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Nonsymbolic and symbolic representations of null numerosity

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Abstract

Previous research has shown that null numerosity can be processed as a numerical entity that is represented together with non-null numerosities on the same magnitude system. The present study examined which conditions enable perceiving nonsymbolic (i.e., an empty set) and symbolic (i.e., 0) representations of null numerosity as a numerical entity, using distance and end effects. In Experiment 1, participants performed magnitude comparisons of notation homogeneous pairs (both numerosities appeared in nonsymbolic or symbolic format), as well as heterogeneous pairs (a nonsymbolic numerosity versus a symbolic one). Comparisons to 0 resulted in faster responses and an attenuated distance effect in all conditions, whereas comparisons to an empty set produced such effects only in the nonsymbolic and symbolic homogeneous conditions. In Experiments 2 and 3, participants performed same/different numerosity judgments with heterogeneous pairs. A distance effect emerged for "different" judgments of 0 and sets of 1 to 9 dots, but not for those with an empty set versus digits 1–9. These findings indicate that perceiving an empty set, but not 0, as a numerical entity is determined by notation homogeneity and task requirements.

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Notes

  1. Furthermore, visual inspection of the data in the symbolic block (see Figure 2, left panel) suggests that the distance effect found for comparisons to empty sets may stem from a significant linear decrease primarily explained by the RT difference between an intrapair distance of 1 and all other intrapair distances, instead of reflecting a gradual linear decrease with the increase in the intrapair distance. An intrapair distance of 1 in comparisons to null numerosity corresponds to a comparison between two semantic end-values, that is, 0 and 1. Such a comparison may be conflicting, thus resulting in longer RTs (Pinhas et al., 2015; Pinhas & Tzelgov, 2012). To examine this impression statistically, we reanalyzed both comparisons to null numerosity and other comparisons in each of the homogeneous blocks excluding an intrapair distance of 1. In each of these four conditions, we examined the significance of the linear trend to evaluate the presence of a distance effect. Comparisons to null numerosity resulted in significant linear trends in both the symbolic block, F(1, 23) = 12.48, MSE = 88.21, p = .004, η2p = .27, and nonsymbolic block, F(1, 23) = 71.12, MSE = 61.88, p < .001, η2p = .82. Similarly, significant linear trends were obtained for other comparisons in the symbolic block, F(1, 23) = 8.17, MSE = 206, p < .001, η2p = .09) and nonsymbolic block, F(1, 23) = 54.46, MSE = 371, p < .001, η2p = .48.

  2. The error rate analyses in the same/different tasks of both Experiments 2 and 3 indicated an increase in the error rates as a function of an increase in the presented numerosity for “same” responses. These findings reflect the inaccuracy of the estimation process in larger quantities. “Different” responses rarely resulted in errors and, thus, their analyses did not result in significant effects. Accordingly, the error rate analyses revealed no speed-accuracy trade-offs or significant effects. Therefore, for the sake of brevity, they were not reported.

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Acknowledgements

This study was carried out by the first author under the supervision of the second and third authors in partial fulfillment of the PhD requirements at Ben-Gurion University of the Negev. This research was supported by the Israel Science Foundation Grant no. 1799/12 awarded to the Center for the Study of the Neurocognitive Basis of Numerical Cognition, and Grant no. 1348/18 awarded to MP.

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  1. Department of Cognitive and Brain Sciences, Ben-Gurion University of the Negev, 84105, Beer Sheva, Israel

    Rut Zaks-Ohayon & Joseph Tzelgov

  2. Department of Behavioral Sciences, Ariel University, 40700, Ariel, Israel

    Michal Pinhas

  3. Department of Psychology, and Zlotowski Center for Neuroscience, Ben-Gurion University of the Negev, 84105, Beer Sheva, Israel

    Joseph Tzelgov

  4. Department of Psychology, Achva Academic College, 79800, Arugot, Israel

    Joseph Tzelgov

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  1. Rut Zaks-Ohayon
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Zaks-Ohayon, R., Pinhas, M. & Tzelgov, J. Nonsymbolic and symbolic representations of null numerosity. Psychological Research 86, 386–403 (2022). https://doi.org/10.1007/s00426-021-01515-4

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