Model of hierarchical complexity

The model of hierarchical complexity is a framework for scoring how complex a behavior is, such as verbal reasoning or other cognitive tasks. 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. This model has been developed by Michael Commons and others since the 1980s. The model of hierarchical complexity is a framework for scoring how complex a behavior is, such as verbal reasoning or other cognitive tasks. 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. This model has been developed by Michael Commons and others since the 1980s. 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, 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. 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: 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. It specifies 16 orders of hierarchical complexity and their corresponding stages. It is different from previous proposals about developmental stage applied to humans; 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). 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. 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. One major basis for this developmental theory is task analysis. The study of ideal tasks, including their instantiation in the real world, has been the basis of the branch of stimulus control called psychophysics. Tasks are defined as sequences of contingencies, each presenting stimuli and each requiring a behavior or a sequence of behaviors that must occur in some non-arbitrary fashion. The complexity of behaviors necessary to complete a task can be specified using the horizontal complexity and vertical complexity definitions described below. Behavior is examined with respect to the analytically-known complexity of the task. Tasks are quantal in nature. They are either completed correctly or not completed at all. There is no intermediate state (tertium non datur). For this reason, the model characterizes all stages as P-hard and functionally distinct. The orders of hierarchical complexity are quantized like the electron atomic orbitals around the nucleus: each task difficulty has an order of hierarchical complexity required to complete it correctly, analogous to the atomic Slater determinant. Since tasks of a given quantified order of hierarchical complexity require actions of a given order of hierarchical complexity to perform them, the stage of the participant's task performance is equivalent to the order of complexity of the successfully completed task. The quantal feature of tasks is thus particularly instrumental in stage assessment because the scores obtained for stages are likewise discrete. Every task contains a multitude of subtasks. When the subtasks are carried out by the participant in a required order, the task in question is successfully completed. Therefore, the model asserts that all tasks fit in some configured sequence of tasks, making it possible to precisely determine the hierarchical order of task complexity. Tasks vary in complexity in two ways: either as horizontal (involving classical information); or as vertical (involving hierarchical information).