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.     

What do the hands externalize in simple arithmetic?

In 4 experiments, the authors examined the use of the hands in simple arithmetic tasks. Experiments 1 and 2 demonstrated that pointing increases both accuracy and speed in counting arrays of items, whether those items are identical or distinctive. Experiment 3 demonstrated that individuals tend to nod their heads when not allowed to point and that nodding is associated with greater accuracy, suggesting that pointing is functional for reasons other than simply providing additional visual information. Experiment 4 examined changes in speech when adding arrays of digits, depending on whether participants were allowed to use their hands to manipulate the tokens on which the digits were presented. Taken together, the results of these experiments are consistent with recent research suggesting that gesture can serve cognitive functions and that the hands can support the binding of representational elements to their functional roles by providing phase markers for cyclic cognitive processes.     

Lana Chimpanzee Learns to Count by “Numath”: A Summary of a Videotaped Experimental Report

This paper summarizes a videotaped presentation (Rumbaugh, Savage-Rumbaugh, Hopkins, Washburn, & Runfeldt, 1987) of computerized training programs whereby an adult female chimpanzee, Lana (Pan troglodytes), learned to use a joystick to remove from a screen the number of boxes appropriate to the value of a randomly selected Arabic numeral 1, 2, or 3. Initial training provided a variety of cues, both numeric and otherwise, to support correct performance. Across software programs, all cues other than numeric ones were deleted. In the final test, Lana was correct on over 80% of trials in which there was no residual feedback of intratrial events and where only her memory of those events could provide the cue to indicate that she had removed boxes in accordance with the value of the target numbers and should terminate the trial. The tape is narrated and consists of video recordings of Lana's performance on each software program.     

Effects of non-symbolic numerical information suggest the existence of magnitude-space synesthesia

In number-space synesthesia, numbers are visualized in spatially defined arrays. In a recent study (Gertner et al. in Cortex, doi: 10.1016/j.cortex.2012.03.019 , 2012), we found that the size congruency effect (SiCE) for physical judgments (i.e., comparing numbers' physical sizes while ignoring their numerical values, for example, 8) was modulated by the spatial position of the presented numbers. Surprisingly, we found that the neutral condition, which is comprise solely of physical sizes (e.g., 3), was affected as well. This pattern gave rise to the idea that number-space synesthesia might entail not only discrete, ordered, meaningful symbols (i.e., Arabic numbers) but also continuous non-symbolic magnitudes (i.e., sizes, length, luminance, etc.). We tested this idea by assessing the performance of two number-space synesthetes and 12 matched controls in 3 comparative judgment tasks involving symbolic and non-symbolic stimuli: (1) Arabic numbers, (2) dot clusters, and (3) sizes of squares. The spatial position of the presented stimuli was manipulated to be compatible or incompatible with respect to the synesthetic number-space perceptions. Results revealed that for synesthetes, but not for controls, non-symbolic magnitudes (dot clusters) as well as symbolic magnitudes (i.e., Arabic numbers) interacted with space. Our study suggests that number-space synesthetes might have a general magnitude-space association that is not restricted to concrete symbolic stimuli. These findings support recent theories on the perception and evaluation of sizes in numerical cognition.     

Creating semantics in tool use

This article presents the first evidence for a functional link between tool use and the processing of abstract symbols like Arabic numbers. Participants were required to perform a tool-use task after the processing of an Arabic number. These numbers represented either a small (2 or 3) or a large magnitude (8 or 9). The tool-use task consisted in using inverse pliers for gripping either a small or a large object. The inverse pliers enable to dissociate the hand action from the tool action in relation to the object (i.e., closing the hand led to an opening of the tool and vice versa). The number/tool hypothesis predicts that the quantity representation associated with Arabic numbers will interact with the action of the tool toward the object. Conversely, the number/hand hypothesis predicts that the quantity associated with numbers will interact with the action of the hand toward the tool. Results confirmed the first hypothesis and rejected the second. Indeed, large numbers interacted with the action of the tool, such that participants were longer to perform an “opening-hand/closing-tool” action after the processing of large numbers. Moreover, no effect was detected for small numbers, confirming previous studies which used only finger movements. Altogether, our finding suggests that the well-known finger/number interaction can be reversed with tool use.     

