Model of Hierarchical Complexity

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= "The Model of Hierarchical Complexity presents a framework for scoring reasoning stages in any domain as well as in any cross cultural setting". [1]


Cory David Barker on the Metamodern Forum:

"my take is that post-modernity is inability to coordinate paradigms beyond the relativism transition step. How it works, is that the people at paradigmatic stage about ideologies who cannot transition beyond the relativism transition step and coordinate the apparent disparities, assume that their coordinative limit necessitates that knowledge is relative. These folks then proclaim this, and ideology gets downward assimilated into lower stage coordinations by their audience, and the audience who inherits the ideas cannot reconcile the paradigmatic disparities because they are trying to coordinate a problem that requires coordinate at one or more magnitudes of complexity higher than they are capable of performing.

The current problem requires integral, unified models that fit together paradigms cross-paradigmatically. Michael’s notion of meta-cross paradigmatic is a different kind of “meta” and should not be confused with meta-systematic. In the MHC schema, correspondence of unified models is an expression of meta-cross paradigmatic performance. The meta-cross paradigmatic stages produces principles, paradigmatic coordinates the principles of a given domain, and cross-paradigmatic stage corresponds the paradigms by their principles. Meta-cross paradigmatic performance has to do with large-scale congruencies across cross-paradigmatic coordinations. Even there, we hit the relativism step since the step exists fractally at all stages, but us folks who coordinate between unifying models at the largest scale know either concisely or intuitively from developing through the paradigmatic relativism transition with the coordination of a wide array of paradigmatic content, is that “relativism” is actually just part of the process of fitting together ideas and actions until a higher order coordination is discovered, which which produces a higher order equilibrium “absolute”.

(April 2021)


From a review by Russ Volckmann of

- a special triple issue of Ervin Laszlo’s World Futures, Vol. 64 Nos. 05–07 (2008): Postformal Thought and Hierarchical Complexity with Guest Editors Michael Lamport Commons and Sara Nora Ross.

1. Michael Commons:

“The Model of Hierarchical Complexity…offers a standard method of examining the universal patterns of evolution and development. It is a quantitative behavioral developmental theory…There are two kinds of hierarchical complexity. The commonly recognized one refers to the ubiquitous linear hierarchies that are described in many fields of study. These are descriptive. By contrast, the Model of Hierarchical Complexity offers a standard method of examining the nonlinear activity of constructing the universal patterns of evolution and development. It accounts for evolution and development by recognizing their patterns are comprised of tasks, or actions, performed at specified orders of hierarchical complexity. Whereas the Model’s unidimensional measure is linear, the tasks it measures are nonlinear performances, as this special issue conveys. The nonlinear activity of tasks is that of organizing, or coordinating, information. Hierarchical complexity applies to any events or occasions in which information is organized. The kinds of entities that organize information include humans and their biological systems as well as their social organizations, non-human organisms, and machines, including computers.”

“The hierarchical complexity of tasks, or actions, is defined in words as follows. Actions at a higher order of hierarchical complexity:

(a) are themselves defined in terms of actions at the next lower order of hierarchical complexity;

(b) organize and transform the lower-order actions;

(c) produce organizations of lower-order actions that are new and not arbitrary. These next higher order actions cannot be accomplished by those lower-order actions alone.”


2. From the Wikipedia:

"The model of hierarchical complexity (MHC) is a formal theory and a mathematical psychology framework for scoring how complex a behavior is. Developed by Michael Lamport Commons and colleagues,[3] it quantifies the order of hierarchical complexity of a task based on mathematical principles of how the information is organized, in terms of information science. Its forerunner was the general stage model.[6]

Behaviors that may be scored include those of individual humans or their social groupings (e.g., organizations, governments, societies), animals, or machines. It enables scoring the hierarchical complexity of task accomplishment in any domain.

It is based on the very simple notions that higher order task actions:

  • are defined in terms of the next lower ones (creating hierarchy);
  • organize the next lower actions;
  • organize lower actions in a non-arbitrary way (differentiating them from simple chains of behavior).

