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Symbolic representation of number in chimpanzees Tetsuro Matsuzawa

This paper aims to summarize the existing evidence for the chimpanzees possess for numerals. Fourth, it introduces symbolic representation of number in chimpanzees. common characteristics of the difficulties experienced by Chimpanzees can represent, to some extent, both the cardinal chimpanzees in various kinds of cognitive tasks. Finally, and the ordinal aspect of number. Through the medium of it discusses the number concept within the larger context Arabic numerals we compared working memory in humans and of cognition, illuminating cognitive development in chimpanzees using the same apparatus and following the same chimpanzees and the unique features of human cognition. procedure. Three young chimpanzees outperformed human adults in memorizing briefly presented numerals. However, we The Ai project: psychophysical measurement found that chimpanzees were less proficient at a variety of and the underlying logic other cognitive tasks including imitation, cross-modal The Ai project – encompassing a series of studies whose matching, symmetry of symbols and referents, and one-to-one principal subject has been a female chimpanzee named Ai correspondence. In sum, chimpanzees do not possess human- – began when Ai, at the age of 1.5 years, first touched an like capabilities for representation at an abstract level. The experimental keyboard on April 15th 1978 [3–5]. The last present paper will discuss the constraints of the number in a succession of ape-language projects launched in the concept in chimpanzees, and illuminate some unique features second half of the 20th century, the Ai-project was also of human cognition. the forerunner of a new research paradigm called Com- parative Cognitive Science (CCS) [6]. CCS is the com- Address bined study of psychophysics and ape-language, using Primate Research Institute, Kyoto University, 41 Kanrin, Inuyama, Aichi computer-controlled apparatus. In its original form, CCS 484-8506, Japan aimed to compare perception, memory, and cognition in Corresponding author: Matsuzawa, Tetsuro humans with those of closely related species such as ([email protected]) chimpanzees. Crucially, such inter-species comparisons rely on identical methods: subjects, irrespective of species, use the same apparatus and follow the same Current Opinion in Neurobiology 2009, 19:92–98 procedure during testing. This review comes from a themed issue on Cognitive neuroscience Psychophysics is the classic psychological study of Edited by Michael Platt and Elizabeth Spelke measuring human sensation, perception, memory, and cognition in general. Psychophysics tries to unravel the Available online 14th May 2009 relationship between physical events and psychological 0959-4388/$ – see front matter events. Psychophysical researchers have established # 2009 Elsevier Ltd. All rights reserved. many laws, including, for example, Weber–Fechner’s DOI 10.1016/j.conb.2009.04.007 law and Steven’s power law. There exist well-established methods for measuring the relationship between the stimuli presented and the corresponding internal psycho- logical states. Thus, psychophysics can be extended to Introduction issues related to concept formation, such as the under- Using the Arabic numerals 0 through 9, the chimpanzee standing of number. Ai can represent both the cardinal and the ordinal aspect of number to some extent [1]. Similar skills have now The Ai project has two important features: the research been partially confirmed in six other chimpanzees [2,3]. presents humans and chimpanzees with exactly the same A recent study has used numerical stimuli to demonstrate tasks so that their performance can be compared in detail, an extraordinary memory capability in young chimpan- and that the research undertakes that comparison by zees [2]. In contrast with the memory test, chimpanzees using the methods of psychophysics. There is the syner- show poor performance in many other cognitive tasks that gistic connection between these two features for the require some form of abstraction. The present paper will enterprise of CCS. CCS aims to compare different species address the following five topics. First, it describes the at the level of cognitive mechanisms, and it is the great logic and framework for the study of the number concept virtue of psychophysical method that serves not only to in nonhuman animals. Second, it reviews the long-run- describe the performance of humans and nonhuman ning Ai project, focusing in particular on studies dealing animals but also to analyze that performance into its with the symbolic representation of number. Third, it component mechanisms. By adopting psychophysical describes the extraordinary memory capacity that young approach, you can go beyond questions of what trained

