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The cross-modal semantic distance effect between tactile and symbolic numerosities. The larger the semantic distance between both numerosities, the shorter the mean response time. Error bars represent 95% within-subject confidence intervals (cf. Loftus and Masson, 1994).
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Evidence for an approximate analog system of numbers has been provided by the finding that the comparison of two numerals takes longer and is more error-prone if the semantic distance between the numbers becomes smaller (so-called numerical distance effect). Recent embodied theories suggest that analog number representations are based on previous s...
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... There have been only a few attempts to investigate how tactile number information is processed in the human brain. In these experiments, tactile numbers were nonsymbolic and were mostly presented sequentially (Cohen et al., 2014;Krause et al., 2013;Sixtus et al., 2020). Krause et al. (2013) asked participants to compare tactually presented numerosities (i.e., simultaneous stimulation of one to four fingers via piezoelectric Braille cells) with visually presented symbolic numbers (Arabic digits). ...
... In these experiments, tactile numbers were nonsymbolic and were mostly presented sequentially (Cohen et al., 2014;Krause et al., 2013;Sixtus et al., 2020). Krause et al. (2013) asked participants to compare tactually presented numerosities (i.e., simultaneous stimulation of one to four fingers via piezoelectric Braille cells) with visually presented symbolic numbers (Arabic digits). They found a crossmodal numerical distance effect (i.e., the larger the distance between two numbers to be compared, the better the performance), which indicates at least a partial representational overlap between those two notations (Krause et al., 2013). ...
... Krause et al. (2013) asked participants to compare tactually presented numerosities (i.e., simultaneous stimulation of one to four fingers via piezoelectric Braille cells) with visually presented symbolic numbers (Arabic digits). They found a crossmodal numerical distance effect (i.e., the larger the distance between two numbers to be compared, the better the performance), which indicates at least a partial representational overlap between those two notations (Krause et al., 2013). Two recent experiments conducted with a group of sighted Braille readers used tactile Braille (symbolic) numbers. ...
The Triple-Code Model stipulates that numerical information from different formats and modalities converges on a common magnitude representation in the Intraparietal Sulcus (IPS). To what extent the representations of all numerosity forms overlap remains unsolved. It has been postulated that the representation of symbolic numerosities (for example, Arabic digits) is sparser and grounded in an existing representation that codes for non-symbolic numerosity information (i.e., sets of objects). Other theories argue that numerical symbols represent a separate number category that emerges only during education. Here, we tested a unique group of sighted tactile Braille readers with numerosities 2, 4, 6 and 8 in three number notations: Arabic digits, sets of dots, tactile Braille numbers. Using univariate methods, we showed a consistent overlap in activations evoked by these three number notations. This result shows that all three used notations are represented in the IPS, which may suggest at least a partial overlap between the representations of the three notations used in this experiment. Using MVPA, we found that only non-automatized number information (Braille and sets of dots) allowed successful number classification. However, the numerosity of one notation could not be predicted above chance from the brain activation patterns evoked by another notation (no cross-classification). These results show that the IPS may host independent number codes in overlapping cortical circuits. In addition, they suggest that the level of training in encoding a given type of number information is an important factor that determines the amount of exploitable information and needs to be controlled for in order to identify the neural code underlying numerical information per se.
... Either way, recent studies have also found a horizontally distributed SPARC effect in non-musicians (Fischer et al. 2013;Weis et al. 2016). Moreover, SNARC-like effects are also seen in the tactile domain (Bollini et al. 2020;Brozzoli et al. 2008;Krause et al. 2013). While Brozzoli et al. (2008) and Krause et al. (2013) investigated the number representation of finger counting, in our previous work, we investigated the role of magnitude in the tactile modality (Bollini et al. 2020). ...
... Moreover, SNARC-like effects are also seen in the tactile domain (Bollini et al. 2020;Brozzoli et al. 2008;Krause et al. 2013). While Brozzoli et al. (2008) and Krause et al. (2013) investigated the number representation of finger counting, in our previous work, we investigated the role of magnitude in the tactile modality (Bollini et al. 2020). We demonstrated with an SRC task in the tactile modality that the effect of magnitude congruency was more substantial than that of spatial congruency. ...
