# Symmetry in the Semantic Representation of Integers

- Jessica M. Tsang,
*Stanford University*
- Daniel L. Schwartz,
*Stanford University*

## Abstract

The integers include more structure than the natural numbers; for
example, they exhibit symmetry about zero. Do adult mental representations
directly encode this increased structure? In two studies, adults completed a
numerical bi-section task in which they were presented with two symbolic integers
and were asked to report the digit at the midpoint of the interval. The reaction
times demonstrated a “tuning curve” such that people were faster when
the midpoint or end point of an interval was close to zero. The results suggest
that the mental representation of negative numbers and zero has incorporated
analog properties to represent the increased structure of the integers.

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