Size invariance in visual number discrimination

In the domain of language research, the simultaneous presentation of a visual scene and its auditory description (i.e., the visual world paradigm) has been used to reveal the timing of mental mechanisms. Here we apply this rationale to the domain of numerical cognition in order to explore the differences between fast and slow arithmetic performance, and to further study the role of spatial-numerical associations during mental arithmetic. We presented 30 healthy adults simultaneously with visual displays containing four numbers and with auditory addition and subtraction problems. Analysis of eye movements revealed that participants look spontaneously at the numbers they currently process (operands, solution). Faster performance was characterized by shorter latencies prior to fixating the relevant numbers and fewer revisits to the first operand while computing the solution. These signatures of superior task performance were more pronounced for addition and visual numbers arranged in ascending order, and for subtraction and numbers arranged in descending order (compared to the opposite pairings). Our results show that the “visual number world”-paradigm provides on-line access to the mind during mental arithmetic, is able to capture variability in arithmetic performance, and is sensitive to visual layout manipulations that are otherwise not reflected in response time measurements.

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Archerfish number discrimination

eLife ◽

10.7554/elife.74057 ◽

2022 ◽

Vol 11 ◽

Author(s):

Davide Potrich ◽

Mirko Zanon ◽

Giorgio Vallortigara

Keyword(s):

Spatial Frequency ◽

Relative Number ◽

Physical Aspect ◽

Physical Stimulus ◽

Numerical Information ◽

Number Discrimination ◽

Large Numbers ◽

Numerical Discrimination ◽

Physical Variables ◽

Performance Results

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.

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Size Invariance in Visual Pattern Recognition by Pigeons

Quantitative Analyses of Behavior ◽

10.4324/9781315788999-3 ◽

2019 ◽

pp. 41-65 ◽

Cited By ~ 1

Author(s):

Celia M. Lombardi ◽

Juan D. Delius

Keyword(s):

Pattern Recognition ◽

Visual Pattern ◽

Visual Pattern Recognition ◽

Size Invariance

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Rapid Shape Adaptation Reveals Position and Size Invariance in the Object-Related Lateral Occipital (LO) Complex.

NeuroImage ◽

10.1016/s1053-8119(18)30876-0 ◽

1998 ◽

Vol 7 (4) ◽

pp. S43 ◽

Cited By ~ 7

Author(s):

R. Malach ◽

K. Grill-Spector ◽

T. Kushnir ◽

S. Edelman ◽

Y. Itzchak

Keyword(s):

Shape Adaptation ◽

Size Invariance

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Honeybees use absolute rather than relative numerosity in number discrimination

Biology Letters ◽

10.1098/rsbl.2019.0138 ◽

2019 ◽

Vol 15 (6) ◽

pp. 20190138 ◽

Cited By ~ 16

Author(s):

Maria Bortot ◽

Christian Agrillo ◽

Aurore Avarguès-Weber ◽

Angelo Bisazza ◽

Maria Elena Miletto Petrazzini ◽

...

Keyword(s):

Absolute Number ◽

Vertebrate Species ◽

Numerical Ability ◽

Basic Properties ◽

Number Discrimination ◽

Ratio Dependent ◽

Better Than

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.

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