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Primate Numerical Competence: Contributions Toward Understanding Nonhuman Cognition
Abstract
Nonhuman primates represent the most significant extant species for comparative studies of cognition, including such complex phenomena as numerical competence, among others. Studies of numerical skills in monkeys and apes have a long, though somewhat sparse history, although questions for current empirical studies remain of great interest to several fields, including comparative, developmental, and cognitive psychology; anthropology; ethology; and philosophy, to name a few. In addition to demonstrated similarities in complex information processing, empirical studies of a variety of potential cognitive limitations or constraints have provided insights into similarities and differences across the primate order, and continue to offer theoretical and pragmatic directions for future research. An historical overview of primate numerical studies is presented, as well as a summary of the 17-year research history, including recent findings, of the Comparative Cognition Project at The Ohio State University Chimpanzee Center. Overall, the archival literature on number-related skills and counting in nonhuman primates offers important implications for revising our thinking about comparative neuroanatomy, cross-species (human/ape) cognitive similarities and differences, and the evolution of cognition represented by the primate continuum.
... Such data suggest that he used a counting strategy for 5: only when beyond the subitizing range of 4 did he, like humans, need time to label the set exactly (for a detailed discussion, see Pepperberg, 2006a). Overall, his data are comparable to those of young children (Mix et al., 2002) and, because he added to six, are more advanced than those published on apes (Boysen and Hallberg, 2000). In a subsequent study (Pepperberg, 2012a), Alex showed that he could perform with equal accuracy when asked to sum three sets of sequentially presented objects—that is, collections of variously sized objects now hidden under three cups. ...
... Occasionally, one cup contained no objects, but even if only those trials are considered in which all three cups contained items, Alex's first trial score was 4/5 correct, p = 0.015 (chance of ¼; for chance of 1/6, p < 0.01); his all trials score was 5/6 or, again, 83.3%. In this three-cup task, all of the addends were within subitizing range (Boysen and Hallberg, 2000;Pepperberg, 2006a); thus Alex could easily have tracked these without specifically counting. However, he still would have needed to remember the values under each of the three cups, for several seconds for each cup, and update his memory after seeing what was under each cup, even if nothing was present. ...
... However, he still would have needed to remember the values under each of the three cups, for several seconds for each cup, and update his memory after seeing what was under each cup, even if nothing was present. Again, because he added up to 6, his competence surpassed that of an ape similarly tested (Sheba:Boysen and Hallberg, 2000). Interestingly, in the two-cup task, Alex did not respond " none " when nothing was under any cup (Pepperberg, 2006a; NB: such trials were not present in the three-cup task). ...
Do humans and nonhumans share the ability to form abstract concepts? Until the 1960s, many researchers questioned whether avian subjects could form categorical constructs, much less more abstract formulations, including concepts such as same-different or exact understanding of number. Although ethologists argued that nonhumans, including birds, had to have some understanding of divisions such as prey versus predator, mate versus nonmate, food versus nonfood, or basic relational concepts such as more versus less, simply in order to survive, no claims were made that these abilities reflected cognitive processes, and little formal data from psychology laboratories could initially support such claims. Researchers like Anthony Wright, however, succeeded in obtaining such data and inspired many others to pursue these topics, with the eventual result that several avian species are now considered "feathered primates" in terms of cognitive processes. Here I review research on numerical concepts in the Grey parrot (Psittacus erithacus), demonstrating that at least one subject, Alex, understood number symbols as abstract representations of real-world collections, in ways comparing favorably to those of apes and young human children. He not only understood such concepts, but appeared to learn them in ways more similar to humans than to apes.
... If language and number skills require the same cognitive capacities, then animals, lacking human language, should not succeed on most number tasks; an alternate view is that humans and animals have similar simple, basic number capacities but that only humans' language skills enable development of numerical representation and thus abilities such as verbal counting, addition, etc. (reviews in Carey, 2009;Pepperberg, 2006b). Possibly, label acquisition simply directs attention to characteristics involved in set formation, providing preparation for dealing with number sets for children and, interestingly, label-trained nonhumans: Nonhumans trained on symbolic labeling can acquire exact understanding of number up to about 8 and of simple mathematical processes (e.g., addition of small numbers), much like young children (review in Pepperberg, 2006b; see also Boysen & Hallberg, 2000;Matsuzawa, 2009). ...
... If 5＋0 trials under the longer time interval are used, his first trial accuracy was 43/48 or 89.6%, p＜0.005. His data are comparable to those of young children (Mix, Huttenlocher, & Levine, 2002) and more advanced than those of apes (Boysen & Hallberg, 2000). His responses on 5＋0 trials suggest, although again cannot prove, that he used a counting strategy for 5: Only when beyond the subitizing range of 4 did he, like humans, need time to label the set exactly (for a detailed discussion, see Pepperberg, 2006a). ...
Do humans and nonhumans share numerical and perceptual abilities? Some researchers argue that nonhumans, lacking human language, possess exact understanding only of quantities up to about 4. Animals trained in human communication systems might, however, be more advanced. ALEX, a Grey parrot, could, for example, quantify sets of ≤8 items (including heterogeneous subsets) using vocal English labels, comprehend these labels fully, sum small quantities, and had a zero-like concept. He understood number symbols as abstract representations of real-world collections, in ways comparing favorably to those of apes and young human children. He appeared to learn in ways more similar to humans than apes.
... Consequently, Davis and Pérusse (1988) argued that numerosity is the last cognitive resort if other means fail. Along with data from other species Frontiers in Psychology | Comparative Psychology (Brannon and Terrace, 1998;Boysen and Hallberg, 2000;Brannon, 2006;Cantlon and Brannon, 2007;Vallortigara et al., 2010), our data clearly argue against this notion, since Blue seemed to spontaneously use numerosity even though other cues were initially available. ...
... Thus, with pairings of higher numbers but constant absolute difference, the relative difference becomes smaller and is therefore more difficult to discriminate. Numerous investigations in human infants (Strauss and Curtis, 1981;Xu and Spelke, 2000), human adults (Xu, 2003;Piazza et al., 2004;Hyde and Spelke, 2008;Cordes and Brannon, 2009;Schmitt and Fischer, 2011), human adults with few number words (see citation inside of Brannon, 2006), other primates (Thomas et al., 1980;Boysen, 1993;Boysen and Hallberg, 2000;Smith et al., 2003;Brannon, 2006;Jordan and Brannon, 2006;van Marle et al., 2006;Addessi et al., 2007;Beran, 2007;Cantlon and Brannon, 2007;Hanus and Call, 2007;Nieder and Merten, 2007;Beran et al., 2008), pigeons (Scarf et al., 2012), New Zealand robins (Hunt et al., 2008), and domestic chicks (Rugani et al., 2008) show similar results. Agrillo et al. (2012) observed this distinction in comparable ways in undergraduate students and guppies, and argued for the existence of two numerical systems that have a long phylogenetic history. ...
A previous study (Kilian et al., 2003) had demonstrated that bottlenose dolphins can discriminate visual stimuli differing in numerosity. The aim of the present study was twofold: first, we sought to determine if dolphins are able to use a numerical category based on “few” vs. “many” when discriminating stimuli according to the number of their constituent patterns. Second, we aimed to extend the previously demonstrated range of numbers, thereby testing the limits of the numerical abilities of bottlenose dolphins. To this end, one adult bottlenose dolphin learned to discriminate between two simultaneously presented stimuli which varied in the number of elements they contained. After initial training, several confounding parameters were excluded to render it likely that discrimination performance indeed depended on numerosity. Subsequently, the animal was tested with new stimuli of intermediate as well as higher numbers of elements. Once discrimination had been achieved, a reversal-training on a subset of stimuli was initiated. Afterward, the subject generalized the reversal successful to new and unreinforced stimuli. Our results reveal two main findings: firstly, our data strongly suggest a magnitude and a distance effect. Thus, coding of numerical information in dolphins might follow logarithmic scaling as postulated by the Weber-Fechner law. Secondly, after learning a reversal of contingencies, the dolphin generalized the reversal successful to new and unreinforced stimuli. Thus, within the limits of a study that was conducted with a single individual, our results suggest that dolphins are able to learn and use a numerical category that is based on abstract qualities of “few” vs. “many.”
... It is become possible to demonstrate that animals are capable not only of decision making and using the experience gained in new situations, but also of using simple grammatical rules, visual symbols and number-related skills. For example, language-trained chimpanzees were found to be able to add and subtract small numbers [1] -the ability that was not available for discovery without the use of intermediary languages. ...
In this review we integrate results of long term experimental study on ant "language" and intelligence which were fully based on fundamental ideas of Information Theory, such as the Shannon entropy, the Kolmogorov complexity, and the Shannon's equation connecting the length of a message (l) and its frequency (p), i.e. for rational communication systems. This approach, new for studying biological communication systems, enabled us to obtain the following important results on ants' communication and intelligence: i) to reveal "distant homing" in ants, that is, their ability to transfer information about remote events; ii) to estimate the rate of information transmission; iii) to reveal that ants are able to grasp regularities and to use them for "compression" of information; iv) to reveal that ants are able to transfer to each other the information about the number of objects; v) to discover that ants can add and subtract small numbers. The obtained results show that Information Theory is not only wonderful mathematical theory, but many its results may be considered as Nature laws.
... The dolphin accurately distinguished all possible pairings except that indicating 5 and 6 fish (Mitchell et al. 1985). Another variant found in studies of numerical competence in chimpanzees required the animals to select a container holding a number of items matching the number of stimuli in a previously presented container, or corresponding to an Arabic numeral (see review in Boysen and Hallberg 2000). ...
... For example, chimpanzees learn a lexigram and use it for naming of things ). They have a numerical competence (Matuzawa 1981;Boysen and Hallberg 2000) and shortterm memory comparable to that of adult human beings . They manufacture a tool and use it for problem-solving tasks . ...
