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

How social influence can undermine the wisdom of crowd effect

Social groups can be remarkably smart and knowledgeable when their averaged judgements are compared with the judgements of individuals. Already Galton [Galton F (1907) Nature 75:7] found evidence that the median estimate of a group can be more accurate than estimates of experts. This wisdom of crowd effect was recently supported by examples from stock markets, political elections, and quiz shows [Surowiecki J (2004) The Wisdom of Crowds]. In contrast, we demonstrate by experimental evidence (N = 144) that even mild social influence can undermine the wisdom of crowd effect in simple estimation tasks. In the experiment, subjects could reconsider their response to factual questions after having received average or full information of the responses of other subjects. We compare subjects' convergence of estimates and improvements in accuracy over five consecutive estimation periods with a control condition, in which no information about others' responses was provided. Although groups are initially "wise," knowledge about estimates of others narrows the diversity of opinions to such an extent that it undermines the wisdom of crowd effect in three different ways. The "social influence effect" diminishes the diversity of the crowd without improvements of its collective error. The "range reduction effect" moves the position of the truth to peripheral regions of the range of estimates so that the crowd becomes less reliable in providing expertise for external observers. The "confidence effect" boosts individuals' confidence after convergence of their estimates despite lack of improved accuracy. Examples of the revealed mechanism range from misled elites to the recent global financial crisis.

Cultural Variation in Numeration Systems and Their Mapping Onto the Mental Number Line

The ability to exactly assess large numbers hinges on cultural tools such as counting sequences and thus offers a great opportunity to study how culture interacts with cognition. To obtain a more comprehensive picture of the cultural variance in number representation, this article argues for the inclusion of cross-linguistic analyses. It scrutinizes the specific counting systems of Polynesian and Micronesian languages that were once derived from an abstract and regular system by extension in three dimensions. The linguistic origins, cognitive properties, and cultural context of these specific counting systems are analyzed, and their implications for the nature of a (putative) mental number line are discussed.

Mathematical skills in 3- and 5-year-olds with spina bifida and their typically developing peers: a longitudinal approach

Preschoolers with spina bifida (SB) were compared to typically developing (TD) children on tasks tapping mathematical knowledge at 36 months (n = 102) and 60 months of age (n = 98). The group with SB had difficulty compared to TD peers on all mathematical tasks except for transformation on quantities in the subitizable range. At 36 months, vocabulary knowledge, visual-spatial, and fine motor abilities predicted achievement on a measure of informal math knowledge in both groups. At 60 months of age, phonological awareness, visual-spatial ability, and fine motor skill were uniquely and differentially related to counting knowledge, oral counting, object-based arithmetic skills, and quantitative concepts. Importantly, the patterns of association between these predictors and mathematical performance were similar across the groups. A novel finding is that fine motor skill uniquely predicted object-based arithmetic abilities in both groups, suggesting developmental continuity in the neurocognitive correlates of early object-based and later symbolic arithmetic problem solving. Models combining 36-month mathematical ability and these language-based, visual-spatial, and fine motor abilities at 60 months accounted for considerable variance on 60-month informal mathematical outcomes. Results are discussed with reference to models of mathematical development and early identification of risk in preschoolers with neurodevelopmental disorder.

Under- and Over-Estimation

Over the last 30 years, numerical estimation has been largely studied. Recently, Castronovo and Seron (2007) proposed the bi-directional mapping hypothesis in order to account for the finding that dependent on the type of estimation task (perception vs. production of numerosities), reverse patterns of performance are found (i.e., under- and over-estimation, respectively). Here, we further investigated this hypothesis by submitting adult participants to three types of numerical estimation task: (1) a perception task, in which participants had to estimate the numerosity of a non-symbolic collection; (2) a production task, in which participants had to approximately produce the numerosity of a symbolic numerical input; and (3) a reproduction task, in which participants had to reproduce the numerosity of a non-symbolic numerical input. Our results gave further support to the finding that different patterns of performance are found according to the type of estimation task: (1) under-estimation in the perception task; (2) over-estimation in the production task; and (3) accurate estimation in the reproduction task. Moreover, correlation analyses revealed that the more a participant under-estimated in the perception task, the more he/she over-estimated in the production task. We discussed these empirical data by showing how they can be accounted by the bi-directional mapping hypothesis ( Castronovo & Seron, 2007 ).