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chimpanzees can do and ask how chimpanzees and enumeration, quantity discrimination, and sequential humans do what they do: What cognitive capacities are responding. Today, much attention continues to be paid shared by the two species and what capacities distinguish to the concept of number in nonhuman animals [16,17]. them. Various researchers have published studies that they described as tests of numerical competence in macaque Ai was the first chimpanzee who learned to discriminate monkeys [18–20], cotton-top tamarin [21], elephant [22], the 26 letters of the alphabet during tests of shape parrot [23], pigeons [24], even salamanders [25] and bees perception and visual acuity [7]. She also mastered [26]. However, none of these compared the performance additional visual symbols such as specially devised geo- of human and nonhuman subjects directly, using the metric shapes (called lexigrams) and Japanese Kanji same methodology. Almost all the literature on nonhu- characters signifying different colors, in the course of man animals has focused on rudimentary forms of the experiments designed to examine her classification of number concept. By contrast, the Ai-project’s series of various colors [8]. number concept studies stands out clearly for two reasons. First, it focuses on the symbolic representation of number Ever since the beginning of the Ai-project, my colleagues using Arabic numerals. This symbolic representation and I have been focusing on the mathematical skills of allowed us to conduct direct comparisons between chimpanzees rather than on any form of bilateral com- humans and chimpanzees. Second, we applied psycho- munication between humans and chimpanzees—the latter physical measurements using a fully automated compu- having been the central theme of previous ape-language ter-controlled apparatus that completely excluded any studies. There were four reasons why we decided to kind of social cueing. concentrate on issues related to number concepts. The fourth reason why we decided to concentrate on First, the world of logico-mathematical skills was small. issues related to number concepts is the connection to the Mathematical cognition is a part of human cognition in psychophysical approach. Most domains of human cogni- general, but the number system is narrower and more tion are not yet amenable to psychophysical analysis, clearly and precisely defined in comparison to the lin- because the proper mathematical characterization of guistic system. The number system includes the levels of the cognitive domain is not clear. Number, however, is Integer that is a part of Real number, and that is a part of highly amenable to psychophysical analysis. Indeed, the Complex number. The scales of the number system Weber–Fechner’s law of psychophysics holds in the advance from Nominal to Ordinal, Interval, and Ratio numerical domain. scales. Therefore, focusing on the Integer, for example, we can examine both cardinal aspects (‘one, two, three, Cardinal and ordinal aspects of number and four...’) and ordinal aspects (‘first, second, third, introducing zero fourth...’) of the number concept in chimpanzees. From Ai is the first chimpanzee who mastered the use of Arabic the perspective of future work, we can examine the numerals to represent numbers [4]. She learned both combination of numerical elements to create new mean- cardinal and ordinal aspects of the number system. She ing: such as putting 1 and 0 together to create ‘10’ in the used the numerals to label real-life items, shown to her in decimal number system. Moreover, further questions a display window, in terms of their numerosity. She also open up regarding numerical operations such as addition became proficient at responding to Arabic numerals in and subtraction. These kinds of numerical manipulations ascending order, selecting them from a touch-screen in can be viewed as corresponding to the syntactical struc- the correct sequence. When the numeral ‘0’ was intro- ture of the language system. duced, Ai mastered its use in both the cardinal and the ordinal domains; however, the acquisition process and the Our second reason for focusing on number concepts was generalization tests in this case clearly highlighted the the accumulation of knowledge about mathematical constraints of the symbolic representation of number thinking in human subjects. Several important papers acquired by the chimpanzee [1]. Further detail on Ai’s had just been published about the child’s understanding experience with numerals follows below. of number, including Gelman and Gallistel’s landmark article [9]. These helped us to discern what we ought to Cardinal number training began when Ai was about five study in chimpanzees. Since then, further studies on years old. She had already learnt to use lexigrams corre- number concepts in humans have continued to shed light sponding to object and color names. Ai mastered the skill on many relevant issues and promoted our understanding of naming 1 through 6, in addition to the naming of 14 of various aspects of numerical cognition (see reviews in objects and 11 colors. Although the ‘word order’ of [10–13]) including its neural mechanisms [14,15]. describing a particular sample (such as ‘five red tooth- brushes’) was free, she spontaneously adopted a favored Third, a handful of studies had reported on topics related sequence, assigning the object and color names first and to the number concept in nonhuman animals, such as then naming the number last. This rule of describing the www.sciencedirect.com Current Opinion in Neurobiology 2009, 19:92–98 94 Cognitive neuroscience