From an evolutionary perspective, understanding chimpanzees offers a way of understanding the basis of human nature. This book on cognitive development in chimpanzees is the first of its kind to focus on infants reared by their own mothers within a natural setting, illustrating various aspects of chimpanzee cognition and the developmental changes that accompany them. The subjects of this book are chimpanzees of three generations inhabiting an enriched environment as well as a wild community in West Africa; and phenomena such as face recognition, concept formation, object manipulation, tool manufacture and use, decision making, learning, communication, self-awareness, intentionality, understanding others’ minds, cooperation, deception, altruism, and reciprocity observed within these groups are reported herein. Unique approaches both in the field and in the laboratory go hand in hand to illustrate the cognitive world of our closest living evolutionary relatives.
... The list of animals that are able to perform numerically would be longer, including primates (Thomas et al. 1980;Boysen 1993;Boysen and Hallberg 2000;Smith et al. 2003;Brannon 2006;Jordan and Brannon 2006;van Marle et al. 2006;Addessi et al. 2007;Beran 2007;Cantlon and Brannon 2007;Hanus and Call 2007;Nieder and Merten 2007;Beran et al. 2008), pigeons (Scarf et al. 2012), or new Zealand robins Hunt et al. 2008). The sum of all this evidence makes it possible to affirm that numerosity is something natural previous to abstract thinking that can be traced throughout the evolutionary phylogenetic tree. ...
... The list of animals that are able to perform numerically would be longer, including primates (Thomas et al. 1980;Boysen 1993;Boysen and Hallberg 2000;Smith et al. 2003;Brannon 2006;Jordan and Brannon 2006;van Marle et al. 2006;Addessi et al. 2007;Beran 2007;Cantlon and Brannon 2007;Hanus and Call 2007;Nieder and Merten 2007;Beran et al. 2008), pigeons (Scarf et al. 2012), or new Zealand robins Hunt et al. 2008). The sum of all this evidence makes it possible to affirm that numerosity is something natural previous to abstract thinking that can be traced throughout the evolutionary phylogenetic tree. ...
The response to subjective probabilities of the Bayesian approach was frequentism, that is, the analysis of long-run series of frequencies of an event from which came the possibilities to extract statistical data. Frequentism became the dominant view in scientific practices during most of the twentieth century. This academic view was espoused by several authors, like Pearson, Fisher, Gosset, and Neyman–Pearson, not all of them agreeing about the best ways to perform this statistical approach. The main ideas and internal debates are analyzed here.
... The list of animals that are able to perform numerically would be longer, including primates (Thomas et al. 1980;Boysen 1993;Boysen and Hallberg 2000;Smith et al. 2003;Brannon 2006;Jordan and Brannon 2006;van Marle et al. 2006;Addessi et al. 2007;Beran 2007;Cantlon and Brannon 2007;Hanus and Call 2007;Nieder and Merten 2007;Beran et al. 2008), pigeons (Scarf et al. 2012), or new Zealand robins Hunt et al. 2008). The sum of all this evidence makes it possible to affirm that numerosity is something natural previous to abstract thinking that can be traced throughout the evolutionary phylogenetic tree. ...
The emergence of a new discipline, epidemiology, contributes to the understanding of the evolution of scientific attitudes and ideas about causality. After an initial and ancient belief in single causes supported by classic philosophers and nineteenth century physicians like Koch that can be expressed as a monocausality view, the complexity of real medical and toxicological problems forced researchers to embrace the notion of multicausality and similar approaches (web of causes, chain of events). All these debates fed the evolution of statistical methodologies employed as well as led to a new way to understand causality within complex systems or contexts.
... The list of animals that are able to perform numerically would be longer, including primates (Thomas et al. 1980;Boysen 1993;Boysen and Hallberg 2000;Smith et al. 2003;Brannon 2006;Jordan and Brannon 2006;van Marle et al. 2006;Addessi et al. 2007;Beran 2007;Cantlon and Brannon 2007;Hanus and Call 2007;Nieder and Merten 2007;Beran et al. 2008), pigeons (Scarf et al. 2012), or new Zealand robins Hunt et al. 2008). The sum of all this evidence makes it possible to affirm that numerosity is something natural previous to abstract thinking that can be traced throughout the evolutionary phylogenetic tree. ...
Rev. Bayes and his friend Richard Price created a new way to deal with the philosophical and theological problems on induction as were explained by Hume. This mathematical formula included the notion of subjective probabilities and, consequently, opened a debate on its validity. French mathematician Pierre-Simon Laplace applied it successfully to astronomical calculations just before starting to change his mind over the correctness of Bayes’ formula. Several objections and practical challenges made the general implementation of Bayes’ ideas impossible.
... The list of animals that are able to perform numerically would be longer, including primates (Thomas et al. 1980;Boysen 1993;Boysen and Hallberg 2000;Smith et al. 2003;Brannon 2006;Jordan and Brannon 2006;van Marle et al. 2006;Addessi et al. 2007;Beran 2007;Cantlon and Brannon 2007;Hanus and Call 2007;Nieder and Merten 2007;Beran et al. 2008), pigeons (Scarf et al. 2012), or new Zealand robins Hunt et al. 2008). The sum of all this evidence makes it possible to affirm that numerosity is something natural previous to abstract thinking that can be traced throughout the evolutionary phylogenetic tree. ...
First chapter analyzes how living systems such as amoebae, insects, fishes, chicks, or dolphins are able to deal with numbers without any symbolic system, explaining the notions of “subitization” or “numerosity,” among others. At the same time, the cognitive limits for humans in relation to number processing are explored, especially those expressed by kids. Once provided this basic naturalistic framework for minds and numbers, the concepts of ignorance, chance, and statistics are introduced as well as their related basic philosophical debates.
... They concentrate on the non-symbolic, associative processes presumed to govern nonhuman cognition, for example trial-and-error experiential learning or behavior chains. This leaves them conceptually and methodologically impoverished concerning symbolic cognition (Anderson 1996;RWB;Rumbaugh 1970;T&C), quantification and logic being important exceptions (e.g., Boysen & Hallberg 2000;Thompson & Oden 2000), so relatively little of the evidence they have generated helps determine whether great apes, or any species, are capable of symbolic cognition. ...
... They also demonstrate that for numbers 1-3 subitization is the basic process followed by dolphins but that from 3 to 6, numerical comparisons are processed logarithmically, as is postulated by the Weber-Fechner law. 12 The list of animals that are able to perform numerically would be longer, including primates (Thomas et al. 1980;Boysen 1993;Boysen and Hallberg 2000;Smith et al. 2003;Brannon 2006;Jordan and Brannon 2006;van Marle et al. 2006;Addessi et al. 2007;Beran 2007;Cantlon and Brannon 2007;Hanus and Call 2007;Nieder and Merten 2007;Beran et al. 2008), pigeons (Scarf et al. 2012), or new Zealand robins Hunt et al. 2008). The sum of all this evidence makes it possible to affirm that numerosity is something natural previous to abstract thinking that can be traced throughout the evolutionary phylogenetic tree. ...
This book analyzes the origins of statistical thinking as well as its related philosophical
questions, such as causality, determinism or chance. Bayesian and frequentist approaches
are subjected to a historical, cognitive and epistemological analysis, making it possible to
not only compare the two competing theories, but to also find a potential solution. The
work pursues a naturalistic approach, proceeding from the existence of numerosity in
natural environments to the existence of contemporary formulas and methodologies to
heuristic pragmatism, a concept introduced in the book’s final section. This monograph
will be of interest to philosophers and historians of science and students in related fields.
Despite the mathematical nature of the topic, no statistical background is required,
making the book a valuable read for anyone interested in the history of statistics and
human cognition.
... If 5+0 trials under the longer time interval are used, his first trial accuracy was 43/48 or 89.6 %, p< 0.005. His data are comparable to those of young children (Mix et al. 2002) and more advanced than those of apes (Boysen and HAllberg 2000). His responses on 5+0 trials suggest, although again cannot prove, that he used a counting strategy for 5: Only when beyond the subitizing range of 4 did he, like humans, need time to label the set exactly (for a detailed discussion, see PePPerberg 2006a). ...
For over 35 years, I have examined Grey parrot cognition via a modeling technique, whereby birds are trained to use elements of English speech referentially, so they can be questioned vocally, much like young children. The oldest bird, Alex, labeled >50 objects, seven colors, five shapes, quantities to eight, three categories (color, shape, material) and used no, come here, wanna go X, and want Y (X, Y being appropriate location or item labels) intentionally. He combined labels to identify, request, comment on, or refuse >150 items and to alter his environment. He understood concepts of category, relative size, quantity, presence or absence of similarity/difference in attributes, showed label comprehension and a zero-like concept; he demonstrated some understanding of phonological awareness and a numerical competence more like that of young children than other nonhumans. He could be queried about optical illusions in ways directly comparable to humans. Younger birds are acquiring similar competence. © 2014 Springer Science+Business Media Dordrecht. All rights are reserved.
... They concentrate on the non-symbolic, associative processes presumed to govern nonhuman cognition, for example trial-and-error experiential learning or behavior chains. This leaves them conceptually and methodologically impoverished concerning symbolic cognition (Anderson 1996;RWB;Rumbaugh 1970;T&C), quantification and logic being important exceptions (e.g., Boysen & Hallberg 2000;Thompson & Oden 2000), so relatively little of the evidence they have generated helps determine whether great apes, or any species, are capable of symbolic cognition. ...
... There is a major difference, however, with regard to what animals and humans make of their knowledge of small numbers. After having mastered integers up to four, chimpanzees need laborious learning of years to acquire the integer list up to nine (Matsuzawa 1985;Boysen and Hallberg 2000;Kawai and Matsuzawa 2000). Children, in turn, use their knowledge of integers up to four to generate a potentially infinite list of integers (Wynn 1992;Carey 2001;Sarnecka and Carey 2008). ...