The cultural constitution of cognition: taking the anthropological perspective

To what extent is cognition affected by culture? And how might cognitive science profit from an intensified collaboration with anthropology in exploring this issue? In order to answer these questions, we will first give a brief description of different perspectives on cognition, one that prevails in most cognitive sciences – particularly in cognitive psychology – and one in anthropology. Three basic assumptions of cognitive science regarding the separability of content and process, the context-independence of processing, and the culture-independence of processing will then be discussed. We argue that these assumptions need to be questioned and scrutinized cross-culturally. A thorough examination of these issues would profit considerably from collaboration with anthropologists, not only by enabling deeper insight into the cultures under scrutiny, but also by synergistic effects that would allow for a more comprehensive understanding of human cognition.

Number line compression and the illusory perception of random numbers

Developmental studies indicate that children initially possess a compressed intuition of numerical distances, in which larger numbers are less discriminable than small ones. Education then "linearizes" this responding until by about age eight, children become able to map symbolic numerals onto a linear spatial scale. However, this illusion of compression of symbolic numerals may still exist in a dormant form in human adults and may be observed in appropriate experimental contexts. To investigate this issue, we asked adult participants to rate whether a random sequence of numbers contained too many small numbers or too many large ones. Participants exhibited a large bias, judging as random a geometric series that actually oversampled small numbers, consistent with a compression of large numbers. This illusion resisted training on a number-space mapping task, even though performance was linear on this task. While the illusion was moderately reduced by explicit exposure to linear sequences, responding was still significantly compressed. Thus, the illusion of compression is robust in this task, but linear and compressed responding can be exhibited in the same participants depending on the experimental context.

Risk-sensitivity in sensorimotor control

Recent advances in theoretical neuroscience suggest that motor control can be considered as a continuous decision-making process in which uncertainty plays a key role. Decision-makers can be risk-sensitive with respect to this uncertainty in that they may not only consider the average payoff of an outcome, but also consider the variability of the payoffs. Although such risk-sensitivity is a well-established phenomenon in psychology and economics, it has been much less studied in motor control. In fact, leading theories of motor control, such as optimal feedback control, assume that motor behaviors can be explained as the optimization of a given expected payoff or cost. Here we review evidence that humans exhibit risk-sensitivity in their motor behaviors, thereby demonstrating sensitivity to the variability of "motor costs." Furthermore, we discuss how risk-sensitivity can be incorporated into optimal feedback control models of motor control. We conclude that risk-sensitivity is an important concept in understanding individual motor behavior under uncertainty.

Extending the Mental Number Line

Multi-digit number processing is ubiquitous in our everyday life – even in school, multi-digit numbers are computed from the first year onward. Yet, many problems children and adults have are about the relation of different digits (for instance with fractions, decimals, or carry effects in multi-digit addition). Cognitive research has mainly focused on single-digit processing, and there is no comprehensive review of the different multi-digit number processing types and effects. The current review aims to fill this gap. First, we argue that effects observed in single-digit tasks cannot simply be transferred to multi-digit processing. Next, we list 16 effect types and processes which are specific for multi-digit number processing. We then discuss the development of multi-digit number processing, its neurocognitive correlates, its cultural or language-related modulation, and finally some models for multi-digit number processing. We finish with conclusions and perspectives about where multi-digit number processing research may or should be heading in following years.

Coding early naturalists' accounts into long-term fish community changes in the Adriatic Sea (1800-2000)

The understanding of fish communities' changes over the past centuries has important implications for conservation policy and marine resource management. However, reconstructing these changes is difficult because information on marine communities before the second half of the 20^th century is, in most cases, anecdotal and merely qualitative. Therefore, historical qualitative records and modern quantitative data are not directly comparable, and their integration for long-term analyses is not straightforward. We developed a methodology that allows the coding of qualitative information provided by early naturalists into semi-quantitative information through an intercalibration with landing proportions. This approach allowed us to reconstruct and quantitatively analyze a 200-year-long time series of fish community structure indicators in the Northern Adriatic Sea (Mediterranean Sea). Our analysis provides evidence of long-term changes in fish community structure, including the decline of Chondrichthyes, large-sized and late-maturing species. This work highlights the importance of broadening the time-frame through which we look at marine ecosystem changes and provides a methodology to exploit, in a quantitative framework, historical qualitative sources. To the purpose, naturalists' eyewitness accounts proved to be useful for extending the analysis on fish community back in the past, well before the onset of field-based monitoring programs.

