Scenes from a thesis: modelling development

“One of the main concerns […] is how to account for quantitative growth in development and how to relate this quantitative growth to qualitative analyses and to the parameters in the model. The definition of such quantitative growth (or development) is an autocatalytic quantitative increase in a growth variable following the emergence of a specific structural possibility in the cognitive system. In other words, language development (or cognitive growth in general) consists of growth which is expressed in numbers (quantitative) and which is not entirely caused by some external factor (autocatalytic). This growth is caused by the system itself, i.e. change is induced by the cognitive system itself.”

From: Going the distance:  A Non-Linear Approach To Change In Language Development. H.G. Ruhland. Groningen, 1998.

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Scenes from a thesis: forms of change

“In sum, I distinguish[ed] six forms of change in time series. There is change which has no end point, i.e. linear and exponential change, and there is change with an end point, i.e. logistic, asymptotic, discrete and cusp. […]. This end point is constant with respect to the score on the y-axis. The difference between logistic/asymptotic and discrete/cusp (all four have an end state) is the suddenness of change. The difference between logistic and asymptotic growth is the starting point. The difference between the discrete step and the cusp is that the cusp has an overlap of states and more than one possible jump from one state to the other. Despite the intuitively appealing descriptions, all forms of growth lack a formal criterion (e.g. how can one distinguish between a rapid gradual change and a discrete step?). Apart from a conclusive definition, the descriptions are also problematic in the sense of testing. Therefore, I present a mathematical approach to quantitative development. [These] Non-linear models and theories […] models and theories allow for an estimation of parameters and [they] state the relationship between x (a time index) and y (the variable) values in terms of a growth indication (e.g. in terms of continuity and discontinuity).”

From: Going the distance:  A Non-Linear Approach To Change In Language Development. H.G. Ruhland. Groningen, 1998.

 

Scenes from a thesis: development

“Development is not an unambiguous concept: there are several meanings (or definitions) of development. Development means growth, and growth is defined as an increase in size or value. This means that something has been present all the time, nothing new is added. Development also means evolution, which derives from the Latin evolve meaning to unfold or to open out. Stage of advancement is [also] listed as a definition of development, advancement being derived from the word advance, which means (among others) to rise or to move forward. [So], If change (e.g. to increase, to open out, to move forward) is the core aspect of development, the next step is to determine the treatment of change (development) in theories on development.”

From: Going the distance:  A Non-Linear Approach To Change In Language Development. H.G. Ruhland. Groningen, 1998.