Arithmetic in newborn chicks

Abstract

Newly hatched domestic chicks were reared with five identical objects. On days 3 or 4, chicks underwent free-choice tests in which sets of three and two of the five original objects disappeared (either simultaneously or one by one), each behind one of two opaque identical screens. Chicks spontaneously inspected the screen occluding the larger set (experiment 1). Results were confirmed under conditions controlling for continuous variables (total surface area or contour length; experiment 2). In the third experiment, after the initial disappearance of the two sets (first event, FE), some of the objects were visibly transferred, one by one, from one screen to the other (second event, SE). Thus, computation of a series of subsequent additions or subtractions of elements that appeared and disappeared, one by one, was needed in order to perform the task successfully. Chicks spontaneously chose the screen, hiding the larger number of elements at the end of the SE, irrespective of the directional cues provided by the initial (FE) and final (SE) displacements. Results suggest impressive proto-arithmetic capacities in the young and relatively inexperienced chicks of this precocial species.

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doi: 10.1098/rspb.2009.0044
, 2451-2460 first published online 1 April 2009276 2009 Proc. R. Soc. B
Rosa Rugani, Laura Fontanari, Eleonora Simoni, Lucia Regolin and Giorgio Vallortigara
Arithmetic in newborn chicks
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Arithmetic in newborn chicks
Rosa Rugani
1,
*, Laura Fontanari
1
, Eleonora Simoni
2
, Lucia Regolin
2
and Giorgio Vallortigara
1
1
Center for Mind/Brain Sciences, University of Trento, Corso Bettini 31, 38068 Rovereto, Italy
2
Department of General Psychology, University of Padova, 35122 Padova, Italy
Newly hatched domestic chicks were reared with five identical objects. On days 3 or 4, chicks underwent
free-choice tests in which sets of three and two of the five original objects disappeared (either
simultaneously or one by one), each behind one of two opaque identical screens. Chicks spontaneously
inspected the screen occluding the larger set (experiment 1). Results were confirmed under conditions
controlling for continuous variables (total surface area or contour length; experiment 2). In the third
experiment, after the initial disappearance of the two sets (first event, FE), some of the objects were visibly
transferred, one by one, from one screen to the other (second event, SE). Thus, computation of a series of
subsequent additions or subtractions of elements that appeared and disappeared, one by one, was needed
in order to perform the task successfully. Chicks spontaneously chose the screen, hiding the larger number
of elements at the end of the SE, irrespective of the directional cues provided by the initial (FE) and final
(SE) displacements. Results suggest impressive proto-arithmetic capacities in the young and relatively
inexperienced chicks of this precocial species.
Keywords: number cognition; counting; number sense; arithmetic; addition; subtraction
1. INTRODUCTION
Only human adults would be considered capable of
counting if numerical and language abilities were
considered to be strictly correlated with one another
(Dehaene 1997;Butterworth 1999;Spelke & Dehaene
1999;Hauser & Spelke 2004). Although this is likely to be
correct for symbolic mathematical capacity (Carey 2004),
recent evidence from clinical neuropsychology suggests a
remarkable degree of independence of mathematical
cognition from language grammar in human adults
(Varley et al. 2005; see also Butterworth et al. 2008).
Moreover, numerical competences have recently been
demonstrated in a variety of species (for mammalian and
bird species, see Hauser et al. 2000;Hauser & Carey 2003;
Lyon 2003;Judge et al. 2005;Pepperberg & Gordon
2005;Beran et al.2006; Cantlon & Brannon 2006a,b,2007;
Pepperberg 2006;Addessi et al. 2008;Rugani et al. 2008).
Animals and human infants are even capable of some
simple arithmetic, such as addition and subtraction
(reviews in Gallistel 1990;Dehaene 1997;Spelke &
Dehaene 1999;Brannon & Roitman 2003).
Some of these studies employed choice paradigms
involving very little or no specific numerical training.
Chimpanzees (Pan troglodytes) presented with two sets of
two food wells, each of which contained a number
of chocolates, selected the pair of quantities whose sum
was greater than the sum of the other pair (Rumbaugh
et al. 1987). To choose the sets of larger overall quantity,
the chimpanzees had to add up the number of chocolates
in each set and then compare the two resulting values.
Chimpanzees solved the task even when, on the critical
trial, the correct set of wells did not contain the larger
single value, demonstrating that performance was not
based on choosing the largest single amount (Rumbaugh
et al. 1988).
Other studies employed specific training on symbols
representing numbers. Washburn & Rumbaugh (1991)
trained two rhesus monkeys (Macaca mulatta) to choose
between two Arabic numbers presented on a touch-
sensitive screen. As a reward, the animals received the
corresponding number of pellets to the number they had
selected. Monkeys always chose the larger number even
when they were presented with new combinations of
numbers. A similar paradigm was used to test squirrel
monkeys (Saimiri sciureus) on tasks requiring them to
choose between pairs or triplets of Arabic numerals.
Monkeys chose the larger sum and their performance
could neither be attributed to choosing the largest single
value nor to avoiding the single smallest value (Olthof et al.
1997). Evidence on symbolic training has been reported
for apes, e.g. chimpanzees (P. troglodytes;Beran &
Rumbaugh 2001).
