Subproject 1: The Paradigm of (Social) Complexity – Part II-2d: System Formation and Maintenance – The Distinction “Element / Relation”

System / environment and element / relation have largely supplanted the much older guiding distinction whole / parts when discussing the formation of a complex system.
I´ve presented the first of these more modern distinctions in the previous blog post [The Distinction “System / Environment” | Valonqua]. The second guiding distinction, element / relation, is the subject of this blog post.

(1) Bottom-up or top-down?

(1a) A bottom-up perspective seems to be prevalent in complexity, esp. complex adaptive systems (CAS) research where simple or even complex elements are sometimes seen as (ontologically) pre-given. The (dynamic) interactions / relations between these elements  are then crucial for a complex system to pop up (see the subsequent blog post on emergence):

Social agents, whether they are bees or people or robots, find themselves enmeshed in a web of connections with one another and, through a variety of adaptive  processes, they must successfully navigate through their world. Social agents interact with one another via connections. These connections can be relatively simple and stable, such as those that bind together a family, or complicated and ever changing, such as those that link traders in a marketplace.  [Miller / Page 2007, 10]

(1b) In contrast, from a difference-based perspective [see, for instance, Cilliers 1998; Luhmann 1995}, the assumption of elements as (ontologically or not) preexistent doesn´t make sense any more. The main reason is that elements and relations are seen as differences:

Just as there are no systems without environments or environments without systems, there are no elements without relational connections or relations without elements. In both cases the difference is a unity (in fact, we say “the” difference), but it operates only as a difference. Only as a difference can it connect processes of information processing. [Luhmann 1995, 20]

But, this perspective can be specified in various ways. For example:

  • as co-constitution in a connectionist network [Cilliers 1998] or
  • from a top-down perspective [Luhmann 1995], as constructs of the emerging (in this case: social) system. In other words, it´s up to the emerging (social) system to determine what is and what isn´t an element / a relation of the system:

If one were to ask what elements (e. g., atoms, cells, or actions) “are,” one would always come upon highly complex facts that must be attributed to the system’s environment. Then an element would be what functions for a system as a unity that cannot be further dissolved (even if, viewed microscopically, it is a highly complex compound). When one says “cannot be further dissolved,” this also means that a system can constitute and change itself only by interrelating its elements, not by dissolving and reorganizing them.  [Luhmann 1995, 22 – my emphasis]

So, the main difference between these bottom up- and top-down perspectives regarding the conceptualisation of the social (here understood as the coordination of human behavior) is:

  • In a  bottom-up approach à la CAS, people (humans, individuals, agents, etc.) represent (social) components of an emerging complex adaptive system such as an organization.
  • In Luhmann´s systems theoretical top-down approach, a human individual is interpreted  as  a kind of agglomeration of various (biological, neural, cerebral, etc.) systems. Each of these systems follows its own operational mode. But, some of them are structurally coupled so that they are able  to perturb each other in a co-evolutionary drift.
    The  structural coupling by means of nonverbal, oral, written, etc. media forms (= perturbation mechanisms) is then seen as crucial for the co-evolution of two or more consciousness systems processing thoughts and the social systems processing communications.

In this context, the social dimension refers to human behavior, action, and communication. But, the underlying coordination problem is much more general and has to be solved by

  • artificial entities such as virtual agents in simulations, artificial neural networks, robot swarms, etc.


  • all kinds of biological enitities [biological neural networks, fungi (Witzany 2012), plants (McGowan 2013; Witzany / Baluska 2012), bacteria (perhaps even viruses, see Hamzelou  2010), social insects, and more complex animals (Witzany 2014), including humans].


As this is an important topic, I´d like to dedicate several blog posts to this problem and its entity- and media-specific comnunication solutions.

(2) Large number of elements with rich and dynamic interactions
According to [Villiers-Botha / Cilliers 2010, pp. 27-28;  Cilliers 1998, pp. 3-4], complex systems consist of a large number of elements.
But, such a vast number isn´t enough. The quality, i.e. the dynamics and richness, of the relations / interactions between these elements is crucial, too. That is:

  • Dynamic means that there are some operations [such as self-organizational (order-from-noise or -chaos) processes, autopoiesis,  conditioned coproduction, etc.] going on that affect the elements of the complex system. In contrast, a static system where nothing happens (for example, a mathemical set of polygons, see Wikipedia 2016h) isn´t a complex system.
  • Rich refers to the fact that elements can somehow (physically, informationally, etc.) influence many other, but not all elements of a complex system.

