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The link between various codes of magnitude and their interactions has been studied extensively for many years. In the current study, we examined how the physical and numerical magnitudes of digits are mapped into a combined mental representation. In two psychophysical experiments, participants reported the physically larger digit among two digits. In the identical condition, participants compared digits of an identical value (e.g., "2" and "2"); in the different condition, participants compared digits of distinct numerical values (i.e., "2" and "5"). As anticipated, participants overestimated the physical size of a numerically larger digit and underestimated the physical size of a numerically smaller digit. Our results extend the shared-representation account of physical and numerical magnitudes.

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Previous research has shown that multi-digit number processing is modulated by both place-value and physical size of the digits. By pitting place-value against physical size, the present study examined whether one of the attributes had a greater impact on the automatic processing of multi-digit numbers. In three experiments, participants were presented with two-digit number pairs that appeared in frames. They were instructed to select the larger frame while ignoring the numbers within the frames. Importantly, we manipulated the physical size of the digits (i.e., both decade/unit digits were physically larger) within the frames, the unit-decade compatibility (i.e., the relationship between the numerical values of both decade and unit digits was consistent or inconsistent), and the congruity between the numerical values of the decade digits and the frames' physical size (i.e., decade-value-frame-size congruity). In Experiment 1, where all pairs were unit-decade compatible, a decade-value-frame-size congruity effect emerged for pairs with physically larger decade, but not unit, digits. However, when adding unit-decade incompatible pairs (Experiments 2-3), in unit-decade compatible pairs, there was a decade-value-frame-size congruity effect regardless of the digits' physical size. In contrast, in unit-decade incompatible pairs, there was no decade-value-frame-size congruity effect, even when the physically larger digit (i.e., unit) contradicted the place-value information, presumably due to the cancellation of the opposing influences of the digits' physical sizes their place-values. Overall, these findings suggest that place-value and physical size are intertwined in the Hindu-Arabic numerical system and are processed as one.

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Numerals (i.e., symbolic representations of numerical magnitude) are widespread in our environment and are fundamental to many decisions we make. It has been suggested that the processing of numerical magnitude is automatic. Various robust psychological effects, such as the distance effect (Moyer & Landauer, Nature, 215 (5109), 1519-1520, 1967) and the physical size-congruity effect (SiCE; Henik & Tzelgov, Memory & Cognition, 10 (4), 389-395, 1982), support this claim. Importantly, these effects demonstrate that the processing of numerical magnitude occurs unintentionally and while irrelevant to the task. These aspects often serve as criteria to assess the automatic nature of mental processes. However, evidence for the involvement of attention in the processing of magnitude of numerals somewhat subverts the automaticity account that was originally put forward. To reconcile between evidence in support of the automaticity account and evidence that compromises this account, we drew on another account of automaticity. This account distinguishes between strongly automatic and partly automatic mental processes based on their susceptibility to attentional influences. In the current study, we manipulated endogenous attention while participants completed numerical and physical comparisons of numerals, separately. We observed modulations of the SiCE for physical comparisons but not for numerical comparisons of numerals. That is, the processing of numerical magnitude when irrelevant was subjected to attentional influences, but the processing of their physical magnitude (i.e., size) was not. Therefore, we concluded that processing the numerical magnitude is partly automatic, whereas processing their physical magnitude is strongly automatic.

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I applied the methodology known as maximum likelihood conjoint measurement (MLCM) to diagnose how numerical magnitude affects the perception of physical size of numerals in the size congruity effect (SCE). Traditional theories of the SCE argue for automatic activation of numerical magnitude, and therefore the obligatory interaction in perception between number and size. Participants in the current study were presented with pairs of numerals varying on physical size and numerical magnitude. They judged which member of the pair was physically larger, while ignoring numerical magnitude. Three nested observer models (i.e. independent, additive, and saturated) of the contribution of physical size and numerical magnitude to perceived size were fit to the data using maximum likelihood. The independent observer model exhibited the best fit for the majority of observers. These results cast doubts on the view that numerical magnitude is activated automatically in judgments of physical size of numerals.

