Exact and approximate arithmetic in an Amazonian indigene group

How Humans Count: Numerosity and the Parietal Cortex

Numerosity (the number of objects in a set), like color or movement, is a basic property of the environment. Animal and human brains have been endowed by evolution by mechanisms based on parietal circuitry for representing numerosity in an highly abstract, although approximate fashion. These mechanisms are functional at a very early age in humans and spontaneously deployed in the wild by animals of different species. The recent years have witnessed terrific advances in unveiling the neural code(s) underlying numerosity representations and showing similarities as well as differences across species. In humans, during development, with the introduction of symbols for numbers and the implementation of the counting routines, the parietal system undergoes profound (yet still largely mysterious) modifications, such that the neural machinery previously evolved to represent approximate numerosity gets partially “recycled” to support the representation of exact number.

Origins of mathematical intuitions: the case of arithmetic

Mathematicians frequently evoke their "intuition" when they are able to quickly and automatically solve a problem, with little introspection into their insight. Cognitive neuroscience research shows that mathematical intuition is a valid concept that can be studied in the laboratory in reduced paradigms, and that relates to the availability of "core knowledge" associated with evolutionarily ancient and specialized cerebral subsystems. As an illustration, I discuss the case of elementary arithmetic. Intuitions of numbers and their elementary transformations by addition and subtraction are present in all human cultures. They relate to a brain system, located in the intraparietal sulcus of both hemispheres, which extracts numerosity of sets and, in educated adults, maps back and forth between numerical symbols and the corresponding quantities. This system is available to animal species and to preverbal human infants. Its neuronal organization is increasingly being uncovered, leading to a precise mathematical theory of how we perform tasks of number comparison or number naming. The next challenge will be to understand how education changes our core intuitions of number.

Arithmetic in newborn chicks

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

From numerical concepts to concepts of number

Many experiments with infants suggest that they possess quantitative abilities, and many experimentalists believe that these abilities set the stage for later mathematics: natural numbers and arithmetic. However, the connection between these early and later skills is far from obvious. We evaluate two possible routes to mathematics and argue that neither is sufficient: (1) We first sketch what we think is the most likely model for infant abilities in this domain, and we examine proposals for extrapolating the natural number concept from these beginnings. Proposals for arriving at natural number by (empirical) induction presuppose the mathematical concepts they seek to explain. Moreover, standard experimental tests for children's understanding of number terms do not necessarily tap these concepts. (2) True concepts of number do appear, however, when children are able to understand generalizations over all numbers; for example, the principle of additive commutativity (a+b=b+a). Theories of how children learn such principles usually rely on a process of mapping from physical object groupings. But both experimental results and theoretical considerations imply that direct mapping is insufficient for acquiring these principles. We suggest instead that children may arrive at natural numbers and arithmetic in a more top-down way, by constructing mathematical schemas.

Compressed Scaling of Abstract Numerosity Representations in Adult Humans and Monkeys

There is general agreement that nonverbal animals and humans endowed with language possess an evolutionary precursor system for representing and comparing numerical values. However, whether nonverbal numerical representations in human and nonhuman primates are quantitatively similar and whether linear or logarithmic coding underlies such magnitude judgments in both species remain elusive. To resolve these issues, we tested the numerical discrimination performance of human subjects and two rhesus monkeys (Macaca mulatta) in an identical delayed match-to-numerosity task for a broad range of numerosities from 1 to 30. The results demonstrate a noisy nonverbal estimation system obeying Weber's Law in both species. With average Weber fractions in the range of 0.51 and 0.60, nonverbal numerosity discriminations in humans and monkeys showed similar precision. Moreover, the detailed analysis of the performance distributions exhibited nonlinearly compressed numerosity representations in both primate species. However, the difference between linear and logarithmic scaling was less pronounced in humans. This may indicate a gradual transformation of a logarithmic to linear magnitude scale in human adults as the result of a cultural transformation process during the course of mathematical education.

Beyond the number domain

In a world without numbers, we would be unable to build a skyscraper, hold a national election, plan a wedding or pay for a chicken at the market. The numerical symbols used in all these behaviors build on the approximate number system (ANS) which represents the number of discrete objects or events as a continuous mental magnitude. Here, we first discuss evidence that the ANS bears a set of behavioral and brain signatures that are universally displayed across animal species, human cultures and development. We then turn to the question of whether the ANS constitutes a specialized cognitive and neural domain - a question central to understanding how this system works, the nature of its evolutionary and developmental trajectory and its physical instantiation in the brain.

