Most of the world modern-day languages are written from left to right – but what about numbers? As it turns out, the majority of people also represent numbers using a ‘mental line’, with smaller numbers on the left and larger numbers on the right. Some researchers argue that this phenomenon results from the way humans learn to read and write: in other words, that it is a by-product of culture, rather than an innate property of the brain.

Recent evidence suggests that newborn infants, as well as certain species of monkeys and birds, also associate smaller numbers with the left and larger numbers with the right side of space. This raises the possibility that human mental number line may stem from an ability that evolved before language, in a common ancestor of humans and other animals. Yet, critics claim that findings in infants and non-human species result from a failure to account for individual biases in responding.

To resolve this controversy, Rugani et al. trained three-day-old domestic chicks to approach a target board sporting five red squares. Chicks were then given the choice to approach two identical boards, which would both show two, five or eight red squares.

Rugani et al. showed that when both boards had two red squares, the chicks tended to approach the left-hand board more often than the right. By contrast, when both boards had eight red squares, the birds approached the right-hand board more often than the left. Importantly, no left-right bias was observed when the number of red squared remained unchanged (five). These results also could not be explained by individual chicks favoring the left or right side.

Instead, the findings suggest that even newborn animals tend to associate numbers with positions on a mental number line. Additional research is needed to determine the role of experience – or culture – in shaping this tendency, and future studies should also examine which brain regions support the association between number and space.

Number knowledge and processing is fundamental for everyday living. A peculiar characteristic of numbers concerns their strong association with space. Galton, 1880 first reported that humans, in many cases, describe and think of numbers as being represented on a mental number line (MNL) oriented from left to right. Dehaene et al., 1993 provided seminal evidence for a left-to-right oriented MNL. Healthy humans are faster in processing small numbers through left-sided responses, and large numbers through right-sided responses. Traditionally, this effect, deemed SNARC (Spatial-Numerical Association of Response Codes), has been attributed to exposure to formal instruction, and therefore considered a by-product of culture, based on reading/writing conventions. Cultural aspects can in fact influence the orientation of the MNL. Arabs, who read from right to left, show an inverted SNARC effect (Zebian, 2005); people with mixed reading habits (e.g., Israelis) show no SNARC at all (Shaki et al., 2009). The placement of numbers along a left-to-right oriented MNL can be also modulated by the experimental context and adjusted by various forms of experience. Participants instructed to conceive numbers as distances along a ruler, showed a left-to-right oriented SNARC effect, whereas conceiving numbers as hours on a clock face elicited an inverted SNARC effect (Bächtold et al., 1998). Increasing evidence, however, has highlighted the importance of pre-linguistic and biologically-determined precursors of spatial-numerical associations (SNA). Evidence from infants rules out a primary influence of verbal counting in SNA orientation. Seven-month olds, habituated to left-to-right sequences of numerical magnitudes either increasing (e.g. 1-2-3) or decreasing (e.g. 3-2-1), at test looked longer at new increasing, but not decreasing, sequences. Whenever during habituation, the sequences were instead displayed from right-to-left, such bias was not reported for both increasing and decreasing sequences (de Hevia et al., 2014). The presentation of a small numerosity (two dots) or of a large numerosity (nine dots) oriented spatial attention of 8-month-old infants, respectively towards the left or the right side of space (Bulf et al., 2015). Nevertheless, these results could be determined by the interactions that few-months olds entertained with adults or their environment (Patro et al., 2016). SNA has been described even in 3-day-old newborns, strongly reducing the possible influence of the interaction with caregivers (de Hevia et al., 2017). Recently, Di Giorgio et al., 2019 reported that newborns habituated to a numerical value (a group of 12 items), spontaneously associated a smaller number (four items) with the left side of space and a larger number (36 items) with the right side. Interestingly enough, the same number, for instance ‘12’, was associated with the left side after habituation with a large number (36), but with the right side after habituation with a smaller number (4).