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Humans not only process and compare magnitude information such as size, duration, and number perceptually, but they also communicate about these properties using language. In this respect, a relevant class of lexical items are so-called scalar adjectives like "big," "long," "loud," and so on which refer to magnitude information. It has been proposed that humans use an amodal and abstract representation format shared by different dimensions, called the generalised magnitude system (GMS). In this paper, we test the hypothesis that scalar adjectives are symbolic references to GMS representations, and, therefore, GMS gets involved in processing their meaning. Previously, a parallel hypothesis on the relation between number symbols and GMS representations has been tested with the size congruity paradigm. The results of these experiments showed interference between the processing of number symbols and the processing of physical (font-) size. In the first three experiments of the present study (total N = 150), we used the size congruity paradigm and the same/different task to look at the potential interaction between physical size magnitude and numerical magnitude expressed by number words. In the subsequent three experiments (total N = 149), we looked at a parallel potential interaction between physical size magnitude and scalar adjective meaning. In the size congruity paradigm, we observed interference between the processing of the numerical value of number words and the meaning of scalar adjectives, on the one hand, and physical (font-) size, on the other hand, when participants had to judge the number words or the adjectives (while ignoring physical size). No interference was obtained for the reverse situation, i.e., when participants judged the physical font size (while ignoring numerical value or meaning). The results of the same/different task for both number words and scalar adjectives strongly suggested that the interference that was observed in the size congruity paradigm was likely due to a response conflict at the decision stage of processing rather than due to the recruitment of GMS representations. Taken together, it can be concluded that the size congruity paradigm does not provide evidence in support the hypothesis that GMS representations are used in the processing of number words or scalar adjectives. Nonetheless, the hypothesis we put forward about scalar adjectives is still is a promising potential line of research. We make a number of suggestions for how this hypothesis can be explored in future studies.

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Previous work using the numerical comparison task has shown that an empty set, the nonsymbolic manifestation of zero, can be represented as the smallest quantity of the numerical magnitude system. In this study, we examined whether an empty set can be represented as such under conditions of automatic processing in which deliberate processing of stimuli magnitudes is not required by the task. In Experiment 1, participants performed physical and numerical comparisons of empty sets (i.e., empty frames) and of other numerosities presented as framed arrays of 1 to 9 dots. The physical sizes of the frames varied within pairs. Both tasks revealed a size congruity effect (SCE) for comparisons of non-empty sets. In contrast, comparisons to empty sets produced an inverted SCE in the physical comparison task, whereas no SCE was found for comparisons to empty sets in the numerical comparison task. In Experiment 2, participants performed an area comparison task using the same stimuli as Experiment 1 to examine the effect of visual cues on the automatic processing of empty sets. The results replicated the findings of the physical comparison task in Experiment 1. Taken together, our findings indicate that empty sets are not perceived as "zero," but rather as "nothing," when processed automatically. Hence, the perceptual dominance of empty sets seems to play a more important role under conditions of automatic processing, making it harder to abstract the numerical meaning of zero from empty sets.

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The size congruity effect in a numerical Stroop task shows that magnitude judgments of two numbers are faster and more accurate when the numerically larger number also appears in a physically larger size, indicating the interaction between numerical and physical magnitudes. It has recently been suggested that spatial shifts of attention between the two numbers may contribute to the size congruity effect. However, a complete line of evidence for the attentional attribution to the size congruity effect remains to be established. Therefore, the present study aimed to provide further demonstrations for the idea that spatial shifts of attention contribute to the size congruity effect during magnitude judgments regarding either the numerical or physical dimension of two numbers. Participants were sequentially or simultaneously presented with a pair of single-digit Arabic numbers whose numerical and physical magnitudes varied independently. They were instructed to perform a magnitude judgment regarding the numerical value or physical size of the paired numbers. Across three experiments, we consistently found that the size congruity effect was reduced or eliminated when number pairs were presented sequentially compared to when they were presented simultaneously. Because in the sequential presentation mode the paired numbers were successively presented at central fixation and therefore spatial attention shifts should be completely precluded by the central presentation of number stimuli, the present findings support the notion that spatial shifts of attention between numbers in the simultaneous presentation mode play an important role in generating the size congruity effect for both numerical and physical tasks.

