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Wim Fias

Publications and source records attributed to Wim Fias.

At least 19 recordsLinked to original sources
PubMed2007

Priming reveals differential coding of symbolic and non-symbolic quantities.

Number processing is characterized by the distance and the size effect, but symbolic numbers exhibit smaller effects than non-symbolic numerosities. The difference between symbolic and non-symbolic processing can either be explained by a different kind of underlying representation or by parametric differences within the same type of underlying representation. We performed a primed naming study to investigate this issue. Prime and target format were manipulated (digits or collections of dots) as well as the numerical distance between prime and target value. Qualitatively different priming patterns were observed for the two formats, showing that the underlying representations differed in kind: Digits activated mental number representations of the place coding type, while collections of dots activated number representations of the summation coding type.

Adult↗
PubMed2006

Automatic response activation of implicit spatial information: Evidence from the SNARC effect.

In the present paper, we focus on how irrelevant implicit spatial information is processed. By irrelevant we mean information that is not required to fulfill the task and by implicit we mean information that is not directly available in the external stimulus. A good example of a task in which such information exists is the SNARC task [Dehaene, S., Bossini, S., & Giraux, P. (1993). The mental representation of parity and number magnitude. Journal of Experimental Psychology: General, 122, 371-396]. The SNARC effect shows that the magnitude of a number, although irrelevant to the task, activates spatial codes that may interfere with the task-related response. These spatial associations exist both for the horizontal and the vertical direction. In Experiment 1, response keys were discriminating in the vertical or the horizontal direction. It is shown that the impact of the numerical spatial codes on overt behavior, although automatic, depends on the response discrimination of the horizontal or the vertical dimension. In Experiment 2, response keys were assigned such that both the horizontal and the vertical direction of the response were discriminating. In this case, the horizontal and the vertical dimension of the irrelevant numerical spatial codes were shown to interact. In general, the results are in line with the response-discrimination account [Ansorge, U., & Wühr, P. (2004). A response-discrimination account of the Simon effect. Journal of Experimental Psychology: Human Perception and Performance, 30, 365-377].

Adult↗
PubMed2006

Further evidence that the SNARC effect is processed along a dual-route architecture: Evidence from the lateralized readiness potential.

In a binary response setting, it has been frequently observed that small numbers are reacted to faster with the left hand and large numbers with the right hand (i. e., the SNARC-effect) which reflects the spatial left-right orientation of the mental number line (Dehaene, Bossini, & Giraux, 1993). In line with the work of Keus and Schwarz (in press), we investigated the locus of the conflict in the SNARC effect in a parity judgment task with the Arabic numerals 1, 2, 8, or 9. Differences between compatible (left-hand response to 1 or 2 and right-hand response to 8 and 9) and incompatible SNARC conditions (left-hand response to 8 or 9 and right-hand response to 1 or 2) were observed in the lateralized readiness potential (LRP) but not in the peak latency of the P300. In accordance with Keus and colleagues (Keus, Jenks, & Schwarz, 2005), we argue that the locus of the conflict is situated at intermediate response-related stages. However, instead of adopting a single-route processing architecture, a dual route account is proposed as the underlying processing architecture explaining the SNARC effect.

Adult↗
PubMed2006

Numbers and space: a computational model of the SNARC effect.

The SNARC (spatial numerical associations of response codes) effect reflects the tendency to respond faster with the left hand to relatively small numbers and with the right hand to relatively large numbers (S. Dehaene, S. Bossini, & P. Giraux, 1993). Using computational modeling, the present article aims to provide a framework for conceptualizing the SNARC effect. In line with models of spatial stimulus-response congruency, the authors modeled the SNARC effect as the result of parallel activation of preexisting links between magnitude and spatial representation and short-term links created on the basis of task instructions. This basic dual-route model simulated all characteristics associated with the SNARC effect. In addition, 2 experiments tested and confirmed new predictions derived from the model.

Adult↗
PubMed2006

Shared spatial representations for numbers and space: the reversal of the SNARC and the Simon effects.

In 4 experiments, the authors investigated the reversal of spatial congruency effects when participants concurrently practiced incompatible mapping rules (J. G. Marble & R. W. Proctor, 2000). The authors observed an effect of an explicit spatially incompatible mapping rule on the way numerical information was associated with spatial responses. The authors also observed an effect of an incompatible numerical mapping rule (if smaller than 5, press right; if larger than 5, press left) on the Simon effect. This effect was observed only when both tasks used the same effectors. The results point to a shared spatial representation for explicit spatial information (locations) and implicit spatial information (numbers).