Using the methodology of the violation of expectancy,
Wynn (1992) showed that five-month-old infants can
solve some simple arithmetic operations. The idea was
that, if infants keep track of the numbers of toys they see
being placed behind a screen, they should look longer at
the screen that, once lowered, violates their expectations
revealing an unexpected outcome. For example, in the
1C1Z2 task, one object was placed on a stage, covered
by the screen, and then another object was introduced
behind the screen. When the screen was removed, infants
looked longer at the ‘impossible’ outcomes of either one
object or three objects, suggesting that infants expected to
see exactly two objects. In the original study, continuous
variables such as volume or surface area were not
controlled for, thus infants might well have attended to
Proc. R. Soc. B (2009) 276, 2451–2460
doi:10.1098/rspb.2009.0044
Published online 1 April 2009
*Author for correspondence (rosa.r ugani@unipd.it; rosa.rugani
@unitn.it.
Received 9 January 2009
Accepted 11 March 2009 2451 This journal is q2009 The Royal Society
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the volume, area or contour length of the objects rather
than to their actual number. Wynn’s results, however,
were then replicated by subsequent studies in which
continuous variables were at least partially controlled for.
Simon et al. (1995) replicated Wynn’s paradigm, but used
‘Elmo’ dolls in the initial phase of the trials and then
surreptitiously replaced ‘Elmo’ dolls with ‘Ernie’ dolls.
The infants’ expectations were not violated by this identity
switch. They looked longer only at the numerically
unexpected outcome and not at the identity of the
outcome. This indicates that, in some sense, infants
represent the number of objects stripped of their non-
numerical features. Moreover, they do so even across
sensory modalities. Five-month-old infants underwent
preliminary familiarization trials in which tones were
paired with objects, thereby, they learned to associate the
two events. At test, the infants were presented alternatively
with two types of arithmetic events: the expected, correct
outcome operations (one objectCone toneZtwo objects;
and one objectCtwo tonesZthree objects) or the
unexpected, incorrect ones (one objectCtwo tonesZtwo
objects; and one objectCone toneZthree objects). Infants
looked longer at the unexpected outcomes rather than at
the expected ones (Kobayashi et al. 2004).
Wynn’s paradigm was also adapted to test arithmetic
reasoning in rhesus monkeys (M. mulatta). Subjects
viewed food items. A screen was then raised to obscure
the items on the stage. Some items were then added or
removed from behind the screen. Finally, the screen was
lowered to reveal an expected or unexpected number of
objects and looking time was measured. Monkeys looked
longer when the unexpected outcome was revealed for
1C1Z1 or 2 and 2K1Z1 or 2 operations (Hauser et al.
1996), even when continuous variables, such as volume
and surface area were partially controlled for ( Hauser &
Carey 2003). Cotton-top tamarins (Saguinus oedipus) and
lemurs (Eulemur fulvus,Eulemur mongoz,Lemur catta and
Varecia rubra), if presented with the 1C1 operation,
looked longer at the unexpected outcome of 3 or 1
compared with the expected value of 2, demonstrating
that subjects expected ‘exactly 2’ (Uller et al. 2001;Santos
et al. 2005). Also, using a choice measure, expressed by
reaching rather than looking time, Sulkowski & Hauser
(2001) have shown that rhesus monkeys are remarkably
precise at calculating the outcome of subtraction
operations for small numbers up to 3. Even domestic
dogs have been shown to be capable of solving simple
additions such as 1C1Z2 rather than 1 or 3 ( West &
Young 2002). In all these studies, regardless of the
paradigm employed, participants were able to compute
the correct outcome of simple arithmetic operations
whenever both sets were small (upper limit of 4 for adult
rhesus monkeys and upper limit of 3 for human babies),
but failed whenever any of the sets exceeded such limit:
rhesus monkeys failed at three versus eight ( Hauser et al.
2000); infants failed at 2 versus 4, 3 versus 6, 1 versus 4
and even 0 versus 4 (Feigenson & Carey 2005). Never-
theless, several other studies showed that animals succeed
when dealing with large as well as small sets. Rhesus
monkeys (Brannon & Terrace 1998,2000), socially
housed hamadryas baboons, socially housed squirrel
monkeys (Papio hamadnjas,Saimiri sciureus;Smith et al.
2003) and brown capuchin monkeys (Cebus apella;Judge
et al. 2005) trained to order numerosities from 1 to 4,
could then generalize to numbers from 5 to 9. Monkeys
trained to respond (in ascending or descending order) to
pairs of numerosities (1–9) spontaneously ordered in the
same direction new pairs of larger values (i.e. 10, 15, 20,
30; Cantlon & Brannon 2006b). Chimpanzees were able
to summate different sets of food items and to select the
larger quantities in the comparison 5 versus 8; 5 versus
10 and 6 versus 10 (Beran & Beran 2004) and 2C2C3
versus 3C4C1(Beran 2001). Monkeys could also sum
different numbers of dots and select the correct response
in a matching-to-sample task even when large numer-
osities were employed (Cantlon & Brannon 2007).