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OBJECTIVES: The objective of the present study was to elucidate the mechanism of bioactive molecule extraction from mineralized dentin by calcium hydroxide (Ca(OH)2) and tricalcium silicate cements (TSC). METHODS AND RESULTS: Transmission electron microscopy was used to provide evidence for collagen degradation in dentin surfaces covered with Ca(OH)2 or a set, hydrated TSC for 1-3 months. A one micron thick collagen degradation zone was observed on the dentin surface. Fourier transform-infrared spectroscopy was used to identify increases in apatite/collagen ratio in dentin exposed to Ca(OH)2. Using three-point bending, dentin exposed to Ca(OH)2 exhibited significant reduction in flexural strength. Using size exclusion chromatography, it was found that the small size of the hydroxyl ions derived from Ca(OH)2 enabled those ions to infiltrate the intrafibrillar compartment of mineralized collagen and degrade the collagen fibrils without affecting the apatite minerals. Using ELISA, TGF-ß1 was found to be extracted from dentin covered with Ca(OH)2 for 3 months. Unlike acids that dissolve the mineral component of dentin to release bioactive molecules, alkaline materials such as Ca(OH)2 or TSC released growth factors such as TGF-ß1 via collagen degradation. SIGNIFICANCE: The bioactive molecule extraction capacities of Ca(OH)2 and TSC render these dental materials excellent for pulp capping and endodontic regeneration. These highly desirable properties, however, appear to be intertwined with the untoward effect of degradation of the collagen matrix within mineralized dentin, resulting in reduced flexural strength.

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Premature birth is a significant risk factor for learning disabilities in general and mathematics learning difficulties in particular. However, the exact reasons for this relation are still unknown. While typical numerical development is associated with a frontal-to-parietal shift of brain activation with increasing age, influences of gestational age have hardly been considered so far. Therefore, we investigated the influence of gestational age on the neural correlates of number processing in 6- and 7-year-old children born prematurely (n=16). Only the numerical distance effect - as a measure of intentional number magnitude processing - elicited the fronto-parietal activation pattern typically observed for numerical cognition. On the other hand, the size congruity effect - as a measure of automatic number magnitude processing - was associated with activation of brain areas typically attributed to cognitive control. Most importantly, however, we observed that gestational age reliably predicted the frontal-to-parietal shift of activation observed for the numerical distance effect. Our findings seem to indicate that human numerical development may start even before birth and prematurity might hamper neural facilitation of the brain circuitry subserving numerical cognition. In turn, this might contribute to the high risk of premature children to develop mathematical learning difficulties.

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We describe Jane Dow (JD), a young right-handed female with acalculia following a cerebral infarction in the left intraparietal sulcus. We investigated automatic processing of different types of magnitudes that were presented visually or through imagery. We employed the size congruity task and the mental clock task that differ in stimuli presentation and in working memory load. In the size congruity task, for physical comparisons, JD presented a lack of facilitation effect, suggesting a deficit in the automatic processing of numerical values. In the mental clock task, JD performed as accurate as controls did but much slower. In both tasks, JD presented a steeper distance effect compared to controls, suggesting a deficit in a domain-general comparison process. Our findings present an atypical pattern of magnitude processing following a left parietal lesion that appears not only for visually presented stimuli but also for imagery-based magnitudes. These finding support recent theories suggesting different types of magnitudes are interconnected with each other.