This perspective of elements and relations / interactions implies a few important points:

(2a) Various types of complexity: 

  • If each and every element of a system with a vast number of elements was connected to every other element, the result would be an incomprehensible complexity that overwhelms an observer of the system (which could be the system itself). So, this kind of complexity resembles a theoretical horizon that a viable complex system can never achieve.
    If we combine this theoretical horizon with the distinction system / environment, we can differentiate between an incomprehensible system complexity and an incomprehensible environmental complexity. These are limit concepts that can´t be further specified. The only thing we can deduce is that there´s a complexity differential between system and environmental complexity because the first is always lesser then the latter. And this complexity differential applies to incomprehensible complexity, too.
  • reduced level of complexity is necessary for the formation of a viable complex system to happen. That is, some elements of the system are connected to many other, but not to all elements of the system:

Complexity, in this sense, means being forced to select; being forced to select means contingency; and contingency means risk. [Luhmann 1995, 25]

In short, system formation equals organized complexity (Warren Weaver) or structured complexity (Niklas Luhmann) where the following equation applies:

reduction =
selection =
(neither impossibility nor necessity)

  • Note:
    – This understanding of structured or organized complexity refers to both system (internal) and environmental (external) complexity. And this means that the structured environmental complexity, which exceeds the complexity of the system, is a construction of the system itself.
    – Further, a selection can be interpreted as an operation that results from the differential of structured environmental and structured system complexity.
    This applies especially to complex systems that operate under extreme time pressure such as human interaction systems where actions and reactions usually occur  in the blink of an eye. But, if it took hours, days, etc. for coordinating human behavior in face-to-face encounters, such a social system would rather sooner than latter collapse.
    In a strict sense, complexity can´t be directly observed – it´s incomprehensible. So, the formation of a complex system is always already engaged in the process of reducing internal and external complexities, which leads to system-dependent structured system and environmental  complexities.
    But, reduction processes by means of selective and contingent abstractions / specializations, functional or other system differentiations, etc. are only one side of the coin.
    The other side of the coin is the possible increase of system-dependent internal and external complexities. Example: When a(n) (human) organization grows in size (that is, it has more specialists, more functional departments, more divisional units, more  branches, etc.), it constructs a more specific system complexity. By doing so, it can handle more structured environmental complexity, too. This means, for example, more contacts to its public, its customers, or to members of other organizations, etc.
    In sum: It´s not only about the reduction of complexity, but also about the increase of a more specific internal and external (structured) complexity.

(2b) Other qualities of dynamic and rich interactions

  • Self-reference / recursion / feedback loops lead to unpredictability

[…] there are systems that have the ability to establish relations with themselves and to differentiate these relations from relations with their environment. ]Luhmann 1995, 15]

The effect of any activity can feed back onto itself, sometimes directly, sometimes after a number of intervening stages. This feedback can be positive (enhancing, stimulating) or negative (detracting, inhibiting). Both kinds are necessary. [Cilliers 1998, 4]

Or, to put it a bit differently: An observer can assume self-referential operations (recursions or negative / positive feedback loops) in some complex systems.
Example: The re-entrant use of the distinction system / environment within  consciousness systems or social systems. This re-entry of the distinction on the side of the system creates a paradoxical indeterminacy for tertium-non-datur-observers, i.e. observers operating with binary logical principles (the laws of identity, non-contradiction, and excluded middle, see Wikipedia 2016m) because the system is, at the same, what it is (system = system) and what it is not (system =  environment).
This means, for instance,  in the case of:
– consciousness systems: thinking (thinking as self-referential operation / thinking about something as other-referential operation),
– communication (i.e. social) systems such as organizations: communicating (communicating as self-referential operation / communicating about something as other-referential operation).
Alternative general wordings could be:
– self-reference = self-reference and self-reference = other-reference, in short: self-reference (self-reference / other-reference)
– inside (inside / outside)
or, in a very general differential sense: the paradoxical re-entry of the two-sided form (marked state / unmarked state) within itself [see Baecker 2012a, 2015b; Wikipedia 2016n].
main consequence of such self-referential or recursive somersaults is: unpredictability.

  • Nonlinearity
    Elements usually influence their immediate neighbors so that interactions are often short-range. But, mediated by other elements that can modify the influences in various ways (suppression, intensification, etc.), long-range influences are possible, too [see Villiers-Botha / Cilliers 2010, 28].
    Because of this and the recursive causality mentioned above, small causes can have large effects and vice versa. This means for complex systems that can be observed as self-referential: There are too many causes, too many effects, and too many recursions so that simple causal attributions fail! 
  • Conditioning of relations

Systems are not merely relations (in the plural!) among elements. The connections among relations must also somehow be regulated. This regulation employs the basic form of conditioning. That is to say, a determinate relation among elements is realized only under the condition that something else is or is not the case. […]
Conditioning can also concern the availability of specific elements, the presence of catalytic agents, or the realization of higher-level relations among relations. [Luhmann 1995, 23 – my emphasis]

If such contingent conditionings are successful, they act as constraints , i.e. as restrictions and enabling conditions [cf. Luhmann 1995, 23].

