Vertical Complexity of Tasks Performed
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, corresponding to the atomic Slater eigenstate. 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 (Overton, 1990). 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).
Read more about this topic: Model Of Hierarchical Complexity
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