How does the mind work? Insights from biology

Cognitive scientists must understand not just what the mind does, but how it does what it does. In this paper, I consider four aspects of cognitive architecture: how the mind develops, the extent to which it is or is not modular, the extent to which it is or is not optimal, and the extent to which it should or should not be considered a symbol-manipulating device (as opposed to, say, an eliminative connectionist network). In each case, I argue that insights from developmental and evolutionary biology can lead to substantive and important compromises in historically vexed debates.

Look Ma, no fingers! Are children numerical solipsists?

I ask whether it is necessary that principles of number be mentally represented and point to the role of language in determining cultural variation. Some cultures possess extensive counting systems that are finite. I suggest that learning number principles is similar to learning conservation and, as such, might be derived from learning about the empirical properties of objects and other individuals in combinations.

Finger counting: The missing tool?

Rips et al. claim that the principles underlying the structure of natural numbers cannot be inferred from interactions with the physical world. However, in their target article they failed to consider an important source of interaction: finger counting. Here, we show that finger counting satisfies all the conditions required for allowing the concept of numbers to emerge from sensorimotor experience through a bottom-up process.

The innate schema of natural numbers does not explain historical, cultural, and developmental differences

Rips et al.'s proposition cannot account for the facts that (1) a historical look at the word number systems suggests that the concept of natural numbers has been progressively elaborated; (2) people from cultures without an elaborate counting system do not master the concept of natural numbers; (3) children take time to master natural numbers; and (4) the competing advantage of the postulated math schema in the natural selection process is not obvious.

Behavioral and prefrontal representation of spatial proportions in the monkey

Primate brains are equipped with evolutionarily old and dedicated neural circuits so that they can grasp absolute quantities, such as the number of items or the length of a line. Absolute magnitude, however, is often not informative enough to guide decisions in conflicting social and foraging situations that require an assessment of quantity ratios. We report that rhesus monkeys can discriminate proportions (1:4, 2:4, 3:4, and 4:4) specified by bars differing in lengths and that they can do so at a precision comparable to that shown by humans; the monkeys thus demonstrate an abstract understanding of proportionality. Moreover, neurons in the lateral prefrontal cortex selectively responded to preferred proportions regardless of the exact physical appearance of the stimuli. These results support the hypothesis that nonhuman primates can judge proportions and utilize the underlying information in behaviorally relevant situations.

Neural correlates of approximate quantification strategies in young and older adults: an fMRI study

Young and older adults assessed the approximate number of dots in collections including between 20 and 50 dots, with two strategies. The benchmark strategy is based on retrieving memory representations of quantities after visually scanning stimulus. The anchoring strategy involves both enumeration and estimation processes. Brain activations and performance were analyzed as a function of strategies, size of collections and age. Executing the benchmark strategy produced faster performance. It was associated with increased activity of a bilateral parieto/occipital and insular cortical network, including the postcentral gyrus, the cuneus, the middle occipital gyrus, and the insula. In addition to these bilateral activations, the benchmark strategy activated right prefrontal area. The anchoring strategy activated right superior parietal lobule, bilateral subcortical structures (putamen), and left dorso-lateral prefrontal cortex. The effects of aging on these cortical networks depended on strategies. These results suggest dissociation between two numerosity estimation strategies underlying different cognitive estimation processes and help to clarify age differences in numerosity estimation.

Delays without mistakes: response time and error distributions in dual-task

Background

When two tasks are presented within a short interval, a delay in the execution of the second task has been systematically observed. Psychological theorizing has argued that while sensory and motor operations can proceed in parallel, the coordination between these modules establishes a processing bottleneck. This model predicts that the timing but not the characteristics (duration, precision, variability…) of each processing stage are affected by interference. Thus, a critical test to this hypothesis is to explore whether the qualitiy of the decision is unaffected by a concurrent task.

