Archerfish number discrimination

Debates have arisen as to whether non-human animals actually can learn abstract non-symbolic numerousness or whether they always rely on some continuous physical aspect of the stimuli, covarying with number. Here we investigated archerfish (Toxotes jaculatrix) non-symbolic numerical discrimination with accurate control for co-varying continuous physical stimulus attributes. Archerfish were trained to select one of two groups of black dots (Exp. 1: 3 vs. 6 elements; Exp. 2: 2 vs. 3 elements); these were controlled for several combinations of physical variables (elements’ size, overall area, overall perimeter, density and sparsity), ensuring that only numerical information was available. Generalization tests with novel numerical comparisons (2 vs. 3, 5 vs. 8 and 6 vs. 9 in Exp. 1; 3 vs. 4, 3 vs. 6 in Exp. 2) revealed choice for the largest or smallest numerical group according to the relative number that was rewarded at training. None of the continuous physical variables, including spatial frequency, were affecting archerfish performance. Results provide evidence that archerfish spontaneously use abstract relative numerical information for both small and large numbers when only numerical cues are available.

Archerfish number discrimination

Debates have arisen as to whether non-human animals actually can learn astract non-symbolic numerousness or whether they always rely on some continuous physical aspect of the stimuli covarying with number. Here we investigated archerfish (Toxotes jaculatrix) non-symbolic numerical discrimination with accurate control for co-varying continuous physical stimulus attributes. Archerfish were trained to select one of two groups of black dots (Exp. 1: 3 vs. 6 elements; Exp. 2: 2 vs. 3 elements); these were controlled for several combinations of physical variables (elements' size, overall area, overall perimeter, density and sparsity), ensuring that only numerical information was available. Generalization tests with novel numerical comparisons (2 vs. 3, 5 vs. 8 and 6 vs. 9 in Exp. 1; 3 vs. 4, 3 vs. 6 in Exp. 2) revealed choice for the largest or smallest numerical group according to the relative number that was rewarded at training. None of the continuous physical variables, including spatial frequency, were affecting archerfish performance. Results provide evidence of the spontaneous use of abstract relative numerical information in archerfish for both small and large numbers.

Attentional bias induced by stimulus control (ABC) impairs measures of the approximate number system

Pervasive congruency effects characterize approximate number discrimination tasks. Performance is better on congruent (the more numerous stimulus consists of objects of larger size that occupy a larger area) than on incongruent (where the opposite holds) items. The congruency effects typically occur when controlling for nonnumeric variables such as cumulative area. Furthermore, only performance on incongruent stimuli seems to predict math abilities. Here, we present evidence for an attentional-bias induced by stimulus control (ABC) where preattentive features such as item size reflexively influence decisions, which can explain these congruency effects. In three experiments, we tested predictions derived from the ABC. In Experiment 1, as predicted, we found that manipulation of size introduced congruency effects and eliminated the correlation with math ability for congruent items. However, performance on incongruent items and neutral, nonmanipulated items were still predictive of math ability. A negative correlation between performance on congruent and incongruent items even indicated that they measure different underlying constructs. Experiment 2 demonstrated, in line with the ABC account, that increasing presentation time reduced congruency effects. By directly measuring overt attention using eye-tracking, Experiment 3 revealed that people direct their first gaze toward the array with items of larger individual size, biasing them towards these arrays. The ABC explains why the relation between performance on approximate number discrimination tasks and math achievement has been fragile and suggests that stimulus control manipulations have contaminated the results. We discuss the importance of using stimuli that are representative of the environment.

Quantification of Dual-task Performance in Healthy Young Adults Suitable for Military Use

ABSTRACT Introduction Dual-task performance, in which an individual performs two tasks simultaneously, is compromised following mild traumatic brain injury (mTBI). Proficient dual-task performance is essential in a military setting for both military member safety and execution of skilled tasks. To address the unique needs of military members, a portable dual-task assessment was developed incorporating an auditory dual-task task as a novel assessment module utilizing mobile-device technology. The aim of this study was to develop and validate a dual-task mobile device-based application that accurately quantifies cognitive and motor function. Materials and Methods Fifty, healthy, military-age civilians completed three cognitive tasks in single- and dual-task conditions with eyes open and closed: visual Stroop, auditory Stroop at 1.5- and 2.5-second stimulus presentation, and number discrimination. All dual-task conditions required the maintenance of postural stability while simultaneously completing a cognitive task. Results There were no differences between single- and dual-task conditions for cognitive performance on any of the tests, and a ceiling effect was observed for the visual Stroop and auditory Stroop 1.5-second stimulus presentation (P > .05). Significant differences in postural stability were observed between the eyes-open and eyes-closed conditions in all single- and dual-task conditions (P < .01). Significant differences in postural stability were observed between the eyes-open single-task condition and all dual-task conditions (P < .01). Conclusions Based on the performance of healthy young adults, the number discrimination task may be optimal for detecting subtle changes in dual-task performance. The detected differences found between the eyes-open and eyes-closed conditions provide discriminatory value and insight into the reliance of vision of postural stability performance. While dual-task cognitive performance was not observed in this healthy population, individuals with mTBI may exhibit decreased dual-task performance. The independent evaluation of cognitive and motor function under dual-task conditions has the potential to transform the management and treatment of mTBI.