Many religious traditions embrace ideas that include boundless elements (i.e., beings that are omnipresent, omniscient, etc.). The origin of ideas with such boundless qualities has not yet been successfully accounted for in the cognitive science of religion. In this study I suggest that the domain-general use of recursion underlies the mental representation of boundless qualities. I also examine the contribution of recursive patterns to other aspects of religiosity: the concep-tualization of divine agency and the emergence of magical rituals. I suggest that the human ability to use recursion in a domain-general way is minimally required for the human Faculty of Religion in a Narrow Sense. In recent years, the cognitive science of religion has put forward explanations for various aspects of religion. Some of these hypotheses have been subjected to empirical tests, which raised a number of new questions. Let me mention two particular hypotheses about the cognitive foundations of god concepts which I will address in more detail in this study. In terms of the hypothesis of minimal counterintuitiveness, formulated by Pascal Boyer, concepts that min-imally violate universally held—innate, or so-called maturationally natural— ontological categories are more memorable than either concepts without such violations or concepts with too many violations (Boyer 1994, 2001; McCauley 2000; Barrett 2008). Whereas the first experiments conducted to test Boyer's theory empirically have entirely confirmed his predictions, even in * I owe thanks to two anonymous reviewers, for their helpful comments on different versions of the manuscript.
... identifying the number of potential opponents) (Agrillo, Dadda, & Bisazza, 2007). Numerical competence has been investigated and demonstrated in a variety of non-human primate species in both laboratory and field settings (for reviews see Boysen & Hallberg, 2000;Gallistel & Gelman, 2000). Specifically, non-human primates have demonstrated the capacity to choose the larger of two unequal choice options (i.e. a relative numerousness judgment, or RNJ) in a variety of contexts, such as straightforward quantity discrimination tasks, reversed contingency tasks, and tasks in which items are presented sequentially rather than simultaneously or item-by-item rather than whole sets. ...
Some non-human primate species have demonstrated the capacity for quantity discrimination and summation with symbolic representation in the form of tokens. I examined this capacity in seven Western lowland gorillas (Gorilla gorilla gorilla). In Phase I of the experiment, the gorillas were asked to make a choice between two unequal values (e.g. 1 cylinder token = 5 blueberries vs. 1 cube token = 1 blueberry). In Phase II, two subjects were presented with homogeneous choice combinations (e.g. 2 pyramid tokens = 6 blueberries vs. 4 cube tokens = 4 blueberries). Three of the gorillas performed successfully in Phase I while one performed successfully in Phase II, utilizing the strategy of 'choose the larger sum,' under some conditions, over the alternative strategies of 'choose the larger number of tokens' or 'choose the higher value token.' This research demonstrates that gorillas have the capacity to perform symbolic quantity discriminations and summation judgments.
... 17 Including the handler of the jocularly named but tragically fortuned Nim Chimpsky. 18 Boysen and Hallberg, 2000. Still, there have been touching revelations. ...
... Two possibilities for research of this type are immediately suggested: (1) comparisons of teaching methods using matched classrooms, in which one group of students experience standard teaching methods regarding a topic (e.g., adding fractions) and the other group of students experience teaching methods that based more strongly on the principles outlined in Section 6, and (2) research using remedial education efforts that are based on the principles outlined in Section 6 (again compared to some control group), perhaps similar to the research conducted by Rozin (1976) on developing reading skills. Finally, there may be some useful implications of this approach, for example, looking at the individual assumptions for fraction use, in relation to research on mathematical abilities of nonhuman species (e.g., Beran, Rumbaugh, & Savage-Rumbaugh, 1998;Boysen & Hallberg, 2000;Brannon & Terrace, 2000;Davis & Perusse, 1988). ...
The initial foundations of human mathematical reasoning appear to be based on “naı̈ve mathematics”—specific and persistent privileged mental representations that develop as a normal part of the human evolved phenotype. Based on the proposed existence of privileged representations in the conceptual domain of mathematics, this paper incorporates findings from early development, childhood mathematical reasoning, and adult statistical decision-making research. The utility of such a framework is demonstrated by analyzing how common errors in fraction and decimal use are explicable in terms of these systematic and reliably developing aspects of human mathematical reasoning. Additionally, the idea that privileged representations continue to exert some influence beyond early childhood holds implications for both research and practice in mathematics education.
... It is become possible to demonstrate that animals are capable not only of decision making and using the experience gained in new situations, but also of using simple grammatical rules, visual symbols and number-related skills. For example, language-trained chimpanzees were found to be able to add and subtract small numbers [18]-the ability that was not available for discovery without the use of intermediary languages. ...
In this review we integrate results of long term experimental study on ant "language" and intelligence which were fully based on fundamental ideas of Information Theory, such as the Shannon entropy, the Kolmogorov complexity, and the Shannon's equation connecting the length of a message (l) and its frequency (p), i.e. for rational communication systems. This approach, new for studying biological communication systems, enabled us to obtain the following important results on ants' communication and intelligence: i) to reveal "distant homing" in ants, that is, their ability to transfer information about remote events; ii) to estimate the rate of information transmission; iii) to reveal that ants are able to grasp regularities and to use them for "compression" of information; iv) to reveal that ants are able to transfer to each other the information about the number of objects; v) to discover that ants can add and subtract small numbers. The obtained results show that Information Theory is not only wonderful mathematical theory, but many its results may be considered as Nature laws.
... Some argue that the term "counting" should be reserved for humans , but several studies have provided evidence of animal behavior that conforms to one or more of the formal counting principles as defined by . For example, research has shown that chimpanzees, like young children, tend to touch or point to each item when judging the number of items in an array Boysen, Berntson, Shreyer, & Hannan, 1995;Boysen & Hallberg, 2000). These gestures, known as indicating acts, may help the child or animal coordinate the tagging process involved in the application of the one-to-one correspondence principle. ...
Over the past few decades, researchers have firmly established that a wide range of nonhuman animals exhibit some form of numerical competence. The focus of this research was to define further the extent of numerical ability in rhesus monkeys, and specifically to determine whether the animals possess a symbolic understanding of Arabic numerals. This required examining the stimulus attributes (e.g., number vs. hedonic value) represented by the numerals, as well as the precision (e.g., absolute vs. relative) and generality of those representations. In chapters 2 and 3, monkeys were required to compare and order numerals and were rewarded with either proportional or probabilistic rewards. The results indicated that monkeys were relying on the ordinal or absolute numerical values associated with each numeral and not hedonic value or learned 2-choice discriminations. The studies in chapters 4 and 5 indicated that monkeys can use numerals to symbolize an approximate number of sequential motor responses. The study in Chapter 6 tested the generality of the monkeys' symbolic number concept using transfer tests. The results indicated that some monkeys are able to abstract number across presentation mode, but this ability is only exhibited under limited conditions. Collectively, these studies provide evidence that rhesus monkeys view Arabic numerals as more than sign-stimuli associated with specific response-reward histories, but that numerals do not have the same precise symbolic meaning as they do for humans. INDEX WORDS: Monkeys, Macaca mulatta, numbers, symbols, numerical ability
... It is become possible to demonstrate that animals are capable not only of decision making and using the experience gained in new situations, but also of using simple grammatical rules, visual symbols and number-related skills. For example, language-trained chimpanzees were found to be able to add and subtract small numbers [18]the ability that was not available for discovery without the use of intermediary languages. ...
... It is become possible to demonstrate that animals are capable not only of decision making and using the experience gained in new situations, but also of using simple grammatical rules, visual symbols and number-related skills. For example, language-trained chimpanzees were found to be able to add and subtract small numbers [18]—the ability that was not available for discovery without the use of intermediary languages. However, it is important to note that this way to communicate with animals is based on adopted human languages. ...
... It is become possible to demonstrate that animals are capable not only of decision making and using the experience gained in new situations, but also of using simple grammatical rules, visual symbols and number-related skills. For example, language-trained chimpanzees were found to be able to add and subtract small numbers [18]—the ability that was not available for discovery without the use of intermediary languages. However, it is important to note that this way to communicate with animals is based on adopted human languages. ...
... Here we summarize a few of the relevant studies. (For reviews, see Sarah T. Boysen & Hallberg, 2000; Elizabeth M. Brannon & Roitman, 2003; S. Dehaene, 1997; Gallistel, 1990; Spelke & Dehaene, 1999) ...
Mathematics is a system for representing and reasoning about quantities, with arithmetic as its foundation. Its deep interest for our understanding of the psychological foundations of scientific thought comes from what Eugene Wigner called the unreasonable efficacy of mathematics in the natural sciences. From a formalist perspective, arithmetic is a symbolic game, like tic-tac-toe. Its rules are more complicated, but not a great deal more complicated. Mathematics is the study of the properties of this game and of the systems that may be constructed on the foundation that it provides. Why should this symbolic game be so powerful and resourceful when it comes to building models of the physical world? And on what psychological foundations does the human mastery of this game rest? The first question is metaphysical—why is the world the way it is? We do not treat it, because it lies beyond the realm of experimental behavioral science. We review the answers to the second question that experimental research on human and non-human animal cognition suggests. The general nature of the answer is that the foundations of mathematical cognition appear does not lie in language and the language faculty. The ability to estimate quantities and to reason arithmetically with those estimates exists in the brains of animals that have no language. The same or very similar non-verbal mechanisms appear to operate in parallel with verbal estimation and reasoning in adult humans. And, they operate to some extent before children learn to speak and before they have had any tutoring in the elements of arithmetic. These findings suggest that the verbal expression of number and of arithmetic thinking is based on a non-verbal system for estimating and reasoning about discrete and continuous quantity, which we share with many non-verbal animals. A reasonable supposition is that the neural substrate for this system arose far back in the evolution of brains precisely because of the puzzle that Wigner called attention to: arithmetic reasoning captures deeply important properties of the world, which the animal brain must represent in order to act effectively in it.
