Can rhesus monkeys spontaneously subtract?
Introduction
Over the past 20 or so years, experimental work in the lab and field has provided considerable evidence that animals have the capacity for numerical representation (for reviews see Boysen, 1997, Gallistel and Gelman, 2000, Hauser, 2000, Shettleworth, 1998). In nature, for example, studies of lions have demonstrated that individuals respond more intensely to the roars of three individuals than to the roars of one individual (McComb, Packer & Pusey, 1994). In the lab, studies of pigeons and rats have demonstrated that subjects can press a lever approximately 20 times (i.e. the number of presses is roughly normally distributed around 20) to obtain food, even when such factors as time, energetic expenditure, and motivational state have been controlled (Gallistel, 1990); moreover, as predicted by Gibbon (1977) and Meck and Church (1983), the standard deviation of the distribution of bar presses by a rat increases as a function of the number of target presses, showing that the representation of large numbers is possible, but only approximately. Finally, studies of an African gray parrot (Pepperberg, 1994) and several chimpanzees (Boysen and Bernston, 1989, Boysen and Berntson, 1995, Matsuzawa, 1985) indicate that these extensively trained individuals can learn the meaning of the Arabic numerals, with the highest level of achievement obtained by Matsuzawa's chimpanzee Ai who understands the ordinal relationships between the numbers zero through nine (Biro and Matsuzawa, 1999, Kawai and Matsuzawa, 2000, Matsuzawa, 1985).
Two models have generally dominated current discussions of numerical representation in non-human animals and preverbal human infants, with empirical evidence providing some support for both models (Carey and Spelke, in press, Dehaene and Changeux, 1993, Gallistel and Gelman, 2000, Hauser and Carey, 1998, Wynn, 1998). On the one hand is the Meck and Church (1983) accumulator model which is based on the idea that each object or event is enumerated or represented as an impulse of activation from the nervous system. To extract number (or time), the accumulator stores each impulse until the end of counting (or timing), and then transfers this information into memory where it outputs one value for the impulses counted. As many have articulated, this can be schematically represented as a growing number line with 1=_, 2=__, 3=___, 4=____, … 8=________, and so on. Because of variability or noise in the remembered magnitude, the output from the accumulator is an approximation of number, with variability increasing in proportion to magnitude, or what is referred to as scalar variability (Gibbon, 1977, Whalen et al., 1999); studies of animals in particular have demonstrated that subjects can keep track of both time and number in such tasks, with some recent evidence of more accurate computation of time (Roberts, Coughlin & Roberts, 2000). As Gallistel and Gelman (2000) have recently articulated, under this model “numerosity is never represented exactly in the nonverbal or preverbal mind, with the possible exception of the first three or four numerosities”. Nonetheless, with number represented as a magnitude with scalar variability it is possible to compute such arithmetical operations as addition, subtraction, multiplication and division.
In contrast to the accumulator model, others have proposed that number, especially small numbers less than about four, may be represented by a different system, one that is used by adults for object-based attention and tracking: the object file model (Kahneman et al., 1992, Scholl, in press, Scholl and Leslie, 1999, Trick and Pylyshyn, 1994). Although the object file model does not provide an explicit representation of number (and was not developed for this purpose), it does provide at least four criteria for constructing numerical representations (Carey & Spelke, in press): (1) using spatiotemporal information, object files are opened based on principles of individuation and numerical identity; (2) if one or more object files are opened, opening a new one provides a mechanism for adding one item to an array of items, an operation that is likely to be important for the successor function that is crucial to the integer count list; (3) object files are based on 1−1 correspondence, and thus contribute to the establishment of numerical equivalence; (4) the number of object files that can be simultaneously opened is limited to about four (at least for adult humans; Trick & Pylyshyn, 1994), but is precise and not subject to Weber's law (distance and magnitude effects; for review see Dehaene, 1997, Gallistel, 1990, Gallistel and Gelman, 2000).
