The origins and structure of quantitative concepts

Abstract

“Number” is the single most influential quantitative dimension in modern human society. It is our preferred dimension for keeping track of almost everything, including distance, weight, time, temperature, and value. How did “number” become psychologically affiliated with all of these different quantitative dimensions? Humans and other animals process a broad range of quantitative information across many psychophysical dimensions and sensory modalities. The fact that adults can rapidly translate one dimension (e.g., loudness) into any other (e.g., handgrip pressure) has been long established by psychophysics research (Stevens, 1975). Recent literature has attempted to account for the development of the computational and neural mechanisms that underlie interactions between quantitative dimensions. We review evidence that there are fundamental cognitive and neural relations among different quantitative dimensions (number, size, time, pitch, loudness, and brightness). Then, drawing on theoretical frameworks that explain phenomena from cross-modal perception, we outline some possible conceptualizations for how different quantitative dimensions could come to be related over both ontogenetic and phylogenetic time scales.

Keywords:

• Numerosity
• Development
• Magnitude
• fMRI

Acknowledgments

The authors wish to thank Bradford Z. Mahon for comments and discussion on earlier drafts of the manuscript and support from NSF Graduate Research Fellowship to C.B. and NIH R01HD064636 to J.C.

Notes

¹ We use “magnitude” and “quantity” interchangeably in this paper.