Modulating neuronal activity produces specific and long-lasting changes in numerical competence

Around 20% of the population exhibits moderate to severe numerical disabilities [1-3], and a further percentage loses its numerical competence during the lifespan as a result of stroke or degenerative diseases [4]. In this work, we investigated the feasibility of using noninvasive stimulation to the parietal lobe during numerical learning to selectively improve numerical abilities. We used transcranial direct current stimulation (TDCS), a method that can selectively inhibit or excitate neuronal populations by modulating GABAergic (anodal stimulation) and glutamatergic (cathodal stimulation) activity [5, 6]. We trained subjects for 6 days with artificial numerical symbols, during which we applied concurrent TDCS to the parietal lobes. The polarity of the brain stimulation specifically enhanced or impaired the acquisition of automatic number processing and the mapping of number into space, both important indices of numerical proficiency [7-9]. The improvement was still present 6 months after the training. Control tasks revealed that the effect of brain stimulation was specific to the representation of artificial numerical symbols. The specificity and longevity of TDCS on numerical abilities establishes TDCS as a realistic tool for intervention in cases of atypical numerical development or loss of numerical abilities because of stroke or degenerative illnesses.

Beyond hemispheric dominance: brain regions underlying the joint lateralization of language and arithmetic to the left hemisphere

Language and arithmetic are both lateralized to the left hemisphere in the majority of right-handed adults. Yet, does this similar lateralization reflect a single overall constraint of brain organization, such an overall "dominance" of the left hemisphere for all linguistic and symbolic operations? Is it related to the lateralization of specific cerebral subregions? Or is it merely coincidental? To shed light on this issue, we performed a "colateralization analysis" over 209 healthy subjects: We investigated whether normal variations in the degree of left hemispheric asymmetry in areas involved in sentence listening and reading are mirrored in the asymmetry of areas involved in mental arithmetic. Within the language network, a region-of-interest analysis disclosed partially dissociated patterns of lateralization, inconsistent with an overall "dominance" model. Only two of these areas presented a lateralization during sentence listening and reading which correlated strongly with the lateralization of two regions active during calculation. Specifically, the profile of asymmetry in the posterior superior temporal sulcus during sentence processing covaried with the asymmetry of calculation-induced activation in the intraparietal sulcus, and a similar colateralization linked the middle frontal gyrus with the superior posterior parietal lobule. Given recent neuroimaging results suggesting a late emergence of hemispheric asymmetries for symbolic arithmetic during childhood, we speculate that these colateralizations might constitute developmental traces of how the acquisition of linguistic symbols affects the cerebral organization of the arithmetic network.

The benefit of symbols: monkeys show linear, human-like, accuracy when using symbols to represent scalar value

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.

On the neuro-cognitive foundations of basic auditory number processing: an fMRI study

Background

It is widely agreed that numbers automatically activate a magnitude representation. Nevertheless, so far no systematic evaluation of the neuro-cognitive correlates has been provided for the case of auditorily presented numbers.

Methods

To address this question, we presented spoken number words in three different tasks (passive listening, magnitude comparison, parity judgement) as well as spoken pseudowords in an fMRI study.

Results

We found IPS activation typically associated with magnitude processing in all tasks with numerical stimuli only. Interestingly, directly contrasting the two semantic tasks magnitude comparison (magnitude-relevant) and parity judgement (magnitude-irrelevant) revealed a left lateralized predominance within the IPS for the processing of parity information as compared to a right lateralization for number magnitude for auditorily presented number words.

Conclusions

In summary, our results suggest a highly automatic activation of number magnitude for spoken number words similar to previous observations for visually presented numbers, but also indicate that the issue of hemispheric asymmetries deserves specific consideration.

