The pupil responds spontaneously to perceived numerosity

The study investigates whether perceived numerosity—considered a basic and spontaneous visual attribute or “number sense”—modulates the pupillary light response independently of luminance. Prior work shows numerosity is rapidly and automatically encoded in both animals and humans, with neural tuning and topographic organization evident early in visual processing. Pupil size, while primarily driven by luminance, is known to be influenced by attention, visual illusions, and semantic content, indicating higher-level modulation of subcortical pupillary circuits. The authors test the hypothesis that perceived numerosity scales the pupillary response magnitude, even during passive viewing, implying numerosity is spontaneously encoded and linked to perceptual strength.

Evidence for an innate or early-developing number sense includes single neurons tuned to numerosity in monkeys and crows, and newborn human sensitivity to numerosity. Numerosity representations are topographic, with rapid encoding in occipital cortex (~75 ms) and fast saccadic choices toward more numerous targets (~190 ms), suggesting primitive, possibly subcortical circuits. Pupillary responses are modulated by attention, brightness and size illusions, and implied brightness in images (e.g., sun/moon), demonstrating cortical modulation of the pupil light reflex. Connectedness between items reduces perceived numerosity in psychophysics, a robust illusion leveraged here. Neural substrates of numerosity span prefrontal and occipito-parietal areas, with evidence for subcortical encoding, and the connectedness effect emerges early (~150 ms) in V3 and continues in parietal cortex. These literatures motivate testing whether numerosity spontaneously affects pupil responses when luminance is matched.

Participants: Sixteen adults (six males; mean age 30 ± 3 years) with normal or corrected vision. All 16 completed pupillometry experiment 1; 14 completed the numerosity discrimination (psychophysics) after experiment 1; 13 completed pupillometry and psychophysics experiment 2. Ethics approval and informed consent obtained.

Stimuli: Arrays of either 18 or 24 dots, black or white, on a gray background (129.3 cd/m^2). Luminance extremes ~12.6 and 256 cd/m^2. Two connectedness manipulations:

• Experiment 1 (displaced-lines control): In connected condition, pairs of dots were joined by lines (dumbbells). In isolated condition, connecting lines were displaced to random positions between dots. Dot diameter: 2.2° (N18), 1.9° (N24); line width: 1.03°; line length: 2–3°.
• Experiment 2 (removed-lines control): In connected condition, dots were joined by thinner lines. In isolated condition, lines were removed and their pixels added to dots, enlarging them (~40%). Dot diameter: connected 2.2° (N18), 1.9° (N24); isolated 2.44–2.64° (N18) and 2.10–2.28° (N24); line width: 0.6°; line length: 1.6–2.8°. Across all conditions within each experiment, total number of white/black pixels was matched to equate mean luminance; convex hull area was fixed at 513 deg^2. Total pixel coverage: 92.7 deg^2 (exp. 1) and 82.3 deg^2 (exp. 2). Fourier spectra of stimuli were measured to assess potential confounds.

Procedure (pupillometry): Passive viewing. Trials began with 1 s fixation, followed by a 6 s stimulus presentation, then 1 s post-stimulus (2 s interstimulus interval). Participants maintained fixation and performed no task. Connected and isolated patterns were intermixed; numerosities (18, 24) and polarities (black, white) were in separate sessions; order pseudo-randomized. Each participant completed four sessions of 60 trials.

Apparatus: Dark room, LCD monitor (1280×720, 60 Hz), viewing distance 57 cm, head stabilized. Pupil recorded at 500 Hz (EyeLink 1000, left eye). Nine-point calibration before each session. Stimulus control via MATLAB with Psychtoolbox-3.

Psychophysics (numerosity and brightness): After pupillometry 1, participants performed 2AFC sequential numerosity judgments (500 ms stimuli at fixation; report which interval contained more dots). In exp. 1, probes were isolated dots with lines (variable numerosity 8–24 dots with half as many lines) compared against a reference of 18 dots and 9 lines (either isolated or connected). In exp. 2, probes were isolated dots (variable numerosity 5–12), reference fixed at 18 connected dots. Sessions were run separately for black and white arrays. Three sessions of 40 trials per condition. Brightness comparisons were also collected (Supplementary Information).

Pupillometry preprocessing and analysis: Excluded blinks/signal losses based on thresholds: pupil size <0.1 mm, abrupt changes >1 mm from trial median, velocity >25 mm/s (±20 ms windows removed). Downsampled to 20 Hz, high-pass filtered with 500 ms square window, baseline-corrected using mean over −200 to 0 ms pre-stimulus. Primary metric: mean pupil difference (dark minus light) over 1–6 s window to index net luminance response, excluding the initial transient. Two-way repeated-measures ANOVAs with factors: numerosity (18, 24) and connectedness (connected, isolated). Bayesian ANOVAs reported as log10 Bayes factors. Eye-movement stability assessed by bivariate confidence interval area; compared across conditions with repeated-measures ANOVAs.

General Linear Model (GLM): Modeled pupil time courses as a linear combination of three predictors—onset and offset impulses and a sustained boxcar (stimulus duration)—each convolved with an individualized pupil response function (gamma function h(t) with parameters n, r, δ optimized per participant). Fits yielded β-weights for each predictor per condition; analyses focused on sustained β-weights of the black-minus-white difference traces to index luminance-driven response strength. Goodness-of-fit averaged 83% variance explained.