... Numerical discrimination has been shown to play a potential role in a variety of choices that affect an individual's success, such as assessing foraging options and selection of food patches (Uller et al. 2003;Farnsworth and Smolinski 2006;Stevens et al. 2007;Hunt et al. 2008), evaluating the group size of conspecifics to reduce individual predation risk (Agrillo et al. 2008) and selecting prey by their numerical abundance (Krause and Godin 1995). Historically, most research on numerical discrimination has been completed in the laboratory (Boysen and Hallberg 2000;Hauser et al. 2000;West and Young 2002;Cooper et al. 2003), although more recent studies have started to explore the importance of cognitive ability in the wild (Shettleworth 2001;Lyon 2003;Emery 2006;Hunt et al. 2008). Evidence from other egg-laying species (Armstrong and Robertson 1988;Beukeboom et al. 1988;Bauchau and Seinen 1997;Lyon 2003;White et al. 2009) suggests that female birds may use clutch size in a variety of reproductive decisions and may, in fact, be able to count. ...
Breeding birds use a variety of cues to choose a nest site. For conspecific brood parasites, the number of eggs in a host nest may be an important indicator of nest stage (laying or incubating) and the resulting prospective value of the nest. In precocial birds, such as wood ducks (Aix sponsa), a parasitic female should lay her eggs during the host's laying stage to ensure hatch synchrony with the host. Incubation and hatching success may also be compromised in large clutches. Accordingly, parasitic females should respond to the number of eggs already present in a potential hosts' nest and should preferentially lay eggs in nests with smaller clutches. We conducted a field experiment using simulated nests containing different numbers of "host" eggs to test this hypothesis. When offered a choice of nests containing clutches of 5, 10, 15, or 20 eggs, females were significantly more likely to lay eggs in the 5- and 10-egg treatments, laid more eggs in total in the smaller clutch treatments, and were more likely to incubate the nests in the 5- and 10-egg treatments. These results indicate that wood ducks are responsive to quantitative cues, such as the number of eggs in a nest, although we do not yet know if they are able to do so directly by numerical discrimination (i.e., counting). Copyright 2010, Oxford University Press.
... We focused on male-male dyads for the majority of the analysis for 2 reasons: 1) Frequency of support is often higher among males than among females (de Waal, 1982; Hemelrijk and Ek, 1991) and 2) extracting data for a temporal analysis is relatively time consuming, so we limited the analysis to the subset of male-male dyads. Chimpanzees are the most suitable nonhuman primate species for such a test because evidence of their complex social cognitive abilities (Byrne and Whiten, 1988; Call, 2001; de Waal, 1982; de Waal and Luttrell, 1988) and numerical competence (Biro and Matsuzawa, 1999; Boysen and Hallberg, 2000; Kawai and Matsuzawa, 2000), which is advantageous if mental scorekeeping is required, already exists. Thus it is not unreasonable to assume that they may possess the abilities required for anticipation in interchange. ...
We investigated the temporal relationship between grooming given and agonistic support received in a group of chimpanzees at Chester Zoo, U.K. We compared grooming levels the day before a conflict-with-support to those the day before a conflict-without-support and to baseline to investigate whether individuals groom potential supporters in anticipation of the need for support. We also compared grooming and aggression levels the day after conflicts-with-support to levels the day after conflicts-without-support and to baseline levels to determine whether chimpanzees reward individuals that support them or punish those that do not. Finally, we compared grooming and aggression levels the day after conflicts-with-unsuccessful-solicitations-for-support to those the day after conflicts-with-support and to baseline to examine the behavioral consequences of not providing support when an individual had solicited but did not receive it. Future recipients of support groomed future supporters more the day before receiving support, compared to the day before conflicts-without-support, indicating that grooming increased the likelihood of support. The relationship between prior grooming and support held true only for aggressor and not victim support and is consistent with behavior expected if chimpanzees anticipated the need for agonistic support and groomed their supporter the day before to increase the likelihood of support. We found evidence of a system of reward and punishment. Individuals experienced significantly lower rates of aggression after conflicts in which they provided support than at baseline and after conflicts in which they did not provide support. The finding was true only for aggressor support. We found no evidence that chimpanzees punished individuals whom or that they unsuccessfully solicited with aggression or a reduction in grooming. However, solicitors groomed individuals that they solicited for support significantly more after unsuccessful solicitations than after individuals provided support (but with no difference from baseline), indicating that individuals may attempt to recement their relationship after an unsuccessful solicitation. The findings are consistent with a mechanism of calculated interchange in chimpanzees.
... Two possibilities for research of this type are immediately suggested: (1) comparisons of teaching methods using matched classrooms, in which one group of students experience standard teaching methods regarding a topic (e.g., adding fractions) and the other group of students experience teaching methods that based more strongly on the principles outlined in Section 6, and (2) research using remedial education efforts that are based on the principles outlined in Section 6 (again compared to some control group), perhaps similar to the research conducted by Rozin (1976) on developing reading skills. Finally, there may be some useful implications of this approach, for example, looking at the individual assumptions for fraction use, in relation to research on mathematical abilities of nonhuman species (e.g., Beran, Rumbaugh, & Savage-Rumbaugh, 1998;Boysen & Hallberg, 2000;Brannon & Terrace, 2000;Davis & Perusse, 1988). ...
The initial foundations of human mathematical reasoning appear to be based on “naı̈ve mathematics”—specific and persistent privileged mental representations that develop as a normal part of the human evolved phenotype. Based on the proposed existence of privileged representations in the conceptual domain of mathematics, this paper incorporates findings from early development, childhood mathematical reasoning, and adult statistical decision-making research. The utility of such a framework is demonstrated by analyzing how common errors in fraction and decimal use are explicable in terms of these systematic and reliably developing aspects of human mathematical reasoning. Additionally, the idea that privileged representations continue to exert some influence beyond early childhood holds implications for both research and practice in mathematics education.
... Many nonhuman species exhibit various forms of numberrelated abilities (see citations and review in Beran 2011; Dehaene 2011), but only those trained to represent quantity symbolically with Arabic and/or vocal numerals (notably, apes and a Grey parrot) appear to exactly map such numerals to precise cardinal values of sets. Some apes and the parrot spontaneously transferred to novel arrays, demonstrated comparable levels of competence in comprehension and production, understood ordinality, and exhibited abilities extending well beyond levels possibly explained by non-exact strategies (e.g., subitizing, estimating, analog magnitude, or object file representations: Biro and Matsuzawa 2001;Boysen 1993;Boysen and Berntson 1989;Boysen and Hallberg 2000;Boysen et al. 1993;Matsuzawa 1985;Matsuzawa et al. 1991;Murofushi 1997;Pepperberg 1987Pepperberg , 1994Pepperberg , 2006aPepperberg and Gordon 2005;note Carey 2009). ...
A Grey parrot (Psittacus erithacus), able to quantify sets of eight or fewer items (including heterogeneous subsets), to sum two sequentially presented sets of 0-6 items (up to 6), and to identify and serially order Arabic numerals (1-8), all by using English labels (Pepperberg in J Comp Psychol 108:36-44, 1994; J Comp Psychol 120:1-11, 2006a; J Comp Psychol 120:205-216, 2006b; Pepperberg and Carey submitted), was tested on addition of two Arabic numerals or three sequentially presented collections (e.g., of variously sized jelly beans or nuts). He was, without explicit training and in the absence of the previously viewed addends, asked, "How many total?" and required to answer with a vocal English number label. In a few trials on the Arabic numeral addition, he was also shown variously colored Arabic numerals while the addends were hidden and asked "What color number (is the) total?" Although his death precluded testing on all possible arrays, his accuracy was statistically significant and suggested addition abilities comparable with those of nonhuman primates.
... Many nonhuman species exhibit various forms of numberrelated abilities (see citations and review in Beran 2011; Dehaene 2011), but only those trained to represent quantity symbolically with Arabic and/or vocal numerals (notably, apes and a Grey parrot) appear to exactly map such numerals to precise cardinal values of sets. Some apes and the parrot spontaneously transferred to novel arrays, demonstrated comparable levels of competence in comprehension and production, understood ordinality, and exhibited abilities extending well beyond levels possibly explained by non-exact strategies (e.g., subitizing, estimating, analog magnitude, or object file representations: Biro and Matsuzawa 2001;Boysen 1993;Boysen and Berntson 1989;Boysen and Hallberg 2000;Boysen et al. 1993;Matsuzawa 1985;Matsuzawa et al. 1991;Murofushi 1997;Pepperberg 1987Pepperberg , 1994Pepperberg , 2006aPepperberg and Gordon 2005;note Carey 2009). ...
A Grey parrot (Psittacus erithacus), able to quantify sets of eight or fewer items (including heterogeneous subsets), to sum two sequentially presented sets of 0–6 items (up to 6), and to identify and serially order Arabic numerals (1–8), all by using English labels (Pepperberg in J Comp Psychol 108:36–44, 1994; J CompPsychol 120:1–11, 2006a; J Comp Psychol 120:205–216,2006b; Pepperberg and Carey submitted), was tested on addition of two Arabic numerals or three sequentially presented collections (e.g., of variously sized jelly beans or nuts). He was, without explicit training and in the absence of the previously viewed addends, asked, "How many total?" and required to answer with a vocal English number label. In a few trials on the Arabic numeral addition, he was also shown variously colored Arabic numerals while the addends were hidden and asked "What color number (is the) total?" Although his death precluded testing on all possible arrays, his accuracy was statistically significant and suggested addition abilities comparable with those of nonhuman primates.
... Although chimps, monkeys and parrots can learn to associate Arabic numerals (or number words) with numbers of items (Ferster 1964; Matsuzawa 1985; Washburn and Rumbaugh 1991; Pepperberg and Gordon 2005), few have so far exhibited any benefit to using such symbolic, rather than one-to-one correspondence, representations. One benefit to an animal of using symbolic representation was shown by Boysen and Hallberg (2000), who found that chimpanzees presented with two sets of objects, in a task where they were given the unchosen number of reward items, were unable to suppress choosing the larger number of items, but when the two reward amounts were represented by numerals, they were able to choose the smaller numeral and receive the larger reward. Furthermore, Matsuno et al. (2006) showed that chimpanzees who had learned color symbols could make more precise color discriminations than chimpanzees who had not. ...