Understanding quantity in semantic dementia

Patients with semantic dementia (SD) show relative preservation of number skills, contrasting with their severe multimodal semantic impairment. Underpinning this preservation, it is argued, is spared understanding of numerical quantity, a competence likened to a spatial map and subserved by the parietal lobes. The study investigated quantity knowledge in 14 SD patients to determine whether it is consistently preserved irrespective of disease severity or whether there are constraints on this preserved knowledge domain. Performance was well preserved on Piagetian conservation tasks, estimating object numerosity, and understanding of basic numerical magnitude. However, patients showed impairment on real-world estimation tasks, increasing with semantic severity. More surprisingly, on an analogue scale task, they produced implausible responses, suggesting degraded knowledge of precise numerical relationships. The findings challenge the view that knowledge of quantity is totally preserved in SD and suggest that the temporal lobes have a contributory role in the conceptual understanding of quantity.

Core multiplication in childhood

A dedicated, non-symbolic, system yielding imprecise representations of large quantities (approximate number system, or ANS) has been shown to support arithmetic calculations of addition and subtraction. In the present study, 5-7-year-old children without formal schooling in multiplication and division were given a task requiring a scalar transformation of large approximate numerosities, presented as arrays of objects. In different conditions, the required calculation was doubling, quadrupling, or increasing by a fractional factor (2.5). In all conditions, participants were able to represent the outcome of the transformation at above-chance levels, even on the earliest training trials. Their performance could not be explained by processes of repeated addition, and it showed the critical ratio signature of the ANS. These findings provide evidence for an untrained, intuitive process of calculating multiplicative numerical relationships, providing a further foundation for formal arithmetic instruction.

What's Lost When Languages Are The Extinction of the World's Languages and the Erosion of Human Knowledge Oxford University Press, Oxford, 2008. 304 pp. Paper, $17.95, £11.99. ISBN 9780195372069

Harrison explores causes and consequences of the loss of human languages.

Number-space mapping in human infants

Mature representations of number are built on a core system of numerical representation that connects to spatial representations in the form of a mental number line. The core number system is functional in early infancy, but little is known about the origins of the mapping of numbers onto space. In this article, we show that preverbal infants transfer the discrimination of an ordered series of numerosities to the discrimination of an ordered series of line lengths. Moreover, infants construct relationships between numbers and line lengths when they are habituated to unordered pairings that vary positively, but not when they are habituated to unordered pairings that vary inversely. These findings provide evidence that a predisposition to relate representations of numerical magnitude to spatial length develops early in life. A central foundation of mathematics, science, and technology therefore emerges prior to experience with language, symbol systems, or measurement devices.

Context affects the numerical semantic congruity effect in rhesus monkeys (Macaca mulatta)

Do monkeys anchor their numerical judgments based on the context in which their choices are presented? We addressed this question by varying the numerical range across sessions while macaque monkeys made ordinal judgments. Monkeys were trained to make a conditional discrimination whereby they were reinforced for ordering arrays of dots in ascending or descending numerical order, dependent on a color cue. Monkeys were tested using two ranges of numerosities that converged on a single pair. Similar to the findings of Cantlon and Brannon (2005), we found a semantic congruity effect whereby decision time was systematically influenced by the congruity between the cue (ascending or descending) and the relative Numerical Magnitude of the stimuli within each range. Furthermore, monkeys showed a context effect, such that decision time for a given pair was dependent on whether it was a relatively small or large set of values compared to the other values presented in that session. This finding suggests that, similar to humans, the semantic congruity effect observed in monkeys is anchored by the context. Thus our data provide further evidence for the existence of a shared numerical comparison process in monkeys and humans.

Contributions of societal modernity to cognitive development: a comparison of four cultures

This study examined how societal changes associated with modernization are related to cognitive development. Data were from 4 cultural communities that represented a broad range of traditional and modern elements: the Garifuna (Belize), Logoli (Kenya), Newars (Nepal), and Samoans (American Samoa). Naturalistic observations and the performances of 3-, 5-, 7-, and 9-year-old children (N = 192) on 7 cognitive measures were examined. Results replicated age-related improvement on all measures. Contributions of modernity were evident in children's play behaviors and cognitive performances, especially in skills related to schooling. Modernization and schooling independently predicted differences on most of the measures. Results are discussed in relation to the Flynn effect, the worldwide increase in cognitive scores across generations, and the ways in which societal modernization may contribute to cognitive development.

