How to discover modules in mind and brain: the curse of nonlinearity, and blessing of neuroimaging. A comment on Sternberg (2011).11 May 2018
Sternberg (2011) elegantly formalizes how certain sets of hypotheses, specifically modularity and pure or composite measures, imply certain patterns of behavioural and neuroimaging data. Experimentalists are often interested in the converse, however: whether certain patterns of data distinguish certain hypotheses, specifically whether more than one module is involved. In this case, there is a striking reversal of the relative value of the data patterns that Sternberg considers. Foremost, the example of additive effects of two factors on one composite measure becomes noninformative for this converse question. Indeed, as soon as one allows for nonlinear measurement functions and nonlinear module processes, even a cross-over interaction between two factors is noninformative in this respect. Rather, one requires more than one measure, from which certain data patterns do provide strong evidence for multiple modules, assuming only that the measurement functions are monotonic. If two measures are not monotonically related to each other across the levels of one or more experimental factors, then one has evidence for more than one module (i.e., more than one nonmonotonic transform). Two special cases of this are illustrated here: a "reversed association" between two measures across three levels of a single factor, and Sternberg's example of selective effects of two factors on two measures. Fortunately, functional neuroimaging methods normally do provide multiple measures over space (e.g., functional magnetic resonance imaging, fMRI) and/or time (e.g., electroencephalography, EEG). Thus to the extent that brain modules imply mind modules (i.e., separate processors imply separate processes), the performance data offered by functional neuroimaging are likely to be more powerful in revealing modules than are the single behavioural measures (such as accuracy or reaction time, RT) traditionally considered in psychology.