The studies that cast most doubts on the importance of language and symbolic thought for the origin of the SNA come from comparative research (Brugger, 2015; Vallortigara, 2018). Adult Clark’s nutcrackers (Rugani et al., 2010) and rhesus monkeys Drucker and Brannon, 2014 have shown unilateral, left-to-right oriented bias in associating numerosity with space. A spatial representation of magnitude has been found also in gorillas and orangutans (Gazes et al., 2017). Though present in most apes, SNA is either left-to-right or right-to-left oriented, depending on the individual. Idiosyncratic experiences, such as the interactions with caregivers, rather than differences related to species or handedness, are reported among the main factors that might determine the orientation of the SNA (Gazes et al., 2017). This interpretation makes it even clearer that the only way to rule out the role of culture as well as of caregiving experience is to test day-old (almost) naive animals. For instance, baby chicks (Gallus gallus) trained to respond to a target numerosity, spontaneously associated a number smaller than the target with the left side of space, and a number larger than the target with the right side (Rugani et al., 2015a). This study strongly renovated the interest on the origin of the SNA (Drucker and Brannon, 2014; Rugani and de Hevia, 2017) and provided insights on testing SNA in non-verbal subjects. The paradigm of Rugani et al., 2015a has been applied onto different species, with mixed results. On one side, studies that merely applied the chicks’ paradigm failed in finding a SNA (Triki and Bshary, 2018; Beran et al., 2019). On the other hand, studies that extrapolated the core idea and tuned the paradigm to the test situation did successfully find a SNA (de Hevia et al., 2017; Di Giorgio et al., 2019). An alternative explanation of the original study by Rugani et al., 2015a pointed at the importance of any, however subtle, individual biases either toward the left or the right which would be magnified over the course of the test (Mangalam and Karve, 2015), but see Rugani et al., 2015b). Furthermore, Núñez and Fias, 2017 sustained that SNA in chicks could critically depend on having used novel stimuli at test with respect to the training. Chicks’ responses might be triggered by novelty, rather than by numerosity. Therefore, Núñez and Fias, 2017 highlighted the importance of testing the chicks on the same numerosity as that of the training (5 vs. 5).

The aim of the present study was to directly investigate the role of number magnitude versus individual spatial bias in 3-day-old domestic chicks.

At test, chicks were presented with the same numerosity already experienced at training (5). In different experiments this test was administered either as first or as last, to ascertain any role of experience in determining the orientation of the SNA. Data from the 5 vs. 5 control test were meant to be very insightful as no preference was expected according to the hypothesis that the bias is solely determined by the differences in numerical magnitude experienced by the animals. Hence, this test could unveil the presence of any idiosyncratic spatial bias. The performance of each chick in the 5 vs. 5 test was to this purpose employed to normalize performance scored in the other tests (2 vs. 2 and 8 vs. 8). This allowed to control for any individual bias as well as for responses guided by non-numerical variables (e.g., novelty). To test for lateralization in processing numerical magnitude, we scored the side from which chicks circumnavigated the panels. Chicks can use their eyes independently to process different visual stimuli; generally, they approached a stimulus from the side which allows an analysis with the eye connected to the most specialized hemisphere (Daisley et al., 2009). A left circumnavigation, which implies to look with the right eye, would indicate a preferential processing with the left hemisphere; a right circumnavigation, which implies to look with the left eye, would indicate a preferential processing with the right hemisphere.

Here, we trained 3-day-old chicks (n = 48) to circumnavigate a central panel depicting five elements to get a food reward. Then chicks underwent three consecutive tests, each consisting of five trials, in which two identical panels were presented. Each panel depicted either 2, 8 or 5 randomly arranged 1-cm-sided red squares. Each chick underwent a smaller number (2 vs. 2), a larger number (8 vs. 8), and the control (5 vs. 5) test. On each test trial we scored the first inspected panel (left or right) and the side from which chicks circumnavigated the panel.

