Is place-value processing in four-digit numbers fully automatic? Yes,but not always

Knowing the place-value of digits in multi-digit numbers allows us to identify, understand and distinguish between numbers with the same digits (e.g., 1492 vs. 1942). Research using the size congruency task has shown that the place-value in a string of three zeros and a non-zero digit (e.g., 0090) is processed automatically. In the present study, we explored whether place-value is also automatically activated when more complex numbers (e.g., 2795) are presented. Twenty-five participants were exposed to pairs of four-digit numbers that differed regarding the position of some digits and their physical size. Participants had to decide which of the two numbers was presented in a larger font size. In the congruent condition, the number shown in a bigger font size was numerically larger. In the incongruent condition, the number shown in a smaller font size was numerically larger. Two types of numbers were employed: numbers composed of three zeros and one non-zero digit (e.g., 0040–0400) and numbers composed of four non-zero digits (e.g., 2795–2759). Results showed larger congruency effects in more distant pairs in both type of numbers. Interestingly, this effect was considerably stronger in the strings composed of zeros. These results indicate that place-value coding is partially automatic, as it depends on the perceptual and numerical properties of the numbers to be processed.     

The effect of structure on scanning strategies

Ss heard four-digit strings and saw a two-digit probe immediately after each. Every possible combination of two digits taken from the string, as well as each member of the string combined with some digit from the negative set was tested. Reaction times for verifying that both probe digits occurred in the string reveal that Ss grouped the members of the string into two ordered pairs. This result argues that the structure Ss might assign to so-called random strings must be considered when discussing scanning strategies. Structural explanations of two common patterns of reaction times are presented.     

I 5683 you: dialing phone numbers on cell phones activates key-concordant concepts

When people perform actions, effects associated with the actions are activated mentally, even if those effects are not apparent. This study tested whether sequences of simulations of virtual action effects can be integrated into a meaning of their own. Cell phones were used to test this hypothesis because pressing a key on a phone is habitually associated with both digits (dialing numbers) and letters (typing text messages). In Experiment 1, dialing digit sequences induced the meaning of words that share the same key sequence (e.g., 5683, LOVE). This occurred even though the letters were not labeled on the keypad, and participants were not aware of the digit-letter correspondences. In Experiment 2, subjects preferred dialing numbers implying positive words (e.g., 37326, DREAM) over dialing numbers implying negative words (e.g., 75463, SLIME). In Experiment 3, subjects preferred companies with phone numbers implying a company-related word (e.g., LOVE for a dating agency, CORPSE for a mortician) compared with companies with phone numbers implying a company-unrelated word.     

Is it a letter? Is it a number? Processing of numbers within SMS shortcuts

For efficiency reasons, words in electronic messages are sometimes formed by combining letters with numbers, as in gr8 for “great.” The aim of this study was to investigate whether a digit incorporated into a letter-digit shortcut would retain its numerosity. A priming paradigm was used with letter-digit shortcuts (e.g., gr8) and matched pseudoshortcuts (e.g., qr8) as primes. The primes were presented simultaneously with sets of dots (targets) for which even/odd decisions were required, or they appeared 250 msec before target onset. When pseudoshortcuts were presented, decision latencies were shorter when the target and the digit in the prime were matched in parity than when they were mismatched. This main effect of match was not significant for shortcuts. The results suggest that the number concepts of digits combined with letters become activated but are quickly suppressed or deactivated when the digit is part of an existing shortcut.     

A memory-based account of automatic numerosity processing

We investigated the mechanisms responsible for the automatic processing of the numerosities represented by digits in the size congruity effect (Henik & Tzelgov, 1982). The algorithmic model assumes that relational comparisons of digit magnitudes (e.g., larger than {8,2}) create this effect. If so, congruity effects ought to require two digits. Memory-based models assume that associations between individual digits and the attributes "small" and "large" create this effect. If so, congruity effects ought only to require one digit. Contrary to the algorithmic model and consistent with memory-based models, congruity effects were just as large when subjects judged the relative physical sizes of small digits paired with letters as when they judged the relative physical sizes of two digits. This finding suggests that size congruity effects can be produced without comparison algorithms.     

