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Symmetry is ubiquitous in nature, in logic and mathematics, and in perception, language, and thought. Although humans are exquisitely sensitive to visual symmetry (e.g., of a butterfly), symmetry in natural language goes beyond visuospatial properties: many words point to abstract concepts with symmetrical content (e.g., equal, marry). For example, if Mark marries Bill, then Bill marries Mark. In both cases (vision and language), symmetry may be formally characterized as invariance under transformation. Is this a coincidence, or is there some deeper psychological resemblance? Here we asked whether representations of symmetry correspond across language and vision. To do so, we developed a novel cross-modal matching paradigm. On each trial, participants observed a visual stimulus (either symmetrical or non-symmetrical) and had to choose between a symmetrical and non-symmetrical English predicate unrelated to the stimulus (e.g., “negotiate” vs. “propose”). In a first study with visual events (symmetrical collision or asymmetrical launch), participants reliably chose the predicate matching the event’s symmetry. A second study showed that this “language-vision correspondence” generalized to objects, and was weakened when the stimuli’s binary nature was made less apparent (i.e., for one object, rather than two inward-facing objects). A final study showed the same effect when nonsigners guessed English translations of signs from American Sign Language, which expresses many symmetrical concepts spatially. Taken together, our findings support the existence of an abstract representation of symmetry which humans access via both perceptual and linguistic means. More broadly, this work sheds light on the rich, structured nature of the language-cognition interface. 

Symmetry is ubiquitous in nature, in logic and mathematics, and in perception, language, and thought. Although humans are exquisitely sensitive to visual symmetry (e.g., of a butterfly), linguistic symmetry goes far beyond visuospatial properties: Many words refer to abstract, logically symmetrical concepts (e.g., equal, marry). This raises a question: Do representations of symmetry correspond across language and vision, and if so, how? To address this question, we used a cross-modal matching paradigm. On each trial, adult participants observed a visual stimulus (either symmetrical or non-symmetrical) and had to choose between a symmetrical and non-symmetrical English predicate unrelated to the stimulus (e.g., "negotiate" vs. "propose"). In a first study with visual events (symmetrical collision or asymmetrical launch), participants reliably chose the predicate matching the event's symmetry. A second study showed that this "matching" generalized to static objects, and was weakened when the stimuli's binary-relational nature was made less apparent (i.e., one object with a symmetrical contour, rather than two symmetrically configured objects). Taken together, our findings support the existence of an abstract relational concept of symmetry which humans access via both perceptual and linguistic means. More broadly, this work sheds light on the rich, structured nature of the language-cognition interface, and points towards a possible avenue for acquisition of word-to-world mappings for the seemingly inaccessible logical symmetry of linguistic terms.