When humans and animals estimate numbers of items, their error rate is proportional to the number. To date, however, only humans show the capacity to represent large numbers symbolically, which endows them with increased precision, especially for large numbers, and with tools for manipulating numbers. This ability depends critically on our capacity to acquire and represent explicit symbols. Here we show that when rhesus monkeys are trained to use an explicit symbol system, they too show more precise, and linear, scaling than they do using a one-to-one corresponding numerosity representation. We also found that when taught two different types of representations for reward amount, the monkeys systematically undervalued the less precise representation. The results indicate that monkeys, like humans, can learn alternative mechanisms for representing a single value scale and that performance variability and relative value depend on the distinguishability of each representation.
... It is become possible to demonstrate that animals are capable not only of decision making and using the experience gained in new situations, but also of using simple grammatical rules, visual symbols and number-related skills. For example, language-trained chimpanzees were found to be able to add and subtract small numbers [18]—the ability that was not available for discovery without the use of intermediary languages. However, it is important to note that this way to communicate with animals is based on adopted human languages. ...
In this review we integrate results of long term experimental study on ant “language” and intelligence which were fully based on fundamental ideas of Information Theory, such as the Shannon entropy, the Kolmogorov complexity, and the Shannon’s equation connecting the length of a message (l) and its frequency (p), i.e., l = –log p for rational communication systems. This approach enabled us to obtain the following important results on ants’ communication and intelligence: (i) to reveal “distant homing” in ants, that is, their ability to transfer information about remote events; (ii) to estimate the rate of information transmission; (iii) to reveal that ants are able to grasp regularities and to use them for “compression” of information; (iv) to reveal that ants are able to transfer to each other the information about the number of objects; (v) to discover that ants can add and subtract small numbers. The obtained results show that information theory is not only excellent mathematical theory, but many of its results may be considered as Nature laws.
... With respect to phylogeny, the most that we can say is that there is currently a good deal of evidence for at least rudimentary arithmetic abilities in non-human primates (Boysen and Hallberg 2000), but there is no known case of the use of artifacts in this process, let alone an artifact as complex as an abacus. The abacus, which traces its origins back several thousand years to Sumer in the fertile crescent, was introduced into Japan from China where it appears to come into used in the 14 th century, AD. ...
The chapter explores the relationship between technology and intelligence with an emphasis on technologies as forms of tool-mediated social practices. This involves the argument that although tools are constituents of a technology, it is the way in which tools are deployed as part of a social practice that is crucial. Artifacts are considered as the foundation blocks of technology.
This paper discusses the notion of quantity and related notions from the perspective of their lexicalisation in the area of the so-called (functional, auxiliary) grammatical expressions. Such units, founded on the notion of quantity, create a microsystem composed of the following semantic and functional classes: interrogative pronouns, relators, prepositions, metapredicative operators (of gradation, limitation, approximation), conjunctions, particles, metatextual commentaries, and modifi er of declarativity. The semantic relationships between these units are similar to the ones noticeable between expressions from the relevant level of language; apart from that, they form pairs based on such relationships with units from outside the examined lexical and conceptual fi eld. The paper also discusses the variant groups among the analysed expressions and units that are formally similar yet functionally different.
Comparative analysis of higher cognitive abilities in animals provides for assessment of the evolutionary underpinnings of the formation of human thought and language. This review will address the main approaches to studies of thought in animals and analyze the data obtained using these approaches. The results of a diversity of tests indicate that animals with high levels of brain development have a wide spectrum of cognitive abilities. As expected, the widest spectrum is found in the great apes. A quite similar spectrum is found in higher members of the class Aves (corvids and psittacines) despite their different brain structure. Convergent similarity in the level of development of cognitive abilities in higher mammals and birds reflects the operation of common factors determining their evolution. Comparison of several corvid and psittacine species indicates that the high levels of development of their cognitive abilities are due to the high levels of organization of the brains of these species rather than ecological characteristics.
Human language based on symbolization or sign-referent equivalence relations. The paper focuses on methods of studying the process of developing of sign-referent equivalence. Subject is trained in Matching-To-Sample task: for example, reinforcing of stimulus B if the sample was A, and stimulus D if the sample was C. Following test allows to reveal if new relations (for example, symmetry, if subject chooses stimulus A if the sample was B) appeared spontaneously. Human subjects usually pass this test successfully. This result may be explained by repeated demonstration of sign-referent symmetry during language learning and using. Our paper is dedicated to methods features which can be used to study sign-reference developing in human and animals. We discuss factors that leads to appearance of this crucial property of stimulus equivalence.
Monografia jest próbą przedstawienia aktualnego stanu wiedzy z zakresu psychologii porównawczej oraz etologii poznawczej. Maciej Trojan skupia się szczególnie na pięciu obszarach: komunikacji i języku, kompetencjach numerycznych, użyciu i wytwarzaniu narzędzi, teorii umysłu oraz mentalnych podróżach w czasie. Podejmuje też kwestię budzącą powszechne zainteresowanie: problem świadomości i samoświadomości u zwierząt.
Approximate number sense (ANS), the ability to rapidly and accurately compare quantities presented non-symbolically, has been proposed as a precursor to mathematics skills. Earlier work reported low heritability of approximate number sense, which was interpreted as evidence that approximate number sense acts as a fitness trait. However, viewing ANS as a fitness trait is discordant with findings suggesting that individual differences in approximate number sense acuity correlate with mathematical performance, a trait with moderate genetic effects. Importantly, the shared etiology of approximate number sense, mathematics, and general cognitive ability has remained unexamined. Thus, the etiology of approximate number sense and its overlap with math and general cognitive ability was assessed in the current study with two independent twin samples (N = 451 pairs). Results suggested that ANS acuity had moderate but significant additive genetic influences. ANS also had overlap with generalist genetic mechanisms accounting for variance and covariance in mathematics and general cognitive ability. Furthermore, ANS may have genetic factors unique to covariance with mathematics beyond overlap with general cognitive ability. Evidence across both samples was consistent with the proposal that the etiology of approximate number sense functions similar to that of mathematics and general cognitive skills.
Sarah the chimpanzee was the primary participant in David Premack’s language studies initiated at University of California at Santa Barbara in 1967. The first author was an undergraduate assistant training Sarah from 1967 to 1969. This article describes some of the early work with Sarah and our recent search for her. Sarah’s whereabouts during the intervening years, and subsequent reunion with her in 2016 at Chimp Haven, a chimpanzee sanctuary in Louisiana, are described. It was found that despite her illness, Sarah engaged with the first author and demonstrated that she remembered him and the mechanics of the communication procedure that served as the foundation for testing Sarah’s cognitive reasoning abilities as they pertained to language. There was no evidence she remembered any of the 5 symbolic nouns that were presented during a matching-to-sample procedure. The authors expressed their gratitude to the staff at Chimp Haven for the excellent care of Sarah.
I define a natural accountant as an individual who can keep track of quantities coming into or leaving an account containing some type of commodity. I will argue that chimpanzees are very good at this type of accounting although in some instances their performance breaks down in ways that offer interesting insights into the emergence of arithmetic capacities. I will discuss how chimpanzees deal with operations that involve addition and subtraction of discrete quantities and other forms of quantity accounting. After outlining this evidence in favor of chimpanzee accounting in these kinds of tests, I offer some preliminary data from more naturalistic experimental methods that might further refine our understanding of how chimpanzees deal with quantitative and numerical information in foraging-like situations that better approximate real world situations. These accounting capacities reflect the emergence of arithmetic competence and the evolutionary foundations of mathematics.
A methodological approach to investigate the ability of animals to the formation of concepts and symboliza-tion is discussed. The data on the ability of birds with the high level of brain complexity (parrots and corvids) to comprehend equivalent relationships between tokens and the concept of number, as well as the use of nu-merical symbols are analyzed. The results of these experiments confirm the ideas that the ability of symbol-ization is inherent not only to higher mammals, but also to birds.
For over 30 years, I have used a modeling technique (the model/rival or M/R procedure) to train Grey parrots to use an allospecific code (English speech) referentially, and then employed the code to test their cognitive abilities. The oldest bird, Alex, labeled 〉50 objects, seven colors, five shapes, quantities to eight, three categories (color, shape, material) and used "no," "come here," "wanna go X," and "want Y" (X, Y being appropriate location or item labels). He combined labels to identify, request, comment on, or refuse 〉150 items and to alter his environment. He processed queries to judge category, relative size, quantity, presence or absence of similarity/difference in attributes, show label comprehension and a zero-like concept; he demonstrated some understanding of phonological awareness, and numerical competence more comparable to that of young children than to nonhumans. His requests were intentional. He consequently exhibited capacities presumed limited to humans or nonhuman primates. Younger birds are acquiring similar competence.
Wild chimpanzees (Pan troglodytes) live in a surrounding environment that includes mountains, rivers, forests, grasslands, and an enormous variety of plants and animals that inhabit it. Through coexistence and competition with those living things, wild chimpanzees learn numerous strategies to survive throughout their lives. They learn, for example, to identify poisonous and edible foods, the locations and times for getting food, and how to access a food patch, find a food at the patch, and process the food for consumption. Along with that learning, they acquire knowledge of materials that are available as tools. Moreover, through identification of other members of a party to which they themselves belong, chimpanzees form social groups.Members of a group sometimes cooperate to hunt and share prey.
The main approaches to studying the ability of animals to form concepts and symbolization are discussed. The available data on the capabilities of highly organized birds (parrots and corvids) to comprehend equivalence between signs and the concept of number are analyzed. The new own data on the ability of hooded crows for symbolization are described. The considered results confirm the concept that the capability for symbolization is inherent not only to higher mammals, but also to highly organized representatives of birds.