In Experiment 1, test presentation Order was: 2 vs. 2, 8 vs. 8, 5 vs. 5 (N = 12 chicks) or 8 vs. 8, 2 vs. 2, 5 vs. 5 (another sample of N = 12 chicks); chicks were randomly assigned to either group. In Experiment 2, the Order of the three tests was: 5 vs. 5, 2 vs. 2, 8 vs. 8 (N = 12 chicks) or 5 vs. 5, 8 vs. 8, 2 vs. 2 (another sample of N = 12 chicks); chicks were randomly assigned to either group. Sample size for each group was calculated, as indicated by the Ethical committee for animal welfare of the University of Padova, using the formula for quantitative variables: n=(2σ²)/(μ1-μ2)² x f(α,β); with the following values α = 0.05 e ß = 0.80 average = 70% standard deviation = 17%.

For each experiment, we calculated the percentage of trials in which the chick chose the left panel (Left Choices: LC). LC ranged from 0 (left panel never chosen) to 100 (left panel always chosen). Our main prediction was that Test (2 vs. 2; 8 vs. 8; 5 vs. 5) would affect LC; in particular we expected the following order restriction on ‘Test’ variable: LC(2 vs. 2)>LC(5 vs. 5)>LC(8 vs. 8). To assess whether chicks’ behavior was based on number magnitude or on individual bias, for each chick we calculated a Small Number Bias (SNB): LC(5 vs. 5) – LC(2 vs. 2) and a Large Number Bias (LNB): LC(5 vs. 5) – LC(8 vs. 8). We expected a SNB <0, which indicates a left bias in responding to small magnitudes and a LNB >0, which indicates a right bias in responding to large magnitudes.

We conducted Bayes factor analyses using the version 0.9.12–4.2 of the Bayes Factor package in R, and using the default parameter values and JASP 0.11.1. We used the classification by Lee and Wagenmakers, 2013 to interpret Bayes factor (BF). We conducted frequentist analyses using JASP 0.11.1.

Experiment 1

We first considered the effect of Order and Test on the percentage of Left-sided Choices (LC; Figure 1A; Source data 1). Against the ‘Intercept only’ model, the Bayesian ANOVA(BfANOVA) produced an extreme evidence in favor of a Test effect (BF >100), (repeated measures Anova: F(2,44)=36.375; p<0.01, η² = 0.423); but no effect of Order (BF = 0.263), (repeated measures Anova: F(1,44) = 0.336; p=0.714, η² = 0.004), (Source data 2).

Figure 1

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We then tested the equality constraints of our model by comparing the unconstrained model (LC_2 vs. 2 ≠ LC_8 vs. 8 ≠ LC_5 vs. 5) with every other possible somewhat constrained model (e.g.: LC_2 vs. 2 ≠ LC_8 vs. 8 = LC_5 vs. 5). The unconstrained model was preferred to all the possible constrained models by a factor ranging from 12 to >100. This is an evidence, ranging from strong to extreme, in favor of a differential performance in the three tests. To compare the order restrictions model (2 vs. 2 > 5 vs. 5 > 8 vs. 8) with the unconstrained full model (LC_2 vs. 2 ≠ LC_8 vs. 8 ≠ LC_5 vs. 5) we firstly ran a Markov Chain Monte Carlo (MCMC) which showed 9983/10000 cases consistent with our hypothesis. We found a moderate evidence in favor of the order restriction: LC_2 vs. 2>LC_5 vs. 5>LC_8 vs. 8 (BF = 5.990). Frequentist analyses confirmed that: LC_2 vs. 2 was significantly larger than chance (50%): mean = 71.667, SD = 19.486, t(23)=5.447, p<0.001, Cohen's d = 1.572; LC_8 vs. 8 was significantly smaller than chance: mean = 28.333, SD = 20.359, t(23) = −5.214, p<0.001, Cohen's d = 1.505; the LC_5 vs. 5 was not statistically different from chance: mean = 52.500, SD = 23.452, t(23) = 0.522, p=0.604, Cohen's d = 0.151, (Source data 2).

