Beyond the mental number line: A neural network model of number–space interactions

It is commonly assumed that there is an interaction between the representations of number and space (e.g., Dehaene et al., 1993, Walsh, 2003), typically ascribed to a mental number line. The exact nature of this interaction has remained elusive, however. Here we propose that spatial aspects are not inherent to number representations, but that instead spatial and numerical representations are separate. However, cultural factors establish ties between them. By extending earlier models (Gevers et al., 2006, Verguts et al., 2005) based on this hypothesis, the authors present computer simulations showing that a model incorporating this idea can account for data from a series of studies. These results suggest that number–space interactions are emergent properties resulting from the interaction between different brain areas.     

Where's the beef? Putting personality back into personality assessment

This article attempts to demonstrate the value of using a psychoanalytic theory of personality for psychological testing. This approach has more clinical utility than a solely research-based one. It recasts test data into conceptually related constructs that have internal consistency to each other and are directly relevant to psychotherapeutic treatment. Such theoretical recasting serves an organizing function, an integrative function, a clarification function, and a predictive function for the clinical inference process. Furthermore, a psychoanalytically oriented approach to testing allows for the expansion in sources of data that one considers in the testing situation. Five different sources of data emerge from the testing situation once one refocuses on theoretical constructs rather than test signs. These include test scores, test content, the patient-examiner interaction, patient behavior, and examiner countertransference.     

Children’s early mental number line: Logarithmic or decomposed linear?

Recently, the nature of children’s mental number line has received much investigation. In the number line task, children are required to mark a presented number on a physical number line with fixed endpoints. Typically, it was observed that the estimations of younger/inexperienced children were accounted for best by a logarithmic function, whereas those of older/more experienced children were reflected best by a linear function. This led to the conclusion that children’s mental number line transforms from logarithmic to linear with age and experience. In this study, we outline an alternative interpretation of children’s performance in a number line task. We suggest that two separate linear representations for one- and two-digit numbers may exist in young children and that initially the integration of these two representations into the place value structure of the Arabic number system is not fully mastered. When testing this assumption in a sample of more than 120 first graders, we observed that the two-linear model consistently provided better fit indexes. We conclude that instead of assuming a transition from logarithmic to linear coding, performance differences could also be accounted for by an improvement in integrating tens and units into the Arabic place value system.     

On the development of the mental number line: more, less, or never holistic with increasing age?

Magnitude is assumed to be represented along a holistic mental number line in adults. However, the authors recently observed a unit-decade compatibility effect for 2-digit numbers that is inconsistent with this "holisticness" assumption (H.-C. Nuerk, U. Weger, & K. Willmes, 2001). This study used the compatibility effect to examine whether the mental number line representation of magnitude changes toward greater or less holisticness in children from Grades 2-5. The results indicate that decades and units of 2-digit numbers are processed separately rather than holistically from Grade 2 on. However, this separate processing seems to develop from a more sequential (left-to-right) to a more parallel processing mode. Moreover, children may use different strategies depending on task demands. The results are interpreted in the framework of Siegler's overlapping waves model.     

A colorful walk, but is it on the mental number line? Reply to Cohen Kadosh, Tzelgov, and Henik

Cohen Kadosh, Tzelgov, and Henik [Cohen Kadosh, R., Tzelgov, J., and Henik, A. (2008). A synesthetic walk on the number line: The size effect. Cognition, 106, 548-557] present a new paradigm to probe properties of the mental number line. They describe two experiments which they argue to be inconsistent with the exact small number model proposed by Verguts, Fias, and Stevens [Verguts, T., Fias, W., Stevens, M. (2005). A model of exact small-number representation. Psychonomic Bulletin and Review, 12, 66-80]. We discuss the data, assumptions, and conclusions of Cohen Kadosh et al.'s paper in relation to existing models of numerical cognition.     

Does attention have different effects on line orientation and line arrangement discrimination?

