文章基本信息

标题：The statistical shape of geometric reasoning
本地全文：下载
作者：Yuval Hart ; Moira R. Dillon ; Andrew Marantan 等
期刊名称：Scientific Reports
电子版ISSN：2045-2322
出版年度：2018
卷号：8
期号：1
页码：12906
DOI：10.1038/s41598-018-30314-y
语种：English
出版社：Springer Nature
摘要：Abstract Geometric reasoning has an inherent dissonance: its abstract axioms and propositions refer to perfect, idealized entities, whereas its use in the physical world relies on dynamic perception of objects. How do abstract Euclidean concepts, dynamics, and statistics come together to support our intuitive geometric reasoning? Here, we address this question using a simple geometric task – planar triangle completion. An analysis of the distribution of participants’ errors in localizing a fragmented triangle’s missing corner reveals scale-dependent deviations from a deterministic Euclidean representation of planar triangles. By considering the statistical physics of the process characterized via a correlated random walk with a natural length scale, we explain these results and further predict participants’ estimates of the missing angle, measured in a second task. Our model also predicts the results of a categorical reasoning task about changes in the triangle size and shape even when such completion strategies need not be invoked. Taken together, our findings suggest a critical role for noisy physical processes in our reasoning about elementary Euclidean geometry.