Re: Dynamical Hierarchies

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:

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_a, S/R_b, S/R_c,...}, where the length scale of R_a is less than that of R_b is less than R_c 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,

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,

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.