Loudness counts: Interactions between loudness,number magnitude,and space

ATOM (a theory of magnitude) suggests that magnitude information of different formats (numbers, space, and time) is processed within a generalized magnitude network. In this study we investigated whether loudness, as a possible indicator of intensity and magnitude, interacts with the processing of numbers. Small and large numbers, spoken in a quiet and a loud voice, were simultaneously presented to the left and right ear (Experiments 1a and 1b). Participants judged whether the number presented to the left or right ear was louder or larger. Responses were faster when the smaller number was spoken in a quiet voice, and the larger number in a loud voice. Thus, task-irrelevant numerical information influenced the processing of loudness and vice versa. This bi-directional link was also confirmed by classical SNARC paradigms (spatial–numerical association of response codes; Experiments 2a–2c) when participants again judged the magnitude or loudness of separately presented stimuli. In contrast, no loudness–number association was found in a parity judgment task. Regular SNARC effects were found in the magnitude and parity judgment task, but not in the loudness judgment task. Instead, in the latter task, response side was associated with loudness. Possible explanations for these results are discussed.     

Rapid parallel semantic processing of numbers without awareness

In this study, we investigate whether multiple digits can be processed at a semantic level without awareness, either serially or in parallel. In two experiments, we presented participants with two successive sets of four simultaneous Arabic digits. The first set was masked and served as a subliminal prime for the second, visible target set. According to the instructions, participants had to extract from the target set either the mean or the sum of the digits, and to compare it with a reference value. Results showed that participants applied the requested instruction to the entire set of digits that was presented below the threshold of conscious perception, because their magnitudes jointly affected the participant’s decision. Indeed, response decision could be accurately modeled as a sigmoid logistic function that pooled together the evidence provided by the four targets and, with lower weights, the four primes. In less than 800 ms, participants successfully approximated the addition and mean tasks, although they tended to overweight the large numbers, particularly in the sum task. These findings extend previous observations on ensemble coding by showing that set statistics can be extracted from abstract symbolic stimuli rather than low-level perceptual stimuli, and that an ensemble code can be represented without awareness.     

The size congruity effect: is bigger always more?

When comparing digits of different physical sizes, numerical and physical size interact. For example, in a numerical comparison task, people are faster to compare two digits when their numerical size (the relevant dimension) and physical size (the irrelevant dimension) are congruent than when they are incongruent. Two main accounts have been put forward to explain this size congruity effect. According to the shared representation account, both numerical and physical size are mapped onto a shared analog magnitude representation. In contrast, the shared decisions account assumes that numerical size and physical size are initially processed separately, but interact at the decision level. We implement the shared decisions account in a computational model with a dual route framework and show that this model can simulate the modulation of the size congruity effect by numerical and physical distance. Using other tasks than comparison, we show that the model can simulate novel findings that cannot be explained by the shared representation account.     

The role of vision in the development of finger-number interactions: Finger-counting and finger-montring in blind children

Previous research has suggested that the use of the fingers may play a functional role in the development of a mature counting system. However, the role of developmental vision in the elaboration of a finger numeral representation remains unexplored. In the current study, 14 congenitally blind children and 14 matched sighted controls undertook three different test batteries that examined (a) general cognitive abilities, (b) the spontaneous use of finger-counting and finger-montring strategies (where “finger-montring” is a term used to characterize the way people raise their fingers to show numerosities to other people), and (c) the canonicity level of the finger-counting and finger-montring habits. Compared with sighted controls, blind children used their fingers less spontaneously to count and in a less canonical way to count and show quantities. These results demonstrate that the absence of vision precludes the development of a typical finger numeral representation and suggest that the use of canonical finger-counting and finger-montring strategies relies on the visual recognition of particular hand shapes.     

Young adult female fragile X premutation carriers show age- and genetically-modulated cognitive impairments

The high frequency of the fragile X premutation in the general population and its emerging neurocognitive implications highlight the need to investigate the effects of the premutation on lifespan cognitive development. Until recently, cognitive function in fragile X premutation carriers (fXPCs) was presumed to be unaffected by the mutation. Here we show that young adult female fXPCs show subtle, yet significant, age- and FMR1 gene mutation-modulated cognitive impairments as tested by a quantitative magnitude comparison task. Our results begin to define the neurocognitive endophenotype associated with the premutation in adults, who are at risk for developing a neurodegenerative disorder associated with the fragile X premutation. Results from the present study may potentially be applied toward the design of early interventions wherein we might be able to target premutation carriers most at risk for degeneration for preventive treatment.     

Operation-specific encoding in single-digit arithmetic

Solving simple arithmetic problems involves three stages: encoding the problem, retrieving or calculating the answer, and reporting the answer. This study compared the event-related potentials elicited by single-digit addition and multiplication problems to examine the relationship between encoding and retrieval/calculation stages. Results showed that the operation effect appeared as early as the encoding of the first operand and continued to the retrieval/calculation stage: compared to addition, multiplication elicited larger negative potentials in the left anterior electrodes and larger positive potentials in the right posterior electrodes. The consistency of this operation effect across the first two stages of arithmetic processing suggests that encoding of arithmetic problems can be modulated by the nature of representation of the to-be-retrieved arithmetic facts, and thus these two stages are additive rather than interactive.     

How to cook a SNARC: Number placement in text rapidly changes spatial–numerical associations

Most theoreticians believe that reading habits explain why Western adults associate small numbers with left space and large numbers with right space (the SNARC effect). We challenge this belief by documenting, in both English and Hebrew, that SNARC changes during reading: small and large numbers in our texts appeared near the left or right ends of the lines, positioned either spatially congruent or incongruent with reading habits. In English, the congruent group showed reliable SNARC before and after reading and the incongruent group’s SNARC was significantly reduced. In Hebrew the incongruent reading condition even induced a reverse SNARC. These results show that SNARC is a fleeting aspect of number representation that captures multiple spatial associations.     

Evidence for knowledge of the syntax of large numbers in preschoolers

The aim of this study was to provide evidence for knowledge of the syntax governing the verbal form of large numbers in preschoolers long before they are able to count up to these numbers. We reasoned that if such knowledge exists, it should facilitate the maintenance in short-term memory of lists of lexical primitives that constitute a number (e.g., three hundred forty five) compared with lists containing the same primitives but in a scrambled order (e.g., five three forty hundred). The two types of lists were given to 5-year-olds in an immediate serial recall task. As we predicted, the lists in syntactic order were easier to recall, suggesting that they match some knowledge of the way lexical primitives must be ordered to express large numerosities.     

Disconfirming Expectations: Incorrect Imprecise (vs. Precise) Estimates Increase Source Trustworthiness and Consumer Loyalty

Estimations that include numerical information are ubiquitous in our daily lives, for example, housing prices, calories, etc. In the present work, we investigate how the type of information used in an estimate, particularly its level of imprecision, influences evaluations of source trustworthiness after the target value of the estimate is revealed. Specifically, building upon prior work suggesting that (a) imprecise estimates are perceived to be less accurate than precise estimates and (b) performing below expectations results in negative source evaluations, we hypothesize that if the estimate is revealed to be incorrect, imprecise estimates (i.e., 400) elicit higher source trustworthiness than precise estimates (i.e., 417), even if the imprecise estimate is objectively more incorrect (i.e., target value: 570). In addition, we find that this effect also influences consumers’ loyalty toward the source of the estimate. Four studies and a single‐paper meta‐analysis offer triangulating evidence for this prediction and its underlying psychological mechanism. Overall, this work contributes to research on estimates, source evaluations, numerical information, and the influence of errors on consumer behavior.