Light Location Influences the Perceived Locations of Internal Sounds

Numerous studies have shown that visual stimuli can bias the perceived location of auditory stimuli. Here, we sought to determine if a visual stimulus can also bias the perceived location of multiple internal auditory stimuli. Fifty subjects were presented with a train of eight binaural click-pairs over headphones while a single flash of light was presented either to the left or to the right side of a central fixation point on an otherwise black CRT screen. A no-flash baseline was also implemented, as was a no-fixation control. The subjects used a rating scale to indicate the perceived location of each of the eight click-pairs within their heads. The results showed that the flash of light significantly influenced the perceived location of the click-pairs, biasing them in the same direction as the flash of light. This suggests that, even without perceptual correspondence, cross-modal interactions can occur.

Numerical representation in the parietal lobes: abstract or not abstract?

The study of neuronal specialisation in different cognitive and perceptual domains is important for our understanding of the human brain, its typical and atypical development, and the evolutionary precursors of cognition. Central to this understanding is the issue of numerical representation, and the question of whether numbers are represented in an abstract fashion. Here we discuss and challenge the claim that numerical representation is abstract. We discuss the principles of cortical organisation with special reference to number and also discuss methodological and theoretical limitations that apply to numerical cognition and also to the field of cognitive neuroscience in general. We argue that numerical representation is primarily non-abstract and is supported by different neuronal populations residing in the parietal cortex.

How numeracy influences risk comprehension and medical decision making

We review the growing literature on health numeracy, the ability to understand and use numerical information, and its relation to cognition, health behaviors, and medical outcomes. Despite the surfeit of health information from commercial and noncommercial sources, national and international surveys show that many people lack basic numerical skills that are essential to maintain their health and make informed medical decisions. Low numeracy distorts perceptions of risks and benefits of screening, reduces medication compliance, impedes access to treatments, impairs risk communication (limiting prevention efforts among the most vulnerable), and, based on the scant research conducted on outcomes, appears to adversely affect medical outcomes. Low numeracy is also associated with greater susceptibility to extraneous factors (i.e., factors that do not change the objective numerical information). That is, low numeracy increases susceptibility to effects of mood or how information is presented (e.g., as frequencies vs. percentages) and to biases in judgment and decision making (e.g., framing and ratio bias effects). Much of this research is not grounded in empirically supported theories of numeracy or mathematical cognition, which are crucial for designing evidence-based policies and interventions that are effective in reducing risk and improving medical decision making. To address this gap, we outline four theoretical approaches (psychophysical, computational, standard dual-process, and fuzzy trace theory), review their implications for numeracy, and point to avenues for future research.

Representation of number in the brain

Number symbols have allowed humans to develop superior mathematical skills that are a hallmark of technologically advanced cultures. Findings in animal cognition, developmental psychology, and anthropology indicate that these numerical skills are rooted in nonlinguistic biological primitives. Recent studies in human and nonhuman primates using a broad range of methodologies provide evidence that numerical information is represented and processed by regions of the prefrontal and posterior parietal lobes, with the intraparietal sulcus as a key node for the representation of the semantic aspect of numerical quantity.

Possible dendritic contribution to unimodal numerosity tuning and weber-fechner law-dependent numerical cognition

Humans and animals are known to share an ability to estimate or compare the numerosity of visual stimuli, and this ability is considered to be supported by the cortical neurons that have unimodal tuning for numerosity, referred to as the numerosity detector neurons. How such unimodal numerosity tuning is shaped through plasticity mechanisms is unknown. Here, I propose a testable hypothetical mechanism based on recently revealed features of the neuronal dendrite, namely, cooperative plasticity induction and nonlinear input integration at nearby dendritic sites, on the basis of the existing proposal that individual visual stimuli are represented as similar localized activities regardless of the size or the shape in a cortical region in the dorsal visual pathway. Intriguingly, the proposed mechanism naturally explains a prominent feature of the numerosity detector neurons, namely, the broadening of the tuning curve in proportion to the preferred numerosity, which is considered to underlie the known Weber-Fechner law-dependent accuracy of numerosity estimation and comparison. The simulated tuning curves are less sharp than reality, however, and together with the evidence from human imaging studies that numerical representation is a distributed phenomenon, it may not be likely that the proposed mechanism operates by itself. Rather, the proposed mechanism might facilitate the formation of hierarchical circuitry proposed in the previous studies, which includes neurons with monotonic numerosity tuning as well as those with sharp unimodal tuning, by serving as an efficient initial condition.

