An insect brain organizes numbers on a left-to-right mental number line.

The "mental number line" (MNL) is a form of spatial numeric representation that associates small and large numbers with the left and right spaces, respectively. This spatio-numeric organization can be found in adult humans and has been related to cultural factors such as writing and reading habits. Yet, both human newborns and birds order numbers consistently with an MNL, thus raising the question of whether culture is a main explanation for MNL. Here, we explored the numeric sense of honey bees and show that after being trained to associate numbers with a sucrose reward, they order numbers not previously experienced from left to right according to their magnitude. Importantly, the location of a number on that scale varies with the reference number previously trained and does not depend on low-level cues present on numeric stimuli. We provide a series of neural explanations for this effect based on the extensive knowledge accumulated on the neural underpinnings of visual processing in honey bees and conclude that the MNL is a form of numeric representation that is evolutionarily conserved across nervous systems endowed with a sense of number, irrespective of their neural complexity.

Relative numerical middle in rhesus monkeys.

Animals show vast numerical competence in tasks that require both ordinal and cardinal numerical representations, but few studies have addressed whether animals can identify the numerical middle in a sequence. Two rhesus monkeys (Macaca mulatta) learned to select the middle dot in a horizontal sequence of three dots on a touchscreen. When subsequently presented with longer sequences composed of 5, 7 or 9 items, monkeys transferred the middle rule. Accuracy decreased as the length of the sequence increased. In a second test, we presented monkeys with asymmetrical sequences composed of nine items, where the numerical and spatial middle were distinct and both monkeys selected the numerical middle over the spatial middle. Our results demonstrate that rhesus macaques can extract an abstract numerical rule to bisect a discrete set of items.

Response of male and female domestic chicks to change in the number (quantity) of imprinting objects.

When facing two sets of imprinting objects of different numerousness, domestic chicks prefer to approach the larger one. Given that choice for familiar and novel stimuli in imprinting situations is known to be affected by the sex of the animals, we investigated how male and female domestic chicks divide the time spent in the proximity of a familiar versus an unfamiliar number of objects, and how animals interact (by pecking) with these objects. We confirmed that chicks discriminate among the different numerousnesses, but we also showed that females and males behave differently, depending on the degree of familiarity of the objects. When objects in the testing sets were all familiar, females equally explored both sets and pecked at all objects individually. Males instead selectively approached the familiar numerousness and pecked more at it. When both testing sets comprised familiar as well as novel objects, both males and females approached the larger numerousness of familiar objects. However, chicks directed all their pecks toward the novel object within the set. Differences in the behavior of males and females can be accounted for in terms of sex difference in the motivation to reinstate social contact with the familiar objects and to explore novel ones, likely associated with the ecology and the social structure of the species before domestication.

A mental number line in human newborns.

Humans represent numbers on a mental number line with smaller numbers on the left and larger numbers on the right side. A left-to-right oriented spatial-numerical association, (SNA), has been demonstrated in animals and infants. However, the possibility that SNA is learnt by early exposure to caregivers' directional biases is still open. We conducted two experiments: in Experiment 1, we tested whether SNA is present at birth and in Experiment 2, we studied whether it depends on the relative rather than the absolute magnitude of numerousness. Fifty-five-hour-old newborns, once habituated to a number (12), spontaneously associated a smaller number (4) with the left and a larger number (36) with the right side (Experiment 1). SNA in neonates is not absolute but relative. The same number (12) was associated with the left side rather than the right side whenever the previously experienced number was larger (36) rather than smaller (4) (Experiment 2). Control on continuous physical variables showed that the effect is specific of discrete magnitudes. These results constitute strong evidence that in our species SNA originates from pre-linguistic and biological precursors in the brain.

What is a number? The interplay between number and continuous magnitudes.

Leibovich et al. argue that it is impossible to control for all continuous magnitudes in a numerical task. We contend that continuous magnitudes (i.e., perimeter, area, density) can be simultaneously controlled. Furthermore, we argue that shedding light on the interplay between number and continuous magnitudes - rather than considering them independently - will provide a much more fruitful approach to understanding mathematical abilities.

Mapping number to space in the two hemispheres of the avian brain.