AGE DIFFERENCES IN CUMULATIVE LEARNING OF MEANINGFUL AND MEANINGLESS MATERIAL

Age differences in cumulative learning were explored using a technique developed by Hebb. In the first experiment Finnish subjects recalled messages of English digits and in two subsequent experiments English subjects recalled messages of Finnish and of English digits. The finding from the first experiment was that young subjects exhibited cumulative learning while old subjects did not but it was concluded on the basis of the two further experiments that both age groups could show cumulative learning under the conditions used. An age difference in immediate memory for meaningful and meaningless material is noted and the possibility of increasing vulnerability with age to different forms of interference is discussed.     

Perceptual selectivity is task dependent: The pop-out effect poops out

An attempt was made to determine why evidence for perceptual selectivity based on conceptual category (e.g., digits vs. letters) has been found in some experiments but not in others. Experiments using the partial-report paradigm find no partial-report superiority when the report is cued by category, whereas, in recent visual search studies, evidence for perceptual selectivity has been obtained for arrays containing a single item that was categorically different from the other items (e.g., a digit among letters). Using a search task, Experiment 1 investigated the possibility that the number of categorically different items in the arrays could be a determinant of selectivity. One, two, or three digits and a variable number of letters were presented on each trial, and subjects determined if a particular digit was present. No evidence of selectivity was obtained, even for the one-digit condition. Experiment 2 verified this result, and Experiment 3 extended the failure of selectivity to a search task in which the possible targets differed in color from the distractor items. In Experiment 4, subjects counted the number of digits or red letters in arrays in which black letters were the distractor items. The counting task was used to eliminate the requirement in our previous tasks that the subjects search forspecific items. Evidence was obtained in the counting task for selectivity based on the color difference but not on the categorical difference. The color stimuli used in the counting task were essentially the same as those that did not yield any evidence of selectivity in the search task. The results suggest that task demands are an important determinant of whether or not perceptual selectivity will occur.     

Mirror reading of words and numbers: Practice and transfer effects

It remains unknown whether mirror reading represents a genuine text processing skill or is based on recognition of visual patterns. The present study attempts to determine whether (1) systematic practice with a particular mirrored typography also improves reading performance for other mirrored typographies, and whether (2) this transfer extends from lexical to numerical material and vice versa. The results show that short-term intensive practice with mirror-reversed words significantly improves reading performance not only for the trained typography but also for other mirrored typographies and mirror-reversed Arabic digits. Practice with mirror-reversed Arabic digits showed a mixed pattern of transfer effects with regard to other digit transformations and there were no transfer effects to lexical material. Hence, for lexical material, at least, improvement after training seems to be based on generalized skill with transfer effects beyond lexical material, rather than on mere improvement of visual recognition of the material used in training.     

Handedness, eye-dominance, and immediate memory

Twenty male university students varying in handedness and eye-dominance recalled conventional and unconventional digits under two conditions: (1) when the same type of digit was projected simultaneously to each eye, and (2) when a different type of digit was projected simultaneously to each eye.

Forty trials were given, each consisting of four pairs of digits with a different numeral projected to each eye. Performance was analysed in terms of percentage recalled correctly and time of onset of each response.

Right eye-dominant groups, particularly a right handed and right eye-dominant group, were superior in both accuracy of recall and speed of response to left eye-dominant groups. Least able in recall were left handed, left eye-dominant subjects. Superiority of right eye-dominant groups was especially marked when a different type of digit was projected to each eye.

In accord with results reported by Broadbent for the ears (1956, 1957), other results suggest it is possible for the eyes to operate simultaneously as independent information sources. However, unlike the case for audition, present subjects did not report all information from one eye before that from the other, but gave it in pairs. It seems that the capacity of the eyes to function independently depended upon eye-dominance and handedness, while serial ordering of responses reflected imposition of an habitual response organization.     

Spatial modulation of repetition blindness and repetition deafness

When two identical visual items are presented in rapid succession, people often fail to report the second instance when trying to recall both (e.g., Kanwisher, 1987). We investigated whether this temporal processing deficit is modulated by the spatial separation between the repeated stimuli within both audition and vision. In Experiment 1, lists of one to three digits were rapidly presented from loudspeaker cones arranged in a semicircle around the participant. Recall accuracy was lower when repeated digits were presented from different positions rather than from the same position, as compared to unrepeated control pairs, demonstrating that auditory repetition deafness (RD) is modulated by the spatial displacement between repeated items. A similar spatial modulation of visual repetition blindness (RB) was reported when pairs of masked letters were presented visually from either the same or different positions arranged on a semicircle around fixation (Experiment 2). These results cannot easily be accounted for by the token individuation hypothesis of RB (Kanwisher, 1987; Park & Kanwisher, 1994) and instead support a recognition failure account (Hochhaus & Johnston, 1996; Luo & Caramazza, 1995, 1996).     