Until recently, these models, and the form of numerical representation that they operate upon, have been pitted against one another. However, theoretical arguments developed by Carey (in press) and Carey and Spelke (in press), together with empirical work on human infants and non-human primates (Hauser et al., 2000, Uller et al., 1999, Uller et al., submitted for publication), suggest that both models together may provide a more comprehensive explanation of the results to date. In particular, and as Carey and Spelke (in press) have explicitly argued, if number is represented as a magnitude, then it is not possible to account for the fact that human infants successfully discriminate two from three dots, but fail to discriminate four from six and eight from 12 dots (Starkey and Cooper, 1980, Xu and Spelke, 2000); specifically, if infants tapped a magnitude representation of number, in which Weber's law holds (i.e. the discriminability of two perceived magnitudes is determined by the ratio of objective magnitudes), then these pairs should be discriminable since they differ by the same ratio. On the other hand, a magnitude system can account for the fact that human infants are able to discriminate eight from 16 dots, numerical values that well exceed the presumed limits of an object file representation (Xu & Spelke, 2000). Putting these findings together leads to the suggestion that an object file mechanism may underlie success with small numbers, whereas an analog magnitude system may underlie success with larger numbers. More precisely, the object file model provides a mechanism for precise small number quantification, whereas the accumulator model provides a mechanism for approximate large number quantification.
The goal of the present paper is to further explore the extent to which non-human animals can spontaneously compute (i.e. in the absence of training) arithmetic operations over small numbers of objects. More specifically, given the extensive work on the operations of addition (Boysen and Bernston, 1989, Hauser et al., 2000, Hauser et al., 1996, Olthof et al., 1997) and ordering (Biro and Matsuzawa, 1999, Brannon and Terrace, 1998), we designed a series of experiments to assess whether rhesus monkeys are capable of computing the outcome of subtraction events, an operation that has been relatively neglected in the animal literature (e.g. Brannon et al., unpublished data; Gibbon and Church, 1981; Hauser et al., 1996). In addition to this general problem, two more specific issues guided the particular details of our experiments. First, current accounts of the object file model are based on featureless object files (Scholl, in press, Scholl and Leslie, 1999, Simon, 1997, Uller et al., 1999). Specifically, to establish or maintain an object file, information about the object's features is not used. The only relevant operation is 1−1 correspondence. Thus, when a display is occluded and then revealed, the object file system simply checks for a match at the object level, independent of the object's properties or features. However, recent studies of rhesus monkeys, reviewed more completely below, suggest that object features are tracked, remembered, and used to determine the precise number of objects occluded when that number is less than five. These data suggest that either the object file mechanism can, under certain circumstances, keep track of object features or that a different mechanism is in play, one that tracks objects features and is limited to small numbers; the suggestion by Cowan (2001) of a short-term memory mechanism with a limit of four is a candidate mechanism.
The second issue stems from recent studies by Wynn and Chiang (1998). Human infants are surprised (i.e. look longer on an expectancy violation task) by a magical disappearance of an object (1+1=1), but are not surprised by a magical appearance (2−1=2). Based on these findings, Wynn and Chiang argue that human infants cannot represent zero, a finding that they consider to be consistent with the accumulator model. Specifically, so they argue, the accumulator is not engaged unless there is an object or event to initiate the process of impulse activation. If Wynn and Chiang are correct, then tests involving animals' capacities for subtraction are particularly relevant because subtraction is necessary to get to zero.
