The interaction between time and number in a temporal bisection task: a reply to Vicario (2011)

Abstract. We discuss the results of Vicario (2011, Perception 40 23-29), in the light of an experiment designed to bypass some of the limits of that study. There, participants were asked to perform a temporal bisection on numerical stimuli (small or large digits) presented either for 700/900 ms or 2000/2200 ms. For the two longest durations only, bisections of larger digits occurred later than those of smaller digits. Here, subjects judged the temporal position of a flick occurring during the visual presentation of a digit (1, 5, or 9) which lasted on the screen for either 700 ms or 2000 ms. Results revealed no difference in the perceived temporal midpoints of large compared to small digits. In contrast, they showed a response bias: only with the shortest-duration stimuli the digit's magnitude affected the subject's response.     

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.     

亮度对空间-数字反应编码联合效应的影响

本研究探讨亮度对空间-数字反应编码联合效应（Spatial-Numerical Association of Response Codes,简称SNARC效应）的影响及其机制。通过三个实验设计不同的亮度对比水平,要求被试对阿拉伯数字1~9（5除外）进行奇偶判断。实验一将数字亮度设为最高值255时,结果出现了数字的SNARC效应。实验二将数字的亮度值分别设为255和213时,结果仍存在SNARC效应。实验三将亮度值分别设置为213和42时,数字的SNARC效应却消失了。这些结果表明亮度会激活或抑制数字的空间表征,可能与亮度对比值的高低及所消耗认知资源的多少有关。     

Oculomotor bias induced by number perception

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

Coming to grips with weight perception: effects of grasp configuration on perceived heaviness

We investigated how changes in grasp configuration affect perceived heaviness in a weight discrimination task in which participants compared the weights of a series of test objects with the weight of a reference object. In different experiments, we varied the width of the grasp, the number of digits employed, the angle of the grasp surface, and the size of the contact area between the digits and the object. We show that objects are perceived to be lighter when lifting with (1) a wide grip in comparison with a narrow grip, (2) five digits in comparison with two digits, and (3) a large contact area in comparison with a small contact area. However, the angle of the contact surfaces did not influence perceived weight. We suggest that changes in central motor commands associated with grasp differences may influence perceived weight, at least under some conditions.     

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.     

Does unattended information facilitate change detection?

Changes between alternating visual displays are difficult to detect when the successive presentations of the displays are separated by a brief temporal interval. To assess whether unattended changes attract attention, observers searched for the location of a change involving either a large or a small number of features, in pairs of displays consisting of 4, 7, 10, 13, or 16 letters (Experiment 1) or digits (Experiments 2 and 3). Each display in a pair of displays was presented for 200 ms, and either a blank screen (Experiments 1 and 2) or a screen of equal luminance to the letters and digits (Experiment 3) was presented for 80 ms between the alternating displays. In all experiments, the search function for locating the larger change was shallower than the search function for locating the smaller change. These results indicate that unattended changes play a functional role in guiding focal attention.     

Developing number–space associations: SNARC effects using a color discrimination task in 5-year-olds

Human adults’ numerical representation is spatially oriented; consequently, participants are faster to respond to small/large numerals with their left/right hand, respectively, when doing a binary classification judgment on numbers, known as the SNARC (spatial–numerical association of response codes) effect. Studies on the emergence and development of the SNARC effect remain scarce. The current study introduces an innovative new paradigm based on a simple color judgment of Arabic digits. Using this task, we found a SNARC effect in children as young as 5.5 years. In contrast, when preschool children needed to perform a magnitude judgment task necessitating exact number knowledge, the SNARC effect started to emerge only at 5.8 years. Moreover, the emergence of a magnitude SNARC but not a color SNARC was linked to proficiency with Arabic digits. Our results suggest that access to a spatially oriented approximate magnitude representation from symbolic digits emerges early in ontogenetic development. Exact magnitude judgments, on the other hand, rely on experience with Arabic digits and, thus, necessitate formal or informal schooling to give access to a spatially oriented numerical representation.     

Mental set and mental arithmetic

State University of New York, Buffalo, New York 14226 Ss performed mental arithmetic problems in which they added, subtracted, or multiplied two one-digit numbers. The presentation order of the operator symbol and the digits was varied. With three possible operators, presentation of the operator prior to the digits (OD) led to faster RTs. With two possible operators, the opposite order (digits prior to operator, DO) led to faster RTs, because RTs in the OD condition were unaffected by the number of possible operators. These results are discussed in terms of the trade off between accessing active memory for a small number of items in the DO condition vs retrieving information from relatively large tables in long-term memory in the OD condition.     

Adaptation to prisms: Do proprioceptive changes mediate adapted behaviour with ballistic arm movements?

