Sequential or parallel decomposed processing of two-digit numbers? Evidence from eye-tracking

While reaction time data have shown that decomposed processing of two-digit numbers occurs, there is little evidence about how decomposed processing functions. Poltrock and Schwartz (1984) argued that multi-digit numbers are compared in a sequential digit-by-digit fashion starting at the leftmost digit pair. In contrast, Nuerk and Willmes (2005) favoured parallel processing of the digits constituting a number. These models (i.e., sequential decomposition, parallel decomposition) make different predictions regarding the fixation pattern in a two-digit number magnitude comparison task and can therefore be differentiated by eye fixation data. We tested these models by evaluating participants' eye fixation behaviour while selecting the larger of two numbers. The stimulus set consisted of within-decade comparisons (e.g., 53_57) and between-decade comparisons (e.g., 42_57). The between-decade comparisons were further divided into compatible and incompatible trials (cf. Nuerk, Weger, & Willmes, 2001) and trials with different decade and unit distances. The observed fixation pattern implies that the comparison of two-digit numbers is not executed by sequentially comparing decade and unit digits as proposed by Poltrock and Schwartz (1984) but rather in a decomposed but parallel fashion. Moreover, the present fixation data provide first evidence that digit processing in multi-digit numbers is not a pure bottom-up effect, but is also influenced by top-down factors. Finally, implications for multi-digit number processing beyond the range of two-digit numbers are discussed.     

Holistic or compositional representation of two-digit numbers? Evidence from the distance, magnitude, and SNARC effects in a number-matching task

Whether two-digit numbers are represented holistically (each digit pair processed as one number) or compositionally (each digit pair processed separately as a decade digit and a unit digit) remains unresolved. Two experiments were conducted to examine the distance, magnitude, and SNARC effects in a number-matching task involving two-digit numbers. Forty undergraduates were asked to judge whether two two-digit numbers (presented serially in Experiment 1 and simultaneously in Experiment 2) were the same or not. Results showed that, when numbers were presented serially, unit digits did not make unique contributions to the magnitude and distance effects, supporting the holistic model. When numbers were presented simultaneously, unit digits made unique contributions, supporting the compositional model. The SNARC (Spatial-Numerical Association of Response Codes) effect was evident for the whole numbers and the decade digits, but not for the unit digits in both experiments, which indicates that two-digit numbers are represented on one mental number line. Taken together, these results suggested that the representation of two-digit numbers is on a single mental number line, but it depends on the stage of processing whether they are processed holistically or compositionally.     

Sequential or parallel processes? A longitudinal field study concerning determinants of identity-management strategies

Using a longitudinal field design, this study tested the dynamics of an integrative model of social identity theory (SIT) and relative deprivation theory (RDT) with regard to relations between perceived socio-structural characteristics, perceived in-group identification, perceived fraternal deprivation (i.e., resentment) and identity-management-strategy preference. Trait-state analyses revealed that the dynamic relationship among constructs in the model can best be explained in terms of trait-dependent variation rather than sequentially ordered processing. The trait components of the variables replicate previous findings concerning SIT and RDT. However. stable functional relations between variables and their traitlike character contradict the notion that their underlying processes are linear and sequential. Rather, variables and their relations can be regarded as the product of parallel processes. The authors discuss the results as a challenge to core assumptions of SIT.     

The source of dual-task limitations: Serial or parallel processing of multiple response selections?

Although it is generally recognized that the concurrent performance of two tasks incurs costs, the sources of these dual-task costs remain controversial. The serial bottleneck model suggests that serial postponement of task performance in dual-task conditions results from a central stage of response selection that can only process one task at a time. Cognitive-control models, by contrast, propose that multiple response selections can proceed in parallel, but that serial processing of task performance is predominantly adopted because its processing efficiency is higher than that of parallel processing. In the present study, we empirically tested this proposition by examining whether parallel processing would occur when it was more efficient and financially rewarded. The results indicated that even when parallel processing was more efficient and was incentivized by financial reward, participants still failed to process tasks in parallel. We conclude that central information processing is limited by a serial bottleneck.     

