Anatomy of Complexity


For the sake of argument understanding complexity can be reset around two postulates:

  • It can only be assessed through symbolic representations
  • It can be set in terms of problems and solutions spaces

Taking a leaf from thermodynamics, complexity can be described through the micro- and macro-states representing problems and solutions spaces, respectively. When put through ontological prisms, micro-states represent facts from environments, macro-states the categories meant to dealt with them, and entropy the part of the former that cannot be accounted for by the latter.

Complexity viewed through Ontological Prism

Complexity is thus determined by the alternative paths between problems and solutions:

  • 2D (local or logical) complexity, when the symbolic representation of problem and solution spaces can be directly mapped
  • 3D (global or conceptual) complexity, when time and uncertainties introduce a level of indirection between the representations of problem and solution spaces

2D complexity is a matter of self-contained issues subject to reasoned solutions; by contrast 3D complexity corresponds to open-ended issues that entail values and judgments in support of decision-making.

2D Complexity

The direct mapping of symbolic representation of problems and solutions spaces can be achieved when all relevant facts of the former can be taken into account by the latter, in other words when uncertainties about data can be assessed and all stakes and causal chains can be identified. That can be done by crossing anchors and taxonomies:

  • Anchors (#) identify the relevant facts (objects and activities) in problem space
  • Taxonomies (/) define the relevant variants (structures and behaviors) in problem space
2D Complexity

With problems and solutions spaces fully set in 2D, anchors can be used to align facts with categories and taxonomies with corresponding subtypes. Explicit complexity will be determined by subtypes and branches in causal chains introduced to deal with overlapping categories; implicit complexity (aka entropy) would correspond to facts left unexplained, taking into account known uncertainties (aka known unknowns) about data, stakes, and causal chains.

3D Complexity

Contrary to self-contained 2D problems, 3D issues are open-ended with regard to facts, stakes, and causal chains; which brings back cybernetics and the exchange of information between organizations and their environment. That makes for two kinds of complexity: extensional with regard to environments, intensional with regard to organizations.

Extensional complexity is determined by environments and purposes. To begin with, putting names on facts determines the number of micro-states and thus the size of problems space. Then, naming facts entails a selection of the ones deemed to be relevant, and as a corollary the hiding of alternatives ones possibly more explanatory; that caveat can be overcome with statistics and deep-learning.

3D Complexity

Intensional complexity stems from the way organizations represent their context and purpose, from straightforward mapping (no additional complexity) to conjectural or conflicting stakes and causal chains raising issues about the status of facts (observed, asserted, assessed, …) and concepts (symbolic or physical, actual or virtual, …:).

Both types of complexity entail the pairing of decision-making and knowledge management processes, typically along the Observation, Orientation, Decision, Action (OODA) loop:

  • Observation: carried out by avatars of the Maxwell’s demon standing at enterprises’ gates monitoring changes in extensional complexity.
  • Orientation: assessing the effectiveness of representations
  • Decision: improving the effectiveness of representations in order to reduce intensional complexity
  • Action: improving the collect of facts in order to reduce extensional complexity

That pairing, and the management of complexity, is made possible by the digital immersion of enterprises in their environment, and can be effective with ontological prisms used to build EA digital twins.

Complexity & Governance Horizons

Complexity appears as a fundamental characteristic of enterprises’ architectures, making its management a core governance issue. That convergence is illustrated by the alignment of the complexity taxonomy with traditional governance horizons:

  • Operational (2D): facts can be directly mapped to information and put to use as knowledge, allowing for routine decision-making.
  • Tactical (3D, extensional): the reliability of information can be improved with time, enabling rational decisions about predetermined stakes
  • Strategic (3D, intensional): characterized by multiple agents, conflicting stakes, and alternative causal chains

Extensional and intensional complexity can also be aligned with zero- and non zero-sum issues as defined by Game theory.

Further Reading

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