Semantic processing of Arabic,Kanji, and Kana numbers: Evidence from interference in physical and numerical size judgments

Two experiments were conducted with the following objectives (1) to replicate the finding of similar semantic representation of Arabic and written-word (Kanji and Kana) numbers with a direct numerical task, (2) to investigate the automatic semantic processing of Arabic and written-word numbers, and (3) to verify whether the assumption of a common semantic representation is valid in an indirect numerical task. Subjects were asked to judge which of two numbers (e.g, 6-8) was larger either in its numerical size (Experiment 1) or in its physical size (Experiment 2) using the three notations. Effects of two factors were analyzed: the congruity between numerical and physical size and the numerical distance. The effects of these factors were very similar across the three notations in Experiment 1, but were drastically different in Experiment 2. The results of Experiment 2 demonstrated the nonsemantic processing of Kana numbers, and suggest that there may be separate semantic representations for Arabic and Kanji numbers.     

Relative numerosity discrimination by chimpanzees (Pan troglodytes): evidence for approximate numerical representations

Two adult chimpanzees were trained on a relative “numerosity” discrimination task. In each trial, two arrays containing different numbers of red dots were presented on a CRT monitor. The subjects were required to choose the array containing the larger number of dots. In Experiment 1, using numerosities between 1 and 8, 28 different pairs were presented repeatedly, and accuracy scores were analyzed to explore which cues the chimpanzee subjects utilized to perform the task. Multiple regression analyses revealed that the subjects’ performance was (1) not simply controlled by the “numerical” difference between arrays, but that it was (2) best described by Fechner’s Law–that is accuracy increased linearly with the logarithmic value of the numerical difference between arrays divided by the number in the larger of the two arrays. This relationship was maintained when using much larger numerosities (Experiment 3). In Experiment 2, the chimpanzees were tested on the effects of total area and density by manipulating dot size and presentation area. The results revealed that these factors clearly affected the subjects’ performance but that they could not alone explain the results, suggesting that the chimpanzees did use relative numerosity difference as a discriminative cue.     

Too much to count on: impaired very small numbers in corticobasal degeneration

Patients with corticobasal degeneration (CBD) have calculation impairments. This study examined whether impaired number knowledge depends on verbal mediation. We focused particularly on knowledge of very small numbers, where there is a precise relationship between a cardinality and its number concept, but little hypothesized role for verbal mediation. We evaluated accuracy and reaction time (RT) for matching dot arrays and Arabic numerals involving smaller (2-4) and larger (5-9) cardinalities in non-aphasic patients with CBD (n=16), frontotemporal dementia (FTD; n=23), and healthy controls (n=15). CBD were less accurate and slowed at judging smaller Arabic numeral-dot array stimuli compared to FTD patients and controls. Moreover, only CBD showed longer RTs judging successively larger number-dot array pairs among the smaller cardinalities. Difficulty judging very small numbers is impaired in CBD, suggesting degraded representation of precise number knowledge that does not depend on language functioning.     

Rapid proportion comparison with spatial arrays of frequently used meaningful visual symbols

It has been shown that when two arrays of Arabic numerals were briefly presented, observers could accurately indicate which array contained the larger number of a target numeral. This study investigated whether this rapid proportion comparison can be extended to other meaningful symbols that share some of notable properties of Arabic numerals. We tested mainly several Japanese Kanji letters, each of which represents a meaning and can work as a word. Using physically identical stimulus sets that could be interpreted as different types of letters, Experiment 1 first confirmed the rapid proportion comparison with Arabic numerals for Japanese participants. Experiment 2 showed that the rapid proportion comparison can be extended to Kanji numerals. Experiment 3 successfully demonstrated that rapid proportion judgments can be found with non-quantitative Kanji letters that are used frequently. Experiment 4 further demonstrated the rapid proportion comparison with frequently used meaningful non-letter symbols (gender icons). The rapid processing cannot be attributed to fluent processing of familiar items, because it was not found with familiar phonograms (Japanese Kana letters). These findings suggest that the rapid proportion comparison can be commonly found with frequently used meaningful symbols, even though their meaning is not relevant to the task.     

Long-term retention of the differential values of Arabic numerals by chimpanzees (<Emphasis Type="Italic">Pan troglodytes</Emphasis>)

As previously reported (Beran and Rumbaugh, 2001), two chimpanzees used a joystick to collect dots, one-at-a-time, on a computer monitor, and then ended a trial when the number of dots collected was equal to the Arabic numeral presented for the trial. Here, the chimpanzees were presented with the task again after an interval of 6 months and then again after an additional interval of 3.25 years. During each interval, the chimpanzees were not presented with the task, and this allowed an assessment of the extent to which both animals retained the values of each Arabic numeral. Despite lower performance at each retention interval compared to the original study, both chimpanzees performed above chance levels in collecting a quantity of dots equal to the target numeral, one chimpanzee for the numerals 1-7, and the second chimpanzee for the numerals 1-6. For the 3.25-year retention, errors were more dispersed around each target numeral than in the original study, but the chimpanzees' performances again appeared to be based on a continuous representation of magnitude rather than a discrete representation of number. These data provide an experimental demonstration of long-term retention of the differential values of Arabic numerals by chimpanzees.     