Two-digit number processing: holistic,decomposed or hybrid? A computational modelling approach

Currently, there are three competing theoretical accounts concerning the nature of two-digit number magnitude representation: a holistic, a strictly decomposed, and a hybrid model. Observation of the unit-decade compatibility effect (Nuerk et al. in Cognition 82:B25–B33, 2001) challenged the view of two-digit number magnitude to be represented as one integrated entity. However, at the moment there is no study distinguishing between the decomposed and the hybrid model. The present study addressed this issue using a computational modelling approach. Three network models complying with the constraints of all three theoretical models were programmed and trained on two-digit number comparison. Models were compared as to how well they accounted for empirical effects in the most parsimonious way. Generally, this evaluation indicated that the empirical data were simulated best by the strictly decomposed model. Implications of these results for our understanding of the nature of human number magnitude representation are discussed.     

Preattentive processing or prefocal processing?

The concept of preattentive processing is analyzed and alternative views of it are presented. A basic question is whether processing required for preattentive input selection is qualitatively different from post-selection processing. In order to study this, subjects were presented in one set of conditions with one stimulus at either of two locations, and in another set of conditions, simultaneously with two stimuli. The stimuli could be green or red, or large or small. Subjects were asked to indicate the location (or the color, or the size) of the single stimulus in the single-stimulus conditions, or of a predesignated stimulus (say, the red one) in the dual-stimulus conditions. Responses were generally slower in the dual-stimulus conditions. The increases in reaction time were accounted for by the times it takes to process for response selection the properties by which the target stimulus could be selected, as indicated by the results of two control conditions. The results as well as some other considerations do not support the view that preattentive processing is necessarily of a type that qualitatively differs from post-selection processing.     

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.     

What's different in second-language processing? Evidence from event-related brain potentials

German sentences which were either correct, contained a selectional restriction violation, or a word category violation were presented auditorily to 16 native speakers of German (L1 group) and to 16 native speakers of Russian, who had learned German after the age of 10 (L2 group). Semantic violations elicited an N400 effect for both groups, but with a reduced amplitude and a longer peak latency in the L2 group. Compared to correct sentences, sentences with a phrase structure violation elicited an early anterior negativity followed by a broad centro-parietal positivity in native speakers. By contrast, there was no differential modulation of the early anterior negativity in the L2 group. A late positivity was also elicited in the second language learners, but it was slightly delayed compared to that shown by native speakers. This pattern is discussed in terms of different degrees of automaticity with respect to the subprocesses involved in sentence comprehension.     

Where do dialectal effects on speech processing come from? Evidence from a cross-dialect investigation

Accented speech has been seen as an additional impediment for speech processing; it usually adds linguistic and cognitive load to the listener's task. In the current study we analyse where the processing costs of regional dialects come from, a question that has not been answered yet. We quantify the proficiency of Basque–Spanish bilinguals who have different native dialects of Basque on many dimensions and test for costs at each of three levels of processing–phonemic discrimination, word recognition, and semantic processing. The ability to discriminate a dialect-specific contrast is affected by a bilingual's linguistic background less than lexical access is, and an individual's difficulty in lexical access is correlated with basic discrimination problems. Once lexical access is achieved, dialectal variation has little impact on semantic processing. The results are discussed in terms of the presence or absence of correlations between different processing levels. The implications of the results are considered for how models of spoken word recognition handle dialectal variation.     

Levels of processing: Qualitative differences or task-demand differences?

In nearly all reported orienting task studies, the question is asked before the item or items are presented. This paper reports two experiments wherein the question was asked after the item was presented. These experiments found that an orthographic orienting task did not produce poorer retention than a semantic orienting task when (1) the orthographic task was presented in such a way to ensure that the list items would be encoded as units and (2) the test was designed to eliminate the effect of encoding elaboration to positive-response orienting questions. It was concluded that the depth-of-processing effect was composed of two components. One of these is a task-demand component that affects the probability of encoding target items as identifiable units. The second component of processing depth is trace elaboration to positive-response questions. In most experiments, the two components combine to produce better memory performance for targets presented with semantic orienting questions. However, the two components can be examined independently of each other to determine the degree to which each contributes to a particular experimental effect.     

The processing of non-target words: Semantic or not?

It is known that people reacting to visual words may be affected by the meaning of accompanying non-target words. On the approach to perception developed by Treisman (e.g. 1986), this is surprising, because meaning might be thought to require analysis of conjunctions of physical features and so should remain uncomputed for non-target words. Treisman's approach does, however, assert that analysis of the target may unleash further processes that would prime the system for detection of related words. If this were so, then presentation of the target earlier than the distractors would increase the effect of the latter; whereas if analysis of non-targets were independent of priming, they might be expected to have a smaller effect when delayed. Further, if the sets of words involved are small and familiar, then individual features of primed non-targets, rather than conjunctions of features, might trigger interference. They might especially do so when spatial separation of target and non-target is small.

