Abstract
ABSTRACTSpatial relations are central to geometrical thinking. With respect to the classical elementary geometry of Euclid’s Elements, a distinction between co-exact, or qualitative, and exact, or metric, spatial relations has recently been advanced as fundamental. We tested the universality of intuitions of these relations in a group of Senegalese and Dutch participants. Participants performed an odd-one-out task with stimuli that in all but one case display a particular spatial relation between geometric objects. As the exact/co-exact distinction is closely related to Kosslyn’s categorical/coordinate distinction, a set of stimuli for testing all four types was used. Results suggest that intuitions of all spatial relations tested are universal. Yet, culture has an important effect on performance: Dutch participants outperformed Senegalese participants and stimulus layouts affect the categorical and coordinate processing in different ways for the two groups. Differences in level of education within the Senegalese participants did not affect performance.
Highlights
Euclid’s theory of geometry presented in the Elements is a highly influential achievement of western culture
Wulff argues that the central feature of Euclidean geometry is its demonstrative character and its logical structure, rather than what can be seen in graphical pictures of geometric objects
We examined the effect of culture by comparing the Dutch and Senegalese participants, Figure 2(a)
Summary
Euclid’s theory of geometry presented in the Elements is a highly influential achievement of western culture. Izard and colleagues (2011) have provided evidence that the Mundurucu possess intuitions of geometric concepts beyond perceptual experience, such as infinite lines. The premise of these empirical investigations has been criticised by Wulff in the discussion of Wulff et al (2006) in his commentary to Dehaene et al (2006). Wulff thereby follows the modern view on geometric reasoning according to which pictures do not, and should not, play any role in geometric demonstrations (Hilbert, 1971) From this point of view, an empirical investigation of Euclidean geometry, which only involves pictures of geometric objects, necessarily misses the central feature of Euclidean geometry as a mathematical theory.
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