“A Dynamic Systems Model of Cognitive and Language Growth”, 1991 (; backlinks):
In the first part of the article, a conceptual framework is sketched to define cognitive growth, including language growth, as a process of growth under limited resources. Important concepts are the process, level, and rate of growth; minimal structural growth level; carrying capacity and unutilized capacity for growth; and feedback delay.
Second, a mathematical model of cognitive growth under limited resources is presented, with the conclusion that the most plausible model is a model of logistic growth with delayed feedback.
Third, the model is transformed into a dynamic systems model based on the logistic growth equation. This model describes cognitive growth as a system of supportive and competitive interactions between growers. Models of normal logistic growth, U-shaped growth, bootstrap growth, and competitive growth are also presented.
An overview is presented of forms of adaptation of resources (eg. parental and tutorial assistance and support) to the growth characteristics of a cognitive or linguistic competence.
Finally, the question of how the model can account for stages of growth is discussed.
…Cognitive takeover phenomena and competitive growth: Under various conditions, the growth in one dimension may force another dimension to change qualitatively. For instance, a multicellular organism that exceeds a specific number of cells is, through evolution, forced to abandon its direct cell-environment contacts as a major form of energy exchange and to develop an inner structure (eg. a structure with a digestive tract). Cognitive and linguistic rules and strategies can be considered as information-management and production systems. Just as with the biological example, the form of information systems is not independent of quantitative properties of the information they have to manage. Manageability is a function of resources; that is, it poses no problems if one has all the time, space, and energy of the world. If an information-management system reaches a management limit—for example, in addressing problems that require more information than the system can cope with because of memory limitations—then it is likely either to remain constrained by that limit or to be replaced by another, more powerful information-management system. If the latter is the case, it is called a takeover. In the previous examples, the takeover is the effect of scarcity in internal resources, such as time or memory extension. In other cases, takeovers may be the result of external resource limitations. For instance, children often use “wrong” linguistic forms that are based on their immature grammars. Adults initially accept such forms but become increasingly intolerant as the child’s mastery of the correct form increases.
Cognitive development is full of takeover phenomena. Examples are the takeover of one-word by two-word sentence rules, takeover of concrete operatory logic by formal operatory logic in specific domains of application, or the takeover of one balance scale rule by another in the balance scale task (1983). In a substantial number of cases, takeover phenomena usually result in developmental regression (1982), U-shaped behavioral growth, or oscillatory growth (1982; 1982). Such regression is either a complete abandoning of the older rule or principle or a temporary decrease of the field of an initially successful application of a specific production rule, concept, and so on. Regressions have been found in the fields of early object cognition, concept development, ratio comparison, early imitation, language acquisition, face recognition, artistic development, intuitive thinking, gender identity development, and so on (1982; 1982).
A good example of regression toward zero performance level caused by a quantitative increase in the information to be managed by a rule system is provided by the development of conservation in 2–5-year-olds (1982). According to Mehler, 2-year-olds use a perceptual memory strategy and are capable of correctly solving many simple conservation problems. As perceptual differentiation increases, the amount of information encoded within a situation to be remembered increases correspondingly. At a specific point, the average amount to be remembered is simply too much to be managed by the perceptual memory strategy. This is the point at which a new strategy, based on the inference of rules and regularities, is adopted, while the old strategy quickly disappears. The new strategy, however, leads to a spectacular reduction—toward zero—of correct conservation performance. Only at the age of 5 is the regularities strategy back at the performance level of the 2-year-old using the memory strategy. The regularities approach, however, is much more powerful and has a much higher performance ceiling.
[cf. inverse & u-scaling in deep learning]
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