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
). Nonetheless, 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
; 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 apparent. 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.