For what concerns the Number Bias, we firstly computed the SNB and the LNB, then we compared each Number Bias with the null = 0. T-test Bayes factor analysis yielded a very strong evidence in favor of the Number Bias for SNB, (BF = 49.037; One sample t test: t(23)=-3.922; p<0.001, Cohen’s d = −0.801), (Source data 3) and an extreme evidence in favor of the Number Bias for LNB (BF >100; One sample t test: t(23)=4.872; p<0.001, Cohen’s d = 0.994) (Source data 4). For what concerns the side of circumnavigation, we did not find any consistent evidence for each numerical magnitude: 2 vs. 2 (BF = 0.301; X² = 0.403; p=0.525, Phi = 0.058); 5 vs. 5 (BF = 3.314; X² = 5.444; p=0.020, Phi = 0.213); 8 vs. 8 (BF = 0.249; X² = 0.062; p=0.804, Phi = 0.023), see Table 1, Experiment 1; (Source data 5).

Table 1

Experiment 1
		Left panel		Right panel		BF	X2	P	Phi
Test	Side	Left	Right	Left	Right
2 vs. 2	Count	51	35	18	16	0.301	0.403	0.525	0.058
	%	59.302	40.698	52.941	47.059
5 vs. 5	Count	41	22	25	32	3.314	5.444	0.020	0.213
	%	65.079	34.921	43.860	56.140
8 vs. 8	Count	21	13	51	35	0.249	0.062	0.804	0.023
	%	61.765	38.235	59.302	40.698
Experiment 2
		Left Panel		Right Panel		BF	X2	p	Phi
Test	Side	Left	Right	Left	Right
2 vs. 2	Count	62	22	20	16	1.512	3.880	0.049	0.180
	%	73.810	26.190	55.556	44.444
5 vs. 5	Count	36	25	34	25	0.224	0.024	0.877	0.014
	%	58.333	41.667	57.626	42.373
8 vs. 8	Count	24	16	23	57	49.104	10.930	<0.001	0.302
	%	60	40	28.750	71.250

On the basis of these analyses we concluded that chicks’ performance is affected by the number magnitude of elements faced at test.

The results of Experiments 1 and 2 support the hypothesis that number magnitude affects chicks’ performance. Interestingly, the numerical bias reported in Experiment two seems to be less strong than that reported in Experiment 1: the evidence in favor of the Number Bias was very strong-to-extreme in Experiment 1, but moderate in Experiment 2. Plausibly this reduced strength of the SNA is related to the first test, in which chicks experienced a magnitude identical to the training one. A recent paper showed that the effect of spatial-motor experience could modulate the SNA in pre-literate children. A short-term (≈15 min) spatial –and not numerical– training (i.e. playing a video game which required either left-to-right or right-to-left oriented movements) is sufficient to modulate the orientation of the spatial numerical association in 3- and 4-year-old children (Patro et al., 2016). Even if we did not find any consistent bias on the side of circumnavigation, side differences in circumnavigation seemed stronger in Experiment 2, where evidence of spatial numerical association were found to be somewhat weaker than in Experiment 1. This allows to speculate that experience may modulate the processing underlying numerical perception and its association with space.

On the contrary in Experiment 1, chicks experienced an appreciable variation in numerical magnitude in the very first test, in either direction: smaller (2) or larger (8). Such difference in the strength of the SNA opens new challenging opportunities to study the role of experience in modulating the SNA.

Taken together, our two experiments showed that number magnitude and space are strongly associated in young and naïve chicks. In presence of very limited numerical and environmental/spatial experience this association is left-to-right oriented. But is this effect sensitive to experience? Future studies are needed to assess whether and how the association of number and space, however predisposed, can be modulated by experience.

