Making Cognitive Niches Explicit: On the Importance of External Cognitive Representations in Accounting for Cumulative Culture.

Cumulative transmission and innovation are the hallmark properties of the cultural achievements of human beings. Cognitive scientists have traditionally explained these properties in terms of social learning and creativity. The non-social cognitive dimension of cumulative culture, the so-called technical reasoning, has also been accounted for recently. These explanatory perspectives are methodologically individualistic since they frame cumulative and innovative culture in terms of the processing of inner cognitive representations. Here we show that going beyond methodological individualism could facilitate an understanding of why some inventions are disseminated in a stable form and constitute the basis for further modifications. Drawing on three cases of cognitive history of prominent achievements of Antiquity, i.e., Homerian epics, Euclidean geometry, and Roman law, we investigate which properties of cognitive artifacts shaped cognitive niches for modifying original cognitive tasks or developing new ones. These niches both constrained and enabled the cognitive skills of humans to promote cumulative culture and further innovations. At the same time, we claim that "wide cognition," incorporating both intracranial resources and external cognitive representations, constitutes a platform for building explanations of cognitive phenomena developing over a historical time scale.

Professional mathematicians do not differ from others in the symbolic numerical distance and size effects.

The numerical distance effect (it is easier to compare numbers that are further apart) and size effect (for a constant distance, it is easier to compare smaller numbers) characterize symbolic number processing. However, evidence for a relationship between these two basic phenomena and more complex mathematical skills is mixed. Previously this relationship has only been studied in participants with normal or poor mathematical skills, not in mathematicians. Furthermore, the prevalence of these effects at the individual level is not known. Here we compared professional mathematicians, engineers, social scientists, and a reference group using the symbolic magnitude classification task with single-digit Arabic numbers. The groups did not differ with respect to symbolic numerical distance and size effects in either frequentist or Bayesian analyses. Moreover, we looked at their prevalence at the individual level using the bootstrapping method: while a reliable numerical distance effect was present in almost all participants, the prevalence of a reliable numerical size effect was much lower. Again, prevalence did not differ between groups. In summary, the phenomena were neither more pronounced nor more prevalent in mathematicians, suggesting that extremely high mathematical skills neither rely on nor have special consequences for analogue processing of symbolic numerical magnitudes.

Professional mathematicians differ from controls in their spatial-numerical associations.

While mathematically impaired individuals have been shown to have deficits in all kinds of basic numerical representations, among them spatial-numerical associations, little is known about individuals with exceptionally high math expertise. They might have a more abstract magnitude representation or more flexible spatial associations, so that no automatic left/small and right/large spatial-numerical association is elicited. To pursue this question, we examined the Spatial Numerical Association of Response Codes (SNARC) effect in professional mathematicians which was compared to two control groups: Professionals who use advanced math in their work but are not mathematicians (mostly engineers), and matched controls. Contrarily to both control groups, Mathematicians did not reveal a SNARC effect. The group differences could not be accounted for by differences in mean response speed, response variance or intelligence or a general tendency not to show spatial-numerical associations. We propose that professional mathematicians possess more abstract and/or spatially very flexible numerical representations and therefore do not exhibit or do have a largely reduced default left-to-right spatial-numerical orientation as indexed by the SNARC effect, but we also discuss other possible accounts. We argue that this comparison with professional mathematicians also tells us about the nature of spatial-numerical associations in persons with much less mathematical expertise or knowledge.