The present study aimed at extending comparative
research on the spontaneous representation of number to
very young birds, employing filial imprinting to familiarize
the animals with a certain number of elements (see
Vallortigara (2004,2006) for general reviews on the use of
imprinting as a tool for comparative cognitive investi-
gation). Thus, no specific numerical training was
performed and the results obtained allow some con-
clusions to be drawn on the spontaneous ability of animals
to deal with simple arithmetic tasks. Moreover, the use of
very young and inexperienced animals may enlighten us
with regard to core knowledge mechanisms (Spelke 2000,
2003) in the vertebrate brain, in particular, concerning the
extent to which arithmetic capacities depend on acquired
experience versus inborn predispositions (for similar
research in the domain of geometry cognition see
Vallortigara (in press a,b)).
2. EXPERIMENT 1
Chicks were required to identify the larger between a set
of two and a set of three elements (i.e. small balls, all
identical) by walking to the location where such sets had
been seen to disappear. Chicks have been shown capable
of rejoining a social goal (a single imprinting ball) in the
correct spatial location up to 180 s from its disappearance
(Vallortigara et al. 1998;Regolin et al. 2005a,b). Here,
chicks were expected to approach the larger set because,
in simultaneous free-choice tests when both choice
sets were visible, these birds have been shown to prefer
the larger set of imprinting objects, irrespective of the
number of elements that they had been exposed to during
imprinting (Rugani et al. submitted). Rugani and
colleagues tested chicks for their sensitivity to number
versus continuous extent of artificial objects they had
been reared with. When objects used during exposure
were all identical to each other and were also identical to
the objects used at test, chicks faced with choices between
different numerosities (i.e. 1 versus 2 or 2 versus 3
objects) chose the set of larger numerosity, irrespective of
the number of objects they had been reared with. When
chicks were reared with objects of different aspect
(colour, size and shape) and then tested with completely
novel objects (of different colour and shape but
controlled for continuous extent), they chose to associate
with the set of objects comprising the same number of
elements they had been reared with during imprinting.
Note,however,thatinthestudy presented here,
the choice could not be based on direct perceptual
cues associated with visible elements, but must have
relied on the memory of the disappeared sets and of
their spatial position.
2452 R. Rugani et al. Arithmetic in newborn chicks
Proc. R. Soc. B (2009)
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(a)Materials and methods
(i) Subjects and rearing conditions
Subjects were 17 female ‘hybro’ (a local variety derived
from the white leghorn breed) domestic chicks (Gallus
gallus), obtained weekly from a local commercial hatchery
(Agricola Berica, Montegalda, Vicenza, Italy) when they
were only a few hours old. On arrival at the laboratory,
chicks were immediately housed singly in standard metal
home cages (28 cm wide!32 cm long!40 cm high) at
controlled temperature (28–318C) and humidity (68%),
with food and water available ad libitum in transparent
glass jars (5 cm in diameter, 5 cm high) placed at each
corner of the home cage. The cages were constantly
(24 h d
K1
) lit by fluorescent lamps (36 W), located 45 cm
above each cage. Each chick was placed in one cage
together with a set of five identical rounded objects
made of yellow plastic. Each object was a ‘Kinder surprise’
capsule (Ferrero S.P.A. Alba, Cuneo, Italy) measuring
4!3!3 cm, which we will hereafter refer to as a ‘ball’.
Previous studies have shown that this kind of object is very
effective in producing social attachment through filial
imprinting in this strain of chicks ( Vallortigara & Andrew
1991). The five balls placed in each cage constituted the
chicks’ imprinting stimulus and were each suspended in
the centre of the cage by a fine thread, at approximately
4–5 cm from the floor, so that they were all located at
about chicks’ head height.
Chicks were reared in these conditions from the
morning (11.00) of the first day (i.e. Monday, the day of
their arrival, which was considered as day 1) to the third
day (Wednesday). All chicks underwent two testing
phases. In the morning (11.00) of day 3, chicks underwent
the training, and approximately 1 hour later, they took
part in the first testing session. A second testing session
took place in the morning (09.00) of day 4.
(ii) Apparatus
Training and testing took place in an experimental room
located near the rearing room. In the experimental room,
temperature and humidity were controlled (respectively,
at 258C and 70%). The room was kept dark, except for
the light coming from a 40 W lamp placed approximately
80 cm above the centre of the apparatus. The testing
apparatus (figure 1) consisted of a circular arena (95 cm
in diameter and 30 cm outer wall height) with the floor
uniformly covered by a white plastic sheet. Within
the arena, adjacent to the outer wall, was a holding box
(10!20!20 cm), in which each subject was confined
shortly before the beginning of each trial. The box was
made of opaque plastic sheets, with an open top allowing
the insertion of the chick before each trial. The side of the
holding box facing the centre of the arena consisted of
a removable clear glass partition (20!10 cm), in such a
way that the subjects, while confined, could see the centre
of the arena. During the training phase, a single opaque
cardboard screen (16!8 cm; with 3 cm sides bent back
to prevent the chicks from spotting the hidden ball) was
used, positioned in the centre of the arena, in front of and
35 cm away from the front of the holding box. During
testing, two opaque cardboard screens (16!8cm),
identical in colour and pattern (i.e. blue coloured with
a yellow ‘X’ on them), were positioned in the centre of
the arena, symmetrically with respect to the front of the
confining box (i.e. 35 cm away from it and 20 cm apart
from one another).
