Perceived numerosity

In Experiments 1 and 2, dots appeared less numerous when bunched together on a sheet than when spread out over a larger area, and apparent numerosity proved to be a power function, with exponents of 0.72 (Experiment 1) and 0.78 (Experiment 2), of objective numerosity. In Experiment 3, where Xs were shown instead of dots, the exponent was 0.77. In Experiment 4, where Ss made magnitude productions rather than magnitude estimations of the Xs, the exponent was 0.94. The overall results indicate an exponent of about 0.85 for dots or Xs presented.     

Perceived numerosity of spatiotemporal events

Numerosity discrimination was examined when items were varied in space-time position rather than in space only. Observers were instructed to indicate which of two adjacent streamsof visual events contained more items. The precision of numerosity discrimination of dynamic events was not remarkably different from that of static patterns. Two basic numerosity biases previously found for static dot patterns—inhibitory overestimation and satellite underestimation—were demonstrated for items distributed randomly over a spatiotemporal interval. It was also demonstrated that two streams, equated in the number and luminous energy of items, are not judged equal in their visible number if items in one of these two streams have longer duration than items in the second stream. These findings can be accounted for by the occupancy model of perceived numerosity (Allik & Tuulmets, 1991a) if it is supposed that the impact that each element has on its neighborhood is spread along both spatial and temporal coordinates. Perceived numerosity decreases with both spatial and temporal proximity between the-visual-items. Space and time have interchangeable effects on perceived numerosity: the amount of numerosity bias caused by the spatial proximity of items can also be produced by the properly chosen temporal proximity of items     

Temporal information affects the performance of numerosity discrimination: Behavioral evidence for a shared system for numerosity and temporal processing

In this study, we tested whether and how temporal information would affect the performance of numerosity discrimination in sequential events, in an attempt to make the relationship clear between temporal and numerosity processing. We manipulated the duration of event presentation (i.e., the stimulus duration) and the duration of the sequence (i.e., the total interval). We also employed three levels of standard event numbers (i.e., 5, 10, and 20) to test whether and how the effect would differ among event numbers. The results showed that temporal information affected the performance of numerosity discrimination; precision deteriorated when stimulus duration and the total interval were manipulated, and the number of events in the longer total interval were judged as less numerous than those in the shorter total interval across standard numbers. Accordingly, our results suggested the existence of a shared system between time and numerosity processing.     

Perceived numerosity as a function of item size

In a sample of 48 subjects, there was a significant inverse relation between item size and estimation of numerosity. This result was shown to be consistent with Gestalt theory. According to this approach, the components of good figures appear more numerous, and smaller items produce better figures.     

Perceived numerosity, item arrangement, and expectancy

Ten sets of dots ranging in number from 7 to 91 per set were presented to 54 subjects. Half were arranged regularly and half randomly. The regular sets were overestimated by an average of 22%, while the random were underestimated by 16% compared with the physical number. Evidence was presented showing that subjects expect results in the opposite direction. The findings are discussed in relation to the expectancy-contrast model of Birnbaum and Veit.     

A memory-based account of automatic numerosity processing

We investigated the mechanisms responsible for the automatic processing of the numerosities represented by digits in the size congruity effect (Henik & Tzelgov, 1982). The algorithmic model assumes that relational comparisons of digit magnitudes (e.g., larger than {8,2}) create this effect. If so, congruity effects ought to require two digits. Memory-based models assume that associations between individual digits and the attributes "small" and "large" create this effect. If so, congruity effects ought only to require one digit. Contrary to the algorithmic model and consistent with memory-based models, congruity effects were just as large when subjects judged the relative physical sizes of small digits paired with letters as when they judged the relative physical sizes of two digits. This finding suggests that size congruity effects can be produced without comparison algorithms.     

