The Shape of Geometric Reasoning: Geometry Intuition as a Dynamic Visual Process

Summary

Date: 
December 7, 2016 - 1:00pm - 2:00pm
Location: 
Northwest 243
About the Speaker
Name: 
Yuval Hart
Speaker Title: 
Postdoctoral Fellow
Speaker Affiliation: 
Harvard SEAS

The field of geometric reasoning portrays an inherent dissonance - in its abstract form of axioms and propositions it contradicts our perception of dots with finite size and parallel lines that seem to intersect at the horizon. Thus, it is of interest to infer the mechanisms governing our geometric estimations. Previous studies suggested Euclidean rules as an innate, developing intuition in people. Here, we study how changes in triangle size effect people estimations of a missing corner location and angle size. We find that people's answers conflict with Euclidean rules and depend on triangle size manipulations. In turn, this suggests a dynamic visual process for geometric estimations. We analyzed the third vertex location distributions and find a downward bias of the mean position, linearly dependent on the triangle’s side length. The bias downward is further reflected in negative skewness values. The standard deviation of the position shows a sub-linear dependence on side length, STD~ s^0.77. We propose a model that describes the triangle completion mental process in terms of two mechanisms- a local noisy angle estimation and a global error-correction to the base angle value. A single parameter, the correlation length, reflecting the relative strength of the two mechanisms, can explain the behavioral experimental results. The model further captures the distribution of answers in categorical tests and verestimations of angle size. Taken together, our findings suggest that a dynamic visual process drives our geometric intuition. It further underlines geometric reasoning as a viable testbed for underlying principles of our thought.