Five experiments using a paradigm developed by Shaffer and LaBerge confirm that the meaning of non-target words affects response to targets; but (1) this is more true for early than for late arrival of the target; (2) it is affected by target/non-target separation in space; (3) it is true for familiar sets of repeated words but not, in these data, for words used once only in the experiment. It is therefore concluded that the results are more consistent with a Treisman type of explanation than with a theory of universal and automatic full analysis.     

How parallel is visual processing in the ventral pathway?

Visual object perception is usually studied by presenting one object at a time at the fovea. However, the world around us is composed of multiple objects. The way our visual system deals with this complexity has remained controversial in the literature. Some models claim that the ventral pathway, a set of visual cortical areas responsible for object recognition, can process only one or very few objects at a time without ambiguity. Other models argue in favor of a massively parallel processing of objects in a scene. Recent experiments in monkeys have provided important data about this issue. The ventral pathway seems to be able to perform complex analyses on several objects simultaneously, but only during a short time period. Subsequently only one or very few objects are explicitly selected and consciously perceived. Here, we survey the implications of these new findings for our understanding of object processing.     

Two-digit comparison: decomposed, holistic, or hybrid?

We investigate whether two-digit numbers are decomposed for purposes of numerical comparison (e.g., choosing the larger one). Earlier theorists concluded that numbers are processed holistically (Brysbaert, 1995; Dehaene, Dupoux, & Mehler, 1990), or that holistic and decomposed processes operate in parallel (Nuerk, Weger, & Willmes, 2001). In the present experiment, we presented pairs of two-digit numbers with a decade distance of either zero (e.g., 54-57) or one (54-61). If a holistic process contributes to two-digit comparison, there should be an overall distance effect for number pairs with a decade distance of one. On the other hand, if numbers are decomposed and a holistic comparison does not contribute, this overall distance effect should be absent for these number pairs. Evidence is found that, at least in the present task settings, numbers are not compared holistically. The results are interpreted in terms of a recently proposed theory of numerical cognition (Verguts & Fias, 2004; Verguts, Fias, & Stevens, in press).     

Can auditory deviant stimuli temporarily suspend cognitive processing? Evidence from patients with anxiety

While anxiety is typically thought to increase distractibility, this notion mostly derives from studies using emotionally loaded distractors presented in the same modality as the target stimuli and tasks involving crosstalk interference. We examined whether pathological anxiety might also increase distractibility for emotionally neutral irrelevant sounds presented prior to target stimuli in a task where these stimuli do not compete for selection. Patients with anxiety and control participants categorized visual digits preceded by task-irrelevant sounds that changed on rare trials (auditory deviance). Both groups exhibited an equivalent increase in response times following a deviant sound but patients showed a reduction of response accuracy, which was entirely due to an increase in response omissions. We conclude that the involuntary capture of attention by unexpected stimuli may, in patients with anxiety, result in a temporary suspension of cognitive activity.     

Errors in proofreading: Evidence for syntactic control of letter processing?

The present study compared the rates of detection of misspellings in content and in function words, controlling for the effects of familiarity by studying verbs that could be either content words or function words according to the context. In agreement with previous studies, it was found that errors were more readily detected in content words than in function words, thereby clearly demonstrating the importance of syntactic factors in processing the words in a text. Unlike previous studies, we did not find consistent evidence that errors changing the overall word shape were detected more easily than errors preserving word shape, and we found no evidence that the position of the error in the word affected its rate of detection. These findings were interpreted in the framework of an interactive approach to the reading process.     