This chapter advances a theory about the relation between technology and intelligence. The chapter proposes that there are three privileged ways for individuals to relate to technology. First, individuals invent new technologies to solve past and present practical problems. Second, individuals receive a technology as a part of their cultural heritage. Third, individuals adapt to technologies that are new innovations in their cultural background. These different paths to technology involve different processes of assimilation and accommodation. By inventing new technologies, the individual is shaping the environment, so his or her relation with the technology is more or less transparent. Technologies that are received by cultural transmission involve the transmission of intentional affordances and, accordingly, shape human behavior. Finally, adaptation to new technologies involves a process of reciprocal adjustment between the technology and the individual. The authors propose that these three paths to technology represent "ideals." In effect, these paths cohabit so the relation between mind and technology is not a deterministic one. The chapter closes by suggesting that an intelligent (and wise) use of technology involves awareness of the modifiability of both mind and technology. (PsycINFO Database Record (c) 2008 APA, all rights reserved) (from the preface)
Fruit foragers are known to use spatial memory to relocate fruit, yet it is unclear how they manage to find fruit in the first place. In this study, we investigated whether chimpanzees (Pan troglodytes verus) in the Taï National Park make use of fruiting synchrony, the simultaneous emergence of fruit in trees of the same species, which can be used together with sensory cues, such as sight and smell, to discover fruit. We conducted observations of inspections, the visual checking of fruit availability in trees, and focused our analyses on inspections of empty trees, so to say "mistakes". Learning from their "mistakes", we found that chimpanzees had expectations of finding fruit days before feeding on it and significantly increased inspection activity after tasting the first fruit. Neither the duration of feeding nor density of fruit-bearing trees in the territory could account for the variation in inspection activity, which suggests chimpanzees did not simply develop a taste for specific fruit on which they had fed frequently. Instead, inspection activity was predicted by a botanical feature-the level of synchrony in fruit production of encountered trees. We conclude that chimpanzees make use of the synchronous emergence of rainforest fruits during daily foraging and base their expectations of finding fruit on a combination of botanical knowledge founded on the success rates of fruit discovery, and a categorization of fruit species. Our results provide new insights into the variety of food-finding strategies employed by primates and the adaptive value of categorization capacities.
This chapter addresses the proposition that the study of the role of culture in cognitive development must be conducted in a broad, historical perspective that includes the history of the human species, the cultural history of the human group into which children are born, and their engagement in the cultural practices that serve as the proximal environments of development. The issue of phylogenetic history is pursued in two complementary ways: evidence of a “two-way path of causation” between biological and cultural change in the process of hominization following the appearance of Australopithecus and comparative studies on nonhuman primates, especially chimpanzees and bonobos which has produced abundant recent evidence that these near cousins of homo sapiens manifest the presence of culture, defined as behavioral conformity spread or maintained by nongenetic means through processes of social learning. The importance of cultural history is discussed in terms of several strategies. The first is illustrated by “cross-sectional” studies from societies that have undergone very rapid cultural change; in this research, people of the same age who have or have not been exposed to the cultural change are compared. The second strategy involves “longitudinal” studies in which psychologists have been able to return to areas undergoing cultural change at intervals of approximately 20 years and studied the changes in cognitive performance among the population that have occurred in relation to the nature of the cultural change. The third strategy is to study cognitive changes associated with the historically specific institution of formal education. The fourth strategy, akin to the second, is to trace changes in IQ scores over historical time. The role of participation in cultural practices is analyzed in several ways including: cognitive development in “core domains” such as number, naive psychology, theory of mind and biology, noncore domains of social significance, and autobiographical memory. This work draws upon both within-culture and cross-cultural comparisons as key data. The chapter concludes by pointing to a variety of converging evidence to support the basic idea that the role of culture in cognitive development is indeed productively viewed in a broad developmental/historical perspective in which phylogeny, cultural-history, and participation in cultural practices in ontogeny are seen as co-constituting human ontogeny.
Keywords:
activity;
co-evolution;
core domain;
culture;
cultural practice;
schooling;
skeletal principle
It is unclear whether nonhuman animals can use physical tokens to flexibly represent various quantities by combining token values. Previous studies showed that chimpanzees (Pan troglodytes) and a macaque (Macaca mulatta) were only partly successful in tests involving sets of different-looking food containers representing different food quantities, while some capuchin monkeys (Cebus apella) have shown greater success in tests involving sets of various concrete objects representing different food quantities. Some of the discrepancy in results between these studies may be attributed to the different methods used. In an effort to reconcile these discrepancies, we presented two primates species, chimpanzees and capuchin monkeys, with two token tasks. The critical test in each task involved summing the value of multiple tokens of different types to make accurate quantity judgments. We found that, using either method, individuals of both species learned to associate individual tokens with specific quantities, as well as successfully compare individual tokens to one another or to sets of visible food items. However, regardless of method, only a few individuals exhibited the capacity to sum multiple tokens of different types and then use those summed values to make an optimal response. This suggests that flexible combination of symbolic stimuli in quantity judgments tasks is within the abilities of chimpanzees and capuchins but does not characterize the majority of individuals. Furthermore, the results suggest the need to carefully examine specific methodological details that may promote or hinder such possible representation.
Abstract: To explore the degree to which chimpanzee (Pan troglodytes) food vocalizations specifically reference a particular food (e.g. carrot, apple, grape, etc.) or more generally reflect categorical food value (low, medium, or high), a critical elaboration of Hallberg, Nelson, and Boysen (2003) was undertaken. Three phases of this experimental endeavor included: 1) stimuli recording and assembly, 2) experimental presentation of the stimuli via playback paradigm to gather behavioral response data, 3) in-depth acoustic analysis of the stimuli in an attempt to explain chimpanzee response patterns. Stimuli were digitally captured (video and acoustic) during controlled presentation of specific food items to captive chimpanzees. Stimuli were randomly presented to five adult subjects at their "work station" via speaker. Digital photos of four foods immediately appeared in a 2x2 matrix on a touch screen monitor (one photo matching the food presented during the initial recording of the vocalization). Subjects were non-differentially rewarded for selecting a food item. Statistical analysis determined percent correct for food specificity and category value, error patterns as well as context bias relative to food picture placement in the matrix (bias for food categories represented more than once in each choice array). Acoustic analysis of the 36 vocalizations used during the playback experiment included identification of salient features (e.g. bout element structure, element pulse structure, amplitude, etc.) that may contribute to referential qualities. As hypothesized, subjects exhibited statistically significant food specific and category associations, particularly for those vocalizations associated with high value foods. Discriminant function analysis of acoustic features grouped vocalizations by category value. 1.83 MB Title from first page of PDF file. Thesis (Ph. D.)--Ohio State University, 2007. Includes bibliographical references (p. 60-63). Available online via OhioLINK's ETD Center System requirements: World Wide Web browser and PDF viewer.
With nonnumerousness dimensions (e.g., pattern, area) controlled, three cards with two to seven black-filled circles were presented on each trial. If the center of three conditional cue lights was illuminated, the monkey was reinforced for selecting the card with the fewest circles; if two lights were on, the card with the intermediate number of circles was correct; and if three lights were on, the card with the most circles was correct. Training began with one conditional cue light and proceeded to the three-light condition. Then the one- and three-light conditions were presented randomly and concurrently, followed by the two-light condition. Finally, one, two, or three lights were presented randomly and concurrently. Only one monkey met criterion on all training stages, but another monkey succeeded also through the intermediate-number condition. It was concluded that the squirrel monkey is capable of relative numerousness judgments, including ordinal numerousness judgments. Additional discussion was concerned with the hypothesis suggested by Brown, Lenneberg, and Ettlinger (1978) that the ability to use quantitative concepts is a prerequisite to the acquisition of language.
Considers a number of models that specify how children and adults solve single-digit addition problems. It is shown that the most adequate of these for children's response latencies is a model that assumes the existence of a counter with 2 operations: setting and incrementing. The child adds 2 digits, m and n, by setting this counter to max (m,n) and then incrementing it min (m,n) times. This model also accounts for adults' latencies, though with a drastically reduced incrementing time. Some theoretical issues raised by this reduced time are considered, and an alternative model is suggested which assumes that adults usually use a memory look-up process with homogeneous retrieval times, but occasionally revert back to the counting process used by children. (2l ref.) (PsycINFO Database Record (c) 2012 APA, all rights reserved)
Examined the patterns of reaction times that emerge when a child is taught a specific problem-solving procedure and then given extensive practice over many weeks. In 2 experiments, 10 pre-schoolers (average age 4 yrs 8 mo) who knew how to count but were unacquainted with arithmetic were taught a simple algorithm for solving single-digit addition problems and were then given extended practice. An S performing this algorithm would generate reaction times proportional to the sum of the addends. The main finding shows that, at the end of the extended practice phase, data of many Ss were best fitted by a different model predicting reaction times proportional to the minimum addend. This implies that these Ss were no longer using the algorithm they were originally taught. It is also interpreted as suggesting that they invented a more efficient procedure. (PsycINFO Database Record (c) 2012 APA, all rights reserved)
Four major conclusions were supported in 7 runway experiments: Rats count; rats routinely and perhaps automatically count reinforcing events; counting reinforcing events is of importance for understanding instrumental learning and performance; and counting is the result of several independent coordinated cognitive processes. The results suggested counting rather than some simpler numerical ability because (a) they cannot be ascribed to other mechanisms (e.g., an identical–nonidentical discrimination or subitizing; (b) qualitatively different reinforcers were categorized as both similar and different for counting purposes; (c) the order-irrelevance principle was followed; (d) abstract tags were assigned on the basis of number of events; and (e) assignment occurred according to complex and situationally determined rules that were themselves abstract. Number cues associated with reinforcing events are often valid in learning investigations but are invariably confounded with various, equally valid number and duration cues (related to trials, responses, etc.). Reinforcers were counted when confounded with these other cues, which supported the sequential view that rats are highly disposed to using number cues associated with reinforcers and normally do so in instrumental situations. There was some evidence that one or more of the confounded events (unidentified) provided cues that were used by the rat, but this was of minor significance. (PsycINFO Database Record (c) 2012 APA, all rights reserved)
Three chimpanzees (
Pan troglodytes) were trained to discriminate among pairs of boxes in an ABCDE-ordered series. The 2nd member of each pair was reinforced, until all 4 training pairs were learned. During novel tests the nonadjacent BD pair was presented, and all 3 animals reliably selected D. In Exp 2, numerals 1–5 served as stimuli. One chimpanzee reliably selected the larger numeral 4 during testing with a nonadjacent pair (2–4), and 2 chimps showed no preference. In a 2nd phase, the same chimp demonstrated proficiency at reversing the task, reliably selecting the smaller of the 2–4 pair. In Exp 4, after additional training, a 2nd test, which included novel test pairs composed of numbers that had not been used during training, was completed. Two of 3 animals were 100% correct on Trial 1 for all novel pairs. The results suggest that chimpanzees with experience in number concepts may recognize the ordinal character of numbers. (PsycINFO Database Record (c) 2012 APA, all rights reserved)
This paper reports the establishment of a discrimination based upon the number three in a male raccoon. Following a 6-month
training period, the subject was able to select a clear Plexiglas cube containing 3 objects (grapes or small metal bells)
from an array of cubes containing 1, 2, 3, 4, and 5 items. The results confirm previous reports of “intelligence” in the raccoon,
and extend the number of species in which sensitivity to number has been demonstrated (see review by Davis & Memmott, 1982).