number in the final position was preserved in the case of item in a sequence was short when this item was a small new objects and new colors. It was preserved even when number; she took longer to decide on the first item when the number of objects was limited to just one. In a sense, this was large. The symbolic distance effect describes the the chimpanzee spontaneously developed her own ‘gram- finding that latency decreases when two numerals being mar’ to describe the world [4]. compared are far apart (in terms of their position in the sequence); the task becomes more difficult when the Patterns in the ease with which Ai acquired object, color, numerals are close. In sum, Ai (as well as other chimpan- and numerical labels provide an interesting contrast. zees we subsequently trained) clearly mastered the During the initial phase of learning to use visual symbols sequencing of numerals along the ordinal scale [30,31]. to label corresponding objects, Ai experienced consider- able difficulties: the first two objects required a long In a follow-up study, we attempted to add the number 0 to period of training. However, once past this early hurdle, Ai’s repertoire, training her in the meaning of ‘zero’ first in learning to name a third object became easier, and the the cardinal and then in the ordinal domain [1]. She was fourth easier yet. The same pattern was evident in the initially required to use the numeral 0 to describe the case of color naming [8]. This suggests that the chim- absence of dots in the display frame. After she had learned panzee ‘learned to learn’ in terms of objects and color to use zero in this cardinal setting, we introduced the naming. On the contrary, no comparable improvement numeral 0 in the ordinal sequence task. She did not was observed in the case of numerical naming: The spontaneously place the numeral 0 before 1; there was, sessions required to reach the learning criterion did not thus, no immediate transfer of the meaning of zero from decrease as the numerals 3, 4, 5, and 6 were successively the cardinal to the ordinal domain. However, once again, introduced. these negative data do not imply that chimpanzees cannot possess the concept of zero—in fact, Ai eventually suc- After becoming proficient at the numerical naming of real ceeded in mastering both the cardinal and the ordinal life objects, Ai learned to label white dots projected onto a meaning of the numeral. Nevertheless, whether chim- touch-screen monitor [27,28]. Her range of numerosities panzees are capable of bilateral transfer between cardinal and associated labels was also extended, up to nine. and ordinal domains of number remains an open question. Transferring the task on to a fully automated, computer- ized system further allowed us to measure precisely Ai’s Working memory of numerals in chimpanzees response latencies in numerical naming. We found that the People’s general view of the chimpanzee mind is that it is response latency remained constant up to about five dots; inferior to that of humans [32]. My colleagues and I thereafter we saw a gradual increase in the time taken to showed for the first time that young chimpanzees have label progressively larger sets. At a look, this tendency an extraordinary working memory capacity for numerical reminded us of the two phases of numerical labeling in the recollection [33,2]. Their performance was better than case of human subjects, subitizing and counting. However, that of human adults tested on the same apparatus fol- Ai’s response latency reached its maximum at eight dots, lowing the same procedure. rather than the largest of the sets, at nine. In fact, this tendency was clear throughout the process of acquisition: The subjects of this study were six chimpanzees, three The latency was always at maximum at n À 1 dots, when mother–offspring pairs, including Ai. We started training the largest set being tested was of size n. This strongly the three young chimpanzees at the age of four years; the suggests that instead of counting the dots one by one, the two mothers who were also naı¨ve to the task received the chimpanzee seemed to be performing analog magnitude same training in parallel. All of them succeeded in learn- estimation of the number of dots. Such magnitude esti- ing the sequence of Arabic numerals from 1 to 9, using a mation of quantity is well documented not only in chim- touch-screen monitor connected to a computer. A mem- panzees [29] but also in other animals [18]. Of course, Ai’s ory task called ‘masking task’ was then introduced, at performance does not necessarily imply that chimpanzees around the time when the young chimps reached five cannot count; it simply proves that it is not a straightforward years of age. In this task, after touching the first numeral, task to teach them to solve problems by counting items one all other numerals were replaced by white squares. The by one. subjects had to remember which numeral had appeared in which location, and then touch the squares in the correct In addition to the cardinal aspect of number, we also ascending order. Ayumu, one of the three young chim- trained Ai in the ordinal domain. First she learned to panzees, can memorize the nine numerals in 0.67 s. His select Arabic numerals from 1 to 9 on a touch-screen, in performance is much faster and more accurate than ascending order [30]. After initial training with consecu- human adults (Figure 1). tive items, we introduced sequences of nonadjacent numerals—these tests revealed both a positional and a We next invented a novel variation of the memory test, symbolic distance effect in Ai’s performance. The pos- the so-called ‘limited-hold memory task’ [2]. In this itional effect means that Ai’s latency to select the first task, after touching the initial white circle that served as