It is cross-culturally and cross-species valid. The reason it applies cross-culturally is that the scoring is based on the mathematical complexity of the hierarchical organization of information. Scoring does not depend upon the content of the information (e.g., what is done, said, written, or analyzed) but upon how the information is organized.

The MHC is a non-mentalistic model of developmental stages.[2] It specifies 16 orders of hierarchical complexity and their corresponding stages. It is different from previous proposals about developmental stage applied to humans;[10] instead of attributing behavioral changes across a person's age to the development of mental structures or schema, this model posits that task sequences of task behaviors form hierarchies that become increasingly complex. Because less complex tasks must be completed and practiced before more complex tasks can be acquired, this accounts for the developmental changes seen, for example, in individual persons' performance of complex tasks. (For example, a person cannot perform arithmetic until the numeral representations of numbers are learned. A person cannot operationally multiply the sums of numbers until addition is learned. However, as much as natural intelligence helps human to understand some numbers, it does not play a complete role in multiplying large numbers without learning additions.

The creators of the MHC claim that previous theories of stage have confounded the stimulus and response in assessing stage by simply scoring responses and ignoring the task or stimulus.[2] The MHC separates the task or stimulus from the performance. The participant's performance on a task of a given complexity represents the stage of developmental complexity.

Previous stage theories were unsatisfying to Commons and Richards because the theories did not show the existence of the stages more than describing sequential changes in human behavior. This led them to create a list of two concepts they felt a successful developmental theory should address.

The two ideas they wanted to study were

(1) the hierarchical complexity of the task to be solved and

(2) the psychology, sociology, and anthropology of the task performance (and the development of the performance."



Summary of higher stages:

"Few individuals perform at stages above formal operations. More complex behaviors characterize multiple system models ( Kallio, 1995; Kallio & Helkama, 1991). Some adults are said to develop alternative to, and perspectives on, formal operations. They use formal operations within a “higher” system of operations and transcend the limitations of formal operations. In any case, these are all ways in which these theories argue and present converging evidence that adults are using forms of reasoning that are move complex than formal operations.

At the systematic stage (11), the new concepts are referred to as 3rd order abstractions. These coordinate elements of abstract systems. Words like bureaucratic, capitalist, functional, and structural are common. The systematic stage concept, structure, for example, can be employed to ask whether the structure of camp helps instill the qualities we want in future citizens. The logical structure of this stage coordinates multiple aspects of two or more abstractions, as in: “relationships are built on trust and though we can’t always keep them, making promises is one way we build trust, so it’s generally better to make promises than not to make them.” Here, the importance of trust to relationships, building trust, and the possibility that promises can be broken, are all taken into account while formulating the conclusion that promises are desirable.

At the metasystematic stage (12), the new concepts are referred to as 1st order principles. These coordinate formal systems. Words like autonomy, parallelism, heteronomy, and proportionality are common. The metasystematic stage concept of parallelism, for example, can be employed to compare the structures of the military and of camp as institutions. The logical structure of this stage identifies one aspect of a principle or an axiom that coordinates several systems, as in: “contracts and promises are articulations of a unique human quality, mutual trust, which coordinates human relations.” Here, contracts and promises are seen as the instantiation of a broader principle coordinating human interactions.

At the paradigmatic stage (13), people create new fields out of multiple metasystems. The objects of paradigmatic acts are metasystems. When there are metasystems that are incomplete and adding to them would create inconsistences, quite often a new paradigm is developed. Usually, the paradigm develops out of a recognition of a poorly understood phenomenon. The actions in paradigmatic thought form new paradigms from supersystems (metasystems).

Paradigmatic actions often affect fields of knowledge that appear unrelated to the original field of the thinkers. Individuals reasoning at the paradigmatic order have to see the relationship between very large and often disparate bodies of knowledge, and co-ordinate the metasystematic supersystems. Paradigmatic action requires a tremendous degree of decentration. One has to transcend tradition and recognize one's actions as distinct and possible troubling to those in one's environment. But at the same time one has to understand that the laws of nature operate both on oneself and one’s environment—a unity. This suggests that learning in one realm can be generalized to others.