Pre-verbal infants and non-human animals associate small numbers with the left space and large numbers with the right space. Birds and primates, trained to identify a given position in a sagittal series of identical positions, whenever required to respond on a left/right oriented series, referred the given position starting from the left end. Here, we extended this evidence by selectively investigating the role of either cerebral hemisphere, using the temporary monocular occlusion technique. In birds, lacking the corpus callosum, visual input is fed mainly to the contralateral hemisphere. We trained 4-day-old chicks to identify the 4th element in a sagittal series of 10 identical elements. At test, the series was identical but left/right oriented. Test was conducted in right monocular, left monocular or binocular condition of vision. Right monocular chicks pecked at the 4th right element; left monocular and binocular chicks pecked at the 4th left element. Data on monocular chicks demonstrate that both hemispheres deal with an ordinal (sequential) task. Data on binocular chicks indicate that the left bias is linked to a right hemisphere dominance, that allocates the attention toward the left hemispace. This constitutes a first step towards understanding the neural basis of number space mapping.

The use of proportion by young domestic chicks (Gallus gallus).

We investigated whether 4-day-old domestic chicks can discriminate proportions. Chicks were trained to respond, via food reinforcement, to one of the two stimuli, each characterized by different proportions of red and green areas (» vs. ¾). In Experiment 1, chicks approached the proportion associated with food, even if at test the spatial dispositions of the two areas were novel. In Experiment 2, chicks responded on the basis of proportion even when the testing stimuli were of enlarged dimensions, creating a conflict between the absolute positive area experienced during training and the relative proportion of the two areas. However, chicks could have responded on the basis of the overall colour (red or green) of the figures rather than proportion per se. To control for this objection, in Experiment 3, we used new pairs of testing stimuli, each depicting a different number of small squares on a white background (i.e. 1 green and 3 red vs. 3 green and 1 red or 5 green and 15 red vs. 5 red and 15 green). Chicks were again able to respond to the correct proportion, showing they discriminated on the basis of proportion of continuous quantities and not on the basis of the prevalent colour or on the absolute amount of it. Data indicate that chicks can track continuous quantities through various manipulations, suggesting that proportions are information that can be processed by very young animals.

Use of kind information for object individuation in young domestic chicks.

In this paper, we studied the ability of newborn chicks to use kind information (sortal objects) provided by social and food attractors to determine the number of distinct objects present in an event (object individuation). Newly hatched chicks were reared with five imprinting objects and were fed mealworms. Chicks' spontaneous tendency to approach the larger group of items was exploited. At test, on day 2 post-hatching, chicks observed two events in which objects, differing in kind, were each hidden behind one of two identical screens. Approaching either screen was considered a preferential choice. In Experiment 1, chicks presented with two social versus two food attractors did not exhibit any preference. In contrast, in Experiment 2, when chicks saw two different attractors (one social and one food) hidden behind a screen and one attractor hidden twice (i.e. moved back and forth two times) behind the other screen, they spontaneously approached the two different attractors rather than the single one seen twice. An explanation based on the preference for the more varied set was ruled out in Experiment 3: chicks did not preferentially choose between two different versus two identical objects when both groups were simultaneously presented. Results suggest for the first time that a non-human species uses kind information for individuating objects in a cross-basic-level contrast (i.e. food and social items) with minimal experience. As social and food stimuli differ in property as well as in kind information, the alternative explanation accounting for use of property information alone is also discussed.

Magnitude shifts spatial attention from left to right in rhesus monkeys as in the human mental number line.

Humans typically represent numbers and quantities along a left-to-right continuum. Early perspectives attributed number-space association to culture; however, recent evidence in newborns and animals challenges this hypothesis. We investigate whether the length of an array of dots influences spatial bias in rhesus macaques. We designed a touch-screen task that required monkeys to remember the location of a target. At test, monkeys maintained high performance with arrays of 2, 4, 6, or 10 dots, regardless of changes in the array's location, spacing, and length. Monkeys remembered better left targets with 2-dot arrays and right targets with 6- or 10-dot arrays. Replacing the 10-dot array with a long bar, yielded more accurate performance with rightward locations, consistent with an underlying left-to-right oriented magnitude code. Our study supports the hypothesis of a spatially oriented mental magnitude line common to humans and animals, countering the idea that this code arises from uniquely human cultural learning.

One, two, three, four, or is there something more? Numerical discrimination in day-old domestic chicks.

Human adults master sophisticated, abstract numerical calculations that are mostly based on symbolic language and thus inimitably human. Humans may nonetheless share a subset of non-verbal numerical skills, available soon after birth and considered the evolutionary foundation of more complex numerical reasoning, with other animals. These skills are thought to be based on the two systems: the object file system which processes small values (<3) and the analogue magnitude system which processes large magnitudes (>4). Infants' ability to discriminate 1 vs. 2, 1 vs. 3, 2 vs. 3, but not 1 vs. 4, seems to indicate that the two systems are independent, implying that the conception of a continuous number processing system is based on precursors that appear to be interrupted at or about the number four. The findings from the study being presented here indicating that chicks are able to make a series of discriminations regarding that borderline number (1 vs. 4, 1 vs. 5, 2 vs. 4) support the hypothesis that there is continuity in the number system which processes both small and large numerousness.

