Perceiving infinity: An interplay between numerical and physical magnitude

Our mental representation of the infinite has received little research attention in cognitive psychology. In countably infinite sets, the infinity symbol (∞), which usually represents “potential infinity”—an unending process such as counting—is presumed to be perceived as larger than any finite natural number. The present study sought to explore if infinity is indeed processed as “larger than” natural numbers, and, if so, whether it is associated with the special status of “the largest.” In a series of four experiments (N = 40, 20, 20, and 40, respectively), participants performed numerical and physical comparisons of infinity against single- and multi-digit numbers. Overall, numerical comparisons yielded slower responses for comparisons between infinity and a number than for comparisons between two numbers. Furthermore, distance-like effects were obtained for comparisons to infinity, suggesting it was treated as larger than all numbers presented. Importantly, however, physical comparisons revealed a normal size congruity effect for comparisons of infinity and single digits, but a reversed effect for comparisons of infinity and multi-digit numbers, suggesting that infinity was automatically processed as smaller than multi-digit numbers. These findings indicate that infinity is not perceived as “the largest” and can be misconceived as a “number” mapped onto the numerical magnitude system. Furthermore, the results seem to reflect a crude, automatic evaluation of numerical magnitude based on the physical magnitude of the stimuli, namely, their overall length and the number of symbols of which they are comprised.