Search

Numbers are not only used for quantification (cardinals), but also for sequencing (ordinals), and identifying entities (nominals). For example, the sentence ‚ÄúPlayer number 23 took 2nd place by scoring 3 goals‚Äù features nominal, ordinal, and cardinal uses of numbers, in that order. Claims about the relative prevalence of these uses (Wiese, 2004, Niederer 2005) have never been tested. We present the first large-scale analysis of 3,600 numbers in context, showing that cardinal uses are dominant (83.4%), followed by ordinals (11.8%), and then nominals (4.8%). Round numbers, which are associated with approximation, dominate for cardinals (76.4%) but not ordinals (31.1%) or nominals (23.3%). The prevalence of round numbers increases with magnitude only for the cardinals. We discuss implications for the logarithmic scaling of the mental number line (Dehaene & Mehler, 1992), the approximate number system (e.g., Rinaldi & Marelli, 2020), and children's acquisition of number concepts (e.g., Colomé & Noël, 2012).

Numbers and space are associated in the mind, and in language. We investigate 6,400 instances of verbs indicating vertical movement (e.g., rise, fall, decline) or size-based changes (e.g., contract, grow, extend) in four corpora, showing that 60% of all uses occur in quantitative contexts (e.g., ‘prices rose'). For concrete spatial language, it has been found that movement goals are more likely encoded than sources (e.g., Lakusta & Landau 2005, Stefanowitsch, 2018). We demonstrate that this asymmetry carries over to spatial-numerical language, which more often encodes goals (e.g., ‘revenue went up to 48 million') than sources (e.g., ‘share prices rose from $7.13'). In line with their path-related meaning, vertical verbs showed a much higher propensity to encode endpoints (20%) than size-based verbs (10%), a large effect (Cohen's d = 2.0). These results show that the goal bias attested for spatial language carries over to abstract conceptual domains.

Round numbers are often interpreted approximately (Krifka, 2002), with "pragmatic halos" (Lasersohn, 1999) that encompass multiple permissible values. For example, stating "there were 200 people at the meeting" would be acceptable even if the exact count were 197 or 204. In line with the idea that larger numbers have more approximate representations (e.g., Cheyette & Piantadosi, 2020), we demonstrate that rounding and pragmatic halos are magnitude-dependent. First, an analysis of every single number in two large corpora (COCA, BNC) shows that indicators of rounding predict frequency (cf. Woodin et al., 2023), but crucially in interaction with magnitude, with round numbers over-represented for larger magnitudes. Second, we show that jigsaw puzzles often systematically deviate from what is advertised on the box in a way that depends on magnitude, e.g., a 1,000-piece puzzle may contain 1,024 pieces, whereas a 50-piece puzzle is more likely to contain the stated value exactly.

There are three main types of number used in modern, industrialized societies. Cardinals count sets (e.g., people, objects) and quantify elements of conventional scales (e.g., money, distance), ordinals index positions in ordered sequences (e.g., years, pages), and nominals serve as unique identifiers (e.g., telephone numbers, player numbers). Many studies that have cited number frequencies in support of claims about numerical cognition and mathematical cognition hinge on the assumption that most numbers analyzed are cardinal. This paper is the first to investigate the relative frequencies of different number types, presenting a corpus analysis of morphologically unmarked numbers (not, e.g., "eighth" or "21st") in which we manually annotated 3,600 concordances in the Corpus of Contemporary American English. Overall, cardinals are dominant—both pure cardinals (sets) and measurements (scales)—except in the range 1,000–10,000, which is dominated by ordinal years, like 1996 and 2004. Ordinals occur less often overall, and nominals even less so. Only for cardinals do round numbers, associated with approximation, dominate overall and increase with magnitude. In comparison with other registers, academic writing contains a lower proportion of measurements as well as a higher proportion of ordinals and, to some extent, nominals. In writing, pure cardinals and measurements are usually represented as number words, but measurements—especially larger, unround ones—are more likely to be numerals. Ordinals and nominals are mostly represented as numerals. Altogether, this paper reveals how numbers are used in American English, establishing an initial baseline for any analyses of number frequencies and shedding new light on the cognitive and psychological study of number. [ABSTRACT FROM AUTHOR]