The operator hierarchy offers a 'backbone' for the analysis of organisation in nature. For this purpose, we will use three aspects of organisation: 1. The operator hierarchy, 2. The organisation inside any operator, and 3. Complex systems resulting from interactions between operators. We view these three options as independent 'dimensions'. Because of these dimensions, it is no longer advisable to work with the classical linear approach to systems hierarchy.

The following studies offer additional information:
General laws and centripetal science.
Jagers op Akkerhuis G.A.J.M. (2014). European Review 22: 113-144
Analysing hierarchy in the organisation of biological and physical systems.
Jagers op Akkerhuis G.A.J.M. (2008). Biological reviews 83: 1-12

Three dimensions for analysing natural organisation

The operator hierarchy constructs, from the ground up, new types of operators. It uses topological criteria for every step. The resulting steps offer a basis for analysing 'from the ground up' other forms of organisation. As is illustrated in Figure 1, one can use the ranking of the operators (horizontal) as a basis for analysing interaction systems (top) or the internal organisation of any operator (bottom). Examples of interaction systems are e.g. ecosystems, society, companies, etc. As an example of the analysis of internal organisation, one can look at a mammal, its brain, tissues, organs, eukaryotic cells, etc.
Three dimensions.jpg
Figure 1: Different directions for analysing organisation in nature. (1) The hierrarchy of the operator types. (2) Organisation in systems that consist of interacting operators. 3) Organisation inside any operator (internal differentiation). The figure has been published e.g. in Eurpean Review 2014.

Dispersal, Information, Construction, Energy: DICE

Depending on the point of view, the same objects can be ranked in different ways. If one adopts the viewpoint of feeding relationships, this leads to a ranking that is called a 'food chain'. A food chain may for example start with primary producers (plants, algae), and continue with primary consumers (organisms that eat plants/algae), and higher level consumers (e.g. predators that eat animals). Size is not relevant, because a bacterium may cause a deadly disease by preying on a large animal. As an alternative, one could also choose a viewpoint in which organisms make use of each others construction. Now, a chain can be formed showing how certain organisms create structures that are used by other organisms. This may cause a different ranking than the foodchain. Interestingly, the levels in both example chains are never stringent, because organisms feed on things from different trophic levels, and because an organism may offer different strucures to different users. Two more viewpoints for creating rankings may be 'information' (e.g. mating realtionships and signalling relationships) and 'Dispersal', focusing on the changes of position of organisms and whether they use other organisms for their transport. Because of the possibility of different perspectives, each showing specific levels, and because levels are not fixed, the organisation of an ecosystem can best be viewed as multifaceted. Any projection of this complexity into a single dimension, for example a food chain, necessarily represents a marked simplification of reality.

Relationships with classical system hierarchy

Figure 2: Miller's 'Living system theory' as an example of the classical ranking of system organisation.
In the literature one can find many rankings of complex systems. One of these is that proposed by Miller (Figure 2). Miller-like classifications are used by many people, because they fit to general ideas about organisation. However accessibility such figures are, the price is that they are based on a mixture of types of rankings and types of elements.

More than one type of organisms

Miller's scheme offers a single position (or 'level') for the 'organism'. The assumption that seems to be made, is that organisms are multicellular, because the scheme mentions the lower levels of the organ and the cell. This implies that organisms bacteria and eukaryotic unicellulars are not in the scheme. In addition, it is not clear whether the 'organism' in the scheme is a plant or an animal, even though this has marked consequences for the type of organisation. When used this way, the 'organism' is a overly general container concept.

Different internal organisations

Because Miller's scheme, and others schemes like it, do not include different types of organisms, such approaches can not account for differences in the internal organisation. Meanwhile, Miller has chosen the ranking organism-organ-cell for good reasons. This ranking focuses on the most complex example of a multicellular organism. This choice offers a simple means to illustrate that one may find 'levels' of internal organisation in an organism. Unfortunately, this focus implies that a number of important aspects of analysing natural organisation are being negelected. The first aspect is that different kinds of organisms exist, each with a different internal organisation. For example, inside the cell of a bacterium one may find 'organelles'. And inside an elephant one can find 'organs'. The second aspect is that the internal organisation of an organism can be looked at from different perspectives, each of which may lead to a different ranking. For example energetic considerations, structural considerations, displacement considerations, or informational considerations all lead to a different ranking of relationships.

What determines the 'levels' from 'group' to 'supranational'?

Miller considers 'group' and 'organisation' as different 'levels'. Both these concepts can be viewed as a group. A group, an organisation, a population and a community all consist of individuals and represent abstractions that are based on the mental circles we draw around a selection of individuals. Such abstract levels based on behaviour represent a different logic than levels based on construction. As long as operators and interaction systems are mixed, and both physical units and abstract units are included in a ranking, the conclusions must be that such a ranking, e.g. Miller's scheme, represents a hodgepodge of principles.