(iii) Procedure
Training
On day 3 of life, in the morning, chicks underwent a
preliminary training session. Each chick, together with
a single ball, identical to one of the five balls constituting
the chick’s imprinting object, was placed within the testing
arena, in front of one of the screens. The ball was held
from above by the experimenter (not visible to the chick),
via a fine thread, and kept between the holding box and the
screen. The chick was left free to move around and get
acquainted with the environment for approximately
5 min. Thereafter, the experimenter slowly moved the
ball towards the screen, and then behind it, until the ball
disappeared from the chick’s sight. This procedure was
repeated a few times, until the chick responded by
following and rejoining the ball behind the screen.
Thereafter, the chick was confined within the holding
box, from where it could see the ball being moved behind
the screen. As soon as the ball had completely disappeared
from sight, the chick was set free in the arena by lifting the
transparent frontal partition. Every time the chick rejoined
the ball, as a reward, it was allowed to spend a few seconds
with it. The whole procedure was restarted and the
training ended when the chick had rejoined the ball three
consecutive times. On average, approximately 15 min
were required to complete the training for each chick.
Testing
During testing, the chick was confined to the holding box,
behind the transparent partition, from where it could see
the two screens positioned in the arena. The chick was
shown two sets of elements, one made of three of the five
imprinting balls and the other made of two such balls
(placed at first at approx. 10 cm from the front of the
holding box containing the chick). Both sets disappeared,
each behind one of the two screens. Immediately after
the disappearance of both sets (with a delay of 5 s), the
transparent partition was removed and the chick was left
free to move around and search for its imprinting balls
within the arena. To prevent the chicks from seeing the
hidden balls before having circled almost completely
Figure 1. The test apparatus employed in all of the
experiments described. The holding box is visible to the left,
both screens are present, as during the test phase. One ball is
visible behind one of the screens.
Arithmetic in newborn chicks R. Rugani et al. 2453
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around the screen, the screens were provided with 3 cm
bent back edges on the two vertical sides. A choice was
defined as when the chick’s head had entered the area
behind one of the two screens (beyond the side edges),
only the choice for the first screen visited was scored and
thereafter the trial was considered over. At the end of each
trial, chicks were allowed to spend 1–2 s with their ‘social
companions’ behind the screen chosen by the chick. The
behaviour of the chicks was entirely video-recorded and it
was scored blind both online and later offline.
If the chick did not approach either screen within
3 min, the trial was considered null and void and it was
repeated immediately afterwards. After three consecutive
null trials, the chick was placed back within its own rearing
cage (in the presence of the imprinting balls) for
approximately 1 hour before being resubmitted to further
trials. After another three consecutive null trials, the same
procedure was repeated and if, once again, the chick
scored for the third time three consecutive null trials, it
was discarded from the experiment.
Each chick underwent two complete testing sessions of
20 valid trials each. The two test sessions differed in the
procedure by which the balls were made to disappear
behind the two screens:
Simultaneous disappearance test (SDT ). Both sets of
three and two elements were placed in the arena in front
of the chick confined in the holding box. After approxi-
mately 3 s, both sets were simultaneously made to slowly
move and disappear each behind one different screen
(the whole procedure took approx. 8–10 s).
Consecutive disappearance test (CDT ). For each trial,
each of the balls of the first set was placed singly in front of
the confined chick and then made to disappear before the
next ball was introduced in the arena. In this way, all balls
of the first set were made to disappear one by one behind
one screen, and then the same procedure was employed
for the second set. For both sets, each ball was kept for
approximately 3 s in front of the chick before making it
move and disappear behind either screen (the whole
procedure took approx. 50 s). During the disappearance
phase, the speed of motion of the items of each set was
manipulated so that it took the same total time to
disappear for the set of three and for the set of two.
Disappearance of each whole set took approximately 18 s
(i.e. 6 s for each element in the set of three and 9 s for each
element in the set of two).
For both the SDT and the CDT, the order (3–2 versus
2–3) as well as the direction (left–right) of disappearance
of the two sets was counterbalanced within each chick’s
20 test session trials.
The number of trials in which each chick chose the
screen hiding three balls (correct choice) was considered
and percentages were computed as: number of correct
choices/20!100. Parametric paired t-tests (to compare
different conditions) or one-sample t-tests (to assess
significant departures from chance level, i.e. 50%) were
used. Non-parametric statistics were performed employ-
ing the binomial test.
(b)Results and discussion
All chicks took part in the first test administered (whether
SDT or CDT), but four chicks were discarded from the
second test (two chicks did not take part in the SDT, and
two did not take part in the CDT) due to unsatisfactory
health condition. Chicks preferentially chose the screen
hiding three balls over the screen hiding two balls both
in the SDT (nZ15; meanZ65.000, s.e.m.Z2.536;
one-sample t-test: t
14
Z5.915; p!0.001) and in the
CDT (nZ15; meanZ70.000, s.e.m.Z3.047; one-sample
t-test: t
14
Z6.564; p!0.001) trials (figure 2). There was
no statistically significant difference between correct
choices in the two testing conditions (two-sample t-test:
t
28
Z1.261; pZ0.218).