Adolescent↗
PubMed2005

The representation of multiplication facts: developmental changes in the problem size, five, and tie effects.

In this study, we investigated the development of basic effects that have been found in single-digit multiplication arithmetic: the problem size, five, and tie effects. Participants (9-, 10-, and 11-year-olds and adults) performed a production task on simple multiplication. The procedure replicated study [Canadian Journal of Psychology, Vol. 39, pp. 338-366], but the results show that the gradual decrease of the problem size effect ends in sixth grade. We report analyses on raw latencies and state trace analyses that take into account reaction time scaling as a function of age. The results show that 11-year-olds do not differ significantly from adults on any of the three effects. Before 11 years of age, interesting developmental changes occur.

Adult↗
PubMed2005

Naming two-digit arabic numerals: evidence from masked priming studies.

The authors investigated how 2-digit Arabic numerals are named by looking at the effects of masked primes on the naming latencies. Target numerals were named faster when prime and target shared a digit at the same position (e.g., the target 28 primed by 18 and 21). In contrast, naming latencies were slower when prime and target shared 1 or 2 digits at non-corresponding places (e.g., the target 28 primed by 82, 86, or 72). Subsequent experiments showed that these priming effects were situated at the level of the verbal production of the Arabic numerals. The data point to a non-semantically mediated route from visual input to verbal output in the naming of 2-digit Arabic numerals.

Adolescent↗
PubMed2005

Negative priming with numbers: no evidence for a semantic locus.

Selective attention has been studied extensively using the negative priming (NP) paradigm. An important issue regards the representational level at which NP occurs. We investigated this issue by using numbers as stimuli. Because numbers have a well-defined semantic organization, which can be clearly measured by means of the distance effect, they are very suitable for testing the assumption that NP is situated at a central semantic level. Four experiments are presented in which the numerical distance between prime distractor and probe target was manipulated. The task was magnitude comparison. Target and distractor were defined on the basis of colour. In Experiment 1, all numbers were presented in Arabic format; NP was observed only with identical prime distractor and probe target, and no distance-related NP was observed. This could not be explained by a decay of inhibition since in Experiment 2 similar results were obtained with a shortened response-to-stimulus interval. Experiment 3 showed that these observations also hold for numbers presented verbally. Nevertheless, a cross-notational experiment with Arabic prime and verbal probe (Experiment 4) revealed no NP whatsoever and excluded the possibility that the absence of distance-related negative priming was the result of a fine-tuned inhibitory mechanism operating at the semantic level. The results are considered in the light of current theories of negative priming.

Adolescent↗
PubMed2005

Interacting neighbors: a connectionist model of retrieval in single-digit multiplication.

For most adults, retrieval is the most common way to solve a single-digit multiplication problem (Campbell & Xue, 2001). Many theories have been proposed to describe the underlying mechanism of arithmetical fact retrieval. Testing their validity hinges on evaluating how well they account for the basic findings in mental arithmetic. The most important findings are the problem size effect (small multiplication problems are easier than larger ones; cf. 3 x 2 and 7 x 8), the five effect (problems with 5 are easier than can be accounted for by their size), and the tie effect (problems with identical operands are easier than other problems; cf. 8 x 8 and 8 x 7). We show that all existing theories have difficulties in accounting for one or more of these phenomena A new theory is presented that avoids these difficulties. The basic assumption is that candidate answers to a particular problem are in cooperative/competitive interactions and these interactions favor small, five, and tie problems. The theory is implemented as a connectionist model, and simulation data are described that are in good accord with empirical data.

Adult↗
PubMed2005

A model of exact small-number representation.

To account for the size effect in numerical comparison, three assumptions about the internal structure of the mental number line (e.g., Dehaene, 1992) have been proposed. These are magnitude coding (e.g., Zorzi & Butterworth, 1999), compressed scaling (e.g., Dehaene, 1992), and increasing variability (e.g., Gallistel & Gelman, 1992). However, there are other tasks besides numerical comparison for which there is clear evidence that the mental number line is accessed, and no size effect has been observed in these tasks. This is contrary to the predictions of these three assumptions. Moreover, all three assumptions have difficulties explaining certain symmetries in priming studies of number naming and parity judgment. We propose a neural network model that avoids these three assumptions but, instead, uses place coding, linear scaling, and constant variability on the mental number line. We train the model on naming, parity judgment, and comparison and show that the size effect appears in comparison, but not in naming or parity judgment. Moreover, no asymmetries appear in primed naming or primed parity judgment with this model, in line with empirical data. Implications of our findings are discussed.