Unconscious Number Discrimination in the Human Visual System

How do humans compute approximate number? According to one influential theory, approximate number representations arise in the intraparietal sulcus and are amodal, meaning that they arise independent of any sensory modality. Alternatively, approximate number may be computed initially within sensory systems. Here we tested for sensitivity to approximate number in the visual system using steady state visual evoked potentials. We recorded electroencephalography from humans while they viewed dotclouds presented at 30 Hz, which alternated in numerosity (ranging from 10 to 20 dots) at 15 Hz. At this rate, each dotcloud backward masked the previous dotcloud, disrupting top-down feedback to visual cortex and preventing conscious awareness of the dotclouds’ numerosities. Spectral amplitude at 15 Hz measured over the occipital lobe (Oz) correlated positively with the numerical ratio of the stimuli, even when nonnumerical stimulus attributes were controlled, indicating that subjects’ visual systems were differentiating dotclouds on the basis of their numerical ratios. Crucially, subjects were unable to discriminate the numerosities of the dotclouds consciously, indicating the backward masking of the stimuli disrupted reentrant feedback to visual cortex. Approximate number appears to be computed within the visual system, independently of higher-order areas, such as the intraparietal sulcus.

Transfer from number to size reveals abstract coding of magnitude in honeybees

Number discrimination has been documented in honeybees. It is not known, however, whether it reflects, as in vertebrates, the operating of an underlying general magnitude system that estimates quantities irrespective of dimensions (e.g., number, space, time) and format (discrete, continuous). We investigated whether bees spontaneously transfer discrete discrimination of number to continuous discrimination of size. Bees were trained to discriminate between different numerical comparisons having either a 0.5 (2 vs. 4 and 4 vs. 8) or 0.67 ratio (2 vs. 3 and 4 vs. 6). Half of the subjects learnt to choose the smaller quantity and the other half the larger quantity. Bees were then tested for spontaneous choice (in the absence of reward) using comparisons with identical numbers but different sizes. Irrespective of the ratio of the stimuli, bees trained to select the smaller numerical quantity chose the congruent smaller size; bees trained to choose the larger numerical quantity chose the congruent larger size. This finding provides the first evidence for a cross-dimensional transfer between discrete (numerical) and continuous (spatial) dimensions in an invertebrate species and supports the hypothesis of a cognitive universality of a coding for general magnitude.

Certainty in Numerical Judgments Develops Independently of the Approximate Number System

Recent work has shown that the precision with which children reason about their ANS certainty improves with age: when making simple number discrimination decisions, like deciding whether there are more blue or yellow dots on the screen, older children are better able to differentiate trials that they answered correctly vs. incorrectly. Here, in two experiments, we examine whether the age-related improvement in ANS certainty is accounted for by children’s: (1) increasing ability to properly “calibrate” their certainty judgements (i.e., a reduction in over-confidence with age); (2) improving precision of the ANS representations themselves; and/or (3) the improvement of children’s ability to represent and reason about certainty in general. By testing children in a child-friendly “relative” certainty task, we find that 3-7 year-olds’ (N = 161) certainty in their ANS decisions develops independently of both ANS acuity and calibration abilities. These results hold even when non-numeric perceptual features, such as the density and cumulative area, are controlled for. We discuss these results in a broader context of children’s general ability to reason about certainty and confidence.

Honeybees use absolute rather than relative numerosity in number discrimination

Various vertebrate species use relative numerosity judgements in comparative assessments of quantities for which they use larger/smaller relationships rather than absolute number. The numerical ability of honeybees shares basic properties with that of vertebrates but their use of absolute or relative numerosity has not been explored. We trained free-flying bees to choose variable images containing three dots; one group (‘larger’) was trained to discriminate 3 from 2, while another group (‘smaller’) was trained to discriminate 3 from 4. In both cases, numbers were kept constant but stimulus characteristics and position were varied from trial to trial. Bees were then tested with novel stimuli displaying the previously trained numerosity (3) versus a novel numerosity (4 for ‘larger’ and 2 for ‘smaller’). Both groups preferred the three-item stimulus, consistent with absolute numerosity. They also exhibited ratio-dependent discrimination of numbers, a property shared by vertebrates, as performance after 2 versus 3 was better than after 3 versus 4 training. Thus, bees differ from vertebrates in their use of absolute rather than of relative numerosity but they also have some numeric properties in common.

Number detectors spontaneously emerge in a deep neural network designed for visual object recognition

Humans and animals have a “number sense,” an innate capability to intuitively assess the number of visual items in a set, its numerosity. This capability implies that mechanisms to extract numerosity indwell the brain’s visual system, which is primarily concerned with visual object recognition. Here, we show that network units tuned to abstract numerosity, and therefore reminiscent of real number neurons, spontaneously emerge in a biologically inspired deep neural network that was merely trained on visual object recognition. These numerosity-tuned units underlay the network’s number discrimination performance that showed all the characteristics of human and animal number discriminations as predicted by the Weber-Fechner law. These findings explain the spontaneous emergence of the number sense based on mechanisms inherent to the visual system.