Methodology/Principal Findings

In number comparison–as in most decision comparison tasks with a scalar measure of the evidence–the extent to which two stimuli can be discriminated is determined by their ratio, referred as the Weber fraction. We investigated performance in a rapid succession of two non-symbolic comparison tasks (number comparison and tone discrimination) in which error rates in both tasks could be manipulated parametrically from chance to almost perfect. We observed that dual-task interference has a massive effect on RT but does not affect the error rates, or the distribution of errors as a function of the evidence.

Conclusions/Significance

Our results imply that while the decision process itself is delayed during multiple task execution, its workings are unaffected by task interference, providing strong evidence in favor of a sequential model of task execution.

The evolution of comparative cognition: is the snark still a boojum?

In "The Snark is a Boojum", Beach [Beach, F.A., 1950. The snark was a boojum. American Psychologist. 5, 115-124] famously asserted that animal psychology embraced too few species and too few problems to deserve the name comparative. Later in the 20th century, others [e.g. Kamil, A.C., 1988. A synthetic approach to the study of animal intelligence. In: Leger, D.W. (Ed.), Comparative Perspectives in Modern Psychology. Nebraska Symposium on Motivation, vol. 35. University of Nebraska Press, Lincoln, NE, pp. 230-257; Shettleworth, S.J., 1993. Where is the comparison in comparative cognition? Alternative research programs. Psychological Science. 4, 179-184] expressed similar concerns about the new subfield of comparative cognition, suggesting that a more biological approach to choice of species and problems was needed to balance a dominant anthropocentrism. The last 10-15 years have seen many new developments, and a recent survey like Beach's reveals a very different picture. Not only are many more species being studied, contributions by researchers from different backgrounds are increasing, and research on comparative cognition is better connected with developmental psychology, behavioral neuroscience, primatology, behavioral ecology, and other fields. Contemporary research addresses three major aspects of cognition about equally: basic processes, physical cognition, and social cognition. This article describes a selected research program from each area, chosen to exemplify current trends and challenges for the field.

Nonsymbolic, approximate arithmetic in children: abstract addition prior to instruction

Do children draw upon abstract representations of number when they perform approximate arithmetic operations? In this study, kindergarten children viewed animations suggesting addition of a sequence of sounds to an array of dots, and they compared the sum to a second dot array that differed from the sum by 1 of 3 ratios. Children performed this task successfully with all the signatures of adults' nonsymbolic number representations: accuracy modulated by the ratio of the sum and the comparison quantity, equal performance for within- and cross-modality tasks and for addition and comparison tasks, and performance superior to that of a matched subtraction task. The findings provide clear evidence for nonsymbolic numerical operations on abstract numerical quantities in children who have not yet been taught formal arithmetic.

Numerical thought with and without words: Evidence from indigenous Australian children

Are thoughts impossible without the words to express them? It has been claimed that this is the case for thoughts about numbers: Children cannot have the concept of exact numbers until they know the words for them, and adults in cultures whose languages lack a counting vocabulary similarly cannot possess these concepts. Here, using classical methods of developmental psychology, we show that children who are monolingual speakers of two Australian languages with very restricted number vocabularies possess the same numerical concepts as a comparable group of English-speaking indigenous Australian children.

Development of neural networks for exact and approximate calculation: a FMRI study

Neuroimaging findings in adults suggest exact and approximate number processing relying on distinct neural circuits. In the present study we are investigating whether this cortical specialization is already established in 9- and 12-year-old children. Using fMRI, brain activation was measured in 10 third- and 10 sixth-grade school children and 20 adults during trials of symbolic approximate (AP) and exact (EX) calculation, as well as non-symbolic magnitude comparison (MC) of objects. Children activated similar networks like adults, denoting an availability and a similar spatial extent of specified networks as early as third grade. However, brain areas related to number processing become further specialized with schooling. Children showed weaker activation in the intraparietal sulcus during all three tasks, in the left inferior frontal gyrus during EX and in occipital areas during MC. In contrast, activation in the anterior cingulate gyrus, a region associated with attentional effort and working memory load, was enhanced in children. Moreover, children revealed reduced or absent deactivation of regions involved in the so-called default network during symbolic calculation, suggesting a rather general developmental effect. No difference in brain activation patterns between AP and EX was found. Behavioral results indicated major differences between children and adults in AP and EX, but not in MC. Reaction time and accuracy rate were not correlated to brain activation in regions showing developmental changes suggesting rather effects of development than performance differences between children and adults. In conclusion, increasing expertise with age may lead to more automated processing of mental arithmetic, which is reflected by improved performance and by increased brain activation in regions related to number processing and decreased activation in supporting areas.