Controls for artifacts: Compared spatial frequency amplitude spectra across conditions (0.3–10 cpd). Assessed fixation stability and perceived brightness (forced-choice psychophysics).

• Pupillary responses scaled with perceived numerosity despite identical mean luminance across conditions. White arrays elicited constriction and black arrays dilation; their difference (dark minus light) increased with higher perceived numerosity.
• Experiment 1 (displaced-lines control; N=16): Mean pupil difference (1–6 s) was highest for 24 isolated dots and lowest for 18 connected dots, with intermediate values for 18 isolated and 24 connected (similar apparent numerosity). Paired t-test 24 isolated vs 18 connected: t(15)=4.5, p<0.001, Cohen’s d=1.1, log10BF=1.9. Two-way RM-ANOVA: main effect of connectedness F(1,15)=20.5, p<0.001, ηp²=0.6, log10BF=0.8; main effect of numerosity F(1,15)=6.2, p=0.025, ηp²=0.3, log10BF=0.8; interaction F(1,15)=0.13, p=0.72, log10BF=−0.5.
• Experiment 2 (removed-lines control; N=13): Same pattern: strongest for 24 isolated, weakest for 18 connected; t(12)=2.9, p=0.014, d=0.8, log10BF=0.6. Two-way RM-ANOVA: connectedness F(1,12)=6.7, p=0.024, ηp²=0.4, log10BF=0.5; numerosity F(1,12)=2.6, p=0.13, log10BF=0; interaction F(1,12)=0.005, p=0.95, log10BF=−0.5.
• GLM sustained-response analysis corroborated windowed means. Sustained β-weights: highest for 24 isolated, lowest for 18 connected; Exp.1 t(15)=3.8, p=0.002, d=0.9, log10BF=1.4; Exp.2 t(12)=2.2, p=0.047, d=0.6, log10BF=0.2. ANOVAs on β-weights showed significant or trending main effects of connectedness; numerosity effects weaker in Exp.2.
• Psychophysics confirmed the connectedness illusion magnitude: With a reference of 18 isolated dots, PSEs for connected probes shifted left by ~28–30% (Exp.1, displaced lines) and ~22–23% (Exp.2, removed lines). Thus, a 24 connected-dot pattern appeared ~17 (Exp.1) or ~19 (Exp.2), similar to 18 isolated dots.
• Artifact checks: Spatial frequency spectra differences did not align with pupillary effects across both experiments; fixation stability did not differ by condition; perceived brightness showed no significant differences between conditions.

Findings show that pupil size, beyond being a reflexive luminance response, is spontaneously modulated by perceived numerosity during passive viewing. When physical luminance is equated, higher perceived numerosity—whether due to more dots or to reduced grouping (fewer connections)—enhances both constriction to bright and dilation to dark stimuli, consistent with multiplicative scaling of effective stimulus strength. Control analyses argue against alternative explanations: matched pixel counts eliminate mean luminance confounds; spatial frequency differences are small and inconsistent across experiments; fixation stability and perceived brightness do not differ; and task demands were minimal, reducing mental effort or memory load as likely drivers. The pattern suggests numerosity increases perceptual salience and that numerosity is encoded automatically. Mechanistically, modulation could be mediated by attention or higher-level cortical feedback to subcortical pupillary circuits (OPN/EW), consistent with known effects of attention on the pupil light reflex and with neural substrates of numerosity in prefrontal and occipito-parietal areas, as well as possible subcortical contributions. Early emergence of connectedness effects (~150 ms, V3) provides a plausible timescale for influencing sustained pupil responses during the 6 s presentation window.

The study demonstrates that perceived numerosity spontaneously modulates the pupillary light response independently of luminance, reinforcing the view that numerosity is a primary visual attribute with automatic encoding. Both physical increases in numerosity and reductions in grouping (via removing or displacing connectors) enhance the effective strength of stimuli as read out by pupil size. Pupillometry thus offers a simple, objective, task-free tool to probe numerical cognition across populations and species where standard psychophysics may be challenging. Future work should clarify the neural mechanisms (attentional vs. direct cortical/subcortical pathways), assess developmental and clinical populations, and refine stimuli to dissect contributions of grouping, density, and spatial frequency content.

• Mechanism not directly tested: while attention is posited as a candidate mediator, the causal pathway by which numerosity modulates the pupil light reflex remains unresolved.
• Subtle brightness effects cannot be entirely ruled out: authors note that although psychophysics found no significant brightness differences, extremely small effects might exist.
• Reduced effect sizes in experiment 2: overall weaker pupillary responses (possibly due to fewer pixels) and slightly reduced illusion strength suggest sensitivity to stimulus design.
• Modest sample sizes (N=16 and N=13 for pupillometry) may limit detection of smaller effects (e.g., numerosity main effect in experiment 2 was nonsignificant).
• Spatial frequency content differed subtly across conditions; while controls argue against it as a confound across both experiments, complete equivalence is unattainable with these manipulations.