Connectedness affects dot numerosity judgment: Implications for configural processing

Participants judged the number of dots in visual displays with brief presentations (200 msec), such that the numerosity judgment was based on an instantaneous impression without counting. In some displays, pairs of adjacent dots were connected by line segments, whereas, in others, line segments were freely hanging without touching the dots. In Experiments 1, 2A, and 2B, connecting pairs of dots by line segments led to underestimation of dot numbers in those patterns. In Experiment 3, we controlled for the number of freely hanging line segments, whereas Experiment 4 showed that line segments that were merely attached to dots without actually connecting them did not produce a considerable underestimation effect. Experiment 5 showed that a connectedness effect existed when stimulus duration was reduced (50 msec) or extended (1,000 msec). We conclude that connectivity affects dot numerosity judgments, consistent with earlier findings of a configural effect in numerosity processing. Implications of the role of connectedness in object representation are discussed.     

The role of numerosity in processing nonsymbolic proportions

The difficulty in processing fractions seems to be related to the interference between the whole-number value of the numerator and the denominator and the real value of the fraction. Here we assess whether the reported problems with symbolic fractions extend to the nonsymbolic domain, by presenting fractions as arrays of black and white dots representing the two operands. Participants were asked to compare a target array with a reference array in two separate tasks using the same stimuli: a numerosity task comparing just the number of white dots in the two arrays; and a proportion task comparing the proportion of black and white dots. The proportion task yielded lower accuracy and slower response, confirming that even with nonsymbolic stimuli accessing proportional information is relatively difficult. However, using a congruity manipulation in which the greater numerosity of white dots could co-occur with a lower proportion of them, and vice versa, it was found that both task-irrelevant dimensions would interfere with the task-relevant dimension suggesting that both numerosity and proportion information was automatically accessed. The results indicate that the magnitude of fractions can be automatically and holistically processed in the nonsymbolic domain.     

Voluntary timing and brain function: an information processing approach.

This article takes an information processing perspective to review current understanding of brain mechanisms of human voluntary timing. Theoretical accounts of timing of the production of isochronous tapping and rhythms and of bimanual responding repetitive responding are reviewed. The mapping of higher level temporal parameter setting and memory processes and of lower level motor implementation process onto cortical and subcortical brain structures is discussed in relation to evidence from selective lesions in a range of neurological motor disorders. Brain activation studies that have helped identify key brain structures involved in the control of timing are reviewed.     

Perceived numerosity: A comparison of magnitude production,magnitude estimation,and discrimination judgments

In previous studies, modalities with a higher Weber fraction have tended to have a lower power-function exponent. Within a modality, however, the Weber fraction and power-function exponent for individual subjects were unrelated, and the present study largely confirms this finding for the numerosity dimension. More important than discriminability in the judgment of numerosity were cognitive factors. A single feedback trial considerably reduced intersubject variability on the magnitude-estimation exponent, although it failed to eliminate individual differences completely (precue and postcue exponents correlated signigicantly, r=+.50). Intrasubject variability, by contrast, seemingly did not involve the underlying exponent. As in previous studies, numerosity generally was underestimated and the power-function exponent was 1.08 for magnitude production and .80 for precue magnitude estimation. Contrary to previous results, however, males and females did not differ in exponent, perhaps because the present procedure allowed self-selection of individuals more interested in numerosity tasks.     

Embodied numerosity: Implicit hand-based representations influence symbolic number processing across cultures

In recent years, a strong functional relationship between finger counting and number processing has been suggested. Developmental studies have shown specific effects of the structure of the individual finger counting system on arithmetic abilities. Moreover, the orientation of the mental quantity representation (“number line”) seems to be influenced by finger counting habits. However, it is unclear whether the structure of finger counting systems still influences symbolic number processing in educated adults.In the present transcultural study, we pursued this question by examining finger-based sub-base-five effects in an Arabic number comparison task with three different groups of participants (German deaf signers, German and Chinese hearing adults). We observed sub-base-five effects in all groups, but particularly so for both German groups who use an explicit sub-base-five system in their finger counting habits. It is concluded that bodily experiences – namely finger counting – influence the structure of the abstract mental number representations even in adults. Thus, the present findings support the general idea that even seemingly abstract cognition may at least partially be rooted in our bodily experiences.     