In Experiment I subjects pointed repeatedly at a target viewed through laterally displacing prisms and received terminal visual feedback. In one task the pointing movements were slow (proprioceptively controlled), and in the other they were fast (pre-programmed). In both tasks adaptation proceeded at the same rate and to the same level of performance. Following fast pointing with prisms a large amount of arm-body adaptation was found with slow and fast test movements, while following slow pointing with prisms a large amount of arm-body adaptation was found with slow test movements, but only a small amount with fast test movements. The result suggests that adapted behaviour with preprogrammed movements is not mediated by a proprioceptive change. In Experiment II pointing movements were passive. No arm-body adaptation was found with fast test movements, and, contrary to expectation, only a small amount with slow test movements.     

The effect of attending to feeling on memory for internally generated stimuli

The present experiments examined the effects of self-focus, as produced by focusing on feelings, on memory. In an initial experiment subjects did complex mental arithmetic significantly faster after self-focus. Because complex mental addition involves internally generated stimuli, the remaining experiments compared the effects, on memory, of self-focus on internally generated stimuli to the effect of self-focus on stimuli supplied by the experimenter. In a second experiment, self-focus facilitated memory for digits recalled in reverse order but not for digits when recalled in the given order. In a third experiment, self-focus facilitated the memory for the classification of digits but not for the digits themselves. In a fourth and fifth experiment, self-focus aided memory for classification of objects into categories such as small, medium, or large but did not aid memory for the objects themselves. In general, improved performance due to feeling focus was attributed to the role that self-focus may play in increasing attention to internally generated stimuli.     

The effects of abrupt onset of 2-D and 3-D distractors on prehension movements

This article includes two experiments aimed at investigating how two-dimensional (2-D) and three-dimensional (3-D) distractors affect the kinematics of prehension and aiming movements in order to understand the attentional processes involved in visuomotor control. In Experiment 1, subjects grasped large targets in the presence of both large and small 3-D distractors and their corresponding 2-D photographs. The distractors appeared for either 10 sec or appeared simultaneously with the target presentation. It was found that reach and grasp kinematics were influenced primarily by the small, suddenly appearing 3-D distractors. In Experiment 2, the purpose was to examine the conclusion that competition between objects (target and distractor) is related to the behavioral goal of the task. Experiment 2 is a replication of Experiment 1, with the exception that pointing movements were made instead of grasping movements. Results show that both 3-D and 2-D distractors interfered with pointing kinematics, supporting the hypothesis that attentional mechanisms are related to the goal of the task.     

The effects of abrupt onset of 2-D and 3-D distractors on prehension movements

This article includes two experiments aimed at investigating how two-dimensional (2-D) and threedimensional (3-D) distractors affect the kinematics of prehension and aiming movements in order to understand the attentional processes involved in visuomotor control. In Experiment 1, subjects grasped large targets in the presence of both large and small 3-D distractors and their corresponding 2-D photographs. The distractors appeared for either 10 sec or appeared simultaneously with the target presentation. It was found that reach and grasp kinematics were influenced primarily by the small, suddenly appearing 3-D distractors. In Experiment 2, the purpose was to examine the conclusion that competition between objects (target and distractor) is related to the behavioral goal of the task. Experiment 2 is a replication of Experiment 1, with the exception that pointing movements were made instead of grasping movements. Results show that both 3-D and 2-D distractors interfered with pointing kinematics, supporting the hypothesis that attentional mechanisms are related to the goal of the task.     

Perception of signals presented in the periphery of the visual field

Two experiments were performed which tested the type of information that can be extracted from the periphery of the visual field, i.e. content information or position information. In both studies two digits were compared, one presented at the left and one at the right of the subject's meridian, seperated by a binocular visual angle, comprising either an eye-field (45°) or a head-field display (100°). In the first experiment the right signal was presented in separate blocks of either degraded or undegraded digits. In the case of undegraded digits, processing efficiency was better in the eye-field than in the head-field. With degraded digits this eye-field advantage was significantly smaller, but did not altogether disappear, suggesting that information about both the content and the position of digits in the periphery is acquired in the eye-field as opposed to the head-field. In the second experiment degraded and undegraded digits occured randomly within the same block of trials. This was done to investigate whether peripheral information is acquired automatically or through controlled processing. The results indicate a small eye-field advantage, about equal for both degraded and undegraded digits. This supports the controlled processing hypothesis, at least with regard to the acquisition of content information from the periphery.     