Hybro chicks outperform Ross308 in a numerical-ordinal task. Cognitive and behavioral comparisons between 2 broiler strains of newborn domestic chicks (Gallus gallus).

Domestic chickens (Gallus gallus) are among those species subject to intensive selection for production. Among the most widely used broiler strains are the Ross308 and the Hybro. From the perspective of animal production, Ross308 were superior to Hybro in weight gain, final body mass, and feed conversion. Intensive selection is thought to also cause behavioral changes and to negatively affect cognitive abilities. Up to date, though, no evidence has been provided on broiler breeds. The aim of this study was to explore cognitive differences among Hybro and Ross308 chickens by assessing their ordinal-numerical abilities. Chicks learned learnt to find a food reward in the 4th container in a series of 10 identical and sagittally aligned containers. We designed a standard training procedure ensuring that all chicks received the same amount of training. The chicks underwent 2 tests: a sagittal and a fronto-parallel one. In the former test, the series was identical to that experienced during training. In the fronto-parallel test, the series was rotated by 90°, thus left-to-right oriented, to assess the capability of transferring the learnt rule with a novel spatial orientation. In the sagittal test, both chicken hybrids selected the 4th item above chance; interestingly the Hybro outperformed the Ross308 chicks. In the fronto-parallel test, both strains selected the 4th left and the 4th right container above chance; nevertheless, the Hybro chicks were more accurate. Our results support the hypothesis that intense selection for production can influence animal cognition and behavior, with implications on animal husbandry and welfare.

Children perform better on left than right targets in an ordinal task.

Francis Galton first reported that humans mentally organize numbers from left to right on a mental number line (1880). This spatial-numerical association was long considered to result from writing and reading habits. More recently though, newborns and animals showed a left-to-right oriented spatial numerical association challenging the primary role assigned to culture in determining the link between number and space. Despite growing evidence supporting the intrinsic association between number and space in different species, its adaptive value is still largely unknown. Here we tested for an advantage in identification of left versus right target positions in 3- to 6-year-old children. Children watched as a toy was hidden under one of 10 linearly arranged identical cups and were then asked to help a stuffed animal retrieve the toy. On each trial, the toy was hidden in the 2nd, 3rd, or 4th cup, from the left or right. To prevent children from staring at the target cup, they were asked to pick up the stuffed animal from under their chair after witnessing the hiding of the toy and then to help the stuffed animal find the toy. Older children were more accurate than younger children. Children exhibited a serial position effect, with performance higher for more exterior targets. Remarkably, children also showed a left bias: they remembered the left targets better than the right targets. Only the youngest children were dramatically influenced by the location of the experimenter during search. Additional analyses support the hypothesis that children used a left-to-right oriented searching strategy in this spatial/ordinal task.

Processing Individually Distinctive Schematic-Faces Supports Proto-Arithmetical Counting in the Young Domestic Chicken.

A key signature of small-number processing is the difficulty in discriminating between three and four objects, as reported in infants and animals. Five-day-old chicks overcome this limit if individually distinctive features characterize each object. In this study, we have investigated whether processing individually different face-like objects can also support discrimination between three and four objects. Chicks were reared with seven face-like stimuli and tested in the proto-arithmetic comparison 1 + 1 + 1 vs. 1 + 1 + 1 + 1. Birds reared and tested with all different faces discriminated and approached the larger group (Exp. 1), whereas new birds reared and tested with seven identical copies of one same face failed (Exp. 2). The presence at test of individually different faces allowed discrimination even when chicks were reared with copies of one face (Exp. 3). To clarify the role of the previous experience of at least one specific arrangement of facial features, in Experiment 4, featureless faces were employed during rearing. During testing, chicks were unable to discriminate between three and four individually distinct faces. Results highlight the importance of having experienced at least one "face" in prompting individual processing and proto-arithmetical calculation later during testing. We speculate that mechanisms effective at the non-symbolic level may positively affect numerical performance.

Are Rational Numbers Spontaneous? Natural Numbers Suffice all Processing by the Number Sense.

The presence of preverbal numerical abilities in animals and infants is widely established, but an important discussion remains about which cognitive systems support these abilities. In particular, a great amount of research is dedicated to the approximate number system (ANS) for the elaboration of non-symbolic numbers and their possible types of mental numeric representations. In a recently published article, Clarke and Beck (2021) provide a series of evidence that supports its existence (ANS) and argue that the mental referents of this system are both natural and rational numbers. In the current commentary, we introduce the notion of the "whole-entity bias" that permeates perception and cognition and favors an automatic processing of discrete mental magnitudes while hindering the representations of fractional numbers. Further, we argue that a hierarchical structure of the ANS that represents natural numbers and supports the understanding of proportions through a series of computations is a more ecological theorization. To conclude, we believe that such a view is still compatible with the proposal of a single representational system (the ANS) supporting both number kinds but offers a different perspective on the computational level of explanation.