At the cross-paradigmatic, paradigms and coordinated. This is the fourth postformal stage. Cross-paradigmatic actions integrate paradigms into a new field or profoundly transform an old one. A field contains more than one paradigm and cannot be reduced to a single paradigm. One might ask whether all interdisciplinary studies are therefore cross-paradigmatic? Is psycho biology cross-paradigmatic? The answer to both questions is ‘no’. Such interdisciplinary studies might create new paradigms, such as psychophysics, but not new fields.

This order has not been examined in much detail because there are very few people who can solve tasks of this complexity. It may also take a certain amount of time and perspective to realize that behavior or findings were cross-paradigmatic. All that can be done at this time is to identify and analyze historical examples."


Horizontal vs Vertical Complexity

From the Wikipedia:

  • Horizontal complexity

"Classical information describes the number of "yes–no" questions it takes to do a task. For example, if one asked a person across the room whether a penny came up heads when they flipped it, their saying "heads" would transmit 1 bit of "horizontal" information. If there were 2 pennies, one would have to ask at least two questions, one about each penny. Hence, each additional 1-bit question would add another bit. Let us say they had a four-faced top with the faces numbered 1, 2, 3, and 4. Instead of spinning it, they tossed it against a backboard as one does with dice in a game of craps. Again, there would be 2 bits. One could ask them whether the face had an even number. If it did, one would then ask if it were a 2. Horizontal complexity, then, is the sum of bits required by just such tasks as these.

  • Vertical complexity

Hierarchical complexity refers to the number of recursions that the coordinating actions must perform on a set of primary elements.

Actions at a higher order of hierarchical complexity:

(a) are defined in terms of actions at the next lower order of hierarchical complexity;

(b) organize and transform the lower-order actions;

(c) produce organizations of lower-order actions that are qualitatively new and not arbitrary, and cannot be accomplished by those lower-order actions alone.

Once these conditions have been met, we say the higher-order action coordinates the actions of the next lower order.

To illustrate how lower actions get organized into more hierarchically complex actions, let us turn to a simple example. Completing the entire operation 3 × (4 + 1) constitutes a task requiring the distributive act. That act non-arbitrarily orders adding and multiplying to coordinate them. The distributive act is therefore one order more hierarchically complex than the acts of adding and multiplying alone; it indicates the singular proper sequence of the simpler actions. Although simply adding results in the same answer, people who can do both display a greater freedom of mental functioning. Additional layers of abstraction can be applied. Thus, the order of complexity of the task is determined through analyzing the demands of each task by breaking it down into its constituent parts.

The hierarchical complexity of a task refers to the number of concatenation operations it contains, that is, the number of recursions that the coordinating actions must perform. An order-three task has three concatenation operations. A task of order three operates on one or more tasks of vertical order two and a task of order two operates on one or more tasks of vertical order one (the simplest tasks)."



Brendan Graham Dempsey:

"Commons’s Model completes the Piagetian research program with a full and comprehensive articulation of the stages of cognitive development. Commons’s model adds stages on either end of Piaget’s, extending its application to non-human animals as well as filling in the post-Formal stages of human development that Piaget’s work did not cover.

It also distinguishes amongst some of the stages Piaget had identified with greater clarity:

  1. Automatic Stage
  2. Sensory or Motor Stage
  3. Circular Sensory-Motor Stage
  4. Sensory-Motor Stage
  5. Nominal Stage
  6. Pre-Operational Stage
  7. Primary Stage
  8. Concrete Stage
  9. Abstract Stage
  10. Formal Stage
  11. Systematic Stage
  12. Meta-Systematic Stage
  13. Paradigmatic Stage
  14. Cross-Paradigmatic Stage "


More information

  • For a summary of the cognitive capacities that come online with each new stage, see Hanzi Freinacht’s essay “What is the Model of Hierarchical Complexity?”
  • Book: Emergentism: A Religion of Complexity for the Metamodern World. By Adyahanzi, Brendan Graham Dempsey. Metamodern Spirituality Series, Vol. VI. [2] For more, see also: Emergentism as a Religion of Complexity