Response-retrieval and negative priming

The existence of across-notation automatic numerical processing of two-digit (2D) numbers was explored using size comparisons tasks. Participants were Arabic speakers, who use two sets of numerical symbols—Arabic and Indian. They were presented with pairs of 2D numbers in the same or in mixed notations. Responses for a numerical comparison task were affected by decade difference and unit-decade compatibility and global distance in both conditions, extending previous findings with Arabic digits (Nuerk, Weger, & Willmes, 2001). Responses for a physical comparison task were affected by congruency with the numerical size, as indicated by the size congruency effect (SiCE). The SiCE was affected by unit-decade compatibility but not by global distance, thus suggesting that the units and decades digits of the 2D numbers, but not the whole number value were automatically translated into a common representation of magnitude. The presence of similar results for same- and mixed-notation pairs supports the idea of an abstract representation of magnitude.     

Further evidence for addition and numerical competence by a Grey parrot (Psittacus erithacus)

A Grey parrot (Psittacus erithacus), able to quantify sets of eight or fewer items (including heterogeneous subsets), to sum two sequentially presented sets of 0–6 items (up to 6), and to identify and serially order Arabic numerals (1–8), all by using English labels (Pepperberg in J Comp Psychol 108:36–44, 1994; J Comp Psychol 120:1–11, 2006a; J Comp Psychol 120:205–216, 2006b; Pepperberg and Carey submitted), was tested on addition of two Arabic numerals or three sequentially presented collections (e.g., of variously sized jelly beans or nuts). He was, without explicit training and in the absence of the previously viewed addends, asked, “How many total?” and required to answer with a vocal English number label. In a few trials on the Arabic numeral addition, he was also shown variously colored Arabic numerals while the addends were hidden and asked “What color number (is the) total?” Although his death precluded testing on all possible arrays, his accuracy was statistically significant and suggested addition abilities comparable with those of nonhuman primates.     

Use of numerical symbols by the chimpanzee (Pan troglodytes): Cardinals, ordinals, and the introduction of zero

An adult female chimpanzee with previous training in the use of Arabic numerals 1–9 was introduced to the meaning of "zero" in the context of three different numerical tasks. The first two were cardinal tasks where the subject was required either to select numerals corresponding to the number of items presented on a computer screen (productive use of numerals) or to match sets of the appropriate size to numerals presented as samples (receptive use). The third task addressed the ordinal meaning of the same symbols where the subject was required to respond to numerals sequentially, arranging them into an ascending series. The subject mastered the recognition of the meaning of zero in all three tasks. However, details of her usage of the symbol revealed that transfer of the meaning between different kinds of tasks was incomplete, suggesting that the level of abstraction characteristic of human numerical ability was not attained in the chimpanzee. Over the course of acquisition leading to the high levels of accuracy eventually observed, the newly introduced zero appeared to shift along the length of a continuous numerical scale toward the lower end, while confusions with 1 remained the most frequently encountered mistakes. Such patterns of error thus suggest that Ai's understanding of the meaning of zero in relation to the rest of the number symbols was not consistent with an "absence of items versus presence of items" scheme. Electronic Publication     

Inversion Errors in Arabic Number Reading: Is There a Nonsemantic Route?

This article reports on a mildly aphasic patient with major disorders in reading, writing, and number processing. His predominant error type in reading aloud Arabic numbers and in matching heard numerals with Arabic numbers was the violation of the inversion rule of the German Arabic number reading system. According to this rule most of the two-digit numbers or numbers in the final and prefinal position of longer digit strings have to be read beginning with the final digit (e.g., 26 → sechsundzwanzig (literally translated: six-and-twenty)). It is argued that AT's inversion errors (e.g., 26 → zweiundsechzig (literally translated: two-and-sixty)) are not consistent with the predictions of single route models of Arabic number reading but are in agreement with proposals of a visually based asemantic reading routine in addition to a semantically mediated reading routine.     

