Spontaneous, modality-general abstraction of a ratio scale

Abstract

The existence of a generalized magnitude system in the human mind and brain has been studied extensively but remains elusive because it has not been clearly defined. Here we show that one possibility is the representation of relative magnitudes via ratio calculations: ratios are a naturally dimensionless or abstract quantity that could qualify as a common currency for magnitudes measured on vastly different psychophysical scales and in different sensory modalities like size, number, duration, and loudness. In a series of demonstrations based on comparisons of item sequences, we demonstrate that subjects spontaneously use knowledge of inter-item ratios within and across sensory modalities and across magnitude domains to rate sequences as more or less similar on a sliding scale. Moreover, they rate ratio-preserved sequences as more similar to each other than sequences in which only ordinal relations are preserved, indicating that subjects are aware of differences in levels of relative-magnitude information preservation. The ubiquity of this ability across many different magnitude pairs, even those sharing no sensory information, suggests a highly general code that could qualify as a candidate for a generalized magnitude representation.

The Relational SNARC: Spatial Representation of Nonsymbolic Ratios

“…Recent research in numerical cognition has begun to systematically detail the ability of humans and nonhuman animals to perceive the magnitudes of nonsymbolic ratios—that is, ratios instantiated by pairs of nonsymbolic quantities like line segments or dot arrays (e.g., Bonn & Cantlon, ; Drucker, Rossa, & Brannon, ; Jacob, Vallentin, & Nieder, ; Matthews & Chesney, , see Fig. ).…”

“…Indeed, consideration of nonsymbolic ratio stimuli inherently involves relational properties of numbers that are not always readily apparent in research that involves perception of symbolic whole numbers or their nonsymbolic analogs, numerosities (e.g., dot arrays). Unlike studies that focus primarily on discriminating the larger of two numerosities, recent work on ratio perception takes the comparative relation between a pair of quantities as the unit of analysis (Bonn & Cantlon, ; Jacob et al, ; Matthews et al, ). These ratio magnitudes do not correspond to individual components; instead, their magnitudes are determined relationally.…”

Is Emotional Magnitude Spatialized? A Further Investigation

“…Magnitude information is ubiquitous in human experience, whether embedded in numerical symbols such as Arabic digits or in non‐numerical cues such as object size or event duration. Some investigators have proposed that different magnitudes (e.g., number, size, and duration) are processed as part of an integrated system that draws on common neural and cognitive resources (Bonn & Cantlon, ; Bueti & Walsh, ; Lourenco, ; Walsh, ). Support for such a general magnitude system comes from evidence of overlapping activation in parietal cortex (Cantlon, Platt, & Brannon, ; Cohen Kadosh, Lammertyn, & Izard, ) and of cognitive interactions between different magnitudes (e.g., Henik & Tzelgov, ; Lourenco, Ayzenberg, & Lyu, ).…”

Cross‐magnitude interactions across development: Longitudinal evidence for a general magnitude system

“…On one side of the debate, there are those who argue that representations of space, time, and number converge within a general magnitude system (Walsh, ; see also Bonn & Cantlon, ; Capelletti et al., 2013; Lourenco, Azyenberg, & Lyu, ). Though there remains ambiguity in this literature about the precise nature of the convergence, we suggest that the core feature is a direct link between magnitude representations.…”