Visual search and texture segregation studies have led to the inference that stimuli differing in the orientation of their component line segments can be distinguished without focal attention, whereas stimuli that differ only in the arrangement of line segments cannot. In most of this research, the locus of attention has not been explicitly manipulated. In the first experiment presented here, attention was directed to a relevant peripheral target by a cue presented near the target location or at the fovea. Effects of attention on orientation discrimination were assessed in a two-alternative forced-choice task with targets that were either: (1) lines that slanted obliquely to the right or left, or were horizontal or vertical, or (2) Y-like targets that had a short arm leading obliquely right or left of a vertical line. In some groups, a four-alternative forced-choice test with lines at 0°, 45°, 90°, and 135° orientations was used. Discrimination of these targets (i.e. targets that differ in the orientation of component line segments) was only minimally facilitated as the time between the onset of the valid cue and the onset of the target (cue-target stimulus onset asynchrony, SOA) was increased from 0 or 17 msec to 267 msec. In contrast, discrimination of targets that did not differ in the orientation of component line segments but differed in line arrangement (T-like characters), was greatly facilitated by longer cue-target SOAs. In Experiment 2, a cue misdirected attention on 20% of the trials. A decrement occurred on incorrectly cued trials in comparison to correctly cued trials for both types of stimuli used (lines and Ts). The results from these experiments suggest that discrimination of line orientation benefits less from focal attention than does discrimination of line arrangement, but that both discriminations suffer when attention must be disengaged from an irrelevant spatial location.     

Size congruity effects with two-digit numbers: Expanding the number line?

The size congruity effect is the interesting result that comparisons of the sizes of the physical formats in which numerals appear are affected by the numerical magnitudes of the respective numerals. We demonstrated that separating the physical and the numerical attributes in space leaves the effect unchanged. We then applied the spatially separated version to two-digit numerals and showed the effect to be comparable to that obtained with single numerals. We showed further that the effect is sensitive to the relative salience of the numeric and physical dimensions, to the extent that when the latter is the more salient dimension, a reverse effect obtains by which physical size interferes with number comparison. The results can be explained by a relative speed of processing account, but they are also compatible with an attention account that does not appeal to the notion of automaticity.     

The relationship between mental rotation and arithmetic: do number line estimation,working memory,or place-value concept matter?

Mental rotation is positively related to arithmetic ability; however, the mechanism underlying this relationship remains unclear. The possible roles of working memory, place-value concept, and number line estimation in the correlation between mental rotation and whole-number computation were investigated. One hundred and fifty-five first-grade students were tested to determine their mental rotation ability, arithmetic ability, and non-verbal intelligence. One year later, their working memory, place-value concept, number line estimation, and overall arithmetic ability were assessed. After controlling for age, gender, and prior arithmetic ability, we found that mental rotation uniquely predicted arithmetic ability after one year. Further mediation analyses demonstrated that number line estimation significantly mediated the relationship between mental rotation and arithmetic ability. In contrast, neither working memory nor place-value concept significantly mediated the relationship between mental rotation and arithmetic ability. This study highlights that mental number line estimation is the most important element explaining the influence of a dynamic spatial skill, that is, mental rotation, on arithmetic ability among young Chinese children.     

Attacked by the gods or by mental illness? Hybridizing mental and spiritual health in Okinawa

In 1972, the reversion to Japanese rule brought with it many changes for Okinawans, among them the widespread introduction of psychiatry. Psychiatry was not well received at first due to the extensive presence of shamans, who had traditionally dealt with Okinawans’ spiritual and psychological afflictions. Both psychiatrists and shamans claimed to be able to heal those who were labelled ‘mentally ill’ or ‘mentally disordered’ by psychiatrists. This conflict between systems over the body of the patient/client is relevant to debates today about both the perceived value of generic mental health diagnosis and treatment regimes compared with indigenous healing,1 See Kleinman (, ); WHO (2001).  [Google Scholar] and the question of isolating how markers or symbols of identity are employed in patients’ help-seeking choices. We examine three cases from the 1970s of patients who were diagnosed as suffering from both schizophrenia and an indigenous condition known as kami daarii.     

Who can escape the natural number bias in rational number tasks? A study involving students and experts

Many learners have difficulties with rational number tasks because they persistently rely on their natural number knowledge, which is not always applicable. Studies show that such a natural number bias can mislead not only children but also educated adults. It is still unclear whether and under what conditions mathematical expertise enables people to be completely unaffected by such a bias on tasks in which people with less expertise are clearly biased. We compared the performance of eighth‐grade students and expert mathematicians on the same set of algebraic expression problems that addressed the effect of arithmetic operations (multiplication and division). Using accuracy and response time measures, we found clear evidence for a natural number bias in students but no traces of a bias in experts. The data suggested that whereas students based their answers on their intuitions about natural numbers, expert mathematicians relied on their skilled intuitions about algebraic expressions. We conclude that it is possible for experts to be unaffected by the natural number bias on rational number tasks when they use strategies that do not involve natural numbers.     