We describe the preverbal system of counting and arithmetic reasoning revealed by experiments on numerical representations in animals. In this system, numerosities are represented by magnitudes, which are rapidly but inaccurately generated by the Meck and Church (1983) preverbal counting mechanism. We suggest the following. (1) The preverbal counting mechanism is the source of the implicit principles that guide the acquisition of verbal counting. (2) The preverbal system of arithmetic computation provides the framework for the assimilation of the verbal system. (3) Learning to count involves, in part, learning a mapping from the preverbal numerical magnitudes to the verbal and written number symbols and the inverse mappings from these symbols to the preverbal magnitudes. (4) Subitizing is the use of the preverbal counting process and the mapping from the resulting magnitudes to number words in order to generate rapidly the number words for small numerosities. (5) The retrieval of the number facts, which plays a central role in verbal computation, is mediated via the inverse mappings from verbal and written numbers to the preverbal magnitudes and the use of these magnitudes to find the appropriate cells in tabular arrangements of the answers. (6) This model of the fact retrieval process accounts for the salient features of the reaction time differences and error patterns revealed by experiments on mental arithmetic. (7) The application of verbal and written computational algorithms goes on in parallel with, and is to some extent guided by, preverbal computations, both in the child and in the adult.
A chimpanzee (Pan troglodytes), trained to count foods and objects by using Arabic numbers, demonstrated the ability to sum arrays of 0-4 food items placed in 2 of 3 possible sites. To address representational use of numbers, we next baited sites with Arabic numbers as stimuli. In both cases performance was significantly above chance from the first sessions, which suggests that without explicit training in combining arrays, the animal was able to select the correct arithmetic sum for arrays of foods or Arabic numbers under novel test conditions. These findings demonstrate that counting strategies and the representational use of numbers lie within the cognitive domain of the chimpanzee and compare favorably with the spontaneous use of addition algorithms demonstrated in preschool children.
In this research, we asked whether 2 chimpanzee (Pan troglodytes) subjects could reliably sum across pairs of quantities to select the greater total. Subjects were allowed to choose between two trays of chocolates. Each tray contained two food wells. To select the tray containing the greater number of chocolates, it was necessary to sum the contents of the food wells on each tray. In experiments where food wells contained from zero to four chocolates, the chimpanzees chose the greater value of the summed wells on more than 90% of the trials. In the final experiment, the maximum number of chocolates assigned to a food well was increased to five. Choice of the tray containing the greater sum still remained above 90%. In all experiments, subjects reliably chose the greater sum, even though on many trials a food well on the "incorrect" tray held more chocolates than either single well on the "correct" tray. It was concluded that without any known ability to count, these chimpanzees used some process of summation to combine spatially separated quantities. Speculation regarding the basis for summation includes consideration of perceptual fusion of pairs of quantities and subitization.
Recent studies have examined linguistic abilities in apes. However, although human mathematical abilities seem to be derived from the same foundation as those in language, we have little evidence for mathematical abilities in apes (but for exceptions see refs 7-10). In the present study, a 5-yr-old female chimpanzee (Pan troglodytes), 'Ai', was trained to use Arabic numerals to name the number of items in a display. Ai mastered numerical naming from one to six and was able to name the number, colour and object of 300 types of samples. Although no particular sequence of describing samples was required, the chimpanzee favoured two sequences (colour/object/number and object/colour/number). The present study demonstrates that the chimpanzee was able to describe the three attributes of the sample items and spontaneously organized the 'word order'.
Apart from replicating findings of other experimenters, the present authors show that Ss can make a fast "countability" judgment indicating whether or not they could, if requested, give an accurate numerosity response. These judgments were fast and produced a "yes" response within the subitizing range and a "no" response thereafter. Developmental data have indicated that children count arrays as small as 2 and 3; adults seem to give a more automatic response, shown also in the fast RTs to those array sizes. The suggestion that this response is an acquired one to certain frequently appearing canonical patterns of 2 and 3 events (pairs/lines and triples/triangles) was explored in an experiment in which Ss were given canonical patterns of arrays of up to 10. Results show that within few trials, the response to these canonical patterns was usually as fast and accurate as the response to the smaller (1–3) array sizes. Data also demonstrate that the slope for array sizes from 4 to 6 with short exposure time was indistinguishable from the slope for array sizes from 4 to 15 under an unlimited exposure condition. It is concluded, on the basis of 5 studies with 48 adults, that the RT function found in subitizing consisted of 3 processes: a response to arrays of 1–3 that was fast and accurate and was based on acquired canonical patterns; a response to arrays 4 to 6 or 7 that was based on mental counting; and an estimating response for arrays larger than 6 that could be held in consciousness for mental counting. (36 ref)
A chimpanzee (Pan troglodytes) experienced in counting arrays of 0-7 items and trained for comprehension of number symbols, spontaneously displayed a variety of indicating acts (e.g., pointing, touching, and rearranging items) during counting. Twenty-five sessions were videotaped, and all trials were evaluated for the relations among number of items presented, number of indicating acts displayed, and the Arabic number selected to represent the array. Significant correlations included the relations between number of items and the cardinal number selected by the animal, between the number of items and indicating acts displayed by the chimpanzee, and between the number of indicating acts and the numeral selected. These data suggest that the use of indicating acts by this animal may have functional significance and serves as an organizing schema, comparable to similar behaviors observed in children in the early stages of learning to count.
Two chimpanzees were trained to select among 2 different amounts of candy (1-6 items). The task was designed so that selection of either array by the active (selector) chimpanzee resulted in that array being given to the passive (observer) animal, with the remaining (nonselected) array going to the selector. Neither animal was able to select consistently the smaller array, which would reap the larger reward. Rather, both animals preferentially selected the larger array, thereby receiving the smaller number of reinforcers. When Arabic numerals were substituted for the food arrays, however, the selector animal evidenced more optimal performance, immediately selecting the smaller numeral and thus receiving the larger reward. These findings suggest that a basic predisposition to respond to the perceptual-motivational features of incentive stimuli can interfere with task performance and that this interference can be overridden when abstract symbols serve as choice stimuli.
Five chimpanzees with training in counting and numerical skills selected between 2 arrays of different amounts of candy or 2 Arabic numerals. A reversed reinforcement contingency was in effect, in which the selected array was removed and the subject received the nonselected candies (or the number of candies represented by the nonselected Arabic numeral). Animals were unable to maximize reward by selecting the smaller array when candies were used as array elements. When Arabic numerals were substituted for the candy arrays, all animals showed an immediate shift to a more optimal response strategy of selecting the smaller numeral, thereby receiving the larger reward. Results suggest that a response disposition to the high-incentive candy stimuli introduced a powerful interference effect on performance, which was effectively overridden by the use of symbolic representations.
The results of this experiment show that the rhesus monkey can gain moderate proficiency in acquisition of the concept of threeness. (PsycINFO Database Record (c) 2012 APA, all rights reserved)
This chapter discusses the higher mental functions of a home-raised chimpanzee. The use of human standards of comparison in determining the intellectual range of a nonhuman species imposes considerable demands on the ingenuity of the investigators. They must offer their subject the same opportunity to acquire prerequisite skills as is customarily given to the humans of equivalent age. Apparatus must be designed that the animal can handle physically in a setting that has meaning in terms of its everyday life. Communication can be expected to emerge repeatedly as the worst problem of all. The investigators must convey the rules of the game without giving away the answers. They must provide their nonspeaking subject with a means of unambiguous response. This chapter discusses Viki project to explore chimpanzee capabilities by intensive study of one presumably normal but sophisticated individual. Nothing in Viki's family history or in the course of her physical development suggested that she was an exceptional chimpanzee.
A four-year-old female chimpanzee was trained to use symbols to name 11 colours: red, orange, yellow, green, bluc, purple, pink, brown, grey, and black. The chimpanzee was then required to name various colour chips from the Munsell colour charts. Colour classification by the chimpanzee was similar to that in a human observer tested under the same condition. Both the chimpanzee and the human observer divided the colour space into the clusters of a broad area within which a single colour name was applied consistently. Areas of consistent colour naming were separated by narrower areas in which the names applied to the two adjacent areas were used and the response latencies were long. These results suggest that, not only the perception of colours, but also the use of colour names have characteristics in common between the human and the chimpanzee.
