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Each material system involves subsystems at different scalar,

by S. Salthe:

As viewed from without by the systems modeler, the relationships between different scalar levels in a system are not direct interaction, but mutual constraint, with higher scale systems supplying boundary conditions on those nested within them, while these latter provide “initiating conditions” for events that will emerge between them and the upper levels, which can be referred to as events at a focal level. Initiating conditions propose, boundary conditions dispose. In order to capture the complexity of a system, minimally three scalar levels must be explicitly represented in models. This scheme refers to synchronic subsystems, and does not address diachronic matters or development. Systems models are abstract representations of the underlying structures (form and behavior) of conceptually separable portions of the world. They should consider both form and development (predictable directional changes). Typically these models, as in the ones listed below, are made as if the modeler were outside of the system in question.

(a) Concerning systems form synchronically, we need to employ the scalar hierarchy in order to represent extensional complexity. This involves subsystems at different scalar levels – minimally three in order to prevent reduction of complexity to a favored level. Relationships between different levels do not involve direct interaction, but, instead, mutual constraint, with higher scalar levels imposing boundary conditions on those nested within them. These latter provide (what I call) initiating conditions for events at a focal level that will emerge between them and the upper levels. Initiating conditions propose, boundary conditions dispose. Each scalar level is characterized by its own temporal characteristics – relaxation times and turnaround times; each has its own what I call cogent moment. The moments of higher scale events contain many moments of entrained lower scale events. Examples of scalar hierarchies would be: [rock [molecule [atom]]] or [population [organism [cell [DNA segment ]]]].

(b) Concerning systems diachronically, we need to focus on the predictable, or constitutive, changes of development (evolution, or individuation, is non-systematic and historical). These can be represented as a specification hierarchy, whereby a developmental stage is represented as a subclass of the prior stage, and will come to have subclasses within it as well, representing subsequent stages, each nested within the prior one. The general process involved in development is increased specification, the system developing from a vague primordium to an increasingly definite senescence. We will need vaguer or fuzzier discourse in order to deal with immature systems. The developmental trajectory of a system can be traced all the way back to its inception as a material system, giving rise to the following kinds of representations: {physical system { material system { chemical system { biological system { social system { psychological system }}}}}} or {dissipative structure { oocyte { embryo { larva { immature { mature {senescent }}}}}}}. Development is epigenetic. That is, the acquisitions of prior stages are not typically discarded, but rather modified by later developmental events, which are constrained by them. This gives rise to what I call intensional complexity, which allows a system to be examined from many different viewpoints – say, physically, chemically or (if relevant) psychologically.

© These synchronic and diachronic tools can be used with any system, abiotic, biotic or social. Abiotic systems would not have as much intensional complexity, but all systems are in principle equally complex extensionally.


Salthe, S.N., 1985. Evolving Hierarchical Systems: Their Structure and Representation. Columbia University Press.

Salthe, S.N., 1993. Development and Evolution: Complexity and Change in Biology. MIT Press.

principle_of_scalar_levels.txt · Last modified: 2020/07/27 15:38 (external edit)