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.

Keywords: Generalized magnitude representation; Ratio scale.

Figure 1. Examples of sequence types

At the top is the standard sequence with the horizontal axis representing time (left to right). Arrows lead to possible comparison sequences in the Different, Rank, and Ratio pairs.

Figure 2. Experiment 1 results

All displayed mean ratings are back-transformed from empirical logit space to the data space (0 = most dissimilar, 1 = most similar). Each panel corresponds to a subject group tested in one dimension. Black dots with 95% confidence intervals represent mean ratings generated from 1000 simulations from the fitted model. The small, horizontally jittered dots represent individual subject means, the gray being the raw means and the red being model predictions (fitted means), which take into account the random-effects structure.

Figure 3. Supplementary Brightness dimension data

See Figure 2 for details on calculation of subject means and sequence-type means.

Figure 4. Cross-modality comparisons

See Figure 2 for details on calculation of means. Here the overall means are additionally broken down by the order in which each modality was presented.

Figure 5. Cross-dimension comparisons: space, time, and number

See Figure 2 for details on mean calculations. Panels reflect the particular dimension pairs, as indicated in the panel label.