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Many studies demonstrated interactions between number processing and either spatial codes (effects of spatial-numerical associations) or visual size-related codes (size-congruity effect). However, the interrelatedness of these two number couplings is still unclear. The present study examines the simultaneous occurrence of space- and size-numerical congruency effects and their interactions both within and across trials. In a magnitude judgment task physically small or large digits were presented left or right from screen center. The reaction times analysis revealed that space- and size-congruency effects coexisted in parallel and combined additively. Moreover, a selective sequential modulation of the two congruency effects was found. The size-congruency effect was reduced after size incongruent trials. The space-congruency effect, however, was only affected by the previous space congruency. The observed independence of spatial-numerical and within-magnitude associations is interpreted as evidence that the two couplings reflect different attributes of numerical meaning possibly related to ordinality and cardinality.

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The medical literature is replete with the maxim 'primum non nocere', cautioning health care providers to avoid doing any harm to human subjects in their delivery of medical care. Sodium hypochlorite (NaOCl) is a well-established irrigant for root canal treatment because of its antimicrobial and organic tissue remnant dissolution capability. However, little is known about the deleterious effect of this strong oxidizing agent on the integrity of human mineralized dentin. Iatrogenically-induced loss of dentin integrity may precipitate post-treatment root fracture and has potential medico-legal complications. In the present work, transmission electron microscopy provided evidence for collagen destruction in the surface/subsurface of dentin treated with high NaOCl concentrations and long contact times. Size exclusion chromatography showed that the hypochlorite anion, because of its small size, penetrated the water compartments of apatite-encapsulated collagen fibrils, degraded the collagen molecules and produced a 25-35µm thick, non-uniform "ghost mineral layer" with enlarged, coalesced dentinal tubules and their lateral branches. Fourier transform-infrared spectroscopy identified increases in apatite/collagen ratio in NaOCl-treated dentin. The apatite-rich, collagen-sparse dentin matrix that remained after NaOCl treatment is more brittle, as shown by the reductions in flexural strength. Understanding the deleterious effects of NaOCl on mineralized dentin enables one to balance the risks and benefits in using high NaOCl concentrations for lengthy periods in root canal debridement. Delineating the mechanism responsible for such a phenomenon enables high molecular weight, polymeric antimicrobial and tissue dissolution irrigants to be designed that abides by the maxim of 'primum non nocere' in contemporary medical practices. STATEMENT OF SIGNIFICANCE: The antimicrobial and tissue-dissolution capacities of NaOCl render it a well-accepted agent for root canal debridement. These highly desirable properties, however, appear to be intertwined with the untoward effect of collagen matrix degradation within mineralized dentin. Because of its small size, the hypochlorite anion is capable of infiltrating mineralized collagen and destroying the collagen fibrils, producing a mineral-rich, collagen sparse ghost mineral matrix with reduced flexural strength. Findings from the present work challenge the biosafety of NaOCl when it is used in high concentrations and for lengthy time periods during root canal treatment, and laid the background work for future biomaterials design in debridement of the canal space.

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Physical size modulates the efficiency of digit comparison, depending on whether the relation of numerical magnitude and physical size is congruent or incongruent (Besner & Coltheart, Neuropsychologia, 17, 467-472, 1979), the number-size congruency effect (NSCE). In addition, Henik and Tzelgov (Memory & Cognition, 10, 389-395, 1982) first reported an NSCE for the reverse task of comparing the physical size of digits such that the numerical magnitude of digits modulated the time required to compare their physical sizes. Does the NSCE in physical comparisons simply reflect a number-mediated bias mechanism related to making decisions and selecting responses about the digit's sizes? Alternatively, or in addition, the NSCE might indicate a true increase in the ability to discriminate small and large font sizes when these sizes are congruent with the digit's symbolic numerical meaning, over and above response bias effects. We present a new research design that permits us to apply signal detection theory to a task that required observers to judge the physical size of digits. Our results clearly demonstrate that the NSCE cannot be reduced to mere response bias effects, and that genuine sensitivity gains for congruent number-size pairings contribute to the NSCE.