Comparative judgments with numerical reference points

A model of subjective magnitude comparisons is explored, which assumes that subjects compare symbolic stimulus magnitudes with respect to a reference point. The reference point may be established implicitly by the question (e.g., “Which is larger?” vs “Which is smaller?”) or be presented explicitly (e.g., “Choose the stimulus closer to X.”). The model was tested in five experiments in which subjects judged which of two comparison digits was closer to (or further from) a reference digit. Regression analyses in three experiments revealed that reaction time depended on the ratio of the distances from the comparison items to the reference point. The other two experiments provided evidence that subjects can strategically vary the processes by which they compare stimuli to a reference point. The results indicated that subjects can perform various types of “analog arithmetic” using either the linear number scale or a nonlinear scale of subjective digit magnitude.     

Digit memory of soroban experts: Evidence of utilization of mental imagery

Two experiments were conducted to demonstrate that skilled soroban (Japanese abacus) operators can improve digit memory retention by manipulating the beads of a ‘mental soroban’ which is analogous to the actual one. In Experiment 1, soroban experts and control subjects were given two digit memory tasks. In one task, pictures of a soroban figure and in the other, pictures of digit sequences, were presented to the subjects during the retention interval. Soroban experts experienced greater interference from presentation of the soroban figures than the digits; on the other hand, the reverse was true in the control subjects. In Experiment 2, ther soroban experts and control subjects were given the same digit memory tasks under three conditions—soroban pictures, pictures of digit sequences, and human faces were presented to subjects during the retention period of 15 s. The soroban experts were more affected by the presentation of the soroban figures than by the faces or digits, whereas the controls showed more interference from the digits than by the presentation of faces or soroban pictures.     

Flexible and unique representations of two-digit decimals

We examined the representation of two-digit decimals through studying distance and compatibility effects in magnitude comparison tasks in four experiments. Using number pairs with different leftmost digits, we found both the second digit distance effect and compatibility effect with two-digit integers but only the second digit distance effect with two-digit pure decimals. This suggests that both integers and pure decimals are processed in a compositional manner. In contrast, neither the second digit distance effect nor the compatibility effect was observed in two-digit mixed decimals, thereby showing no evidence for compositional processing of two-digit mixed decimals. However, when the relevance of the rightmost digit processing was increased by adding some decimals pairs with the same leftmost digits, both pure and mixed decimals produced the compatibility effect. Overall, results suggest that the processing of decimals is flexible and depends on the relevance of unique digit positions. This processing mode is different from integer analysis in that two-digit mixed decimals demonstrate parallel compositional processing only when the rightmost digit is relevant. Findings suggest that people probably do not represent decimals by simply ignoring the decimal point and converting them to natural numbers.     

Interactive effects of numerical surface form and operand parity in cognitive arithmetic

In Experiment 1, adults (n = 48) performed simple addition, multiplication, and parity (i.e., odd-even) comparisons on pairs of Arabic digits or English number words. For addition and comparison, but not multiplication, response time increased with the number of odd operands. For addition, but not comparison, this parity effect was greater for words than for digits. In Experiment 2, adults (n = 50) solved simple addition problems in digit and word format and reported their strategies (i.e., retrieval or procedures). Procedural strategies were used more for odd than even addends and much more for word than digit problems. The results indicate that problem encoding and answer retrieval processes for cognitive arithmetic are interactive rather than strictly additive stages.     

Visual field differences in the processing of numerical stimuli

Twenty-four right-handed subjects received random presentations of the numbers 1-6 in the form of words, digits, and dot patterns, to the left and right visual fields. Accuracy and reaction time were recorded for an odd-even judgment requiring a manual response. A significant stimulus type of visual field interaction was obtained, with words showing a left-hemisphere advantage and digits and dot patterns showing a right-hemisphere advantage. This pattern supports Coltheart's (1980, Deep dyslexia: A right hemisphere hypothesis, In M. Coltheart, K. Patterson, & J.C. Marshall (Eds.), Deep dyslexia, London: Routledge & Kegan Paul) right hemisphere reading hypothesis, which suggests that the left hemisphere's general advantage in processing linguistic material may be specific to stimuli which involve phonological processing. When phonological processing is not possible (e.g., for arabic digits and other ideographic orthographies), the right hemisphere may have an advantage because of its superior visuospatial processing capabilities.     