The human brain creates an external world representation based on magnitude judgments by estimating distance, numerosity, or size. The magnitude and spatial representation are hypothesized to rely on common mechanisms shared by different sensory modalities. We explored the relationship between magnitude and spatial representation using two different sensory systems. We hypothesize that the interaction between space and magnitude is combined differently depending on sensory modalities. Furthermore, we aimed to understand the role of the spatial reference frame in magnitude representation. We used stimulus–response compatibility (SRC) to investigate these processes assuming that performance is improved if stimulus and response share common features. We designed an auditory and tactile SRC task with conflicting spatial and magnitude mapping. Our results showed that sensory modality modulates the relationship between space and magnitude. A larger effect of magnitude over spatial congruency occurred in a tactile task. However, magnitude and space showed similar weight in the auditory task, with neither spatial congruency nor magnitude congruency having a significant effect. Moreover, we observed that the spatial frame activated during tasks was elicited by the sensory inputs. The participants' performance was reversed in the tactile task between uncrossed and crossed hands posture, suggesting an internal coordinate system. In contrast, crossing the hands did not alter performance (i.e., using an allocentric frame of reference). Overall, these results suggest that space and magnitude interaction differ in auditory and tactile modalities, supporting the idea that these sensory modalities use different magnitude and spatial representation mechanisms.
... While an increasing number of studies investigated this mental magnitude and spatial systems in visual and auditory domains (Wallace, 1971;Roswarski and Proctor, 2000;Wascher et al., 2001;Phillips and Ward, 2002;Roder et al., 2007;Crollen et al., 2017;Ruzzoli and Soto-Faraco, 2017), only a few studies have examined the tactile mental magnitude effect. The few studies that have involved tactile modality are based on a digital representation of the number (Brozzoli et al., 2008;Krause et al., 2013). Such studies have used tactile modality to investigate the relationship between number representation and finger counting using paradigms as numerical distance effect (Krause et al., 2013) or number-based attentional cueing (Brozzoli et al., 2008). ...
... The few studies that have involved tactile modality are based on a digital representation of the number (Brozzoli et al., 2008;Krause et al., 2013). Such studies have used tactile modality to investigate the relationship between number representation and finger counting using paradigms as numerical distance effect (Krause et al., 2013) or number-based attentional cueing (Brozzoli et al., 2008). These investigate a body-based representation of numbers rather than a possible magnitude effect in tactile modality. ...
... While studies have increasingly investigated numerosity processing and finger-number association, few have examined the association of the tactile modality with space (i.e., low/high frequencies associated with left/right spaces, respectively)that is, until now. A fact that has emerged from studies regarding numerosity and subitizing (Riggs et al., 2006;Brozzoli et al., 2008;Plaisier et al., 2009;Plaisier and Smeets, 2011;Krause et al., 2013) is that touch and vision share the same numerosity representation. Here, to investigate the effect of mental magnitude representation on the spatial S-R compatibility effect, we insert conflicts into two S-R congruency tasks. ...
The human brain uses perceptual information to create a correct representation of the external world. Converging data indicate that the perceptual processing of, space, and quantities frequently is based on a shared mental magnitude system, where low and high quantities are represented in the left and right space, respectively. The present study explores how the magnitude affects spatial representation in the tactile modality. We investigated these processes using stimulus-response (S-R) compatibility tasks (i.e., sensorimotor tasks that present an association/dissociation between the perception of a stimulus and the required action, generally increasing/decreasing accuracy and decreasing/increasing reaction times of the subject). In our study, the participant performed a discrimination task between high- and low-frequency vibrotactile stimuli, regardless of the stimulation’s spatial position. When the response code was incompatible with the mental magnitude line (i.e., left button for high-frequency and right button for low-frequency responses), we found that the participants bypassed the spatial congruence, showing a magnitude S-R compatibility effect. We called this phenomenon the Spatial–Tactile Association of Response Codes (STARC) effect. Moreover, we observed that the internal frame of reference embodies the STARC effect. Indeed, the participants’ performance reversed between uncrossed- and crossed-hands posture, suggesting that spatial reference frames play a role in the process of expressing mental magnitude, at least in terms of the tactile modality.
... Symbolic representation of numbers and mathematical operations has facilitated technological progress throughout human history. However, cultural (Butterworth, Reeve, & Reynolds, 2011;Pica, Lemer, Izard, & Dehaene, 2004), cognitive (Krause, Bekkering, & Lindemann, 2013;Price, Palmer, Battista, & Ansari, 2012;Revkin, Piazza, Izard, Cohen, & Dehaene, 2008), developmental (Izard, Sann, Spelke, & Streri, 2009;Xu & Spelke, 2000), and comparative (Agrillo & Bisazza, 2014;Beran, 2006) psychology provide evidence for the existence of rudimentary numerical abilities that are independent from educational factors and predate the emergence of language. Such abilitiesoften referred to as non-symbolic numerical abilities (Agrillo, Piffer, & Adriano, 2013;Gilmore, McCarthy, & Spelke, 2010;Park, Bermudez, Roberts, & Brannon, 2016) -seem to be evolutionarily ancient, given the unquestionable advantages they provide in terms of fitness and survival in the natural environment. ...
