Going Round in Circles: A Cognitive Bias in Geometric Reasoning

Deductive reasoning is essential to most of our scientific and technological achievements and is a crucial component to scientific education. In Western culture, deductive reasoning first emerged as a dedicated mode of thinking in the field of geometry, but the cognitive mechanisms behind this major intellectual achievement remain largely understudied. Here, we report an unexpected cognitive bias in geometric reasoning that challenges existing theories of human deductive reasoning. Over two experiments involving almost 250 participants, we show that educated adults systematically mistook as valid a set of elementary invalid inferences with points and circles in the Euclidean plane. Our results suggest that people got "locked" on unwarranted conclusions because they tended to represent geometric premisses in specific ways and they mainly relied on translating, but not scaling, the circles when searching for possible conclusions. We conducted two further experiments to test these hypotheses and found confirmation for them. Although mathematical reasoning is considered as the hallmark of rational thinking, our findings indicate that it is not exempt from cognitive biases and is subject to fundamental counter-intuitions. Our empirical investigations into the source of this bias provide some insights into the cognitive mechanisms underlying geometric deduction, and thus shed light on the cognitive roots of intuitive mathematical reasoning.