Numbers in Context: Cardinals, Ordinals, and Nominals in American English.

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.

Large-scale patterns of number use in spoken and written English.

This paper describes patterns of number use in spoken and written English and the main factors that contribute to these patterns. We analysed more than 1.7 million occurrences of numbers between 0 and a billion in the British National Corpus, including conversational speech, presentational speech (e.g., lectures, interviews), imaginative writing (e.g., fiction), and informative writing (e.g., academic books). We find that four main factors affect number frequency: (1) Magnitude - smaller numbers are more frequent than larger numbers; (2) Roundness - round numbers are more frequent than unround numbers of a comparable magnitude, and some round numbers are more frequent than others; (3) Cultural salience - culturally salient numbers (e.g., recent years) are more frequent than non-salient numbers; and (4) Register - more informational texts contain more numbers (in writing), types of numbers, decimals, and larger numbers than less informational texts. In writing, we find that the numbers 1-9 are mostly represented by number words (e.g., 'three'), 10-999,999 are mostly represented by numerals (e.g., '14'), and 1 million-1 billion are mostly represented by a mix of numerals and number words (e.g., '8 million'). Altogether, this study builds a detailed profile of number use in spoken and written English.

Consensus Paper: Current Perspectives on Abstract Concepts and Future Research Directions.

concepts are relevant to a wide range of disciplines, including cognitive science, linguistics, psychology, cognitive, social, and affective neuroscience, and philosophy. This consensus paper synthesizes the work and views of researchers in the field, discussing current perspectives on theoretical and methodological issues, and recommendations for future research. In this paper, we urge researchers to go beyond the traditional abstract-concrete dichotomy and consider the multiple dimensions that characterize concepts (e.g., sensorimotor experience, social interaction, conceptual metaphor), as well as the mediating influence of linguistic and cultural context on conceptual representations. We also promote the use of interactive methods to investigate both the comprehension and production of abstract concepts, while also focusing on individual differences in conceptual representations. Overall, we argue that abstract concepts should be studied in a more nuanced way that takes into account their complexity and diversity, which should permit us a fuller, more holistic understanding of abstract cognition.

Conceptual Metaphor and Graphical Convention Influence the Interpretation of Line Graphs.

Many metaphors in language reflect conceptual metaphors that structure thought. In line with metaphorical expressions such as 'high number', experiments show that people associate larger numbers with upward space. Consistent with this metaphor, high numbers are conventionally depicted in high positions on the y-axis of line graphs. People also associate good and bad (emotional valence) with upward and downward locations, in line with metaphorical expressions such as 'uplifting' and 'down in the dumps'. Graphs depicting good quantities (e.g., vacation days) are consistent with graphical convention and the valence metaphor, because 'more' of the good quantity is represented by higher y-axis positions. In contrast, graphs depicting bad quantities (e.g., murders) are consistent with graphical convention, but not the valence metaphor, because more of the bad quantity is represented by higher (rather than lower) y-axis positions. We conducted two experiments (N = 300 per experiment) where participants answered questions about line graphs depicting good and bad quantities. For some graphs, we inverted the conventional axis ordering of numbers. Line graphs that aligned (versus misaligned) with valence metaphors (up = good) were easier to interpret, but this beneficial effect did not outweigh the adverse effect of inverting the axis numbering. Line graphs depicting good (versus bad) quantities were easier to interpret, as were graphs that depicted quantity using the x-axis (versus y-axis). Our results suggest that conceptual metaphors matter for the interpretation of line graphs. However, designers of line graphs are warned against subverting graphical convention to align with conceptual metaphors.

A Complete Real-World Theory of Language Should Explain How Iconicity Remains a Stable Property of Linguistic Systems.

Murgiano et al. make a compelling case for studying iconicity in multimodal face-to-face interaction, but they appear ambivalent about the importance of iconicity at the level of the linguistic system. We argue that, rather than decreasing over time, iconicity is a stable property of languages. Understanding how and why this is so is critical to building a complete real-world theory of language that bridges the situated context of language use with language as an evolving symbolic system. An important point for future research is to examine the interface between iconic prosody and the latent iconic features of words and signs that are frozen in the linguistic system.

'Tiny numbers' are actually tiny: Evidence from gestures in the TV News Archive.

We report a large-scale, quantitative investigation of manual gestures that speakers perform when speaking metaphorically about numerical quantities. We used the TV News Archive-an online database of over 2 million English language news broadcasts-to examine 681 videos in which 584 speakers used the phrase 'tiny number', 'small number', 'large number', or 'huge number', which metaphorically frame numerical quantity in terms of physical size. We found that the gestures speakers used reflect a number of different strategies to express the metaphoric size of quantities. When referring to greater versus lesser quantities, speakers were far more likely to gesture (1) with an open versus closed hand configuration, (2) with an outward versus inward movement, and (3) with a wider distance between the gesturing hands. These patterns were often more pronounced for the phrases containing more extreme adjectives ('tiny/huge number'). However, we did not find that speakers performed two-handed versus one-handed gestures. Nor did we find that speakers performed right-handed versus left-handed gestures, when referring to greater versus lesser quantities. Overall, this work supports the claim that metaphoric thought is involved in the production of verbal metaphors that describe numerical magnitudes. It demonstrates that size-based numerical associations observed in previous lab experiments are active in real-life communication outside the lab.

Placing Abstract Concepts in Space: Quantity, Time and Emotional Valence.

Research has shown that abstract concepts are often conceptualized along horizontal and vertical axes. However, there are mixed results concerning which axis is preferred for which type of conceptual domain. For instance, it has been suggested that the vertical axis may be preferred for quantity in tasks using linguistic stimuli (e.g., 'more,' 'less'), whereas numerals (e.g., '1,' '2,' '3') may be more prone to horizontal conceptualization. In this study, we used a task with free response options to see where participants would place quantity words ('most,' 'more,' 'less,' 'least'), numerals ('2,' '4,' '7,' '9'), time words ('past,' 'future,' 'earliest,' 'earlier,' 'later,' 'latest') and emotional valence words ('best,' 'better,' 'worse,' 'worst'). We find that for quantity words, the vertical axis was preferred; whereas for numerals, participants preferred the horizontal axis. For time concepts, participants preferred the horizontal axis; and for emotional valence, they preferred the vertical axis. Across all tasks, participants tended to use specific axes (horizontal, vertical), rather than combining these two axes in diagonal responses. These results shed light on the spatial nature of abstract thought.