In order to assess whether the overall performance
depended on learning, occurring during testing, the
first five trials of each session were considered. Since
there was no difference between the two groups (two-
sample t-test: t
28
Z1.684, pZ0.103; SDT: nZ15, meanZ
58.667, s.e.m.Z4.563;CDT: nZ15, meanZ70.667,
s.e.m.Z5.474), data were merged and overall, chicks
preferentially chose the larger set (nZ30; meanZ64.667,
s.e.m.Z3.674; one-sample t-test: t
29
Z3.992, p!0.001).
We also performed a non-parametric (binomial)
analysis on chicks’ initial performance. As this was
the chicks’ behaviour in the very first trial affected by the
response to the novelty of the situation (e.g. two screens
were present in the arena), the first three trials were
considered. Twenty-three chicks were considered success-
ful as they scored at least two correct trials within the first
three, and seven chicks were considered as unsuccessful
(they scored at least two mistaken trials out of three). The
difference (23 versus 7) was significant (binomial test, one
tail, pZ0.0026).
Chicks’ performance could not be based on the average
presentation time of the two sets of stimuli, because this
was identical in the SDT, and was equalized in the CDT.
Results confirmed that, in the absence of any specific
training, chicks spontaneously discriminated between sets
of two and three elements, preferring the larger set
(Rugani et al. submitted), and did so even when such a
discrimination must have been based on the memory of
the disappeared sets and of their relative spatial position.
3. EXPERIMENT 2
Experiment 1 showed that chicks spontaneously master
the discrimination of two versus three identical elements
after these had been hidden from view. In experiment 2,
a similar procedure was employed using new stimuli
allowing us to control for continuous variables, such as
overall area and contour length. Our hypothesis predicted
that chicks should be able to discriminate 2 versus
3 independently of the use of such variables, since such
0
10
20
30
40
50
60
70
80
90
100
SDT CDT
correct responses (%)
Figure 2. Results of experiment 1. Percentage of correct
responses (group meansCs.e.m.) scored by chicks that
underwent the SDT or the CDT. The dashed line ( yZ50)
represents chance level.
2454 R. Rugani et al. Arithmetic in newborn chicks
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discrimination would still be possible when operating
within a system computing small numerosities (Hauser &
Spelke 2004). However, some doubt has been raised
recently as to whether human infants and non-human
animals really compute numerosity: when number is
pitted against continuous dimensions correlating with
number (e.g. area and contour length), infants sometimes
respond to continuous physical dimensions (Feigenson
et al. 2002a,b). Nevertheless, it has been shown that
monkeys are able to compute number rather than other
dimensions in a matching-to-sample numerical task
(Cantlon & Brannon 2007). That is not to say that
preverbal infants cannot respond to number themselves,
but that they do so only sometimes. For instance, when
objects to be discriminated belong to a domain in
which the continuous extent is especially relevant, such
as food, infants indeed tend to respond to the overall
amount rather than to number ( Feigenson et al. 2002a,b).
But, when the task requires reaching for individual
objects, number encoding prevails over physical extent
(Feigenson 2005). Using conditioning procedures, even
newborn chicks are able to discriminate small sets of
elements on the basis of number when both area and
contour length are controlled for (Rugani et al. 2008).
(a)Materials and methods
(i) Subjects
Subjects were a new group of 16 female domestic chicks.
Rearing conditions were identical to those described for
the first experiment.
(ii) Stimuli
Imprinting stimuli were identical for all chicks and
consisted of a set of five identical, two-dimensional
(approx. 1 mm thick), red plastic squares (4!4 cm).
Test stimuli also consisted of red squares, identical in
material and colour to those used for imprinting, but
differing in their dimensions in each of three control
groups. In the two-dimensional stimuli control group
(nZ7), the original dimensions of the stimuli were
maintained, so that the single squares were all identical
in the sets of three and two elements. This control was
aimed at determining whether chicks responded to two-
dimensional imprinting stimuli in the same way as they did
to the solid objects in experiment 1. Both in the contour
length (nZ5) and in the area (nZ4) control groups, the
set of two elements comprised squares of dimensions
identical to those used during imprinting, while the set of
three elements comprised smaller sized squares. The
dimensions of each square in the set of three elements
were computed in order to equate the overall contour
length (with squares measuring 2.66!2.66 cm each) or
the overall area (with squares measuring 3.26!3.26 cm
each) in the two sets. The overall time of disappearance
of the two sets was equalized as detailed in §2a(iii).
(iii) Procedure
The apparatus, the general training and testing procedures
were identical to those described in the CDT of the
previous experiment, with each chick undergoing 20 test
trials on day 3.
(b)Results and discussion
No difference (F
2,13
Z1.824; pZ0.200) emerged at an
analysis of variance (ANOVA) comparing the percentage
of correct responses emitted by the three groups of chicks
(two-dimensional stimuli control group: nZ7, meanZ
67.143, s.e.m.Z1.844; contour length control group:
nZ5, meanZ62.000, s.e.m.Z2.000; and area control
group: nZ4, meanZ63.750, s.e.m.Z3.750). Data were
therefore merged, and the resulting mean (nZ16,
meanZ64.688, s.e.m.Z1.405) was significantly above
chance level (one-sample t-test: t
15
Z10.454, p!0.001).