Exact Equality and Successor Function: Two Key Concepts on the Path towards understanding Exact Numbers

Humans possess two nonverbal systems capable of representing numbers, both limited in their representational power: the first one represents numbers in an approximate fashion, and the second one conveys information about small numbers only. Conception of exact large numbers has therefore been thought to arise from the manipulation of exact numerical symbols. Here, we focus on two fundamental properties of the exact numbers as prerequisites to the concept of exact numbers: the fact that all numbers can be generated by a successor function, and the fact that equality between numbers can be defined in an exact fashion. We discuss some recent findings assessing how speakers of Mundurucu (an Amazonian language), and young western children (3-4 years old) understand these fundamental properties of numbers.

Visual working memory capacity and proactive interference

BACKGROUND

Visual working memory capacity is extremely limited and appears to be relatively immune to practice effects or the use of explicit strategies. The recent discovery that visual working memory tasks, like verbal working memory tasks, are subject to proactive interference, coupled with the fact that typical visual working memory tasks are particularly conducive to proactive interference, suggests that visual working memory capacity may be systematically under-estimated.

METHODOLOGY/PRINCIPAL FINDINGS

Working memory capacity was probed behaviorally in adult humans both in laboratory settings and via the Internet. Several experiments show that although the effect of proactive interference on visual working memory is significant and can last over several trials, it only changes the capacity estimate by about 15%.

CONCLUSIONS/SIGNIFICANCE

This study further confirms the sharp limitations on visual working memory capacity, both in absolute terms and relative to verbal working memory. It is suggested that future research take these limitations into account in understanding differences across a variety of tasks between human adults, prelinguistic infants and nonlinguistic animals.

Monkeys match and tally quantities across senses

We report here that monkeys can actively match the number of sounds they hear to the number of shapes they see and present the first evidence that monkeys sum over sounds and sights. In Experiment 1, two monkeys were trained to choose a simultaneous array of 1-9 squares that numerically matched a sample sequence of shapes or sounds. Monkeys numerically matched across (audio-visual) and within (visual-visual) modalities with equal accuracy and transferred to novel numerical values. In Experiment 2, monkeys presented with sample sequences of randomly ordered shapes or tones were able to choose an array of 2-9 squares that was the numerical sum of the shapes and sounds in the sample sequence. In both experiments, accuracy and reaction time depended on the ratio between the correct numerical match and incorrect choice. These findings suggest monkeys and humans share an abstract numerical code that can be divorced from the modality in which stimuli are first experienced.

Log or linear? Distinct intuitions of the number scale in Western and Amazonian indigene cultures

The mapping of numbers onto space is fundamental to measurement and to mathematics. Is this mapping a cultural invention or a universal intuition shared by all humans regardless of culture and education? We probed number-space mappings in the Mundurucu, an Amazonian indigene group with a reduced numerical lexicon and little or no formal education. At all ages, the Mundurucu mapped symbolic and nonsymbolic numbers onto a logarithmic scale, whereas Western adults used linear mapping with small or symbolic numbers and logarithmic mapping when numbers were presented nonsymbolically under conditions that discouraged counting. This indicates that the mapping of numbers onto space is a universal intuition and that this initial intuition of number is logarithmic. The concept of a linear number line appears to be a cultural invention that fails to develop in the absence of formal education.

Calibrating the mental number line

Human adults are thought to possess two dissociable systems to represent numbers: an approximate quantity system akin to a mental number line, and a verbal system capable of representing numbers exactly. Here, we study the interface between these two systems using an estimation task. Observers were asked to estimate the approximate numerosity of dot arrays. We show that, in the absence of calibration, estimates are largely inaccurate: responses increase monotonically with numerosity, but underestimate the actual numerosity. However, insertion of a few inducer trials, in which participants are explicitly (and sometimes misleadingly) told that a given display contains 30 dots, is sufficient to calibrate their estimates on the whole range of stimuli. Based on these empirical results, we develop a model of the mapping between the numerical symbols and the representations of numerosity on the number line.