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Figure 1

Chimpanzee Ayumu, at the age of 5.5 years, performs the masking task in which the subject has to remember which numeral appeared in which location of the monitor. The latency to touch the first numeral was 0.67 s. The young chimpanzees can memorize the nine numerals much faster and more accurate than human adults [2].

the start key to each trial, the numerals appeared only for as a function of hold duration. However, from the very a certain limited duration, and were then automatically first session, Ayumu’s performance remained at almost replaced by white squares. We tested both chimpanzee the same level irrespective of hold duration, and showed subjects (Ai and her son Ayumu) and human subjects on no decrement. Ayumu outperformed all of the human three different hold duration conditions: 650, 430, and subjects in both speed and accuracy. Our most recent 210 ms. (unpublished) data show that Ayumu can remember eight numerals shown for only 210 ms with an accuracy of 80%. The number of numerals was limited to five. In human Such memory performance has never been obtained in subjects and Ai, the percentage of correct trials decreased human subjects, even after intensive training. Seeing is www.sciencedirect.com Current Opinion in Neurobiology 2009, 19:92–98 96 Cognitive neuroscience

believing: Please enter the keywords ‘chimpanzee mem- to match the symbol to the corresponding color. This kind ory’ in YouTube.com’s search engine, and watch the 10- of bi-directional correspondence between symbols and min video clip entitled ‘Ayumu’ that we have uploaded. referents is referred to as ‘symmetry’. Symmetry is almost automatically established in the early phase of human Not only Ayumu but also the other two young chimpan- language development. However, this is not the case in zees we tested showed the same extraordinary memory chimpanzees, who do not transfer spontaneously but need capability [2]. Young chimpanzees thus appear to have further intensive training [39]. an extraordinary working memory capacity for numerical recollection—better than that of human adults. The Let us return to the issue of number. In true counting results may be reminiscent of the phenomenon known behavior, one-to-one correspondence should provide as ‘eidetic imagery’ or the feats of so-called ‘idiot savants’. the essential basis for further establishment of the Such abilities are known to be present in some human number concept. Imagine that you place five cups children among thousands, with the ability generally upside down in front of a chimpanzee, and then provide declining with age. her with small wooden blocks. Using a gesture, you then ask the chimpanzee to put the wooden blocks on A recent study presented the first examination of eye top of the cups. It is extremely difficult for the chim- tracking in chimpanzees by a computer-based automatic panzee to place the wooden blocks – which can be seen detection system [34]. The eye movements of chimpan- as representing ‘counters’ – on the cups one by one. She zees as they viewed naturalistic pictures were recorded. will more probably stack the blocks on top of one The results were compared with those of humans in the another, the chimpanzees’ preferred way of manipulat- same apparatus following the same procedure. Although ing objects in such situations. Of course, chimpanzees the two species shared many common features such as may learn to solve this particular task, however, it will looking at faces and eyes, chimpanzees shifted the fix- not automatically generalize to variations thereof. One- ation location more quickly and more broadly than to-one correspondence looks easy to us, but it is not so humans. The chimpanzees are good at quickly grasping for the chimpanzees. the pattern as a whole. Human infants assume stable supine posture from right Cognitive tasks that present particular after birth [40]. This enhances face-to-face visual com- difficulties for chimpanzees munication, vocal exchange, as well as bimanual object During my past three decades with the chimpanzees [35], manipulation since the hands are freed from having to it became clear that some cognitive tasks easy for humans cling to the mother. By contrast, chimpanzee infants were not so easy for chimpanzees. For example, although