There are two reasons why rhesus monkeys are ideal subjects for exploring the details of non-linguistic numerical representation. First, recent work by Brannon and Terrace (1998) shows that rhesus monkeys trained to discriminate between the numbers one through four can subsequently discriminate – in the absence of training – between the numbers one through nine. On two counts, these data provide support for the accumulator mechanism of analog magnitude representation. Specifically, rhesus monkeys' success in discrimination exceeds the limits of the object file mechanism (i.e. greater than four) and their performance is subject to magnitude effects (i.e. greater accuracy with increasing differences between number pairs); because the animals were trained on one through four, it is not possible to assess whether they would also show scalar variability within this range. Second, using a spontaneous (i.e. no training, one trial per animal) search task involving addition operations, Hauser et al. (2000) provide evidence for the set size signature of the object file model (i.e. a limit of approximately four), one that keeps track of object features. In the basic task, each subject received only one trial in which they watched different quantities of apple placed into one of two boxes. Thus, for example, a subject watched as an experimenter sequentially placed (i.e. consecutive addition operations) three pieces of apple into one box, followed by four pieces of apple into a second box. Subjects were then allowed to approach one box, and eat its contents. Because the pieces of apple are placed out of sight into the boxes, subjects must keep this information in working memory in order to calculate which box has more food. Subjects succeed up to a contrast of four versus three (controlling for time and volume), but fail at larger numbers, including five versus four, six versus four, and eight versus three; these failures are inconsistent with Weber's law, and stand in striking contrast to the results of Brannon and Terrace (1998) using an operant procedure. In controlling for time, we required the rhesus to keep track of the identity of each object placed in the box. Thus, for example, they saw four apple slices placed into one box versus three apple slices and a rock placed into the other box. Once again, they picked four over three slices, showing that they attended to the features of the objects placed, distinguishing between apple slices and rocks.
In a second series of experiments with rhesus monkeys, using the expectancy violation procedure of Wynn (1992), Hauser and colleagues (Hauser and Carey, 1998, Hauser et al., 1996; unpublished data) have also shown the set size signature of the object file mechanism. Specifically, rhesus monkeys pass tests (i.e. look longer at the impossible outcomes) involving 1+1=1 versus 2 versus 3, 2+1=2 versus 3, and 2−1=1 versus 2, but fail with 2+2=3 versus 4 versus 5. Thus, using two different tasks, Hauser and colleagues provide converging evidence that rhesus monkeys spontaneously represent the numbers one, two and three.
Given the rhesus monkeys' performance on the spontaneous search tasks involving addition operations, the following experiments were designed to explore their capacity to compute subtraction operations. Specifically, we examine whether rhesus monkeys compute the outcome of subtraction events, attending to the identity of the objects placed out of sight, and contrasting the quantities obtained in two spatially separated locations, following subtraction events. Rather than focus on the upper limit of their capacity to compute the outcome of subtraction operations, we focused instead on their ability to track object identity, compute the precise outcome of a subtraction operation, and represent both zero and equality.
Section snippets
Subjects
Experiments were conducted on a population of semi-free-ranging rhesus monkeys (Macaca mulatta) living on the island of Cayo Santiago, Puerto Rico (Rawlins & Kessler, 1987). This population has been observed for over 60 years, thereby providing considerable information concerning demographic parameters, life history characteristics, social behavior, mating system, and vocal and cognitive behavior. Over the past 5 or so years, researchers have conducted several experiments on this population,
Experiment 1: 1 versus 1−1, single subtraction
Fig. 1A provides a schematic illustration of the experimental design. A subject watched as an experimenter placed two foam core platforms on the ground, with one plum on each platform, lowered an occluder in front of each platform, and then removed one plum from one side. The experimenter then walked away, allowing the subject to approach. Given the initial set-up, this experiment provides each subject with a choice of one plum versus zero plums (i.e. 1−1=0).
Results show (Fig. 1B) that 14 out
General discussion
The central aim of these experiments was to determine whether rhesus monkeys can spontaneously compute subtraction operations with small numbers. In contrast to our earlier work with rhesus monkeys (Hauser and Carey, 1998, Hauser et al., 2000, Hauser et al., 1996), where we were able to document the upper limit of spontaneous number discrimination following addition operations, the present studies provide a more in-depth analysis of subtraction. Specifically, studies of addition show that
Acknowledgements
For comments on the data and manuscript, we thank S. Carey, S. Dehaene, R. Gallistel, R. Gelman, B. Scholl, E. Spelke, members of the Primate Cognitive Neuroscience Laboratory, and three anonymous reviewers. For help running the experiments, we thank Damian Moskovitz, Geert Spaepen, and David Goldenberg. Research on the Cayo Santiago rhesus monkeys (PHS grant: P51RR00168-38) was greatly facilitated by Drs J. Berard, M. Kessler, and F. Bercovitch, and approved by the animal care and use
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