The case for a notation-independent representation of number

Cohen Kadosh & Walsh (CK&W) neglect the solid empirical evidence for a convergence of notation-specific representations onto a shared representation of numerical magnitude. Subliminal priming reveals cross-notation and cross-modality effects, contrary to CK&W's prediction that automatic activation is modality and notation-specific. Notation effects may, however, emerge in the precision, speed, automaticity, and means by which the central magnitude representation is accessed.

Symbolic, numeric, and magnitude representations in the parietal cortex

We concur with Cohen Kadosh & Walsh (CK&W) that representation of numbers in the parietal cortex is format dependent. In addition, we suggest that all formats do not automatically, and equally, access analog magnitude representation in the intraparietal sulcus (IPS). Understanding how development, learning, and context lead to differential access of analog magnitude representation is a key question for future research.

Non-abstract numerical representations in the IPS: Further support, challenges, and clarifications

The commentators have raised many pertinent points that allow us to refine and clarify our view. We classify our response comments into seven sections: automaticity; developmental and educational questions; priming; multiple representations or multiple access(?); terminology; methodological advances; and simulated cognition and numerical cognition. We conclude that the default numerical representations are not abstract.

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.

Spontaneous mapping of number and space in adults and young children

Mature representations of space and number are connected to one another in ways suggestive of a 'mental number line', but this mapping could either be a cultural construction or a reflection of a more fundamental link between the domains of number and geometry. Using a manual bisection paradigm, we tested for number line representations in adults, young school children, and preschool children. Non-symbolic numerical displays systematically distorted localization of the midpoint of a horizontal line at all three ages. Numerical and spatial representations therefore are linked prior to the onset of formal instruction, in a manner that suggests a privileged relation between spatial and numerical cognition.

Multiple spatial representations of number: evidence for co-existing compressive and linear scales

Although the spatial representation of number (mental number line) is well documented, the scaling associated with this representation is less clear. Sometimes people appear to rely on compressive scaling, and sometimes on linear scaling. Here we provide evidence for both compressive and linear representations on the same numerical bisection task, in which adult participants estimate (without calculating) the midpoint between two numbers. The same leftward bias (pseudoneglect) shown on physical line bisection appears on this task, and was previously shown to increase with the magnitude of bisected numbers, consistent with compressive scaling (Longo and Lourenco in Neuropsychologia 45:1400-1407, 2007). In the present study, participants held either small (1-9) or large (101-109) number primes in memory during bisection. When participants remembered small primes, bisection responses were consistent with compressive scaling. However, when they remembered large primes, responses were more consistent with linear scaling. These results show that compressive and linear representations may be accessed flexibly on the same task, depending on the numerical context.

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

Dehaene et al. (Reports, 30 May 2008, p. 1217) argued that native speakers of Mundurucu, a language without a linguistic numerical system, inherently represent numerical values as a logarithmically spaced spatial continuum. However, their data do not rule out the alternative conclusion that Mundurucu speakers encode numbers linearly with scalar variability and psychologically construct space-number mappings by analogy.

Intuitive numbers guide decisions

Measuring reaction times to number comparisons is thought to reveal a processing stage in elementary numerical cognition linked to internal, imprecise representations of number magnitudes. These intuitive representations of the mental number line have been demonstrated across species and human development but have been little explored in decision making. This paper develops and tests hypotheses about the influence of such evolutionarily ancient, intuitive numbers on human decisions. We demonstrate that individuals with more precise mental-number-line representations are higher in numeracy (number skills) consistent with previous research with children. Individuals with more precise representations (compared to those with less precise representations) also were more likely to choose larger, later amounts over smaller, immediate amounts, particularly with a larger proportional difference between the two monetary outcomes. In addition, they were more likely to choose an option with a larger proportional but smaller absolute difference compared to those with less precise representations. These results are consistent with intuitive number representations underlying: a) perceived differences between numbers, b) the extent to which proportional differences are weighed in decisions, and, ultimately, c) the valuation of decision options. Human decision processes involving numbers important to health and financial matters may be rooted in elementary, biological processes shared with other species.