Rapid communication Orienting numbers in mental space: Horizontal organization trumps vertical

While research on the spatial representation of number has provided substantial evidence for a horizontally oriented mental number line, recent studies suggest vertical organization as well. Directly comparing the relative strength of horizontal and vertical organization, however, we found no evidence of spontaneous vertical orientation (upward or downward), and horizontal trumped vertical when pitted against each other (Experiment 1). Only when numbers were conceptualized as magnitudes (as opposed to nonmagnitude ordinal sequences) did reliable vertical organization emerge, with upward orientation preferred (Experiment 2). Altogether, these findings suggest that horizontal representations predominate, and that vertical representations, when elicited, may be relatively inflexible. Implications for spatial organization beyond number, and its ontogenetic basis, are discussed

The oculomotor resonance effect in spatial-numerical mapping.

We investigated automatic Spatial-Numerical Association of Response Codes (SNARC) effect in auditory number processing. Two experiments continually measured spatial characteristics of ocular drift at central fixation during and after auditory number presentation. Consistent with the notion of a spatially oriented mental number line, we found spontaneous magnitude-dependent gaze adjustments, both with and without a concurrent saccadic task. This fixation adjustment (1) had a small-number/left-lateralized bias and (2) it was biphasic as it emerged for a short time around the point of lexical access and it received later robust representation around following number onset. This pattern suggests a two-step mechanism of sensorimotor mapping between numbers and space - a first-pass bottom-up activation followed by a top-down and more robust horizontal SNARC. Our results inform theories of number processing as well as simulation-based approaches to cognition by identifying the characteristics of an oculomotor resonance phenomenon

Up or down? Reading direction influences vertical counting direction in the horizontal plane - a cross-cultural comparison

Most adults and children in cultures where reading text progresses from left to right also count objects from the left to the right side of space. The reverse is found in cultures with a right-to-left reading direction. The current set of experiments investigated whether vertical counting in the horizontal plane is also influenced by reading direction. Participants were either from a left-to-right reading culture (UK) or from a mixed (left-to-right and top-to-bottom) reading culture (Hong Kong). In Experiment 1, native English-speaking children and adults and native Cantonese-speaking children and adults performed three object counting tasks. Objects were presented flat on a table in a horizontal, vertical, and square display. Independent of culture, the horizontal array was mostly counted from left to right. While the majority of English-speaking children counted the vertical display from bottom to top, the majority of the Cantonese-speaking children as well as both Cantonese- and English-speaking adults counted the vertical display from top to bottom. This pattern was replicated in the counting pattern for squares: all groups except the English-speaking children started counting with the top left coin. In Experiment 2, Cantonese-speaking adults counted a square array of objects after they read a text presented to them either in left-to-right or in top-to-bottom reading direction. Most Cantonese-speaking adults started counting the array by moving horizontally from left to right. However, significantly more Cantonese-speaking adults started counting with a top-to-bottom movement after reading the text presented in a top-to-bottom reading direction than in a left-to-right reading direction. Our results show clearly that vertical counting in the horizontal plane is influenced by longstanding as well as more recent experience of reading direction

Summing up: A functional role of eye movements along the mental number line for arithmetic.

In Western cultures, small-left and large-right spatial-numerical associations are constantly found in various simple number processing tasks. It has recently been suggested that spatial associations are also involved in more complex number processing, for example that individuals make rightward or upward "mental" movements along the number line during addition, and leftward or downward movements during subtraction. In line with this, it has been shown that participants' spontaneous eye movements on a blank screen during upward and downward counting follow such associations. The present research investigated whether eye movements along the number line are simply an epiphenomenon of the recruitment of a spatial reference frame, or whether they play a functional role for the arithmetic computation. This question was addressed by using multi-step problems (e.g., 59 + 5 + 4 + 3) that show a larger proportion of computation (vs. retrieval) when compared to single-step problems (e.g., 59 + 5), as confirmed in Pretest 1. Moreover, the question was addressed only for addition problems and vertical eye movements, because spatial-arithmetic associations were not found in the other conditions (subtraction, horizontal eye movements) in Pretest 2. In the main experiment, participants (n = 29) solved addition problems while following a moving dot with their eyes (smooth pursuit) either in a congruent (upward) or incongruent (downward) direction, or while keeping their eyes fixated on to the center of the screen, or while moving their eyes freely on a blank screen. Arithmetic performance was faster in the congruent condition (upward eye movements) when compared to the other conditions (downward eye movements, central fixation, free viewing). These results suggest that vertical shifts in spatial attention along the mental number line are functionally involved in addition. The results support the view of shared mechanisms for directing spatial attention in external (visual) and representational (number space). Implications for embodied views of number processing are discussed

