A classical pattern for ranking organisation in nature is the linear 'hierarchy', which runs from atoms and molecules, to cells, organs, organisms, populations, communities, ecosystems, etc. In this ranking entities/transitions are placed in sequence which represent different logical kinds. To solve this problem, we propose an alternative ranking that distinguishes proper hierarchies for: 1. particles/organisms ('operators') of increasing complex structure, 2. compleixty in how particles produce systems of interacting particles, 3. complexity inside particles/organisms. For example atoms, molecules, bacteri and horses are increasingly complex operators. Examples of systems of interacting operators are ponds, villages and bumble-bee colonies, of which more complex forms exist as oceans, cities and bee colonies. Finally, one can find different levels of organization inside every operator. This shows that the classical linear hierarchy in fact shows three 'dimensions'. A more comprehensive approah to presenting 'hierarchy' in figures must be sought, if we want to account for the above three aspects.

The following paper offer more information:
Analysing hierarchy in the organisation of biological and physical systems.
Jagers op Akkerhuis G.A.J.M. (201o). Biological Reviews 1: 1-12

Classical system hierarchy.

Figure 1: Miller's 'Living system theory' as an example of the classical ranking of system organisation.
As an example of the classical ranking, Figure 1 shows a system hierarchy proposed by Miller. Miller-like classifications are used by many people. But the simplicity of the linear ranking comes at a price. It requires the mixing of types of rankings and of types of elements. This can be illustrated by discussing the position of' 'the organism' and the choice for organ and cell as selected aspects of the organisation inside an 'organism'.

Different types of organisms

As Figure 1 illustrates, Miller's scheme offers just one position (or 'level') for the 'organism'. The envisioned organism has a multicellular construction, because the scheme mentions the lower levels of the organ and the cell. There are no separate levels for organisms of different complexity, such as bacterial unicellulars, eukaryotic unicellulars, multicellulars and multicellulars with neural network..

Different internal organisations

Because Miller's scheme, and others schemes like it, do not include different types of organisms, such approaches can not deal with organisms that show differences in their type of internal organisation. Of course, Miller has chosen the ranking organism-organ-cell for good reasons. This ranking focuses on the complex example of a multicellular organism, which offers a way to illustrate many 'levels' of internal organisation. Unfortunately, this focus implies that one is limited to a one-deimensional representation of structural complexity, while we have just proposed that a more comprehensive approach may be needed. There are three reasons for choosing a more comprehensive approach: 1. Different kinds of organisms exist, that differ in their internal organisation. For example, inside the cell of a bacterium one may find 'organelles'. And inside an elephant one can find 'organs'. 2. The internal organisation of any 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. 3. The logical type of the 'organ level' differs fundamentally from that of the 'organism'. The reason is that an organ is a level inside an organism, while an organisms is an abstract concept, which refers to any organism that either is a bacterium, a eukaryotic cell, a bacterial or eukaryotic multicellular, or a neural network organism. 4. The concept of the 'organism' lacks a bottom-up definition, which is a problem when it is used in an analysis of hierarchy.

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

Figure 2: Analysing organisation according to three separate dimenions. The 'upward' dimension represents the ranking of the operator hierarchy.
Miller considers groups of individuals as one 'level', and organisations consisting of groups of individuals as the next 'level'. Similarly, biologists may consider a 'population' as a level, and a 'community' of populations as the next level. Interestingly, it is not logically the same if one talks about a 'leveled' ranking from group->organisation->community or about a 'leveled' ranking from cel->endosymbiontic cell->multicellular. constructed of cells with endosymbionts. The reason is that a multicellular organism is always physically constructed from cells, but an organisation need not be constructed from groups. A group, an organisation, a population and a community all consist of individuals and represent abstract levels that are based on the mental circles we draw around a selection of individuals. The fact that we support our groupings by referring to interactions does not change this reasoning. Abstract levels based on behaviour represent a different logic than constructional levels, e.g. the ranking from atom to molecule and further to cell. Miller's scheme does in a limited way acknowledge this difference by drawing a dashed line between entities in 'biology' and entities in 'sociology'.

The operator theory suggests three dimensions for ranking (Figure 2).

The operator theory now suggests to enrich the presentation by using three separate dimensions for analysing organisation: an 'outward', an 'inward' and an 'upward' dimension. One can compare these dimensions with the possibilities for a next footstep on a ladder (Figure 2). An upward footstep brings a person on the next rung. Subsequent steps upward allow one to klimb the 'ladder'. A step can also be directed into the interiour of an object on the ladder. Such a step stands for the inward dimension, which covers all analyses of the internal organisation of an operator. Finally, a nex footstep can lead away from the ladder. This represents the outward dimension. The outward dimension deals with systems that consist of interacting operators (the systems above the dashed line in Miller's scheme). Here one may dicsuss populations, bee colonies, herds, society, etc.

Extending the ladder: combining levels of matter and life

The above distinction of three dimensions and subsequent analysis of levels along each dimension is not just 'interesting'. In fact, it solves fundamental difficulties that plague classical hierarchies. Moreover, it offers a step towards a more general evolution theory. Darwin's theory focuses on reproduction, variation and selection. While Darwin focuses on organisms, he did mention that other things may evolve as well. But if we want to include other entities than organisms in a theory of evolution, we must have acces to a way of how to define such entities. By using the upward dimension, a generalisation can be based on the observation that not only organisms show stepwise increases in complexity (e.g. from bacteria to multicellular animals). Such stepwise increases can be found also between various complexity levels of abiotic particles, such as quarks, hadrons, atoms and molecules. By focusing on such complexity steps, the abiotic levels of complexity can be joined with the biological levels of complexity. But before one can create a general complexity ladder, the question has to be answered how one can identify the positions of the rungs of the ladder. The next page discusses the construction of a complexity-ladder for particles and organisms.

Questions and References section 1.3.