Effects of spatial frequency cross-adaptation on the visual number sense.

When observing a simple visual scene such as an array of dots, observers can easily and automatically extract their number. How does our visual system accomplish this? We investigate the role of specific spatial frequencies to the encoding of number through cross-adaptation. In two experiments, observers were peripherally adapted to six randomly generated sinusoidal gratings varying from relatively low-spatial frequency (M = 0.44 c/deg) to relatively high-spatial frequency (M = 5.88 c/deg). Subsequently, observers judged which side of the screen had a higher number of dots. We found a strong number-adaptation effect to low-spatial frequency gratings (i.e., participants significantly underestimated the number of dots on the adapted side) but a significantly reduced adaptation effect for high-spatial frequency gratings. Various control conditions demonstrate that these effects are not due to a generic response bias for the adapted side, nor moderated by dot size or spacing effects. In a third experiment, we observed no cross-adaptation for centrally presented gratings. Our results show that observers' peripheral number perception can be adapted even with stimuli lacking any numeric or segmented object information and that low spatial frequencies adapt peripheral number perception more than high ones. Together, our results are consistent with recent number perception models that suggest a key role for spatial frequency in the extraction of number from the visual signal (e.g., Paul, Ackooij, Ten Cate, & Harvey, 2022), but additionally suggest that some spatial frequencies - especially in the low range and in the periphery - may be weighted more by the visual system when estimating number. We argue that the cross-adaptation paradigm is also a useful methodology for discovering the primitives of visual number encoding.

The malleable impact of non-numeric features in visual number perception.

Non-numeric stimulus features frequently influence observers' number judgments: when judging the number of items in a display, we will often (mis)perceive the set with a larger cumulative surface area as more numerous. These "congruency effects" are often used as evidence for how vision extracts numeric information and have been invoked in arguments surrounding whether non-numeric cues (e.g., cumulative area, density, etc.) are combined for number perception. We test whether congruency effects for one such cue - cumulative area - provide evidence that it is necessarily used and integrated in number perception, or if its influence on number is malleable. In Experiment 1, we replicate and extend prior work showing that the presence of feedback eliminates congruency effects between number and cumulative area, suggesting that the role of cumulative area in number perception is malleable rather than obligatory. In Experiment 2, we test whether this malleable influence is because of use of prior experiences about how number naturalistically correlates with cumulative area, or the result of response competition, with number and cumulative area actively competing for the same behavioral decision. We preserve cumulative area as a visual cue but eliminate response competition with number by replacing one side of the dot array with its corresponding Hindu-Arabic numeral. Independent of the presence or absence of feedback, we do not observe congruency effects in Experiment 2. These experiments suggest that cumulative area is not necessarily integrated in number perception nor a reflection of a rational use of naturalistic correlations, but rather congruency effects between cumulative area and number emerge as a consequence of response competition. Our findings help to elucidate the mechanism through which non-numeric cues and number interact, and provide an explanation for why congruency effects are only sometimes observed across studies.

The association of brightness with number/duration in human newborns.

Human neonates spontaneously associate changes in magnitude across the dimensions of number, length, and duration. Do these particular associations generalize to other pairs of magnitudes in the same way at birth, or do they reflect an early predisposition to expect specific relations between spatial, temporal, and numerical representations? To begin to answer this question, we investigated how strongly newborns associated auditory sequences changing in number/duration with visual objects changing in levels of brightness. We tested forty-eight newborn infants in one of three, bimodal stimulus conditions in which auditory numbers/durations increased or decreased from a familiarization trial to the two test trials. Auditory numbers/durations were paired with visual objects in familiarization that remained the same on one test trial but changed in luminance/contrast or shape on the other. On average, results indicated that newborns looked longer when changes in brightness accompanied the number/duration change as compared to no change, a preference that was most consistent when the brightness change was congruent with the number/duration change. For incongruent changes, this preference depended on trial order. Critically, infants showed no preference for a shape change over no shape change, indicating that infants likely treated brightness differently than a generic feature. Though this performance pattern is somewhat similar to previously documented associations, these findings suggest that cross-magnitude associations among number, length, and duration may be more specialized at birth, rather than emerge gradually from postnatal experience or maturation.

At Birth, Humans Associate "Few" with Left and "Many" with Right.

Humans use spatial representations to structure abstract concepts [1]. One of the most well-known examples is the "mental number line"-the propensity to imagine numbers oriented in space [2, 3]. Human infants [4, 5], children [6, 7], adults [8], and nonhuman animals [9, 10] associate small numbers with the left side of space and large numbers with the right. In humans, cultural artifacts, such as the direction of reading and writing, modulate the directionality of this representation, with right-to-left reading cultures associating small numbers with right and large numbers with left [11], whereas the opposite association permeates left-to-right reading cultures [8]. Number-space mapping plays a central role in human mathematical concepts [12], but its origins remain unclear: is it the result of an innate bias or does it develop after birth? Infant humans are passively exposed to a spatially coded environment, so experience and culture could underlie the mental number line. To rule out this possibility, we tested neonates' responses to small or large auditory quantities paired with geometric figures presented on either the left or right sides of the screen. We show that 0- to 3-day-old neonates associate a small quantity with the left and a large quantity with the right when the multidimensional stimulus contains discrete numerical information, providing evidence that representations of number are associated to an oriented space at the start of postnatal life, prior to experience with language, culture, or with culture-specific biases.

Spontaneous, modality-general abstraction of a ratio scale.

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.

Indexical and linguistic processing by 12-month-olds: Discrimination of speaker, accent and vowel differences.

Infants preferentially discriminate between speech tokens that cross native category boundaries prior to acquiring a large receptive vocabulary, implying a major role for unsupervised distributional learning strategies in phoneme acquisition in the first year of life. Multiple sources of between-speaker variability contribute to children's language input and thus complicate the problem of distributional learning. Adults resolve this type of indexical variability by adjusting their speech processing for individual speakers. For infants to handle indexical variation in the same way, they must be sensitive to both linguistic and indexical cues. To assess infants' sensitivity to and relative weighting of indexical and linguistic cues, we familiarized 12-month-old infants to tokens of a vowel produced by one speaker, and tested their listening preference to trials containing a vowel category change produced by the same speaker (linguistic information), and the same vowel category produced by another speaker of the same or a different accent (indexical information). Infants noticed linguistic and indexical differences, suggesting that both are salient in infant speech processing. Future research should explore how infants weight these cues in a distributional learning context that contains both phonetic and indexical variation.

The origins and structure of quantitative concepts.

"Number" is the single most influential quantitative dimension in modern human society. It is our preferred dimension for keeping track of almost everything, including distance, weight, time, temperature, and value. How did "number" become psychologically affiliated with all of these different quantitative dimensions? Humans and other animals process a broad range of quantitative information across many psychophysical dimensions and sensory modalities. The fact that adults can rapidly translate one dimension (e.g., loudness) into any other (e.g., handgrip pressure) has been long established by psychophysics research (Stevens, 1975 ). Recent literature has attempted to account for the development of the computational and neural mechanisms that underlie interactions between quantitative dimensions. We review evidence that there are fundamental cognitive and neural relations among different quantitative dimensions (number, size, time, pitch, loudness, and brightness). Then, drawing on theoretical frameworks that explain phenomena from cross-modal perception, we outline some possible conceptualizations for how different quantitative dimensions could come to be related over both ontogenetic and phylogenetic time scales.