When analysing chicks’ initial performance (consid-
ering the first three trials, as described for the data of
experiment 1), a statistically significant difference was
found as 13 chicks out of 16 were successful (binomial
test, one tail, pZ0.0106).
Chicks preferentially chose the screen hiding the set
of three elements in all conditions.
Results confirmed the ability of chicks to discriminate
sets of 2 versus 3 elements selectively preferring the
larger set even when such discrimination must be based on
the actual number of the non-visible sets of objects and
was not based on differences in continuous variables, such
as contour length, area or time of disappearance.
4. EXPERIMENT 3
In the third experiment, we checked whether chicks can
also update their representation of the sets of stimuli by
processing subsequent events. After the initial disap-
pearance of the two sets of elements (similarly to the
previous experiments), some of the elements were visibly
transferred from behind one screen to behind the other
one. Such condition should represent a more challenging
task than those of the previous experiments, since
the chicks’ final choice would now depend on correctly
taking into account a series of subsequent displacements.
The possible cues provided by the order of disappear-
ance of stimuli in guiding chicks’ discrimination were
controlled for.
(a)Materials and methods
(i) Subjects
Subjects were a new group of 19 female domestic chicks.
Rearing conditions were identical to those described for
the previous experiments.
(ii) Procedure
Apparatus, general training and testing procedures were
the same described for the previous experiments. At test,
one ball at a time was placed in the arena and was slowly
moved towards and behind one screen. The procedure
was repeated for all five balls in such a way that a different
number of them (depending on the experimental con-
dition, see below) was eventually concealed behind either
screen. This disappearance phase constituted the first
event (FE). Approximately 5 s after the last ball had
disappeared, and while the chick was still confined to the
holding box, some of the concealed balls were slowly and
visibly moved (one ball at a time) from one screen towards
and behind the other screen (second event, SE). After a
delay of 5 s from the end of the SE, the chick was released
in the arena. Regardless of the balls position after the FE,
all four tests provided, as a result of the SE, a final
Arithmetic in newborn chicks R. Rugani et al. 2455
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comparison of two versus three balls. Chicks performed a
correct choice when approaching the screen hiding the
three elements.
Each chick underwent only one of two different
test conditions:
—FE controlled (FEC )(nZ8). In order to choose the
screen hiding the larger amount, i.e. the three balls,
the chicks entering this condition would need to
choose against the cue provided by the initial
displacement of the balls. In fact, at the end of the
FE, the larger set was located behind the screen
which hid two balls at the end of the SE (i.e. the
wrong one). This was obtained in two different
manners: ‘(4K2) versus (1C2)’ and ‘(5K3) versus
(0C3)’ (the names refer to the events taking place at
the correct screen).
—(4K2) versus (1C2). The chicks (nZ4) saw four
balls disappearing behind one screen and the
remaining one disappearing behind the other
screen. Subsequently, two balls moved from the
screen hiding four balls to the other screen. At
the end, the screen initially hiding one ball only,
hid three balls and represented the correct choice
(figure 3a).
—(5K3) versus (0C3). In front of the chicks (nZ4),
five balls disappeared behind one screen and none
disappeared behind the other screen. Then, the
chick saw three balls that moved from the screen
hiding the group of five, to the other screen.
Therefore, the screen initially hiding no balls,
at the end hid three balls and constituted the
correct choice.
—Last event controlled (LEC )(nZ11). The SE now
involved a movement from the screen that was to be
considered as correct (hiding the larger number of
elements) to the wrong screen (hiding the smaller
number of elements). Therefore, in order to choose
the correct screen chicks would need to choose
against the directional cue provided by the final visible
displacement. This was obtained in two different
manners: ‘(4K1) versus (1C1)’ and ‘(5K2) versus
(0C2)’ (again, the names refer to the events taking
place at the correct screen).
—(4K1) versus (1C1). Chicks (nZ7) saw four balls
disappear behind one screen and the remaining
one behind the other screen. Then, one ball moved
from the group of four to the other screen.
Therefore, the screen initially hiding four balls
now hid three balls and represented the correct
choice (figure 3b).
—(5K2) versus (0C2). Chicks (nZ4) saw five balls
disappear behind one screen and none behind the
other. Two balls were then moved from the group
(a)
(i) (ii) (i) (ii)
(iii)
(v) (v)
(iv) (iii) (iv)
(b)
Figure 3. Schematic representing, from the perspective of the confined chick, the events occurring in experiment 3 within:
(a) one possible trial of the FEC test (in the ‘(4K2) versus (1C2)’ condition, see text); (b) one possible trial of the last event
controlled test (in the ‘(4K1) versus (1C1)’ condition, see text). (a(i)) FE: one ball is hidden behind one screen. (ii) Four balls
are hidden—one by one—behind the other screen. The sequence of events and the directions were randomized between trials.
(iii) At the end of the first displacement either four or one ball(s) are hidden behind each screen. (iv) SE: two balls move—one by
one—from the screen hiding four to the one hiding a single ball. (v) Test: the chick is released in the arena and should rejoin the
larger number of imprinting balls, which is NOT behind the screen where the larger number of balls had initially disappeared.
