Is approximate numerical judgment truly modality-independent? Visual, auditory, and cross-modal comparisons

Abstract

The numerosity of any set of discrete elements can be depicted by a genuinely abstract number representation, irrespective of whether they are presented in the visual or auditory modality. The accumulator model predicts that no cost should apply for comparing numerosities within and across modalities. However, in behavioral studies, some inconsistencies have been apparent in the performance of number comparisons among different modalities. In this study, we tested whether and how numerical comparisons of visual, auditory, and cross-modal presentations would differ under adequate control of stimulus presentation. We measured the Weber fractions and points of subjective equality of numerical discrimination in visual, auditory, and cross-modal conditions. The results demonstrated differences between the performances in visual and auditory conditions, such that numerical discrimination of an auditory sequence was more precise than that of a visual sequence. The performance of cross-modal trials lay between performance levels in the visual and auditory conditions. Moreover, the number of visual stimuli was overestimated as compared to that of auditory stimuli. Our findings imply that the process of approximate numerical representation is complex and involves multiple stages, including accumulation and decision processes.

Neural basis of approximate number system develops independent of visual experience

“…We find that quantities that are more similar to each other (differ by a smaller ratio) elicited more overlapping neural patterns in the IPS than quantities that differ by a larger ratio. This ratio-dependence of the IPS population code mirrors the ratio-dependence of behavioral discrimination and neural responses to number reported in previous work (Eger et al, 2009;Odic, Libertus, Feigenson, & Halberda, 2013;Piazza et al, 2007;Tokita et al, 2013).…”

“…On the other hand, there are reasons to think that numerical representations in the IPS are abstract, rather than visual. First, numerical information can be represented from non-visual input; adults can approximate the number of events in auditory sequences and enumerate points of tactile stimulation (Gallace, Tan, & Spence, 2006Piazza et al, 2006;Riggs et al, 2006;Tokita, Ashitani, & Ishiguchi, 2013).…”

Modality‐independent representations of small quantities based on brain activation patterns

“…Recent behavioral studies have shown inconsistent findings regarding whether there is truly an abstract code for numbers in different modalities. A study using a psychophysical adaptation technique showed commonality of representations of numbers across different formats and modalities [Arrighi et al, ], whereas another study demonstrated that approximate numerical judgments of sequentially presented stimuli depend on sensory modality, calling into question the claim of modality independence [Tokita et al, ]. Additionally, while a few previous neuroimaging studies indicating common neural representations across notation and modalities have implicated mainly bilateral parietal regions to be associated with these abstract representations (Dehane, 1996; Eger et al, ; Libertus et al, ; Naccache and Dehaene, ), others including an electrophysiological study have provided evidence against the abstract view of number representation [Ansari, ; Bulthé et al, ; Bulthé et al, ; Cohen Kadosh et al, ; Lyons et al, ; Notebaert et al, ; Piazza et al, ; Spitzer et al, ].…”

Judging crowds’ size by ear and by eye in virtual reality

“…21], a recent study has reported differences in approximate numerical judgments between visual and auditory stimuli. In a numerical comparison task, Tokita et al observed a better precision with sequences of tones compared to the precision with sequences of flashes [22] and proposed that quantity judgment involves complex processes, which may be influenced by the sensory presentation of stimuli.…”