We present an account of processing capacity in the ACT-R theory. At the symbolic level, the number of chunks in the current goal provides a measure of relational complexity. At the subsymbolic level, limits on spreading activation, measured by the attentional parameter W, provide a theory of processing capacity, which has been applied to performance, learning, and individual differences data.

We discuss how modified dual-task approaches may be used to verify the degree to which cognitive tasks are capacity demanding. We also delineate some of the complexities associated with the use of the “double easy-to-hard” paradigm for testing claim of Halford, Wilson & Phillips that hierarchical reasoning imposes processing demands equivalent to those of transitive reasoning.

Synchronization of neural activity in oscillatory neural networks is a general principle of information processing in the brain at both preattentional and attentional levels. This is confirmed by a model of attention based on an oscillatory neural network with a central element and models of feature binding and working memory based on multi-frequency oscillations.

We argue that Halford et al.'s characterisation of relational complexity offers an unadaptive principle in terms of cognitive economy, that its relation with the empirical evidence is highly selective, and that the task behaviours used in support of a multivector processing space are better described by linear serial processes which do not require n-dimensional mappings for their emergence.

Relational complexity theory has important virtues, but the present model omits key aspects and evidence. In contrast, skill theory specifies (1) a detailed series of developmental changes in relational complexity from birth to age 30, (2) processes of interaction of content and structure that produce variability in complexity, (3) the role of cortical development, and (4) empirical criteria for complexity levels, including developmental discontinuities. Many findings support these specifications.

Halford et al. have sharpened the concept of processing capacity as applied to various complex tasks. This commentary examines the apparent contradiction between capacity theories and theories in which it is processing speed, rather than capacity, that presumably limits cognitive performance. It explains how capacity and speed often are interrelated and suggests how one might examine whether capacity or speed is the more elementary in processing.

Relational complexity provides a metric for measuring task demands, and in this respect has much in common with the cognitive complexity and control theory. However, relational complexity does not account for the relative difficulty of different relational types, and appears to underestimate the importance of changes in children's ability to act on the basis of their understanding.

Halford, Wilson & Phillips argue that cognitive development is driven by increases in processing capacity. We suggest that changes in relational knowledge are as important or more so. We present evidence that 3-year-olds' analogical abilities are sharply improved by teaching them relational labels; over a 30-minute experimental session children gained approximately 2 years in effective performance. These results mandate caution interpreting age-related change as indicating maturational change, and call for a deeper consideration of the role of epistemological change in cognitive development.

This commentary focusses on the evidence used by Halford et al. to support their postulated links between relational complexity and age differences in children's understanding of concepts. None of their developmental claims is consistent with recent cognitive-developmental research. Relational complexity must be an important variable in cognition, but it does not provide a satisfactory metric for explaining cognitive development.

The discovery of a quaternary complexity limitation to mature cognitive operations raises important theoretical issues. We propose that cognitive limitations arise naturally in a complex dynamic information processing system, and consider problems such as the distinction between parallel and serial processes and the representativeness of the empirical data base used by Halford et al. to support their relational complexity scheme.

In a simple economic decision problem with multi-tasking the dimensionality of the problem is neither a necessary nor a sufficient measure of complexity. Rather, dimension is good measure of complexity when there is an aggregate resource constraint that creates an interaction between the different activities, resulting in a problem with high algorithmic complexity.

Halford et al. are not redefining capacity in the sense of limit on resources but in the sense of limits on what resources can do. Furthermore, the necessity of using resource theory as a theoretical frame is questionable.

Measurements of the dimensionality of chaotic attractors obtained on behavioral data represent the task complexity and also could be hypothesized to reflect the number of synchronized neural groups involved in the generation of the data. The changes in dimensionality for different experimental conditions suggest that limited processing capacity, task complexity, demand, and synchrony in neural firing might be closely related.

Two assertions of Halford et al. are critiqued: their claim of priority in relational complexity analysis and the sufficiency for cognitive development of their relational-complexity analysis of tasks. Critical discussion of concrete task analyses (i.e., the relational complexity of proportionality problems, of balance scale problems, and the Tower of Hanoi) serves, by way of counterexamples, to highlight problems in their method.

Much of Halford et al.'s discussion of vector models for representing relations concerns the perceived inadequacies of alternative methods with respect to chunking, binding, systematicity, and resource requirements. Vector-based models for storing relations are in their infancy, however, and the relative merits of different schemes are not so clearly in favor of their STAR scheme as Halford et al. portray.

The metric devised by Halford, Wilson & Phillips may have considerable potential in distinguishing between the working memory demands of different tasks but may be less effective in distinguishing working memory capacity between individuals. Despite the strengths of the metric, determining whether an effect is caused by relational complexity or by differential levels of expertise is currently problematic.

Halford et al.'s analysis of relational complexity provides a possible framework for characterizing the symbolic functions of the prefrontal cortex. Studies of prefrontal patients have revealed that their performance is selectively impaired on tasks that require integration of two binary relations (i.e., tasks that Halford et al.'s analysis would identify as three-dimensional). Analyses of relational complexity show promise of helping to understand the neural substrate of thinking.

Halford et al. seek to provide a framework that unifies distinct developmental phenomena. However, in pursuit of this goal, they sidestep crucial aspects of some well-known developmental benchmarks (most notably Transitive Inference and Object Concept), and they do not acknowledge “repeated” or “direct” experience as possibly being more fundamental than relational complexity, instead, ascribe all experience a secondary role.

The core issue of our target article concerns how relational complexity should be assessed. We propose that assessments must be based on actual cognitive processes used in performing each step of a task. Complexity comparisons are important for the orderly interpretation of research findings. The links between relational complexity theory and several other formulations, as well as its implications for neural functioning, connectionist models, the roles of knowledge, and individual and developmental differences, are considered.