Self-generated cognitive fluency: consequences on evaluative judgments

ABSTRACTPeople can support abstract reasoning by using mental models with spatial simulations. Such models are employed when people represent elements in terms of ordered dimensions (e.g. who is oldest, Tom, Dick, or Harry). We test and find that the process of forming and using such mental models can influence the liking of its elements (e.g. Tom, Dick, or Harry). The presumed internal structure of such models (linear-transitive array of elements), generates variations in processing ease (fluency) when using the model in working memory (see the Symbolic Distance Effect, SDE). Specifically, processing of pairs where elements have larger distances along the order should be easier compared to pairs with smaller distances. Elements from easier pairs should be liked more than elements from difficult pairs (fluency being hedonically positive). Experiment 1 shows that unfamiliar ideographs are liked more when at wider distances and therefore easier to process. Experiment 2 replicates this effect with non-words. Experiment 3 rules out a non-spatial explanation of the effect while Experiments 4 offers a high-powered replication. Experiment 5 shows that the spatial effect spontaneously emerges after learning, even without a task that explicitly focuses on fluency. Experiment 6 employed a shorter array, but yielded no significant results.

Symbols Are Special: An fMRI Adaptation Study of Symbolic, Nonsymbolic, and Non-Numerical Magnitude Processing in the Human Brain

How are different formats of magnitudes represented in the human brain? We used functional magnetic resonance imaging adaptation to isolate representations of symbols, quantities, and physical size in 45 adults. Results indicate that the neural correlates supporting the passive processing of number symbols are largely dissociable from those supporting quantities and physical size, anatomically and representationally. Anatomically, passive processing of quantities and size correlate with activation in the right intraparietal sulcus, whereas symbolic number processing, compared with quantity processing, correlates with activation in the left inferior parietal lobule. Representationally, neural patterns of activation supporting symbols are dissimilar from neural activation patterns supporting quantity and size in the bilateral parietal lobes. These findings challenge the longstanding notion that the culturally acquired ability to conceptualize symbolic numbers is represented using entirely the same brain systems that support the evolutionarily ancient system used to process quantities. Moreover, these data reveal that regions that support numerical magnitude processing are also important for the processing of non-numerical magnitudes. This discovery compels future investigations of the neural consequences of acquiring knowledge of symbolic numbers.

Development of a Possible General Magnitude System for Number and Space

There is strong evidence for a link between numerical and spatial processing. However, whether this association is based on a common general magnitude system is far from conclusive and the impact of development is not yet known. Hence, the present study aimed to investigate the association between discrete non-symbolic number processing (comparison of dot arrays) and continuous spatial processing (comparison of angle sizes) in children between the third and sixth grade (N = 367). Present findings suggest that the processing of comparisons of number of dots or angle are related to each other, but with angle processing developing earlier and being more easily comparable than discrete number representations for children of this age range. Accordingly, results favor the existence of a more complex underlying magnitude system consisting of dissociated but closely interacting representations for continuous and discrete magnitudes.

Implicit and Explicit Number-Space Associations Differentially Relate to Interference Control in Young Adults With ADHD

Behavioral evidence for the link between numerical and spatial representations comes from the spatial-numerical association of response codes (SNARC) effect, consisting in faster reaction times to small/large numbers with the left/right hand respectively. The SNARC effect is, however, characterized by considerable intra- and inter-individual variability. It depends not only on the explicit or implicit nature of the numerical task, but also relates to interference control. To determine whether the prevalence of the latter relation in the elderly could be ascribed to younger individuals' ceiling performances on executive control tasks, we determined whether the SNARC effect related to Stroop and/or Flanker effects in 26 young adults with ADHD. We observed a divergent pattern of correlation depending on the type of numerical task used to assess the SNARC effect and the type of interference control measure involved in number-space associations. Namely, stronger number-space associations during parity judgments involving implicit magnitude processing related to weaker interference control in the Stroop but not Flanker task. Conversely, stronger number-space associations during explicit magnitude classifications tended to be associated with better interference control in the Flanker but not Stroop paradigm. The association of stronger parity and magnitude SNARC effects with weaker and better interference control respectively indicates that different mechanisms underlie these relations. Activation of the magnitude-associated spatial code is irrelevant and potentially interferes with parity judgments, but in contrast assists explicit magnitude classifications. Altogether, the present study confirms the contribution of interference control to number-space associations also in young adults. It suggests that magnitude-associated spatial codes in implicit and explicit tasks are monitored by different interference control mechanisms, thereby explaining task-related intra-individual differences in number-space associations.