Many studies have investigated whether numerical and spatial abilities share similar cognitive systems. A novel approach to this issue consists of investigating whether the same perceptual biases underlying size illusions can be identified in numerical estimation tasks. In this study, we required adult participants to estimate the number of white dots in arrays made of white and black dots displayed in such a way as to generate horizontal–vertical illusions with inverted T and L configurations. In agreement with previous literature, we found that participants tended to underestimate the target numbers. However, in the presence of the illusory patterns, participants were less inclined to underestimate the number of vertically aligned white dots. This reflects the perceptual biases underlying horizontal–vertical illusions. In addition, we identified an enhanced illusory effect when participants observed vertically aligned white dots in the T shape compared to the L shape, a result that resembles the length bisection bias reported in the spatial domain. Overall, we found the first evidence that numerical estimation differs as a function of the vertical or horizontal displacement of the stimuli. In addition, the involvement of the same perceptual biases observed in spatial tasks supports the idea that spatial and numerical abilities share similar cognitive processes.
... The literature regarding the processing of cardinal meanings of finger sets so far shows inconsistent results, as will be indicated by the following section (for broader reviews, see Domahs, Kaufmann, & Fischer, 2012). Krause, Bekkering, and Lindemann (2013) found that the cardinal meaning of finger sets is mentally processed similar to the cardinal meaning of Arabic numbers. Participants in their study verbally compared a visual Arabic number with the amount of tactually stimulated fingers in a same-different task. ...
... Cohen, Naparstek, and Henik (2014) furthermore found that judgements concerning the amount of tactually stimulated fingers were faster and more accurate when the stimulated sets of fingers consisted of neighbouring fingers than when they consisted of non-neighbouring fingers. While Cohen et al. (2014) did not report an advantage for the simultaneous stimulation of counting-congruent finger configurations (i.e., neighbouring fingers that include the thumb for participants who start to count on their thumb) as compared to other neighbouring configurations, Krause et al. (2013) did. However, in Krause et al.'s (2013) first experiment, the countingincongruent sets of fingers differed substantially from the counting-congruent sets: the latter were sets of neighbouring fingers including the thumb and the former were sets of neighbouring fingers including the pinkie. ...
... However, in Krause et al.'s (2013) first experiment, the countingincongruent sets of fingers differed substantially from the counting-congruent sets: the latter were sets of neighbouring fingers including the thumb and the former were sets of neighbouring fingers including the pinkie. In their second experiment, Krause et al. (2013) used sequential instead of simultaneous stimulations; congruency was defined by the stimulation direction relative to the mid-sagittal plane. Both hands were always prone, so congruent stimulation ran from the thumb outwards and incongruent stimulation ran inwards towards the thumb. ...
Finger counting is one of the first steps in the development of mature number concepts. With a one-to-one correspondence of fingers to numbers in Western finger counting, fingers hold two numerical meanings: one is based on the number of fingers raised and the second is based on their ordinal position within the habitual finger counting sequence. This study investigated how these two numerical meanings of fingers are intertwined with numerical cognition in adults. Participants received tactile stimulation on their fingertips of one hand and named either the number of fingers stimulated (2, 3, or 4 fingers; Experiment 1) or the number of stimulations on one fingertip (2, 3, or 4 stimulations; Experiment 2). Responses were faster and more accurate when the set of stimulated fingers corresponded to finger counting habits (Experiment 1) and when the number of stimulations matched the ordinal position of the stimulated finger (Experiment 2). These results show that tactile numerosity perception is affected by individual finger counting habits and that those habits give numerical meaning to single fingers.
... A few studies to date have investigated how tactile number information is processed. These studies provided important insights into cross-modal number processing; however, they used non-symbolic tactile number coding (number of stimulated fingers; Krause, Bekkering, & Lindemann, 2013;Cohen, Naparstek, & Henik, 2014;Sixtus, Lindemann, & Fischer, 2018). To our knowledge, number coding in a symbolic tactile notation -Braille numbershas not previously been investigated. ...
