Coordinate and categorical relations; Euclidean diagrams; Exact and co-exact relations; Metric and topological relations; Spatial relation processing; Adult; Female; Humans; Male; Photic Stimulation; Reaction Time; Task Performance and Analysis; Visual Fields; Young Adult; Cognition; Dominance, Cerebral; Space Perception; Experimental and Cognitive Psychology; Developmental and Educational Psychology; Arts and Humanities (miscellaneous); General Medicine
Abstract :
[en] The cognitive processing of spatial relations in Euclidean diagrams is central to the diagram-based geometric practice of Euclid's Elements. In this study, we investigate this processing through two dichotomies among spatial relations-metric vs topological and exact vs co-exact-introduced by Manders in his seminal epistemological analysis of Euclid's geometric practice. To this end, we carried out a two-part experiment where participants were asked to judge spatial relations in Euclidean diagrams in a visual half field task design. In the first part, we tested whether the processing of metric vs topological relations yielded the same hemispheric specialization as the processing of coordinate vs categorical relations. In the second part, we investigated the specific performance patterns for the processing of five pairs of exact/co-exact relations, where stimuli for the co-exact relations were divided into three categories depending on their distance from the exact case. Regarding the processing of metric vs topological relations, hemispheric differences were found for only a few of the stimuli used, which may indicate that other processing mechanisms might be at play. Regarding the processing of exact vs co-exact relations, results show that the level of agreement among participants in judging co-exact relations decreases with the distance from the exact case, and this for the five pairs of exact/co-exact relations tested. The philosophical implications of these empirical findings for the epistemological analysis of Euclid's diagram-based geometric practice are spelled out and discussed.
Disciplines :
Theoretical & cognitive psychology
Author, co-author :
Hamami, Yacin ; Université de Liège - ULiège > Traverses ; Centre for Logic and Philosophy of Science, Vrije Universiteit Brussel, Brussels, Belgium. Electronic address: yacin.hamami@gmail.com
van der Kuil, Milan N A; Department Health, Medical and Neuropsychology, Leiden University, Leiden, the Netherlands
Mumma, John; Philosophy Department, California State University of San Bernardino, San Bernardino, CA, USA
van der Ham, Ineke J M; Department Health, Medical and Neuropsychology, Leiden University, Leiden, the Netherlands
Language :
English
Title :
Cognitive Processing of Spatial Relations in Euclidean Diagrams.
This study was partly funded from a Strategic Research Project ( SRP ) of the Vrije Universiteit Brussel (Free University Brussels). YH acknowledges support from a postdoctoral fellowship of the FWO (Research Foundation - Flanders). This study was partly funded from a Strategic Research Project
(SRP) of the Vrije Universiteit Brussel (Free University Brussels). YH
acknowledges support from a postdoctoral fellowship of the FWO
(Research Foundation - Flanders).
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