Comprehension↗
PubMed2004

"I can write seven but I can't say it": a case of domain-specific phonological output deficit for numbers.

While it is established that numbers represent a category-specific semantic domain being dissociable from other semantic domains, it is a debated issue whether the category-specific dissociability persists at a level of lexical processing or whether words and number words are processed by the same lexical mechanisms. In most of the documented cases of brain damage, lexical processing of words and number words was equally spared or impaired. Here, we describe the case of a patient who after recovering from his naming disorders, showed a selective deficit in the spoken production of numbers with spared number writing and number comprehension abilities. After having ruled out alternative interpretations, we can conclude that these results indicate that words and numbers are not only categorically organised at the semantic level but that they are also processed by different lexical mechanisms. In addition, the results argue in favour of the existence of different modality-specific output lexicons for the written and spoken production of numerals.

Cerebral Cortex↗
PubMed2004

Oculomotor bias induced by number perception.

Previous research with manual response methods has found evidence for an association between numbers and space. The present study investigated whether eye movements also show this association. Eye movement responses were recorded from 15 healthy participants as they categorized the digits 0-9 as odd or even. Responses were initiated faster to the left in response to small digits and faster to the right in response to large digits. Movement amplitudes were not systematically affected by either number magnitude or parity. These results provide further evidence for a spatially oriented "mental number line".

Adolescent↗
PubMed2004

Representation of number in animals and humans: a neural model.

This article addresses the representation of numerical information conveyed by nonsymbolic and symbolic stimuli. In a first simulation study, we show how number-selective neurons develop when an initially uncommitted neural network is given nonsymbolic stimuli as input (e.g., collections of dots) under unsupervised learning. The resultant network is able to account for the distance and size effects, two ubiquitous effects in numerical cognition. Furthermore, the properties of the network units conform in detail to the characteristics of recently discovered number-selective neurons. In a second study, we simulate symbol learning by presenting symbolic and nonsymbolic input simultaneously. The same number-selective neurons learn to represent the numerical meaning of symbols. In doing so, they show properties reminiscent of the originally available number-selective neurons, but at the same time, the representational efficiency of the neurons is increased when presented with symbolic input. This finding presents a concrete proposal on the linkage between higher order numerical cognition and more primitive numerical abilities and generates specific predictions on the neural substrate of number processing.

Animals↗
PubMed2003

Parietal representation of symbolic and nonsymbolic magnitude.

The close behavioral parallels between the processing of quantitative information conveyed by symbolic and nonsymbolic stimuli led to the hypothesis that there exists a common cerebral representation of quantity (Dehaene, Dehaene-Lambertz, & Cohen, 1998). The neural basis underlying the encoding of number magnitude has been localized to regions in and around the intraparietal sulcus (IPS) by brain-imaging studies. However, it has never been demonstrated that these same regions are also involved in the quantitative processing of nonsymbolic stimuli. Using functional brain imaging, we explicitly tested the hypothesis of a common substrate. Angles, lines, and two-digit numbers were presented pairwise, one to the left and one to the right of the fixation point. In the three comparison tasks, participants (n = 18) pressed the key on the side of the largest quantity. In the three control tasks, they indicated the side on which dimming occurred. A conjunction analysis between the three subtractions (comparison task-control task) revealed a site in left IPS that is specifically responsive when two stimuli have to be compared quantitatively, irrespective of stimulus format. The results confirm the hypothesis that quantity is represented by a common mechanism for both symbolic and nonsymbolic stimuli in IPS. In addition, the interaction between task and type of stimulus identified a region anterior to the conjunction site, not specific for quantitative processing, but reflecting general processes loaded by number processing.

Adult↗
PubMed2003

The mental representation of ordinal sequences is spatially organized.

In the domain of numbers the existence of spatial components in the representation of numerical magnitude has been convincingly demonstrated by an association between number magnitude and response preference with faster left- than right-hand responses for small numbers and faster right- than left-hand responses for large numbers (Dehaene, S., Bossini, S., & Giraux, P. (1993) The mental representation of parity and number magnitude. Journal of Experimental Psychology: General, 122, 371-396). Because numbers convey not only real or integer meaning but also ordinal meaning, the question of whether non-numerical ordinal information is spatially coded naturally follows. While previous research failed to show an association between ordinal position and spatial response preference, we present two experiments involving months (Experiment 1) and letters (Experiment 2) in which spatial coding is demonstrated. Furthermore, the response-side effect was obtained with two different stimulus-response mappings. The association occurred both when ordinal information was relevant and when it was irrelevant to the task, showing that the spatial component of the ordinal representation can be automatically activated.

Adult↗