Misperception of exocentric directions in auditory space

Previous studies have demonstrated large errors (over 30 degrees ) in visually perceived exocentric directions (the direction between two objects that are both displaced from the observer's location; e.g., Philbeck et al. [Philbeck, J. W., Sargent, J., Arthur, J. C., & Dopkins, S. (2008). Large manual pointing errors, but accurate verbal reports, for indications of target azimuth. Perception, 37, 511-534]). Here, we investigated whether a similar pattern occurs in auditory space. Blindfolded participants either attempted to aim a pointer at auditory targets (an exocentric task) or gave a verbal estimate of the egocentric target azimuth. Targets were located at 20-160 degrees azimuth in the right hemispace. For comparison, we also collected pointing and verbal judgments for visual targets. We found that exocentric pointing responses exhibited sizeable undershooting errors, for both auditory and visual targets, that tended to become more strongly negative as azimuth increased (up to -19 degrees for visual targets at 160 degrees ). Verbal estimates of the auditory and visual target azimuths, however, showed a dramatically different pattern, with relatively small overestimations of azimuths in the rear hemispace. At least some of the differences between verbal and pointing responses appear to be due to the frames of reference underlying the responses; when participants used the pointer to reproduce the egocentric target azimuth rather than the exocentric target direction relative to the pointer, the pattern of pointing errors more closely resembled that seen in verbal reports. These results show that there are similar distortions in perceiving exocentric directions in visual and auditory space.     

Finger–digit compatibility in Arabic numeral processing

Finger–digit response compatibility was tested by asking participants to identify Arabic digits by pressing 1 of 10 keys with all 10 fingers. The direction of the finger–digit mapping was varied by manipulating the global direction of the hand–digit mapping as well as the direction of the finger–digit mapping within each hand (in each case, from small to large digits, or the reverse). The hypothesis of a left-to-right mental number line predicted that a complete left-to-right mapping should be easier whereas the hypothesis of a representation based on finger counting predicted that a counting-congruent mapping should be easier. The results show that when all 10 fingers are used to answer, a mapping congruent with the prototypical finger-counting strategy reported by the participants leads to better performance than does a mapping congruent with a left-to-right oriented mental number line, both in palm-down and palm-up postures of the hands, and they demonstrate that finger-counting strategies influence the way that numerical information is mentally represented and processed.     

Finger-digit compatibility in Arabic numeral processing

Finger-digit response compatibility was tested by asking participants to identify Arabic digits by pressing 1 of 10 keys with all 10 fingers. The direction of the finger-digit mapping was varied by manipulating the global direction of the hand-digit mapping as well as the direction of the finger-digit mapping within each hand (in each case, from small to large digits, or the reverse). The hypothesis of a left-to-right mental number line predicted that a complete left-to-right mapping should be easier whereas the hypothesis of a representation based on finger counting predicted that a counting-congruent mapping should be easier. The results show that when all 10 fingers are used to answer, a mapping congruent with the prototypical finger-counting strategy reported by the participants leads to better performance than does a mapping congruent with a left-to-right oriented mental number line, both in palm-down and palm-up postures of the hands, and they demonstrate that finger-counting strategies influence the way that numerical information is mentally represented and processed.     

Exploring the origin of the number-size congruency effect: Sensitivity or response bias?

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.     

The form of analog size information in memory

The information used to choose the larger of two objects from memory was investigated in two experiments that compared the effects of a number of variables on the performance of subjects who either were instructed to use imagery in the comparison task or were not so instructed. Subjects instructed to use imagery could perform the task more quickly if they prepared themselves with an image of one of the objects at its normal size, rather than with an image that was abnormally big or small, or no image at all. Such subjects were also subject to substantial selective interference when asked to simultaneously maintain irrelevant images of digits. In contrast, when subjects were not specifically instructed to use imagery to reach their decisions, an initial image at normal size did not produce significantly faster decisions than no image, or a large or small image congruent with the correct decision. The selective interference created by simultaneously imaging digits was reduced for subjects not told to base their size comparisons on imagery. The difficulty of the size discrimination did not interact significantly with any other variable. The results suggest that subjects, unless specifically instructed to use imagery, can compare the size of objects in memory using information more abstract than visual imagery.     

Moving the eyes along the mental number line: comparing SNARC effects with saccadic and manual responses

Bimanual parityjudgments about numerically small (large) digits are faster with the left (right) hand, even though parity is unrelated to numerical magnitude per se (the SNARC effect; Dehaene, Bossini, & Giraux, 1993). According to one model, this effect reflects a space-related representation of numerical magnitudes (mental number line) with a genuine left-to-right orientation. Alternatively, it may simply reflect an overlearned motor association between numbers and manual responses--as, for example, on typewriters or computer keyboards--in which case it should be weaker or absent with effectors whose horizontal response component is less systematically associated with individual numbers. Two experiments involving comparisons of saccadic and manual parity judgment tasks clearly support the first view; they also establish a vertical SNARC effect, suggesting that our magnitude representation resembles a number map, rather than a number line.