(2c) Complexity understood as lack of information

When the number is relatively small, the behaviour of the elements can often be given a formal description in conventional terms. However, when the number becomes sufficiently large, conventional means (e.g. a system of differential equations) not only become impractical, they also cease  to assist in any understanding of the system. [Cilliers 1998, 3]

In other words, an observer, who could be the system itself, lacks the information to fully understand a complex system, i.e. structured system complexity,  or its environment, i.e. structured environmental complexity. As a result, an observer is always already overwhelmed by these complexities.
But, language-based observers are able to problematize their lack of knowledge and re-introduce it in language-based systems (families, organizations, etc.), for example, as a concept, as an unknown quantity, as uncertainty, risk, anxiety, etc. [see Luhmann 1995, 28].

On a final note, I´d like to mention that the following blog posts won´t continue this series of complexity features.Rather, they´re blog posts hors série called ComplexiQuickies. These quickies are related to the subject of complexity, but they act as quickly written and open idea sketches.
So, the first ComplexiQuickie discusses the following question: How can we deal with complex systems or situations? And the next regular blog post regarding features of complexity discusses the problem of emergence.


[Allen / Maguire / McKelvey 2011]  Allen, P.  / Maguire, S. / McKelvey, B. (eds.) (2011), The SAGE Handbook of Complexity and Management, Los Angeles et al.: SAGE.

[Baecker 2012a] Baecker, D. (2012a),  Aristotle and George Spencer-Brown, URL: [accessed Sept 18, 2015].

[Baecker 2015b] – (2015b),  Working the Form: George Spencer-Brown and the Mark of Distinction*.
URL: Working the Form [accessed May 26, 2016].

[Cilliers 2010] Cilliers, P. (2010), Difference, Identity and Complexity, in: [Cilliers / Preiser 2010], 3-18.

[Cilliers 1998] – (1998), Complexity and Postmodernism: Understanding Complex Systems, London / New York: Routledge.

[Cilliers / Preiser 2010] – / R. Preiser (eds.) (2010), Complexity, Difference and Identity. An Ethical Perspective, Dordrecht et al.: Springer.

[Hamzelou  2010] Hamzelou, J.(2010), Viruses use ‘hive intelligence’ to focus their attack, in: New Scientist (Jan. 21, 2010),
URL:  [accessed May 24, 2016].

[Luhmann 1995] Luhmann, N. (1995), Social Systems, Stanford California: Stanford University Press.

[McGowan 2013] McGoan, K. (2013), How plants secretly talk to each other, in: Wired (Dec.2013).
URL: [accessed May 26, 2016].

[Mesjasz 2010]  Mesjasz, C.  (2010), Complexity of Social Systems, in: Acta Physica Polonica (2010), vol. 117, no. 4, 706-715.
URL: [accessed March 20, 2016].

[Miller / Page 2007] Miller, J.H. / Page, S.E. (2007),  Complex Adaptive Systems. An Introduction to Computational Models of Social Life, Princeton / Oxford: Princeton University Press.

[Mitleton-Kelly 2003] Mitleton-Kelly, E.(2003), Ten principles of complexity and enabling infrastructures, in: id.  (ed.) Complex Systems and Evolutionary Perspectives on Organisations: the Application of Complexity Theory to Organisations, Oxford, UK: Elsevier, 3-20.
URL:Ten principles of complexity and enabling infrastructures [accessed April 28, 2016].

[Villiers-Botha / Cilliers 2010] Villiers-Botha, T. de / Cilliers, P. (2010),  The Complex “I”: The Formation of Identity in Complex Systems, in: [Cilliers / Preiser 2010], 19-38.

[Wikipedia 2016h] Wikipedia (2016h), Set (mathematics),
URL: [accessed May 23, 2016].

[Wikipedia 2016l] – (2016l), Self-organization,
URL: [accessed May 23, 2016].

[Wikipedia 2016m] – (2016m), Law of thought,
URL: Law of thought [accessed May 26, 2016].

[Wikipedia 2016n] – (2016n), Laws of Form,
URL: Laws of Form [accessed May 26, 2016].

[Witzany 2014]  Witzany G. (ed.) (2014) Biocommunication of Animals, Dordrecht et al.: Springer.

[Witzany 2012]  – (ed.) (2012),Biocommunication of Fungi, Dordrecht: Springer.

[Witzany / Baluska 2012] / Baluska, F. (eds.) (2012), Biocommunication of Plants, Berlin / Heidelberg: Springer.


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