Implicit response-irrelevant number information triggers the SNARC effect: Evidence using a neural overlap paradigm

There is evidence from the SNARC (spatial–numerical association of response codes) effect and NDE (numerical distance effect) that number activates spatial representations. Most of this evidence comes from tasks with explicit reference to number, whether through presentation of Arabic digits (SNARC) or through magnitude decisions to nonsymbolic representations (NDE). Here, we report four studies that use the neural overlap paradigm developed by Fias, Lauwereyns, and Lammertyn (2001) to examine whether the presentation of implicit and task-irrelevant numerosity information (nonsymbolic arrays and auditory numbers) is enough to activate a spatial representation of number. Participants were presented with either numerosity arrays (1–9 circles or triangles) to which they made colour (Experiment 1) or orientation (Experiment 2) judgements, or auditory numbers coupled with an on-screen stimulus to which they made a colour (Experiment 3) or orientation (Experiment 4) judgement. SNARC effects were observed only for the orientation tasks. Following the logic of Fias et al., we argue that this SNARC effect occurs as a result of overlap in parietal processing for number and orientation judgements irrespective of modality. Furthermore, we found stronger SNARC effects in the small number range (1–4) than in the larger number range (6–9) for both nonsymbolic displays and auditory numbers. These results suggest that quantity is extracted (and interferes with responses in the orientation task) but this is not exact for the entire number range. We discuss a number of alternative models and mechanisms of numerical processing that may account for such effects.     

Implicit response-irrelevant number information triggers the SNARC effect: Evidence using a neural overlap paradigm

There is evidence from the SNARC (spatial-numerical association of response codes) effect and NDE (numerical distance effect) that number activates spatial representations. Most of this evidence comes from tasks with explicit reference to number, whether through presentation of Arabic digits (SNARC) or through magnitude decisions to nonsymbolic representations (NDE). Here, we report four studies that use the neural overlap paradigm developed by Fias, Lauwereyns, and Lammertyn (2001) to examine whether the presentation of implicit and task-irrelevant numerosity information (nonsymbolic arrays and auditory numbers) is enough to activate a spatial representation of number. Participants were presented with either numerosity arrays (1-9 circles or triangles) to which they made colour (Experiment 1) or orientation (Experiment 2) judgements, or auditory numbers coupled with an on-screen stimulus to which they made a colour (Experiment 3) or orientation (Experiment 4) judgement. SNARC effects were observed only for the orientation tasks. Following the logic of Fias et al., we argue that this SNARC effect occurs as a result of overlap in parietal processing for number and orientation judgements irrespective of modality. Furthermore, we found stronger SNARC effects in the small number range (1-4) than in the larger number range (6-9) for both nonsymbolic displays and auditory numbers. These results suggest that quantity is extracted (and interferes with responses in the orientation task) but this is not exact for the entire number range. We discuss a number of alternative models and mechanisms of numerical processing that may account for such effects.     

Reading habits for both words and numbers contribute to the SNARC effect

This study compared the spatial representation of numbers in three groups of adults: Canadians, who read both English words and Arabic numbers from left to right; Palestinians, who read Arabic words and Arabic-Indic numbers from right to left; and Israelis, who read Hebrew words from right to left but Arabic numbers from left to right. Canadians associated small numbers with left and large numbers with right space (the SNARC effect), Palestinians showed the reverse association, and Israelis had no reliable spatial association for numbers. These results suggest that reading habits for both words and numbers contribute to the spatial representation of numbers.     

Morphological units in the Arabic mental lexicon: evidence from an individual with deep dyslexia

An ongoing debate in Arabic morphology concerns the nature of the smallest unit governing lexical organization and representation in this language. A standard model maintains that Arabic words are typically analyzable into a three-consonantal root morpheme carrying the core meaning of words and a prosodic template responsible mostly for grammatical information. This view has been largely supported by research in both theoretical linguistics and psycholinguistics. An alternative theory holds that the meaning of words in Arabic is, rather, encoded in the 'etymon' comprising two unordered consonants of the root only. Results from a recent priming experiment have shown that the etymon induces strong morphological priming effects, supporting its morphological/lexical status. In this paper we present data from a patient with deep dyslexia questioning the role of the etymon as a psychologically real representational unit in Arabic and arguing, instead, for the central role of the root in both morphological and lexical representation in this language.     

Ordinality and inferential abilities of a grey parrot (Psittacus erithacus)

A grey parrot (Psittacus erithacus), able to label the color of the bigger or smaller object in a pair (I. M. Pepperberg & M. V. Brezinsky, 1991), to vocally quantify < or =6 item sets (including heterogeneous subsets; I. M. Pepperberg, 1994), and separately trained to identify Arabic numerals 1-6 with the same vocal English labels but not to associate Arabic numbers with their relevant physical quantities, was shown pairs of Arabic numbers or an Arabic numeral and a set of objects and was asked for the color of the bigger or smaller one. The parrot's success showed he (a) understood number symbols as abstract representations of real-world collections, (b) inferred the relationship between the Arabic number and the quantity via stimulus equivalence, and (c) understood the ordinal relationship of his numbers.