An Eye on Numbers: The Processing of Numerical Information in the Context of Visual Perception

The capability of understanding and processing numerical information is a critical skill that allows humans to compare, calculate, judge and remember numbers and numerosities. Without this capability, countless processes in everyday life would be very hard to accomplish. This ranges from simple actions like playing dice to the invention of modern techniques, such as personal computers and satellite-based navigation. Hence, it is important to understand the neural processes underlying the (human) perception of numbers and numerosities. As a contribution to this very complex research field I performed three studies using psychophysical methods and electroencephalography (EEG) with the aim to draw general conclusions on human number perception and the processing of numerical information. In the first two studies, I investigated the effect of spatial numerical association of response codes (SNARC). This effect is commonly seen as evidence for the concept of a mental number line (MNL), which is a metaphor for the fact, that the human brain organizes numbers on a mentally conceived line with small numbers on the left and large numbers on the right. In my first study I showed the effector dependence of the SNARC effect, by measuring the SNARC effect for three different effectors: bimanual finger responses, arm pointing responses and saccadic responses. In my second study, I showed that the concept of the mental number line can be extended to a frontoparallel mental number plane, where small numbers are represented left and down and large numbers are represented right and up. I achieved this result by investigating the SNARC effect for cardinal axes (horizontal and vertical) and for diagonal axes in one and the same subject. This approach allowed me to conclude that the strength of the SNARC effect on the diagonal axes can be expressed as a linear combination of the strength of the SNARC effect along the two cardinal axes. In this second study I measured the SNARC effect also regarding two sensory modalities (visual presented Arabic digits and spoken number words). The comparison of the SNARC effect elicited by these two modalities revealed that the strength of the SNARC effect depended on the modality of number presentation. Together with the results of the effector dependency of the SNARC effect from my first study this led me to propose the existence of a distributed “SNARC network” in the human brain. Within the framework of this proposal the SNARC effect is elicited in a central number stage (CNS) as a consequence of the interaction between numbers and space in the human brain (e.g. as explicated by the MNL). But in addition, the SNARC effect is further modulated by early, modality dependent processing stages and late, effector dependent processing stages. I hypothesize that these stages modulate the SNARC effect, but not the relationship between numbers and space per se. My first two studies, explored the SNARC effect, based on abstract numbers represented in the, so-called, approximate number system (ANS). In addition to the number processing in the ANS, it is known that the human brain is capable of perceiving very small magnitudes (up to four) immediately, a phenomenon called subitizing. Previous studies showed that this perception, although very fast, might be influenced by attentional load (Railo et al., 2008; Olivers & Watson, 2008; Anobile et al., 2012). In my third study, I measured the neural basis of the processing of numerical information non-invasively by means of EEG and used the effect of visual mismatch negativity to demonstrate the pre-attentive processing of quantities in the subitizing range. In this experiment, I rapidly pre-sented stimuli, consisting of one, two or three circular patches. To ensure that numerosity was the relevant factor, patches were varied for low-level visual features (luminance vs. individual patch size). While participants were engaged in a difficult visual detection task, changes of the number of patches (standard vs. deviant) were processed pre-attentively. The results of my study provide evidence for the idea that numerosity in this small (subitizing) range is processed pre-attentively. Taken together, I showed that the mental number line could be extended to a frontoparallel mental number plane and eventually even to a three-dimensional mental number space. I found evidence for the dependence of the SNARC effect on sensory modalities as well as on response effectors, suggesting the existence of a distributed SNARC-brain-network. Finally, I revealed some evidence that number processing of small magnitudes in the subitizing range might be pre-attentive

Which Way Does Time Go?:Differences in Expert and Novice Representations of Temporal Information at Extreme Scales Interferes with Novice Understanding of Graphs