... In our study, we tested sighted people who learned Braille numbers when they were already fluent in recognizing Arabic digits. Such crossmodal number priming is in line with the notion of a generalized magnitude system (Krause et al., 2013;Walsh, 2003). We propose that during Braille acquisition our participants mapped Braille patterns to their internal number representation. ...
Quantities can be represented by different formats (e.g. symbolic or non-symbolic) and conveyed via different modalities (e.g. tactile or visual). Despite different priming curves: V-shape and step-shape for place and summation coded representation, respectively, the occurrence of priming effect supports the notion of different format overlap on the same mental number line. However, little is known about tactile-visual overlap of symbolic numerosities i.e. Braille numbers to Arabic digits on the magnitude number representation. Here, in a priming experiment, we tested a unique group of sighted Braille readers to investigate whether tactile Braille digits would activate a place-coding type of mental number representation (V-shape), analogous to other symbolic formats. The primes were either tactile Braille digits presented on a Braille display or number words presented on a computer screen. The targets were visually presented Arabic digits, and subjects performed a naming task. Our results reveal a V-shape priming function for both prime formats: tactile Braille and written words representing numbers, with strongest priming for primes of identical value (e.g. "four" and "4"), and a symmetrical decrease of priming strength for neighboring numbers, which indicates that the observed priming is due to identity priming. We thus argue that the magnitude information is processed according to a shared phonological code, independent of the input modality.
... Early evidence that magnitudes can arrange along a hypothetical mental line can be found in the seminal work by Moyer and Landauer (1967) on the distance effect: In that study, when participants were asked to decide which number in a pair was the largest, reaction times (RTs) tended to decrease with absolute difference between the numbers. A possible interpretation of this effect is that the farther apart two numbers are on the mental number line, the easier it is to decide which is the largest and therefore the shorter the RTs (see also Dehaene et al. 1990;Krause et al. 2013;Treccani and Umiltà 2011;cf. Fischer and Shaki 2011;Herrera et al. 2008). ...
... Walsh 2003) and distance (e.g. Krause et al. 2013) effects in a weight comparison task. More precisely, participants were asked to press either a left-or a right-side response key to classify a centrally placed target word-describing an animal (e.g. ...
Stimuli associated with large quantities are typically responded to faster with a right-than a left-side key, whereas stimuli associated with small quantities are typically responded to faster with a left-than a right-side key. This phenomenon is known as the spatial-quantity association of response codes (SQUARC) effect. Here, in two experiments, we explored whether a SQUARC effect can emerge for light versus heavy items. Participants judged whether the weight associated with a central target word, describing an animal (e.g. 'cow'; Experiment 1) or a material (e.g. 'iron'; Experiment 2), was lighter or heavier than the weight associated with a reference word. Responses were provided with a left-and a right-side button. Then, participants estimated the weight associated with target and reference words. In both experiments, evidence for a SQUARC effect emerged. Moreover, response times for each target word decreased with absolute difference between its rated weight and the rated weight of the reference word, in line with a distance effect. Overall, these results provide evidence of a possible spatial representation of weight.
... When the task was speeded comparative judgment, the numerical separation between the stimuli did make a difference. A similar numerical distance effect across modalities was reported by Krause et al. (2013) for magnitude comparisons across the visual and tactile modalities. However, we do not interpret the observed effect as one uniquely associated with number processing. ...
In the number-to-position methodology, a number is presented on each trial and the observer places it on a straight line in a position that corresponds to its felt subjective magnitude. In the novel modification introduced in this study, the two-numbers-to-two-positions method, a pair of numbers rather than a single number is presented on each trial and the observer places them in appropriate positions on the same line. Responses in this method indicate not only the subjective magnitude of each single number but, simultaneously, provide a direct estimation of their subjective numerical distance. The results of four experiments provide strong evidence for a linear representation of numbers and, commensurately, for the linear representation of numerical distances. We attribute earlier results that indicate a logarithmic representation to the ordered nature of numbers and to the task used and not to a truly non-linear underlying representation.
... Furthermore, not only active posture production or finger movements are linked to number processing, but also passive finger stimulation (Cohen, Aisenberg, & Henik, 2016;Cohen, Naparstek, & Henik, 2014;Krause, Bekkering, & Lindemann, 2013; but see Brozzoli et al., 2008). Krause et al. (2013) reported that enumeration of tactually stimulated fingers and Arabic numerals were processed in a similar vein. ...