Chicks showed a left bias in the 2 vs. 2, a right bias in the 8 vs. 8 and no bias in the control test 5 vs. 5, irrespectively of testing order (Figure 1A and B). Our results cannot be explained by individual orienting biases or by preference for novelty (Núñez and Fias, 2017). Our results show, instead, that it is the relative numerical magnitude between the training and the testing values, which determines the direction of the bias. Moreover, the presence of a linear trend with three points of reference - LC(2 vs. 2)>LC(5 vs. 5)>LC(8 vs. 8)- poses further restrictions in favor of a spatial-numerical mapping guided by the mental number line (see Núñez and Fias, 2017).

One important issue is the adaptive significance, if any, of a directional number-space association for non-human (and human) animals. One could argue that the basic phenomena is the mapping of number to space, and that the ordering of such mapping is simply the outcome of chance processes. However, if this were the case, then one would expect different individuals showing different directional biases, for there would be no specific reason for an alignment in the direction of the space-number association in different individuals. Some more basic biological phenomenon may, however, be at work here. One hypothesis has been put forward by Vallortigara, 2018. It is based on evidence that the two sides of the brain provide qualitatively different contributions to the control of functions related to motivation and emotion - sometimes referred to as the ‘valence hypothesis’ (Davidson, 2004)- with the left and right sides of the brain specialized for positive (approach) or negative (withdrawal) aspects in the control of behavior. It is plausible that changes towards larger or smaller magnitudes are associated with prevalent activation of, respectively, the left (positive valence) and the right (negative valence) hemisphere, and, thus, that attention to contralateral hemispace arises from it. Even if not explicitly trained to such association, animals can establish that for appetitive stimuli like the ones used in our experiments, larger magnitudes are intrinsically better (and approachable) than smaller magnitudes. According to this hypothesis, when chicks are faced with either abrupt increase or decrease in numerosities this would evoke preferential activation of, respectively, the left hemisphere (positive emotion) or the right hemisphere (negative emotion). In turn, this would promote attending to the contralateral side of the activated hemisphere, i.e. to the left for changes from large to smaller numerosities and to the right for changes from small to larger numerosities. The hypothesis can be tested in future experiments by e.g. establishing specific associations between certain magnitudes and an aversive (rather than an appetitive) stimulus, thus inducing a reduction if not an inversion of the direction of the space–number association.

All data and codes have been uploaded as source data. The R codes used for data analyses, including the full list of parameters used have also been uploaded. Our datasets data are stored and backed up on the Research Data Unipd server (http://researchdata.cab.unipd.it/id/eprint/326). Research Data Unipd is a research data repository that meets the demands of FAIR (Findable, Accessible, Interoperable, Reusable) data storage, in accordance with the Guidelines on FAIR Data Management in Horizon 2020- July 2016.

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Author details

1. Rosa Rugani

   1. Department of General Psychology, University of Padova, Padova, Italy
   2. Department of Psychology, University of Pennsylvania, Philadelphia, United States

   Contribution

   Conceptualization, Data curation, Formal analysis, Funding acquisition, Investigation, Methodology, Writing - original draft, Project administration, Writing - review and editing

   For correspondence

   rosa.rugani@unipd.it

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0001-5294-6306

2. Giorgio Vallortigara

   Center for Mind/Brain Sciences, University of Trento, Rovereto, Italy

   Contribution

   Conceptualization, Funding acquisition, Validation, Visualization, Writing - review and editing

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0001-8192-9062

3. Konstantinos Priftis

   Department of Psychology, University of Pennsylvania, Philadelphia, United States

   Contribution

   Conceptualization, Formal analysis, Supervision, Validation, Visualization, Writing - review and editing

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0002-5215-4621

4. Lucia Regolin

   Department of General Psychology, University of Padova, Padova, Italy

   Contribution

   Conceptualization, Supervision, Funding acquisition, Validation, Visualization, Methodology, Writing - review and editing

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0001-8960-0309

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