Visual representations of data are widely used for communication and understanding, particularly in science, technology, engineering, and mathematics (STEM). However, despite their importance, many people have difficulty understanding data-based visualizations. This work presents a series of three studies that examine how understanding time-based Earth-science data visualizations are influenced by scale and the different directions time can be represented (e.g., the Geologic Time Scale represents time moving from bottom-to-top, whereas many calendars represent time moving left-to-right). In Study 1, 316 visualizations from two top scholarly geoscience journals were analyzed for how time was represented. These expert-made graphs represented time in a range of ways, with smaller timescales more likely to be represented as moving left-to-right and larger scales more likely to be represented in other directions. In Study 2, 47 STEM novices were recruited from an undergraduate psychology experiment pool and asked to construct four separate graphs representing change over two scales of time (Earth’s history or a single day) and two phenomena (temperature or sea level). Novices overwhelmingly represented time moving from left-to-right, regardless of scale. In Study 3, 40 STEM novices were shown expert-made graphs where the direction of time varied. Novices had difficulty interpreting the expert-made graphs when time was represented moving in directions other than left-to-right. The study highlights the importance of considering representations of time and scale in STEM education and offers insights into how experts and novices approach visualizations. The findings inform the development of educational resources and strategies to improve students’ understanding of scientific concepts where time and space are intrinsically related

Estimaciones numéricas espaciales en la recalibración propioceptiva

Research has emphasized that the body's position in space and patterns of visual searching for stimuli are crucial variables to explain the ability to estimate distances numerically. In this paper, we tested the hypothesis that proprioception recalibration interferes in the ability to numerically estimate fixed peri-personal space. The Rubber Hand Illusion (RHI) experimental paradigm was applied as a tool to temporally manipulate the sense of proprioception in participant’s right hand. Seventeen college students were asked to estimate fixed horizontal spatial cues before and after two conditions of tactile stimulation within RHI (synchronous versus asynchronous stroking). Results evidenced that proprioceptive recalibration of the hand were temporally altered by both stroking patterns. However, the effects of numerically estimate fixed horizontal cues towards the body midline were only consistently observed in the synchronous stroking condition. Those findings suggest that numerical estimates of peri-personal fixed cues are strongly associated with proprioceptive recalibration, corroborating the literature on multisensory integration of perception.La literatura en psicología cognitiva ha enfatizado que la posición del cuerpo en el espacio y los patrones de búsqueda visual de estímulos son variables cruciales para explicar la capacidad de estimar distancias numéricamente. En este artículo, hemos probado la hipótesis de que la recalibración de la propiocepción interfiere en la capacidad de estimar numéricamente el espacio peri-personal fijo. El paradigma experimental Rubber Hand Illusion (RHI) se aplicó como herramienta para manipular temporalmente el sentido de propiocepción en la mano derecha del participante. Se pidió a diecisiete estudiantes universitarios que, dentro de la RHI, estimasen señales espaciales fijadas horizontalmente  antes y después de dos condiciones de estimulación táctil (estimulaciones síncronas x asíncronas). Los resultados evidenciaron que la recalibración proprioceptiva de la mano fue temporalmente alterada por ambos patrones de estimulación. Sin embargo, los efectos de estimar las señales fijas numéricamente en dirección de la línea media del cuerpo sólo fueron observados consistentemente en la condición de estimulación síncrona.Estos resultados sugieren que la estimación numérica de señales fijas peri-personales está fuertemente asociadas con la recalibración proprioceptiva, corroborando la literatura sobre integración multisensorial de la percepción

Mental Number Representations in 2D Space

There is evidence both for mental number representations along a horizontal mental number line with larger numbers to the right of smaller numbers (for Western cultures) and a physically grounded, vertical representation where “more is up.” Few studies have compared effects in the horizontal and vertical dimension and none so far have combined both dimensions within a single paradigm where numerical magnitude was task-irrelevant and none of the dimensions was primed by a response dimension. We now investigated number representations over both dimensions, building on findings that mental representations of numbers and space co-activate each other. In a Go/No-go experiment, participants were auditorily primed with a relatively small or large number and then visually presented with quasi-randomly distributed distractor symbols and one Arabic target number (in Go trials only). Participants pressed a central button whenever they detected the target number and elsewise refrained from responding. Responses were not more efficient when small numbers were presented to the left and large numbers to the right. However, results indicated that large numbers were associated with upper space more strongly than small numbers. This suggests that in two-dimensional space when no response dimension is given, numbers are conceptually associated with vertical, but not horizontal space