... Furthermore, not only active posture production or finger movements are linked to number processing, but also passive finger stimulation (Cohen, Aisenberg, & Henik, 2016;Cohen, Naparstek, & Henik, 2014;Krause, Bekkering, & Lindemann, 2013; but see Brozzoli et al., 2008). Krause et al. (2013) reported that enumeration of tactually stimulated fingers and Arabic numerals were processed in a similar vein. Participants compared two numbers cross-modally and exhibited a distance effecta typical marker of analogue number processingwhich indicates that both number representations drew on the same underlying processes. ...
... No-go trials ensured participants' attention towards the visual stimuli. Instructions were given purely visually and not, for instance, by manipulating the participant's fingers; this was done to avoid tactile stimulation of the fingers, which is also known to trigger numerical concepts (Krause et al., 2013). The implied counting direction was manipulated to ensure equally distributed spatial attention to the left and right sides of the display (in the visual priming condition) and of one's own body (in the motor priming condition). ...
Numbers are omnipresent in daily life. They vary in display format and in their meaning so that it does not seem self-evident that our brains process them more or less easily and flexibly. The present thesis addresses mental number representations in general, and specifically the impact of finger counting on mental number representations. Finger postures that result from finger counting experience are one of many ways to convey numerical information. They are, however, probably the one where the numerical content becomes most tangible. By investigating the role of fingers in adults’ mental number representations the four presented studies also tested the Embodied Cognition hypothesis which predicts that bodily experience (e.g., finger counting) during concept acquisition (e.g., number concepts) stays an immanent part of these concepts. The studies focussed on different aspects of finger counting experience. First, consistency and further details of spontaneously used finger configurations were investigated when participants repeatedly produced finger postures according to specific numbers (Study 1). Furthermore, finger counting postures (Study 2), different finger configurations (Study 2 and 4), finger movements (Study 3), and tactile finger perception (Study 4) were investigated regarding their capability to affect number processing. Results indicated that active production of finger counting postures and single finger movements as well as passive perception of tactile stimulation of specific fingers co-activated associated number knowledge and facilitated responses towards corresponding magnitudes and number symbols. Overall, finger counting experience was reflected in specific effects in mental number processing of adult participants. This indicates that finger counting experience is an immanent part of mental number representations. Findings are discussed in the light of a novel model. The MASC (Model of Analogue and Symbolic Codes) combines and extends two established models of number and magnitude processing. Especially a symbolic motor code is introduced as an essential part of the model. It comprises canonical finger postures (i.e., postures that are habitually used to represent numbers) and finger-number associations. The present findings indicate that finger counting functions both as a sensorimotor magnitude and as a symbolic representational format and that it thereby directly mediates between physical and symbolic size. The implications are relevant both for basic research regarding mental number representations and for pedagogic practices regarding the effectiveness of finger counting as a means to acquire a fundamental grasp of numbers.
... More generally, there is a body of literature that suggests numerical processing is intrinsically linked with a variety of sensorimotor processes (e.g. Besner and Coltheart 1979;Henik and Tzelgov 1982;Cohen Kadosh and Henik 2006;Badets et al. 2007;Domahs et al. 2010;Link et al. 2013;Krause et al. 2013;Krause et al. 2016;Fisher 2012;Moeller et al 2012). On the basis of this work, we hypothesised that the sensorimotor control processes involved in writing (with a pen, pencil, piece of chalk or tablet stylus) would be intrinsically intertwined with the 'higher-order' cognitive processes involved in numerical processing (and more generally in any cognitive processing that relies on spatial representations). ...
Mathematics is often conducted with a writing implement. But is there a relationship between numerical processing and sensorimotor ‘pen’ control? We asked participants to move a stylus so it crossed an unmarked line at a location specified by a symbolic number (1–9), where number colour indicated whether the line ran left–right (‘normal’) or vice versa (‘reversed’). The task could be simplified through the use of a ‘mental number line’ (MNL). Many modern societies use number lines in mathematical education and the brain’s representation of number appears to follow a culturally determined spatial organisation (so better task performance is associated with this culturally normal orientation—the MNL effect). Participants (counter-balanced) completed two consistent blocks of trials, ‘normal’ and ‘reversed’, followed by a mixed block where line direction varied randomly. Experiment 1 established that the MNL effect was robust, and showed that the cognitive load associated with reversing the MNL not only affected response selection but also the actual movement execution (indexed by duration) within the mixed trials. Experiment 2 showed that an individual’s motor abilities predicted performance in the difficult (mixed) condition but not the easier blocks. These results suggest that numerical processing is not isolated from motor capabilities—a finding with applied consequences.