Intelligence and information processing during an auditory discrimination task with backward masking: an event-related potential analysis

The relation between mental ability and auditory discrimination ability was examined by recording event-related potentials from 60 women during an auditory oddball task with backward masking. Across conditions that varied in intensity and in the interval between the target and masking stimuli, the higher ability (HA) group exhibited greater response accuracy, shorter response times, larger P3 amplitude, and shorter P3 latency to target stimuli than the lower ability (LA) group. When instructed to ignore the stimuli, the HA group exhibited shorter mismatch negativity latency to deviant tones than the LA group. The greater speed and accuracy of auditory discrimination for the HA group, observed here with multiple measures, is not a consequence of response strategy, test-taking ability, or attention deployment.     

Temporal expectation and information processing: a model-based analysis

People are able to use temporal cues to anticipate the timing of an event, enabling them to process that event more efficiently. We conducted two experiments, using the fixed-foreperiod paradigm (Experiment 1) and the temporal-cueing paradigm (Experiment 2), to assess which components of information processing are speeded when subjects use such temporal cues to predict the onset of a target stimulus. We analyzed the observed temporal expectation effects on task performance using sequential-sampling models of decision making: the Ratcliff diffusion model and the shifted-Wald model. The results from the two experiments were consistent: temporal expectation affected the duration of nondecision processes (target encoding and/or response preparation) but had little effect on the two main components of the decision process: response-threshold setting and the rate of evidence accumulation. Our findings provide novel evidence about the psychological processes underlying temporal-expectation effects on reaction time.     

Aspects of temporal information processing: A dimensional analysis

A major controversy in the field of prospective temporal information processing refers to the question of whether performance in various temporal tasks can be accounted for by the general assumption of an internal clock rather than by distinct, task-specific timing mechanisms. Therefore, the present study was designed to identify dimensions of temporal information processing. For this purpose, 120 subjects performed eight psychophysical temporal tasks. Correlational and principal factor analyses suggested a common pacemaker-based interval timing mechanism involved in duration discrimination, temporal generalization, and temporal order judgment. On the other hand, rhythm perception and perceived simultaneity/successiveness appeared to be controlled by task-specific processes unrelated to interval-based timing.     

The development of automatic numerosity processing in preschoolers: evidence for numerosity-perceptual interference

Three experiments examined developmental changes in the automatic processing of numerosity and perceptual information using a nonsymbolic numerical Stroop paradigm. In Experiments 1 and 2 (E1 and E2), 4-, 5-, and 6-year-olds had to compare the numerosities or the total filled areas of collections of dots (E1) or bars (E2) varying along both dimensions. Experiment 3 replicated E2's results in 3-, 4-, and 5-year-olds. Results demonstrated the existence of reciprocal influences between numerical and perceptual information beginning at age 3. Moreover, the irrelevant perceptual influences remained stable throughout development, whereas the sensitivity to irrelevant numerical cues tended to increase with age despite children's growing inhibition capacities. No significant correlation could be found between these developmental changes and the acquisition of counting knowledge.     

Attentional deficits in head-injured children: An information processing analysis

Attentional problems of closed head-injured (CHI) children were examined using an information processing (IP) approach. Based on Sternberg's (1969) additive factor method (AFM), the study examined attentional processes in terms of four stages and their corresponding task variables. A visual-spatial choice reaction-time task was undertaken with two groups of CHI children (severe and mild to moderate) and corresponding matched control groups. Results indicated that for this task both the CHI and the normal children exhibited a similar mode of linear, sequential information processing. It was found that the severe group was impaired not only in terms of slowed motor execution but also in terms of response selection. This group showed no impairment on the feature extraction, stimulus identification, and motor adjustment stages of processing. No evidence of impairment on any of the stages was found for the mild group. The utility of the AFM and implications of these findings are discussed with reference to CHI children and to neuropsychological assessment and rehabilitation.