Does action make the link between number and space representation? Visuo-manual adaptation improves number bisection in unilateral neglect

If the visual world is artificially shifted by only 10 degrees, people initially experience difficulty in directing their actions toward visual goals, but then rapidly compensate the visual distortion. The consequence of such adaptation can be measured as visual and proprioceptive aftereffects, as well as by performance on pointing tasks without visual feedback. Recent work has shown that more cognitive deficits can be improved following prism adaptation in patients with unilateral neglect. Here we show that a short visuo-manual adaptation to prisms improves performance on a mental number-bisection task recently shown to be impaired in unilateral neglect. The association previously found between space and number representation (the mental number line) may thus be grounded in common action principles. Our results suggest that visuo-motor plasticity functionally links parietal areas involved in space and number representation.     

Number line estimation and complex mental calculation: Is there a shared cognitive process driving the two tasks?

It is widely accepted that different number-related tasks, including solving simple addition and subtraction, may induce attentional shifts on the so-called mental number line, which represents larger numbers on the right and smaller numbers on the left. Recently, it has been shown that different number-related tasks also employ spatial attention shifts along with general cognitive processes. Here we investigated for the first time whether number line estimation and complex mental arithmetic recruit a common mechanism in healthy adults. Participants’ performance in two-digit mental additions and subtractions using visual stimuli was compared with their performance in a mental bisection task using auditory numerical intervals. Results showed significant correlations between participants’ performance in number line bisection and that in two-digit mental arithmetic operations, especially in additions, providing a first proof of a shared cognitive mechanism (or multiple shared cognitive mechanisms) between auditory number bisection and complex mental calculation.     

Outpatient benefits for mental health services in Medicare. Alignment with the private sector?

Revision of Medicare's benefit for outpatient mental health care is long overdue. The Omnibus Reconciliation Act of 1987 expands the covered limit to $2,200 (from the $500 set in 1966) but retains the 50% coinsurance requirement for beneficiaries. There are several strong arguments supporting further changes in the benefit to reduce the coinsurance and include psychologists as covered providers. These are need among the elderly, changes in Medicare's inpatient reimbursement system, and innovations in treatment. Outpatient mental health care is a very small portion of Medicare expenditures, amounting to less than .1% of total costs. Using data from the Bureau of Data Management and Strategy at the Health Care Financing Administration (HCFA), it was estimated that $41.8 million was paid by HCFA for outpatient mental health care in fiscal year 1984. This article estimates the costs to Medicare and beneficiaries of reducing the coinsurance to 20% and including psychologists as eligible providers.     

Evolved sex differences in the number of partners desired? The long and the short of it

Do men seek more short-term mates than women? Buss and Schmitt (1993) showed a pattern of mean difference in the ideal number of sexual partners men and women desired over various time frames. We replicated these mean sex differences (e.g., ideal number over the next 30 years: Ms = 7.69 and 2.78 for men and women, respectively), but in both data sets the sampling distributions were highly skewed. In Study 1, we found few sex differences in medians across time frames (e.g., ideal number over the next 30 years: Mdn = 1 for both men and women). In Study 2, most college men (98.9%) and women (99.2%) said they wanted to settle down with one mutually exclusive sexual partner at some point in their life, ideally within the next 5 years. Neither medians in number of partners desired overall before settling down (replicating Study 1) nor medians in short-term partners desired before settling down (Mdn = 0) differed significantly by gender. Rather, men and women concurred: Short-term mating is not what humans typically seek.     

What is the relationship between synaesthesia and visuo-spatial number forms?

This study compares the tendency for numerals to elicit spontaneous perceptions of colour or taste (synaesthesia) with the tendency to visualise numbers as occupying particular visuo-spatial configurations (number forms). The prevalence of number forms was found to be significantly higher in synaesthetes experiencing colour compared both to synaesthetes experiencing taste and to control participants lacking any synaesthetic experience. This suggests that the presence of synaesthetic colour sensations enhances the tendency to explicitly represent numbers in a visuo-spatial format although the two symptoms may nevertheless be logically independent (i.e. it is possible to have number forms without colour, and coloured numbers without forms). Number forms are equally common in men and women, unlike previous reports of synaesthesia that have suggested a strong female bias. Individuals who possess a number form are also likely to possess visuo-spatial forms for other ordinal sequences (e.g. days, months, letters) which suggests that it is the ordinal nature of numbers rather than numerical quantity that gives rise to this particular mode of representation. Finally, we also describe some consequences of number forms for performance in a number comparison task.