Children's understanding of the relationship between addition and subtraction

In learning mathematics, children must master fundamental logical relationships, including the inverse relationship between addition and subtraction. At the start of elementary school, children lack generalized understanding of this relationship in the context of exact arithmetic problems: they fail to judge, for example, that 12+9-9 yields 12. Here, we investigate whether preschool children's approximate number knowledge nevertheless supports understanding of this relationship. Five-year-old children were more accurate on approximate large-number arithmetic problems that involved an inverse transformation than those that did not, when problems were presented in either non-symbolic or symbolic form. In contrast they showed no advantage for problems involving an inverse transformation when exact arithmetic was involved. Prior to formal schooling, children therefore show generalized understanding of at least one logical principle of arithmetic. The teaching of mathematics may be enhanced by building on this understanding.

Language is not just for talking: redundant labels facilitate learning of novel categories

In addition to having communicative functions, verbal labels may play a role in shaping concepts. Two experiments assessed whether the presence of labels affected category formation. Subjects learned to categorize "aliens" as those to be approached or those to be avoided. After accuracy feedback on each response was provided, a nonsense label was either presented or not. Providing nonsense category labels facilitated category learning even though the labels were redundant and all subjects had equivalent experience with supervised categorization of the stimuli. A follow-up study investigated differences between learning verbal and nonverbal associations and showed that learning a nonverbal association did not facilitate categorization. The findings show that labels make category distinctions more concrete and bear directly on the language-and-thought debate.

Aging and numerosity estimation

In two experiments, young and older participants were asked to find the approximate number of dots in collections including between 40 and 460 dots. Experiment 1 showed that both age groups had comparable performance and no age-related differences in the power-function exponents for numerosity. Experiment 2 found that these age-related similarities were not due to speed-accuracy trade-offs or to compensation by older adults for potential age-related decline in numerosity estimation processes. Furthermore, young and older participants' estimation performance was influenced by physical features of stimuli only for very large numerosities, presumably because these are poorly represented in long-term memory. Implications of these findings for the further understanding of how participants accomplish numerosity estimation tasks and effects of aging in this domain are discussed.

Basic math in monkeys and college students

Adult humans possess a sophisticated repertoire of mathematical faculties. Many of these capacities are rooted in symbolic language and are therefore unlikely to be shared with nonhuman animals. However, a subset of these skills is shared with other animals, and this set is considered a cognitive vestige of our common evolutionary history. Current evidence indicates that humans and nonhuman animals share a core set of abilities for representing and comparing approximate numerosities nonverbally; however, it remains unclear whether nonhuman animals can perform approximate mental arithmetic. Here we show that monkeys can mentally add the numerical values of two sets of objects and choose a visual array that roughly corresponds to the arithmetic sum of these two sets. Furthermore, monkeys' performance during these calculations adheres to the same pattern as humans tested on the same nonverbal addition task. Our data demonstrate that nonverbal arithmetic is not unique to humans but is instead part of an evolutionarily primitive system for mathematical thinking shared by monkeys.

Adult humans possess mathematical abilities that are unmatched by any other member of the animal kingdom. Yet, there is increasing evidence that the ability to enumerate sets of objects nonverbally is a capacity that humans share with other animal species. That is, like humans, nonhuman animals possess the ability to estimate and compare numerical values nonverbally. We asked whether humans and nonhuman animals also share a capacity for nonverbal arithmetic. We tested monkeys and college students on a nonverbal arithmetic task in which they had to add the numerical values of two sets of dots together and choose a stimulus from two options that reflected the arithmetic sum of the two sets. Our results indicate that monkeys perform approximate mental addition in a manner that is remarkably similar to the performance of the college students. These findings support the argument that humans and nonhuman primates share a cognitive system for nonverbal arithmetic, which likely reflects an evolutionary link in their cognitive abilities.

Monkeys have an ability to represent numerical values even though they lack linguistic abilities. The authors show that monkeys can also perform addition on numerical values and that they perform similarly to college students who are asked to add without counting.

