smaller>b </x-tad-smaller>entails S/R<x-tad-smaller>c </x-tad-smaller>
entails....only when S is restricted to being a system which is entirely trivial in the authors sense. In all other cases, there will in general be no entailment relationship between various "levels" of description. To expect a relationship to exist is thus to mandate very special conditions on S. Rosen saw this a long time ago when discussing composition of equations of state in FM [sec. 7.12] and its negative consequences for reductionism [sec.7.13]. Rosen saw that, in general, compositions of equations of state of "elementary systems" will not lead to an equation of state for the composite system. So, in general,
S/R<x-tad-smaller>a</x-tad-smaller> not-entails S/R<x-tad-smaller>b </x-tad-smaller>
not-entails S/R<x-tad-smaller>c </x-tad-smaller>
not-entails....The upshot is that, in my view, it is not profitable to pursue a general program of system analysis by using a paradigm of dynamical hierarchies , since the paradigm applies unproblematically only in trivial cases of S, yet the authors readily agree that emergent properties do occur. To begin with a paradigm which from the outset cannot handle the general case seems a poor choice. In particular, in the case of biological organisms, which seem to be rife with emergent properties, this paradigm appears to have little to offer. 
 
Regards,
Tim