continuously cling to their mothers at least throughout infant chimpanzees show neonatal imitation of facial the first three months of life. It is the stable supine gestures just like humans, this does not develop into posture, not bipedal locomotion, that makes human hands generalized imitation [36]. Chimpanzees can master free and provides important clues to the complexity of our the ‘Do this!’ game to some extent. Although they can object manipulation, a precursor of tool use. When we imitate actions toward objects, it is difficult for them to analyze the development of object manipulation in chim- imitate actions toward their own bodies, and even more panzees using standard tests involving wooden blocks, difficult to imitate simple actions without objects [37]. nesting cups, and so forth, we see interesting differences between the two species in terms of action grammar [41]. Cross-modal matching is also a challenging task for chim- Only one of the three infant chimpanzees we studied panzees. They require intensive training to master started to stack blocks spontaneously—she did so at a matching auditory stimuli to corresponding visual stimuli little less than three years of age, much later than human [38]. Similar difficulties can be observed in symbolic infants [42]. The other two never stacked blocks, despite matching-to-sample tasks. Very little evidence exists having had extensive experience of watching their regarding the symmetry of symbols and their referents. mothers’ stacking behavior. No chimpanzees, not even Let us consider a symbolic matching-to-sample task in Ai, succeeded in making a copy of a simple three-block which a referent needs to be matched to the correspond- structure, such as a ‘bridge’ or ‘arch’ in which two blocks ing symbol. For example, the color ‘red’ must be matched are placed side by side a short distance apart and a third is to the symbol ‘red’, and the color ‘green’ to the symbol placed on top of both [43]. Chimpanzees can manipulate ‘green’. After intensive training on the task, chimpanzees blocks into one-dimensional structures, in a vertical or can become proficient at selecting the correct symbol in horizontal alignment. However, they find two-dimen- response to being presented with a specific color. In turn, sional structures difficult, and three-dimensional con- you can now test the reverse scenario: showing a symbol struction more difficult still. These kinds of first and then providing two choice alternatives, the color hierarchical constraints are seen throughout all examples ‘red’ pitted against the color ‘green’. Chimpanzees, of object manipulation by chimpanzees both in the trained only on color-to-symbol matching, find it difficult laboratory and in the wild [44–47].

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Conclusions: a trade-off theory of memory human, and comparable levels of abstraction have yet to and symbolic representation be demonstrated in the rest of the animal kingdom— Why do chimpanzees have a better memory than humans even in our closest evolutionary neighbor, the chimpan- for immediately capturing visual stimuli? Why do chim- zee. panzees have difficulties representing things at an abstract level? The existing data can be interpreted Acknowledgements according to an evolutionary trade-off hypothesis [40]. The present study was supported by grants from the Ministry of Education, Science, and Culture in Japan (#12002009, #16002001, #20002001), and The common ancestor of humans and chimpanzees five to Japan Society for the Promotion of Science (gCOE-A06, gCOE-D07, ITP- six million years ago may have possessed an extraordinary HOPE). Thanks are due to the staff of the Primate Research Institute, memory capability. At a certain point in evolution, Kyoto University, and to keepers and veterinarians who took care of the chimpanzees at the institute. I thank Dora Biro for her help given in the because of limitations on brain capacity, the human brain course of revising the manuscript. may have acquired new functions in parallel with losing others—such as acquiring language while losing visuo- References and recommended reading spatial temporal storage ability. Papers of particular interest, published within the period of review, have been highlighted as:

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