The specious interaction of time and numerosity perception

Abstract

Magnitude information is essential to create a representation of the external environment and successfully interact with it. Duration and numerosity, for example, can shape our predictions and bias each other (i.e. the greater the number of people queuing, the longer we expect to wait). While these biases suggest the existence of a generalized magnitude system, asymmetric effects (i.e. numerosity affecting duration but not vice versa) challenged this idea. Here, we propose that such asymmetric integration depends on the stimuli used and the neural processing dynamics they entail. Across multiple behavioural experiments employing different stimulus presentation displays (static versus dynamic) and experimental manipulations known to bias numerosity and duration perceptions (i.e. connectedness and multisensory integration), we show that the integration between numerosity and time can be symmetrical if the stimuli entail a similar neural time-course and numerosity unfolds over time. Overall, these findings support the idea of a generalized magnitude system, but also highlight the role of early sensory processing in magnitude representation and integration.

The neural signature of magnitude integration between time and numerosity

“…Judging numerosity or duration usually entails different levels of difficulty. Indeed, at least in vision, judging duration is usually considered a more difficult task compared to a more salient dimension like numerosity, leading to a decreased precision of duration judgments compared to numerosity (Togoli et al, 2021). Although dynamic stimuli, whereby numerosity is defined as the average across several stimuli, have been shown to yield a similar precision of temporal and numerical judgments (Togoli et al, 2021), we further addressed this potential difference by assessing the Weber’s fraction (WF; computed as JND/PSE; see Methods ) as a measure of precision in the task (Fig.…”

“…Although the effect was significant in both directions, we observed an asymmetry: the influence of duration on numerosity was stronger compared to the influence of numerosity on duration. Asymmetric effects in magnitude integration are common in the literature, but usually involve duration being more strongly affected by non-temporal dimensions (e.g., Casasanto & Boroditsky, 2008; Dormal et al, 2006; Togoli et al, 2021; but see Cai & Connell, 2015 for an opposite asymmetry in the tactile modality). Symmetric effects across duration and numerosity have been observed by using either very short stimulus durations (i.e., ∼50-100 ms; Javadi & Aichelburg, 2012) or dynamic stimuli whereby numerosity is conveyed as an average across several individual arrays (Togoli et al, 2021).…”

“…Asymmetric effects in magnitude integration are common in the literature, but usually involve duration being more strongly affected by non-temporal dimensions (e.g., Casasanto & Boroditsky, 2008; Dormal et al, 2006; Togoli et al, 2021; but see Cai & Connell, 2015 for an opposite asymmetry in the tactile modality). Symmetric effects across duration and numerosity have been observed by using either very short stimulus durations (i.e., ∼50-100 ms; Javadi & Aichelburg, 2012) or dynamic stimuli whereby numerosity is conveyed as an average across several individual arrays (Togoli et al, 2021). This has led to the proposal that asymmetric effects across duration and numerosity result from a different processing time-course of these two dimensions, with the fastest one to be represented (i.e., numerosity; see Fornaciai et al, 2017) being able to more strongly interfere with a slowly accumulating dimension (i.e., duration), but not vice versa (Togoli et al, 2021); see also Lambrechts et al, 2013).…”

“…Indeed, different magnitude dimensions have been shown to interact with each other so that the processing of one dimension is influenced by another dimension. For example, an event involving a bigger stimulus or a more numerous set of objects is perceived as lasting longer in time compared to smaller stimuli or less numerous sets (e.g., Rammsayer & Verner, 2014; Togoli et al, 2021; Xuan et al, 2007). Vice versa, a longer duration can lead to an increase in the perceived size of a stimulus (Cai & Connell, 2015) or an increase in perceived numerosity (Javadi & Aichelburg, 2012; Togoli et al, 2021).…”

“…To do so, we used a numerosity and a duration classification task of dynamic dot-array stimuli modulated in duration and in average numerosity (i.e., the average number of dots presented across several briefly flashed arrays). Dynamic stimuli were specifically used to facilitate a mutual interaction between the two dimensions (Togoli et al, 2021), since static stimuli often yield a strong bias induced by numerosity on duration while not showing an effect in the opposite direction (e.g., Dormal et al, 2006). EEG data was then used to assess how changes in stimulus numerosity, duration, or their combination modulate the event-related potentials (ERPs) evoked by the stimuli in the two task conditions.…”