Forecasting exponential growth and exponential decline: similarities and differences

Previous research has demonstrated adults' difficulties with explicitly forecasting exponential processes. Exponential growth is usually grossly underestimated, whereas exponential decline is forecast more accurately. By contrast, the present study examined implicit knowledge about exponential processes and how it is affected by function type (growth versus decline) in samples of 7-, 10-, 14-year-olds, and adults (N=80). Different indicators of the quality of forecasts were investigated. As opposed to previous findings, participants of all age groups estimated exponential decline less adequately than exponential growth. This effect could be attributed mainly to the fact that, in relation to fitted exponential functions, the starting value, or intercept, of the function was approximated well for exponential growth but badly with regard to exponential decline. The accuracy of the non-linear component in forecast functions barely differed between function types within the same age group. Furthermore, even 7-year-olds appeared to have a preliminary understanding of exponential processes, while both intercepts and exponents of forecasts became more accurate with age. Theoretical and practical implications are discussed.

The limits of counting: numerical cognition between evolution and culture

Number words that, in principle, allow all kinds of objects to be counted ad infinitum are one basic requirement for complex numerical cognition. Accordingly, short or object-specific counting sequences in a language are often regarded as earlier steps in the evolution from premathematical conceptions to greater abstraction. We present some instances from Melanesia and Polynesia, whose short or object-specific sequences originated from the same extensive and abstract sequence. Furthermore, the object-specific sequences can be shown to be cognitively advantageous for calculations without notation because they use larger counting units, thereby abbreviating higher numbers, enhancing the counting process, and extending the limits of counting. These results expand our knowledge both regarding numerical cognition and regarding the evolution of numeration systems.

Phylogeny and cultural history in ontogeny

This purpose of this paper is to defend the contention that human culture is constitutive of human psychological processes. Several kinds of evidence are presented in support of this proposition: phenomena associated with the stabilization of images on the retina and their selective disappearance and reappearance when varying degrees of destabilization are introduced; the non-linearity of cultural/cognitive time which acts as a transformative mechanism uniting the material and ideal aspects of culture; data on the operation of culture as a non-linear source of structuration in human ontogeny, and finally, data on the ways in which cultural practices influence the functioning of the brain.

Children’s understanding of posterior probability

Do young children have a basic intuition of posterior probability? Do they update their decisions and judgments in the light of new evidence? We hypothesized that they can do so extensionally, by considering and counting the various ways in which an event may or may not occur. The results reported in this paper showed that from the age of five, children's decisions under uncertainty (Study 1) and judgments about random outcomes (Study 2) are correctly affected by posterior information. From the same age, children correctly revise their decisions in situations in which they face a single, uncertain event, produced by an intentional agent (Study 3). The finding that young children have some understanding of posterior probability supports the theory of naive extensional reasoning, and contravenes some pessimistic views of probabilistic reasoning, in particular the evolutionary claim that the human mind cannot deal with single-case probability.

Priming reveals differential coding of symbolic and non-symbolic quantities

Number processing is characterized by the distance and the size effect, but symbolic numbers exhibit smaller effects than non-symbolic numerosities. The difference between symbolic and non-symbolic processing can either be explained by a different kind of underlying representation or by parametric differences within the same type of underlying representation. We performed a primed naming study to investigate this issue. Prime and target format were manipulated (digits or collections of dots) as well as the numerical distance between prime and target value. Qualitatively different priming patterns were observed for the two formats, showing that the underlying representations differed in kind: Digits activated mental number representations of the place coding type, while collections of dots activated number representations of the summation coding type.

Semantic associations between signs and numerical categories in the prefrontal cortex

The utilization of symbols such as words and numbers as mental tools endows humans with unrivalled cognitive flexibility. In the number domain, a fundamental first step for the acquisition of numerical symbols is the semantic association of signs with cardinalities. We explored the primitives of such a semantic mapping process by recording single-cell activity in the monkey prefrontal and parietal cortices, brain structures critically involved in numerical cognition. Monkeys were trained to associate visual shapes with varying numbers of items in a matching task. After this long-term learning process, we found that the responses of many prefrontal neurons to the visual shapes reflected the associated numerical value in a behaviorally relevant way. In contrast, such association neurons were rarely found in the parietal lobe. These findings suggest a cardinal role of the prefrontal cortex in establishing semantic associations between signs and abstract categories, a cognitive precursor that may ultimately give rise to symbolic thinking in linguistic humans.

Studying mental states is not a research program for comparative cognition

The title of the target article suggests an agenda for research on cognitive evolution that is doubly flawed. It implies that we can learn directly about animals' mental states, and its focus on human uniqueness impels a search for an existence proof rather than for understanding what components of given cognitive processes are shared among species and why.