I Number Words.- 1 Introduction and Overview of Different Uses of Number Words.- 2 The Number-Word Sequence: An Overview of Its Acquisition and Elaboration.- II Correspondence Errors in Counting Objects.- 3 Correspondence Errors in Children's Counting.- 4 Effects of Object Arrangement on Counting Correspondence Errors and on the Indicating Act.- 5 Effects of Object Variables and Age of Counter on Correspondence Errors Made When Counting Objects in Rows.- 6 Correspondence Errors in Children's Counting: A Summary.- III Concepts of Cardinality.- 7 Children's Early Knowledge About Relationships Between Counting and Cardinality.- 8 Later Conceptual Relationships Between Counting and Cardinality: Addition and Subtraction of Cardinal Numbers.- 9 Uses of Counting and Matching in Cardinal Equivalence Situations: Equivalence and Order Relations on Cardinal Numbers.- IV Number Words, Counting, and Cardinality: The Increasing Integration of Sequence, Count, and Cardinal Meanings.- 10 Early Relationships Among Sequence Number Words, Counting Correspondence, and Cardinality.- 11 An Overview of Changes in Children's Number Word Concepts from Age 2 Through 8.- References.- Author Index.
[discusses how] studies of numerical competence in the chimpanzee continue to provide new insights into the range and capacity for quantitatively based information processing in this species / suggests that this area remains a rich and fruitful source of contributions to our understanding of animal cognition and behavior
motor tagging during counting / constraints on counting capabilities (PsycINFO Database Record (c) 2012 APA, all rights reserved)
Three untamed
rhesus monkeys were trained to reach for food upon the larger number of sounds (taps), with a fixed interval of time of 1.5 secs. between them, and to refrain from reaching upon the sounding of the smaller number of taps. The number of sounds, within the varying intervals, varied from 1 to 6, 1 being presented with 2, 1 with 3, 2 with 3, and so on, as comparison stimuli to be discriminated by the animal. All three of the subjects learned to discriminate combinations up to 4 sounds per interval, but beyond that number, as between 4 and 5 or 5 and 6, very little learning occurred. Some transfer characterized two of the animals, on stimuli of 3
vs. 4 sounds. The time interval separating the sound components of a stimulus and the quality of the sound rather than the abstract number of taps were found to be effective factors influencing the discrimination. Hesitation, immediately prior to incorrect responses, suggested a real discriminatory process, as did also the gradual merging of the reaching behavior into a form almost identical with the restraint response, affording the animal a ready means of correctly and speedily reacting to the proper stimulus upon its presentation. 2 references. (PsycINFO Database Record (c) 2012 APA, all rights reserved)
Flashes of light, dots on the top of boxes which concealed food, and successive sounds were used in an attempt to determine whether baboons are able to discriminate in terms of number. Discrimination of number may be demonstrated unequivocally only when "the animal is not choosing on the basis of pattern, the number is appreciated in all the sense modalities, the number is recognized in both spatial and temporal dimensions, the animal is not reacting to any property of the component units of the number constellation." With such factors controlled, there was no sure evidence of number discrimination. (PsycINFO Database Record (c) 2012 APA, all rights reserved)
By means of a special apparatus the author investigated the ability of a monkey to discriminate between one and two sounds and one and three sounds. The first problem was learned in 700 trials, but the second was never learned. Attempts to build up the second discrimination led to a disintegration of the first. The discrepancy between these results and Woodrow's findings is explained on the basis that the present experiment called for discrimination based upon the "absolute property of number," whereas Woodrow's investigation called for a discrimination "of temporal sequences of sound stimuli on the basis of relative 'more'ness." (PsycINFO Database Record (c) 2012 APA, all rights reserved)
1. The first attempts to approach the problem of number conception in animals consisted in a training to identify one object out of many by its relative position.
2. The multiple‐choice method, although an advance on previous work, has yielded relatively poor results. The only apparent exception, namely the striking results obtained with finches, is probably due to a technical error.
3. Experiments with a temporal maze have shown that it is extremely difficult for animals to perform a double alternation, and no animal has yet been trained to perform this more than once successively. Claims that some birds are able to select every third out of a line of similar objects are without convincing foundation owing to the lack of adequate control tests.
4. The experiments of Verlaine and his collaborators led to the belief in a genuine number conception in animals, but the lack of satisfactory controls deprives the results of these cleverly devised experiments of validity.
5. Bierens de Haan repeated these experiments on a sound basis with the necessary controls. He found that the animals trained themselves to perform two or three single actions in a certain rhythm, and that consequently increasing the intervals between the single actions destroyed the training.
6. Systematic investigation of the two basic abilities of performing an action a certain number of times and of discriminating between two quantities of objects gave the interesting result that the limit in both cases is respectively 6 or 5:6 for all animals investigated. The discrimination between 6 and 7 has never been achieved.
7. Experiments with parrakeets gave better results than with pigeons, but both groups were surpassed by the achievements of jackdaws. The latter were able to learn four different kinds of number training, and to make use of them simultaneously. They could also to a certain extent combine both basic abilities. But a close analysis of these surprising accomplishments shows that even here any counting or number conception in the human sense of the word does not exist.
This paper provides a tutorial introduction to numerical cognition, with a review of essential findings and current points of debate. A tacit hypothesis in cognitive arithmetic is that numerical abilities derive from human linguistic competence. One aim of this special issue is to confront this hypothesis with current knowledge of number representations in animals, infants, normal and gifted adults, and brain-lesioned patients. First, the historical evolution of number notations is presented, together with the mental processes for calculating and transcoding from one notation to another. While these domains are well described by formal symbol-processing models, this paper argues that such is not the case for two other domains of numerical competence: quantification and approximation. The evidence for counting, subitizing and numerosity estimation in infants, children, adults and animals is critically examined. Data are also presented which suggest a specialization for processing approximate numerical quantities in animals and humans. A synthesis of these findings is proposed in the form of a triple-code model, which assumes that numbers are mentally manipulated in an arabic, verbal or analogical magnitude code depending on the requested mental operation. Only the analogical magnitude representation seems available to animals and preverbal infants.
Rumbaugh, Savage-Rumbaugh, and Hegel (1987) reported that two chimpanzees (Pan troglodytes) could select, with better than 90% accuracy, the greater of two paired quantities of chocolate chips. In that study, no one quantity of chocolates (from 0 through 5) was used in both pairs on a given trial. We investigated the effect of having one quantity in common (CQ) in both pairs. Whether the other quantities (OQs) of chocolates were both less than or greater than the CQ, summation still occurred. Accuracy was primarily a function of the ratios of sums to be differentiated. This finding substantiated the earlier conclusion that summation was based on both quantities of each pair and not on some simpler process such as the avoidance of the tray with the smallest single amount or selection of the tray with the single largest amount.
Two monkeys were reinforced for responding to the card which displayed fewer number of entities (three randomly selected sizes of filled circles) than the other card in any given pair. Area and brightness cues were controlled (at least for the successive numerousness discriminations), as were specific-pattern learning cues. Training proceeded in the order 2 versus 7 (2:7), 2:6, 2:5...2:3, 3:7, 3:6...3:4, etc., until it was judged that the monkeys were unlikely to attain the stringent criteria for discrimination. Both monkeys met criteria on the 7:8 discrimination, and one monkey met criteria on the 8:9 discrimination. It was concluded that the monkeys' numerousness judgments were made on a conceptual basis and that, among nonhuman animals, the evidence for such judgments appears to be limited to apes and monkeys.
The similarity of animal counting and timing processes was demonstrated in four experiments that used a psychophysical choice procedure. In Experiment 1, rats initially learned a discrimination between a two-cycle auditory signal of 2-sec duration and an eight-cycle auditory signal of 8-sec duration. For the number discrimination test, the number of cycles was varied, and the signal duration was held constant at an intermediate value. For the duration discrimination test, the signal duration was varied, and the number of cycles was held constant at an intermediate value. Rats were equally sensitive to a 4:1 ratio of counts (with duration controlled) and a 4:1 ratio of times (with number controlled). The point of subjective equality for the psychophysical functions that related response classification to signal value was near the geometric mean of the extreme values for both number and duration discriminations. Experiment 2 demonstrated that 1.5 mg/kg of methamphetamine administered intraperitoneally shifted the psychophysical functions for both number and duration leftward by approximately 10%. Experiment 3 demonstrated that the magnitude of cross-modal transfer from auditory signals to cutaneous signals was similar for number and duration. In Experiment 4 the mapping of number onto duration demonstrated that a count was approximately equal to 200 msec. The psychophysical functions for number and duration were fit with a scalar expectancy model with the same parameter values for each attribute. The conclusion was that the same internal mechanism is used for counting and timing. This mechanism can be used in several modes: the "event" mode for counting or the "run" and the "stop" modes for timing.
Comparison of quantitative reasoning in nonhuman animals has suffered, on the one hand, from the methodological failure to do properly controlled studies of number (for review, recent examples and exceptions see refs 1, 2; 3, 4; and 5, 6 respectively), and on the other, from the conceptual failure to consider forms of quantitative reasoning other than number. An approach to mathematical reasoning may profit from the study of proportion, a continuous quantity, in addition to number, a discrete quantity. In the experiments reported here, an adult chimpanzee and four juveniles were tested for their knowledge of `proportion' and `number' with conceptual match-to-sample tasks. The juveniles failed but the adult successfully matched exemplars of the proportions 1/4, 1/2, 3/4 and 1, and the numbers 1, 2, 3 and 4, when the sample and alternatives were highly dissimilar physically (such as in shape, colour) and in other quantitative (for example mass, area, length) dimensions. The results reveal the presence of simple `proportion' and `number' concepts in a nonhuman primate.
Three chimpanzees (Pan troglodytes) were trained to discriminate among pairs of boxes in an ABCDE-ordered series. The 2nd member of each pair was reinforced, until all 4 training pairs were learned. During novel tests the nonadjacent BD pair was presented, and all 3 animals reliably selected D. In Experiment 2, numerals 1-5 served as stimuli. One chimpanzee reliably selected the larger numeral 4 during testing with a nonadjacent pair (2-4), and 2 chimps showed no preference. In a 2nd phase, the same chimp demonstrated proficiency at reversing the task, reliably selecting the smaller of the 2-4 pair. In Experiment 4, after additional training, a 2nd test, which included novel test pairs composed of numbers that had not been used during training, was completed. Two of 3 animals were 100% correct on Trial 1 for all novel pairs. The results suggest that chimpanzees with experience in number concepts may recognize the ordinal character of numbers.
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