Developmental Dyscalculia and Automatic Magnitudes Processing: Investigating Interference Effects between Area and Perimeter

The relationship between numbers and other magnitudes has been extensively investigated in the scientific literature. Here, the objectives were to examine whether two continuous magnitudes, area and perimeter, are automatically processed and whether adults with developmental dyscalculia (DD) are deficient in their ability to automatically process one or both of these magnitudes. Fifty-seven students (30 with DD and 27 with typical development) performed a novel Stroop-like task requiring estimation of one aspect (area or perimeter) while ignoring the other. In order to track possible changes in automaticity due to practice, we measured performance after initial and continuous exposure to stimuli. Similar to previous findings, current results show a significant group × congruency interaction, evident beyond exposure level or magnitude type. That is, the DD group systematically showed larger Stroop effects. However, analysis of each exposure period showed that during initial exposure to stimuli the DD group showed larger Stroop effects in the perimeter and not in the area task. In contrast, during continuous exposure to stimuli no triple interaction was evident. It is concluded that both magnitudes are automatically processed. Nevertheless, individuals with DD are deficient in inhibiting irrelevant magnitude information in general and, specifically, struggle to inhibit salient area information after initial exposure to a perimeter comparison task. Accordingly, the findings support the assumption that DD involves a deficiency in multiple cognitive components, which include domain-specific and domain-general cognitive functions.

Interference between Space and Time Estimations: From Behavior to Neurons

Influences between time and space can be found in our daily life in which we are surrounded by numerous spatial metaphors to refer to time. For instance, when we move files from one folder to another in our computer a horizontal line that grows from left to right informs us about the elapsed and remaining time to finish the procedure and, similarly, in our communication we use several spatial terms to refer to time. Although with some differences in the degree of interference, not only space has an influence on time but both magnitudes influence each other. Indeed, since our childhood our estimations of time are influenced by space even when space should be irrelevant and the same occurs when estimating space with time as distractor. Such interference between magnitudes has also been observed in monkeys even if they do not use language or computers, suggesting that the two magnitudes are tightly coupled beyond communication and technology. Imaging and lesion studies have indicated that same brain areas are involved during the processing of both magnitudes and have suggested that rather than coding the specific magnitude itself the brain represents them as abstract concepts. Recent neurophysiological studies in prefrontal cortex, however, have shown that the coding of absolute and relative space and time in this area is realized by independent groups of neurons. Interestingly, instead, a high overlap was observed in this same area in the coding of goal choices across tasks. These results suggest that rather than during perception or estimation of space and time the interference between the two magnitudes might occur, at least in the prefrontal cortex, in a subsequent phase in which the goal has to be chosen or the response provided.

Developmental Dyscalculia in Adults: Beyond Numerical Magnitude Impairment

Numerous studies have tried to identify the core deficit of developmental dyscalculia (DD), mainly by assessing a possible deficit of the mental representation of numerical magnitude. Research in healthy adults has shown that numerosity, duration, and space share a partly common system of magnitude processing and representation. However, in DD, numerosity processing has until now received much more attention than the processing of other non-numerical magnitudes. To assess whether or not the processing of non-numerical magnitudes is impaired in DD, the performance of 15 adults with DD and 15 control participants was compared in four categorization tasks using numerosities, lengths, durations, and faces (as non-magnitude-based control stimuli). Results showed that adults with DD were impaired in processing numerosity and duration, while their performance in length and face categorization did not differ from controls' performance. Our findings support the idea of a nonsymbolic magnitude deficit in DD, affecting numerosity and duration processing but not length processing.

Adolescents with Developmental Dyscalculia Do Not Have a Generalized Magnitude Deficit - Processing of Discrete and Continuous Magnitudes

The link between number and space has been discussed in the literature for some time, resulting in the theory that number, space and time might be part of a generalized magnitude system. To date, several behavioral and neuroimaging findings support the notion of a generalized magnitude system, although contradictory results showing a partial overlap or separate magnitude systems are also found. The possible existence of a generalized magnitude processing area leads to the question how individuals with developmental dyscalculia (DD), known for deficits in numerical-arithmetical abilities, process magnitudes. By means of neuropsychological tests and functional magnetic resonance imaging (fMRI) we aimed to examine the relationship between number and space in typical and atypical development. Participants were 16 adolescents with DD (14.1 years) and 14 typically developing (TD) peers (13.8 years). In the fMRI paradigm participants had to perform discrete (arrays of dots) and continuous magnitude (angles) comparisons as well as a mental rotation task. In the neuropsychological tests, adolescents with dyscalculia performed significantly worse in numerical and complex visuo-spatial tasks. However, they showed similar results to TD peers when making discrete and continuous magnitude decisions during the neuropsychological tests and the fMRI paradigm. A conjunction analysis of the fMRI data revealed commonly activated higher order visual (inferior and middle occipital gyrus) and parietal (inferior and superior parietal lobe) magnitude areas for the discrete and continuous magnitude tasks. Moreover, no differences were found when contrasting both magnitude processing conditions, favoring the possibility of a generalized magnitude system. Group comparisons further revealed that dyscalculic subjects showed increased activation in domain general regions, whilst TD peers activate domain specific areas to a greater extent. In conclusion, our results point to the existence of a generalized magnitude system in the occipito-parietal stream in typical development. The detailed investigation of spatial and numerical magnitude abilities in DD reveals that the deficits in number processing and arithmetic cannot be explained with a general magnitude deficiency. Our results further indicate that multiple neuro-cognitive components might contribute to the explanation of DD.