(b(i)) FE: one ball is hidden behind one screen. (ii) Four balls are hidden—one by one—behind the other screen. The sequence
of events and the directions were randomized between trials. (iii) At the end of the first displacement either four or one ball(s) are
hidden behind each screen. (iv) SE: one ball moves from the screen hiding four to the one hiding a single ball. (v) Test: the chick
is released in the arena and should rejoin the larger number of imprinting balls, which is NOT behind the screen where the final
hiding of balls has been observed.
2456 R. Rugani et al. Arithmetic in newborn chicks
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of five to the other screen. Therefore, the screen
initially hiding five balls now hid three balls and
constituted the correct choice.
For both conditions (FEC and LEC), whenever the
initial displacement involved two hiding events (i.e. four
balls going behind one screen and one (or two) ball(s)
going behind the other screen), the order of such events
(i.e. which one occurred before and which after the other)
was counterbalanced throughout the 20 testing trials
administered to each chick, as well as the left–right
direction of the disappearance of the two sets. Sets’
disappearance times could not be equalized in this
experiment due to procedural contingencies (e.g. one
set disappeared in one direction and no elements
disappeared in the opposite direction).
Each chick underwent one single testing session
(20 trials). For each chick and for each group, the mean
percentage of choices of the screen hiding three elements
were computed. Non-parametric statistics were per-
formed employing the binomial test.
(b)Results and discussion
Results are represented in figure 4.
(i) FE controlled
No significant difference (two-sample t-test: t
6
Z0.785;
pZ0.463) was found between the groups: (4K2) versus
(1C2) (nZ4, meanZ78.750, s.e.m.Z3.750) and (5K3)
versus (0C3) (nZ4, meanZ73.750, s.e.m.Z5.154).
Overall (nZ8, meanZ76.250, s.e.m.Z3.098) chicks
significantly chose the screen hiding the larger number
of elements (one-sample t-test: t
7
Z8.473, p!0.001).
When limiting the analysis to the first five test trials, no
statistically significant difference was found between the
two conditions (two-sample t-test: t
6
Z0.522, pZ0.620).
Overall, chicks significantly approached, from the very
beginning of the test, the screen hiding the larger set at
the end of the SE (nZ8, meanZ77.500, s.e.m.Z4.531;
one-sample t-test: t
7
Z6.069, p!0.001).
(ii) LE controlled
No significant difference (two-sample t-test: t
10
Z1.053;
pZ0.317) was found between the (4K1) versus (1C1)
(nZ7, meanZ76.586, s.e.m.Z2.978) and the (5K2)
versus (0C2) (nZ5, meanZ71.556, s.e.m.Z3.826)
conditions. Overall, chicks preferentially chose the correct
screen (nZ12, meanZ74.490, s.e.m.Z2.366; one-
sample t-test: t
11
Z10.347, p!0.001).
When limiting the analysis to the first five test trials,
no difference was found (two-sample t-test: t
10
Z0.078;
pZ0.938) between the two test conditions. Overall, chicks
significantly preferred the correct screen even within the
first five test trials (nZ12, meanZ76.667, s.e.m.Z4.820;
one-sample t-test: t
11
Z5.533; p!0.001).
There was no difference between FEC and LEC
conditions (two-sample t-test: t
18
Z0.458; pZ0.652).
Chicks selectively approached the screen hiding the
larger number of elements (nZ20, meanZ75.194,
s.e.m.Z1.843; one-sample t-test: t
19
Z13.667;
p!0.001). Their response was based neither on the first
site, where the larger number of objects had been seen to
disappear, nor on the most recent directional cue provided
by the very last displacement.
When chicks’ initial performance was analysed with
non-parametric statistics (considering the first three trials,
as described for the data of experiment 1), the difference
between successful and unsuccessful chicks (i.e. 13 out
of 19) was marginally non-significant (binomial test, one
tail, pZ0.0835). We expected chicks’ performance to be
worse in experiment 3, as the conditions were much
harder than those of the previous experiments. Never-
theless, when analysing chicks’ overall scores in the 20
trials, and considering successful any chick that took at
least 14 out of 20 (binomial test, one tail, pZ0.0577)
correct trials, then overall 14 out of 19 chicks were
successful (binomial test, one tail, pZ0.0318).
It should be pointed out that, although chicks were
choosing against the initial or the final events, they must
have properly computed such events in order to make a
correct final choice.
5. GENERAL DISCUSSION
The results of experiments 1 and 2 showed that, in the
absence of any specific training, chicks spontaneously
discriminated between two and three, in both cases
preferring the larger stimulus set. The discrimination
was based on the memory of the spatial position of the
disappeared objects, since any direct assessment of
the sensory stimuli associated with the two sets was not
possible at the time when chicks were allowed to choose
between the two screens. Hence chicks’ behaviour seemed
to indicate an ability to perform additions, i.e. combining
two or more quantitative representations (addends) to
form a new representation (i.e. the sum).
Quite interestingly, the discrimination held for both
the simultaneous disappearance of all the elements of a
set of stimuli as well as for the one-by-one (i.e. sequential)
disappearance of the single elements of the set. Indeed,
the performance tended to be slightly better in the latter
case, although this difference could not be due to cues
provided by differences in the time of disappearance of
the two sets as this variable had been equalized in the
first two experiments.