Raven's matrices and working memory: A dual-task approach

The cognitive system does not just act as a mirror from the sensory input; instead, it tends to normalize this information. Given that letter processing seems to be much more specialized than digit processing in the cortex, we examined whether the regularization process occurs differently from digits to letters than from letters to digits: We employed a masked priming same/different experiment (e.g., probe, VESZED; prime, V35Z3D ; and target, VESZED). When embedded in letter strings, digits that resemble letters (e.g., 3 and 5 in V35Z3D -VESZED) tend to be encoded in a letter-like manner, whereas when embedded in digit strings, letters that resemble digits (e.g., E and S in 9ES7E2–935732) tend not to be encoded in a digit-like manner.     

Mental comparison of size and magnitude: size congruity effects

Paivio (1975) found that the latency to choose the larger of two named objects does not depend on congruity between the object sizes and the sizes of the object names. Because size congruity does affect latencies for pictorially presented objects, Paivio interpreted this result as support for the dual coding hypothesis. However, Experiment 1 demonstrated that Paivio's results were an artifact of his experimental design. Size congruity does affect latencies to choose the larger of two named objects when object pairs are not repeated. When the same object pairs are used repeatedly, as in Paivio's experiment, the effect disappears. In this case the response is probably remembered, so that the objects need not be compared. To determine the processing stages affected by size congruity, both the distance between stimulus sizes and the size congruity were manipulated in Experiment 2. Three groups of subjects chose either the greater Arabic digit, the greater named digit, or the larger named object. Size congruity interacted with distance only for Arabic digits. For both Arabic digits and named digits, the interference caused by size incongruity was greater than the facilitation caused by size congruity, whereas for object names, the facilitation was greater than the interference. A model of the interaction between physical size comparisons and conceptual size comparisons is proposed to account for these results.     

Tactile retention: Reading with the skin

In four experiments, subjects were required to identify sequences of random digits, letters, or words drawn on the skin. The passive tactile digit span was determined to be three items when the digits were drawn with an interstimulus interval of 1 sec. Identification was significantly better for words than for random letter sequences. Slower rates of presentation produced better tactile retention. The deficiencies in passive retention were ascribed to two processes, the generation of aftersensations and a difficulty in the generation of a unitary percept. Perceptual activity may normally act to inhibit aftersensations and facilitate the construction of a unitary percept The results supported the notion that the tactile span of immediate memory is labile and may be limited by passivity.     

Serial position effects in the identification of letters, digits, symbols, and shapes in peripheral vision

Three experiments measured serial position functions for character-in-string identification in peripheral vision. In Experiment 1, random strings of five letters (e.g., P F H T M) or five symbols (e.g., λ Б Þ Ψ ¥) were briefly presented to the left or to the right of fixation, and identification accuracy was measured at each position in the string using a post-cued two-alternative forced-choice task (e.g., was there a T or a B at the 4th position). In Experiment 2 the performance to letter stimuli was compared with familiar two-dimensional shapes (e.g., square, triangle, circle), and in Experiment 3 we compared digit strings (e.g., 6 3 7 9 2) with a set of keyboard symbols (e.g., % 4 @ < ?). Eye-movements were monitored to ensure central fixation. The results revealed a triple interaction between the nature of the stimulus (letters/digits vs. symbols/shapes), eccentricity, and visual field. In all experiments this interaction reflected a selective left visual field advantage for letter or digit stimuli compared with symbol or shape stimuli for targets presented at the greatest eccentricity. The results are in line with the predictions of the modified receptive field hypothesis proposed by Tydgat and Grainger (2009), and the predictions of the SERIOL2 model of letter string encoding.     

Selective attention and target search with brief visual displays

In a series of four experiments, subjects were presented with eight item arrays tachistoscopically. In two tasks, the subject was required to recall a digit presented among seven letters or a letter among seven digits. The remaining tasks required the subject to detect the presence of a specific letter either in the context of seven random letters or seven digits. An examination of the effects of a masking stimulus for various target positions suggested that subjects could attend selectively when the target was a different category than its context but had to process the entire array when the target was the same category as the context. The effects of selective attention and masking are explained in terms of parallel and sequential identification processes.