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The size congruity effect refers to the interaction between the numerical and physical (i.e., font) sizes of digits in a numerical (or physical) magnitude selection task. Although various accounts of the size congruity effect have attributed this interaction to either an early representational stage or a late decision stage, only Risko, Maloney, and Fugelsang (Attention, Perception, & Psychophysics, 75, 1137-1147, 2013) have asserted a central role for attention. In the present study, we used a visual search paradigm to further study the role of attention in the size congruity effect. In Experiments 1 and 2, we showed that manipulating top-down attention (via the task instructions) had a significant impact on the size congruity effect. The interaction between numerical and physical size was larger for numerical size comparison (Exp. 1) than for physical size comparison (Exp. 2). In the remaining experiments, we boosted the feature salience by using a unique target color (Exp. 3) or by increasing the display density by using three-digit numerals (Exps. 4 and 5). As expected, a color singleton target abolished the size congruity effect. Searching for three-digit targets based on numerical size (Exp. 4) resulted in a large size congruity effect, but search based on physical size (Exp. 5) abolished the effect. Our results reveal a substantial role for top-down attention in the size congruity effect, which we interpreted as support for a shared-decision account.

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In a comparison task involving numbers, the size congruity effect refers to the general finding that responses are usually faster when there is a match between numerical size and physical size (e.g., 2-8) than when there is a mismatch (e.g., 2-8). In the present study, we used computer mouse tracking to test two competing models of the size congruity effect: an early interaction model, where interference occurs at an early representational stage, and a late interaction model, where interference occurs as dynamic competition between response options. In three experiments, we found that the curvature of responses for incongruent trials was greater than for congruent trials. In Experiment 2 we showed that this curvature effect was reliably modulated by the numerical distance between the two stimulus numbers, with large distance pairs exhibiting a larger curvature effect than small distance pairs. In Experiment 3 we demonstrated that the congruity effects persist into response execution. These findings indicate that incongruities between numerical and physical sizes are carried throughout the response process and result from competition between parallel and partially active response options, lending further support to a late interaction model of the size congruity effect.

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The brain activity associated with processing numerical end values has received limited research attention. The present study explored the neural correlates associated with processing semantic end values under conditions of automatic number processing. Event-related potentials (ERPs) were recorded while participants performed the numerical Stroop task, in which they were asked to compare the physical size of pairs of numbers, while ignoring their numerical values. The smallest end value in the set, which is a task irrelevant factor, was manipulated between participant groups. We focused on the processing of the lower end values of 0 and 1 because these numbers were found to be automatically tagged as the "smallest." Behavioral results showed that the size congruity effect was modulated by the presence of the smallest end value in the pair. ERP data revealed a spatially extended centro-parieto-occipital P3 that was enhanced for congruent versus incongruent trials. Importantly, over centro-parietal sites, the P3 congruity effect (congruent minus incongruent) was larger for pairs containing the smallest end value than for pairs containing non-smallest values. These differences in the congruency effect were localized to the precuneus. The presence of an end value within the pair also modulated P3 latency. Our results provide the first neural evidence for the encoding of numerical end values. They further demonstrate that the use of end values as anchors is a primary aspect of processing symbolic numerical information.

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This study investigated brain activity in numerical processing at early stages of development. Brain activity of preschoolers was measured while they performed a numerical Stroop task. Participants were asked to decide which of two digits was numerically or physically larger. Behavioral distance and size congruity effects (SiCEs) were found. However, a reverse facilitation was observed, where responses to neutral trials were faster than to congruent ones. The event-related potentials data showed the expected distance effect at occipitoparietal scalp areas. Moreover, conflict was related to effects both at frontal and parietal scalp areas. In addition, there was a difference between the timing of the interference compared to the facilitation components in the SiCE. In parietal scalp areas, facilitation was significant in an early time window and interference was significant at a later time window. This is consistent with the idea that facilitation and interference are separate processes. Our findings indicate that children as young as 5-6 years old can automatically process the numerical meaning of numerals. In addition, our findings are consistent with the idea that, children might use both frontal and parietal areas in order to process irrelevant numerical information.