Asymmetrical number-space mapping in the avian brain.

When trained to peck a selected position in a sagittally-oriented series of identical food containers, and then required to generalize to an identical series rotated by 90°, chicks identify as correct only the target position from the left end, while choosing the right one at chance. Here we show that when accustomed to systematic changes in inter-elements distances during training or faced with similar spatial changes at test, chicks identify as correct both the target positions from left and right ends. However, ordinal position is spontaneously encoded even when inter-element distances are kept fixed during training (in spite of the fact that distances between elements suffice for target identification without any numerical computation). We explain these findings in terms of intra-hemispheric coupling of bilateral numerical (ordinal) representation and unilateral (right hemispheric) spatial representation of the number line, producing differential allocation of attention in the left and right visual hemifields.

Spontaneous discrimination of possible and impossible objects by newly hatched chicks.

Four-month-old infants can integrate local cues provided by two-dimensional pictures and interpret global inconsistencies in structural information to discriminate between possible and impossible objects. This leaves unanswered the issue of the relative contribution of maturation of biologically predisposed mechanisms and of experience with real objects, to the development of this capability. Here we show that, after exposure to objects in which junctions providing cues to global structure were occluded, day-old chicks selectively approach the two-dimensional image that depicted the possible rather than the impossible version of a three-dimensional object, after restoration of the junctions. Even more impressively, completely naive newly hatched chicks showed spontaneous preferences towards approaching two-dimensional depictions of structurally possible rather than impossible objects. These findings suggest that the vertebrate brain can be biologically predisposed towards approaching a two-dimensional image representing a view of a structurally possible three-dimensional object.

Object individuation in 3-day-old chicks: use of property and spatiotemporal information.

Object individuation was investigated in newborn domestic chicks. Chicks' spontaneous tendency to approach the larger group of familiar objects was exploited in a series of five experiments. In the first experiment newborn chicks were reared for 3 days with objects differing in either colour, shape or size. At test, each chick was presented with two groups of events: two objects differing in one property vs. two presentations of the same object. In both cases, all objects involved in the same group of events were sequentially presented and eventually concealed in a different spatial location, and the number of events taking place at each location was equalized. Chicks spontaneously approached the two different objects rather than the single object seen twice. Chicks did not just prefer the more varied set as they did not choose it when the two elements of each group of events were simultaneously presented (Experiment 2). Chicks succeeded when two different objects simultaneously presented were confronted with three identical ones simultaneously presented (Experiment 3), though they failed with sequential presentation of two different objects vs. one object presented three times if they had been familiarized with up to three identical objects (Experiment 4). Chicks instead succeeded if they had been familiarized with objects that were all different from one another (Experiment 5). These young birds thus proved able to use property and spatiotemporal information for object individuation.

Approach direction and accuracy, but not response times, show spatial-numerical association in chicks.

Chicks trained to identify a target item in a sagittally-oriented series of identical items show a higher accuracy for the target on the left, rather than that on the right, at test when the series was rotated by 90°. Such bias seems to be due to a right hemispheric dominance in visuospatial tasks. Up to now, the bias was highlighted by looking at accuracy, the measure mostly used in non-human studies to detect spatial numerical association, SNA. In the present study, processing by each hemisphere was assessed by scoring three variables: accuracy, response times and direction of approach. Domestic chicks were tested under monocular vision conditions, as in the avian brain input to each eye is mostly processed by the contralateral hemisphere. Four-day-old chicks learnt to peck at the 4th element in a sagittal series of 10 identical elements. At test, when facing a series oriented fronto-parallel, birds confined their responses to the visible hemifield, with high accuracy for the 4th element. The first element in the series was also highly selected, suggesting an anchoring strategy to start the proto-counting at one end of the series. In the left monocular condition, chicks approached the series starting from the left, and in the right monocular condition, they started from the right. Both hemispheres appear to exploit the same strategy, scanning the series from the most lateral element in the clear hemifield. Remarkably, there was no effect in the response times: equal latency was scored for correct or incorrect and for left vs. right responses. Overall, these data indicate that the measures implying a direction of choice, accuracy and direction of approach, and not velocity, i.e., response times, can highlight SNA in this paradigm. We discuss the relevance of the selected measures to unveil SNA.