The results of experiment 2 showed that discrimination
was based on the number, and not on the continuous
physical variables that may covary with number, such as
area, contour length or time of disappearance during
stimuli presentation. Evidence has been reported that
when the number is pitted against continuous dimensions
that correlate with number (e.g. area and contour length),
infants sometimes seem to respond to continuous physical
dimensions (Feigenson et al. 2002a,b). Nonetheless,
0
10
20
30
40
50
60
70
80
90
100
FEC LEC
correct responses (%)
Figure 4. Results of experiment 3. Percentage of correct
responses (group meansCs.e.m.) shown by chicks that
underwent the FEC or the LEC conditions. The dashed
line ( yZ50) represents chance level.
Arithmetic in newborn chicks R. Rugani et al. 2457
Proc. R. Soc. B (2009)
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evidence has been collected showing that human infants
also encode discrete numbers as well as continuous extent
(Feigenson & Carey 2003). It seems that when the objects
in an array differ in their individual characteristics (such as
colour, shape, texture), infants rely on the number rather
than spatial extent, whereas the reverse is true for sets of
homogeneous objects ( Feigenson 2005). Somewhat
similar results were obtained in the study by Rugani
et al.(submitted; see §2) in which chicks, were directly
facing the two sets of objects while choosing between them
at test, so that encoding them as a homogeneous or
heterogeneous array of elements was perceptually appa-
rent. In the task studied here, by contrast, summation and
subtraction required an updating of stored memory
representations of small arrays that were no longer visible.
Updating of stored representations by chicks is
particularly impressive in experiment 3. Here, after the
initial disappearance of the two sets of objects behind both
screens, some of the objects were again visibly transferred
from one screen to the other before the chick was allowed
to search. Thus, an initial addition and a subsequent
subtraction of elements were needed in order to determine
the screen hiding the larger number of elements at the end
of the two events. Chicks correctly chose the screen hiding
the larger number of elements irrespective of the
directional cues provided by the initial or final movement
of the elements.
Human infants seem to show a failure when an exact
numerical representation has to include more than three
objects (review in Hauser & Spelke 2004). A signature
limit similar to that described for young infants has been
reported for adult monkeys ( Hauser & Spelke 2004), and
it was also observed in chicks, although in a different
task and on animals a few days older than those used here
(Rugani et al. 2008). In the present study, however,
chicks seem to go beyond such a limit, for, in order
to perform the arithmetic discriminations described in
experiment 3, they must have represented five distinct
individuals exactly.
It can be speculated that altricial and precocial species
may differ in signature limits (or in their timing of
appearance in life) in exact numerical representations.
Moreover, the signature limit may be task specific, in
the sense that it is shaped by the specific demands of the
ecological conditions in which a certain numerical
computation has evolved. If so, we could perhaps expect
that chicks’ signature limits would be defined by their
typical brood size (i.e. approx. 8–10 siblings).
The capacities exhibited by young chicks appear to
be really noteworthy, particularly considering that, in
the very brief period of rearing that preceded testing, the
animals had no possibility to experience the sorts of events
they were faced with at test, since the chicks were reared
singly with the suspended balls (and without any
experience of occluding surfaces in their home cage). We
cannot exclude of course that, over their first days of life,
chicks experience (in their home cage) would contribute to
some familiarization with quantity manipulation. Besides
the imprinting objects, chicks in their home cages were
exposed to food, water and the dishes. For example, chicks
may learn that the level of chicks’ starter food decreases
over the time spent eating. Nevertheless, we regard it
unlikely for the chicks to experience precise computation
of actual subtraction of food elements (we see no possible
way for them to experience additions) while eating, as
their food (i.e. standard chicks’ starter crumbs) was not
made of discrete elements (as would occur, for example, if
the chicks were fed seeds), but rather of clumped
aggregate of grain flour. Moreover, although food amount
in the dish could somewhat diminish daily, new food was
constantly added so that its level was kept constant.
Chicks could apparently maintain a record of the
number of hidden objects comprising two distinct sets,
updated by arithmetic operations of addition and
subtraction computed on the basis of only the sequential
visual appearance and disappearance of single separate
objects. Models based on the idea of an operating
‘accumulator’ are common in the theoretical analyses of
how animals can perform counting in the absence of verbal
tags (Meck & Church 1983). However, to the best of our
knowledge, this is the first evidence showing that
sequential addition and subtraction can be successfully
performed by animals on the same sets.
We believe that the findings presented here provide
striking support to the ‘core knowledge’ hypothesis ( Pica
et al. 2004;Dehaene et al. 2006;Spelke & Kinzler 2007)
according to which mental representations of number (as
well as other basic representations such as those of
physical objects, animate objects and geometry) would
be in place at birth and shared among vertebrates.
All procedures were in accordance with the Italian
and European Community laws on animal research
and treatment.
The authors wish to thank Paola De Martini Di Valle Aperta
for the help provided with animal care and testing. This study
was supported by grants ‘Intellat’ and MIPAF ‘Benolat’
(to G.V.).
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