Magnitude Processing in the Brain: An fMRI Study of Time, Space, and Numerosity as a Shared Cortical System

Continuous dimensions, such as time, space, and numerosity, have been suggested to be subserved by common neurocognitive mechanisms. Neuroimaging studies that have investigated either one or two dimensions simultaneously have consistently identified neural correlates in the parietal cortex of the brain. However, studies investigating the degree of neural overlap across several dimensions are inconclusive, and it remains an open question whether a potential overlap can be conceptualized as a neurocognitive magnitude processing system. The current functional magnetic resonance imaging study investigated the potential neurocognitive overlap across three dimensions. A sample of adults (N = 24) performed three different magnitude processing tasks: a temporal discrimination task, a number discrimination task, and a line length discrimination task. A conjunction analysis revealed several overlapping neural substrates across multiple magnitude dimensions, and we argue that these cortical nodes comprise a distributed magnitude processing system. Key components of this predominantly right-lateralized system include the intraparietal sulcus, insula, premotor cortex/SMA, and inferior frontal gyrus. Together with previous research highlighting intraparietal sulcus, our results suggest that the insula also is a core component of the magnitude processing system. We discuss the functional role of each of these components in the magnitude processing system and suggest that further research of this system may provide insight into the etiology of neurodevelopmental disorders where cognitive deficits in magnitude processing are manifest.

A common metric magnitude system for the perception and production of numerosity, length, and duration

Numerosity, length, and duration processing may share a common functional mechanism situated within the parietal cortex. A strong parallelism between the processing of these three magnitudes has been revealed by similar behavioral signatures (e.g., Weber–Fechner's law, the distance effect) and reciprocal interference effects. Here, we extend the behavioral evidence for a common magnitude processing mechanism by exploring whether the under- and overestimation patterns observed during numerical perception and production tasks are also present in length and duration perception and production. In a first experiment, participants had to perform two estimation tasks (i.e., perception and production) on three magnitudes (i.e., numerosities, lengths, and durations). The results demonstrate similar patterns for the three magnitudes: underestimation was observed in all perception tasks, whereas overestimation was found in all production tasks. A second experiment ensured that this pattern of under- and over-estimation was not solely generated by the mere process of perceiving or producing something. Participants were required to estimate the alphabetical position of a letter (i.e., perception task) or to produce the letter corresponding to a given position (i.e., production task). No under- or overestimation were observed in this experiment, which suggests that the process of perceiving or producing something alone cannot explain the systematic pattern of estimation observed on magnitudes. Together, these findings strengthen the idea that magnitude estimations share a common metric system, requiring similar mechanisms and/or representations.

The mental representations of fractions: adults' same-different judgments

Two experiments examined whether the processing of the magnitude of fractions is global or componential. Previously, some authors concluded that adults process the numerators and denominators of fractions separately and do not access the global magnitude of fractions. Conversely, others reported evidence suggesting that the global magnitude of fractions is accessed. We hypothesized that in a fraction matching task, participants automatically extract the magnitude of the components but that the activation of the global magnitude of the whole fraction is only optional or strategic. Participants carried out same/different judgment tasks. Two different tasks were used: a physical matching task and a numerical matching task. Pairs of fractions were presented either simultaneously or sequentially. Results showed that participants only accessed the representation of the global magnitude of fractions in the numerical matching task. The mode of stimulus presentation did not affect the processing of fractions. The present study allows a deeper understanding of the conditions in which the magnitude of fractions is mentally represented by using matching tasks and two different modes of presentation.

Magnitude processing in non-symbolic stimuli

Dot arrays are often used to study basic numerical skills across cultures, species and development. Researchers investigate the ability of subjects to discriminate between dot arrays, as a function of the ratio or distance between their numerosities. Such studies have contributed significantly to the number sense theory (i.e., that humans are born with the ability to process numerosities, and share this ability with various species)—possibly the most influential theory in numerical cognition literature today. However, a dot array contains, in addition to numerosity, continuous properties such as the total surface area of the dots, their density, etc. These properties are highly correlated with numerosity and therefore might influence participants' performance. Different ways in which different studies choose to deal with this confound sometimes lead to contradicting results, and in our opinion, do not completely eliminate the confound. In this work, we review these studies and suggest several possible reasons for the contradictions in the literature. We also suggest that studying continuous properties, instead of just trying to control them, may contribute to unraveling the building blocks of numerical abilities.

Discrete and analogue quantity processing in the parietal lobe: a functional MRI study

The human intraparietal sulcus (IPS) is implicated in processing symbolic number information and possibly in nonsymbolic number information. Specific IPS activity for discrete quantities (numerosities) as compared with continuous, analogue quantity has not been demonstrated. Here we use a stimulus-driven paradigm to distinguish automatic estimation of "how many things" from "how much" and "how long." The discrete analogue response task (DART) uses the perception of hues which can change either abruptly (discrete, numerous stimuli) or smoothly (analogue, nonnumerous stimuli) in space or in time. Subjects decide whether they saw more green or more blue. A conjunction analysis of spatial and temporal conditions revealed that bilateral IPS was significantly more active during the processing of discrete stimuli than during analogue stimuli, as was a parietal-occipital transition zone. We suggest that processing numerosity is a distinct process from processing analogue quantity, whether extended in space or time, and that an intraparietal network connects objects' segmentation to the estimation of their numerosity.