The Model of Hierarchical Complexity, Explained

Introduction

The Model of Hierarchical Complexity, usually shortened to MHC, is a framework for measuring how complex a task or a piece of reasoning actually is. It was developed by Michael Commons and Francis Richards, and it has been used in developmental psychology for decades. ¹

Its central move is simple to state and powerful in practice. Instead of defining developmental stages by age, by content, or by description, the MHC defines them by structure: by how the parts of an action are organized. Each higher order of complexity coordinates the actions of the order below it into a new whole that could not exist at the lower level.

This is the framework underneath how Arq.training thinks about levels. When Arq talks about cognitive complexity growing in stages, the MHC is the model that gives those stages a precise, scoreable definition rather than a vague impression.

The problem it solves

For most of the twentieth century, developmental stages were defined by what people could do at a certain age. Piaget's stages, for all their influence, were tied to childhood and to specific content like conservation of volume. ² That left two problems. Stages defined by age cannot explain adult development, and stages defined by content cannot transfer across domains.

Commons and Richards asked a different question. What if you could define the complexity of a task without reference to who performs it or what it is about? If difficulty could be measured structurally, then the same ruler would work for a child sorting blocks, an adult weighing an ethical dilemma, and a leader designing an organization. ¹

That ruler is the order of hierarchical complexity, and it is what makes the model general rather than tied to one age group or one subject.

How an order of complexity is defined

The MHC defines a higher-order task by three conditions. A higher-order action is defined in terms of the actions at the next lower order. It organizes those lower actions in a way that is non-arbitrary, meaning the coordination itself carries meaning. And it coordinates two or more lower-order actions rather than simply repeating one. ¹

An everyday illustration helps. Performing single arithmetic operations is one order. Coordinating those operations into the logic of an algebraic equation, where the operations themselves become objects you manipulate, is a higher order. Stepping up again to reason about systems of relationships among equations is higher still. Each level treats the products of the level below as the raw material it now operates on.

Because the definition is formal, every task can in principle be assigned a number, its order of hierarchical complexity. That number is not a score of how well someone did. It is a measure of how complex the task itself is. A person's stage is then the highest order of task they can reliably coordinate.

The stages, from concrete to metasystematic

The MHC describes a long sequence of orders, from the earliest sensory and motor actions up through the kinds of reasoning that most formal schooling targets and beyond. The orders most relevant to education and work cluster near the top of the everyday range.

• The concrete order coordinates specific actions and simple logic about particular cases.

• The abstract order forms variables and categories out of concrete instances, the move from this dog to dogs in general.

• The formal order reasons with relationships between variables: if-then logic, controlling for one factor while varying another. Much of standardized schooling tops out here.

• The systematic order coordinates multiple relationships into whole systems, seeing how variables interact rather than treating them one at a time.

• The metasystematic order operates on whole systems as objects, comparing, integrating, and critiquing entire frameworks against one another.

Most adults reason comfortably at the formal order on familiar problems and reach systematic or metasystematic reasoning only on questions they have genuinely wrestled with. This is precisely the territory where complex real-world problems live, and where developmental gains pay off most. ³

Why it makes thinking measurable

The reason the MHC matters for assessment is that an analytic definition can be scored reliably. If a stage is just a description, two raters will disagree about who is in it. If a stage is defined by structure, raters can be trained to identify that structure consistently, and machines can be trained to detect it too.

This is the foundation under developmental scoring systems like the Lectical Assessment System, built by Theo Dawson and Lectica, which scores the complexity of reasoning against a validated scale derived from this tradition. ⁴ It is also why a number assigned by the model is more useful than a vague label: it supports growth tracking, because you can see movement from one order to the next over time.

Arq builds on this lineage. Rather than asking whether an answer is right, Arq reads the order of complexity a person is operating at while they reason through a problem, then designs the next challenge to sit just above it.

What the model does and does not claim

The MHC is a measure of structural complexity, not a verdict on a person's worth, creativity, or character. A response at a higher order is not automatically wiser or kinder. It coordinates more, which is an advantage for genuinely complex problems and irrelevant for simple ones.

Stage is also task-specific and supported, not a fixed global rank. Performance rises with familiarity, motivation, and scaffolding and falls under stress or novelty, a point Kurt Fischer's dynamic skill theory makes central. ⁵ The honest reading of a developmental level is therefore a range, the band a person works within across conditions, not a single permanent number.

Held to those limits, the model is a precise instrument for one important thing: seeing how much of a problem a person can coordinate, and watching that capacity grow.

Originally published on Arq.