Are historic years understood as numbers or events? An fMRI study of numbers with semantic associations

While numbers generally cue processing of quantity or order, they can also contain semantic information, as in the case of historic years (e.g., “1492” calls forth associations of Columbus sailing the ocean blue). Whether these dates are processed as quantities or events may depend on the context in which they occur. We examined such “ambiguous number” processing in two different contexts using a paired-comparison task, recording both behavioral responses and brain activity. Participants were either asked to think of all items as numbers and to choose the larger number, or were told to treat the comparators as events and to choose the later event. Behaviorally, all events showed a normal distance effect, establishing that they may be understood and compared in an ordinal sequence. Functional magnetic resonance imaging (fMRI) demonstrated significant differences between years when treated as numbers versus as events. Dates in both contexts shared activity in parietal lobe regions previously implicated in number processing. Dates as numbers showed no extra-numeric activity, while dates thought of as events evoked activity in temporal semantic processing and frontal semantic retrieval areas. These differences suggest that extra-numeric information may be easily accessed and incorporated during processing when supported by even a weak context. This work supports previous studies showing a dissociation between quantity and meaning, and illustrates the brain areas involved in these different aspects.     

Are historic years understood as numbers or events? An fMRI study of numbers with semantic associations

While numbers generally cue processing of quantity or order, they can also contain semantic information, as in the case of historic years (e.g., “1492” calls forth associations of Columbus sailing the ocean blue). Whether these dates are processed as quantities or events may depend on the context in which they occur. We examined such “ambiguous number” processing in two different contexts using a paired-comparison task, recording both behavioral responses and brain activity. Participants were either asked to think of all items as numbers and to choose the larger number, or were told to treat the comparators as events and to choose the later event. Behaviorally, all events showed a normal distance effect, establishing that they may be understood and compared in an ordinal sequence. Functional magnetic resonance imaging (fMRI) demonstrated significant differences between years when treated as numbers versus as events. Dates in both contexts shared activity in parietal lobe regions previously implicated in number processing. Dates as numbers showed no extra-numeric activity, while dates thought of as events evoked activity in temporal semantic processing and frontal semantic retrieval areas. These differences suggest that extra-numeric information may be easily accessed and incorporated during processing when supported by even a weak context. This work supports previous studies showing a dissociation between quantity and meaning, and illustrates the brain areas involved in these different aspects.     

Is there parallel and independent hemispheric processing of intonational and phonetic components of dichotic speech stimuli?

The possibility of hemisphere interaction in the processing of spoken language was studied in two dichotic listening experiments. The stimulus material consisted of six CV syllable triplets each spoken with each one of six intonation contours. In Experiment I, 15 aphasic patients, 8 patients with unilateral right hemisphere lesions, and 10 normal controls were asked to identify the four components of a dichotic item from a multiple-choice (MC) set comprising all possible CV triplets and intonation contours. In Experiment II, 30 normal subjects were required to identify either the right or left ear stimulus alone from an MC set comprising the right and left ear stimulus together with the two wrong combinations of right ear CV triplet with left ear intonation and vice versa. It is concluded from the results that the left hemisphere is capable of processing both phonetic and intonational information and that there is neither the necessity nor the tendency for right hemisphere participation in the perception of spoken language.     

Features of laterally displayed faces: Saliency or top-down processing?

Facial features differ in their importance for face recognition. However, it remains uncertain if this phenomenon reflects actual feature saliency or an effect of their top vs. down position in the stimulus (face). Consequently, the saliency of hair, eyes, and mouth has been studied with 32 female subjects by presenting the material right-side up or upside-down in a multiple-choice recognition task. In addition, stimuli were laterally displayed in the visual hemifields since it was possible that both interpretations would be correct, each specifically linked to a given cerebral hemisphere. In one condition, a feature was removed from the displayed face; in the other condition, this isolated feature only was shown. The usual saliency was observed and was maintained in the reversed orientation, which did not support the top-down interpretation. In addition, the inversion did not affect the processing of isolated features. Finally, the order of conditions affected the processing of isolated features in the right field only.     

Lexical processing of ambiguous words: dominance or associative strength?

Four experiments examined the role of meaning frequency (dominance) and associative strength (measured by associative norms) in the processing of ambiguous words in isolation. Participants made lexical decisions to targets words that were associates of the more frequent (dominant) or less frequent (subordinate) meaning of a homograph prime. The first two experiments investigated the role of associative strength at long SOAs (Stimulus Onset Asynchrony) (750 ms.), showing that meaning is facilitated by the targets' associative strength and not by their dominance. The last two experiments traced the role associative strength at short SOAs (250 ms), showing that the manipulation of the associative strength has no effect in the semantic priming. The conclusions are: on the one hand, semantic priming for homographs is due to associative strength manipulations at long SOAs. On the other hand, the manipulation of the associative strength has no effect when automatic processes (short SOAs) are engaged for homographs.