# Getting off at the end of the line: the estimation of large numbers

- David Landy,
*University of Richmond*
- Noah Silbert,
*Center for the Advanced Study of Language, University of Maryland*
- Aleah Goldin,
*University of Richmond*

## Abstract

Despite their importance in public discourse, numbers in the range
of one million to one trillion are notoriously difficult to understand. We
examine magnitude estimation by adult Americans when placing large numbers on a
number line and when qualitatively evaluating descriptions of imaginary
geopolitical scenarios. Common conceptions of the number line suggest a
logarithmic compression of the numbers (Dehaene, 2003). Theories of abstract
concept learning suggest that in situations where direct experience is
unavailable, people will use the structure of notation systems as a proxy for the
actual system. (Carey, 2009; Landy & Goldstone, 2007).
Evaluations across two subject populations largely matched the predictions of the
latter account. Approximately 40% of participants estimated one million
approximately halfway between one thousand and one billion, but placed numbers
linearly across each half, as though they believed that the number words
“thousand, million, billion, trillion” constitute a uniformly spaced
count list. Very brief training procedures proved partially successful both in
correcting number line placement and in shifting participants’ judgments of
geopolitical situations. These results reinforce notions of abstract concepts as
grounded in external notation systems, as well as having direct implications for
lawmakers and scientists hoping to communicate effectively with the public.

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