Salillas Semenza, Number processing
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Effects of attention to location and motion on number
processing.
Elena Salillas and Carlo Semenza
Universitá degli Studi di Trieste, Italy
Corresponding author:
Elena Salillas Pérez.
e-mail:
salillas@psico.units.it
Department of Psychology
University of Trieste
Via S. Anastasio 12
34100 Trieste - ITALY
Phone: +39 040 558 2727
Fax: +39 040 4528022
Effects of attention to location
and motion on number processing
ABSTRACT
In this study we aimed at exploring the impact of exogenous covert attention to
static and moving stimuli on the process of numerical comparison. Number comparison
is thought to imply the direct activation of the core quantity system, analogous to a
mental “number line” oriented from left to right (e.g. Dehaene et al, 2003). The first two
experiments show that shifts of covert attention exogenously induced by visual
lateralized stimuli or by non-predictive arrows influence the time of number
comparison. Interactions between the shift of attention to location caused by these cues
and the size of the number were found, which agrees with the proposals of a number
line with spatial nature. Experiments 3 and 4 test the influence of motion perception in
the process of number comparison. This process showed to be sensitive both to the
direction of the signal on concurrent random dots kinematograms (RDKs) and to their
level of coherence. Vertical and horizontal motion had an impact on number
comparison times, which were facilitated when the target numbers concurred with
rightward or upward motion. Overall, the results show that not only attention to location
but also attention to motion can affect the process of number comparison, and that these
effects may be independent. Thus, we propose motion as a mechanism operating on the
representation of numbers.
Keywords: Number comparison; Attention; Space; Motion; RDK.
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Effects of attention to location
and motion on number processing
INTRODUCTION
There are different theories about the way numbers are processed and
represented (Clark and Campbell, 1991; McCloskey, 1992; Nöel and Seron, 1997).
Some models conceive the semantic representation of number magnitude as an analogue
continuum (Dehaene, 1992; Gallistel and Gelman, 1992), in the form of a “mental
number line” oriented from left to right (Dehaene, Bossini, & Giraux, 1993) that may be
related to space (Walsh, 2003).
On one hand, the
distance effect
(Moyer and Landauer, 1967) means that
greater
distances between numbers are easier to compare than smaller distances. This effect is
taken as evidence for the transformation of numbers into analogue magnitudes that are
subsequently compared, and it suggests that numbers and the relationships between
them are spatially organized (Dehaene, 1997).
Another effect that has been taken as evidence for the analogue quantity
continuum is the
magnitude effect
, i.e. the fact that the time necessary to compare two
numbers increases with the increase of their magnitude (eg. 8 and 9 vs 1 and 2)
Specifically, the ratio between the two numbers to be compared predicts the time
required to compare them.
Finally, the
SNARC
(Spatial-Numerical Association of Response Codes)
effect
provides evidence for access to magnitude representation in a left-to-right orientation.
Large numbers are responded to faster with the right hand, whereas relatively low
numbers achieve a faster response from the left hand (Dehaene et al, 1993), even when
numerical information is not relevant to the task (Fias, Brysbaert, Geypens, &
d´Ydewalle et al, 1996; Fias, Lauwereyns, & Lammertyn, 2001). The effect has been
proven to depend on the direction of writing (Dehaene, et al. 1993) and it has also been
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Effects of attention to location
and motion on number processing
shown for other non-numerical, sequential stimuli, such as the months of the year and
the letters of the alphabet (Gevers, Reynvoet, & Fias, 2003).
Other studies have tested more specifically for the relationship between number
and spatial attention. For instance, Fischer, Castel, Dodd and Pratt (2003) reported shifts
of covert attention caused by the perception of numbers that were irrelevant to the task.
In their study, a number was presented in the middle of the screen for 300msec. and,
after a variable delay, it was followed by a lateral visual target presented on the right or
on the left. The subject’s task was to detect the target. An interaction was obtained
between the size of the number and the location of the target: right targets following a
high number and left targets following a low number were detected faster than left
targets following a high number and right targets following low numbers. The
maximum effect was at delays of 400 to 1000msec. These results can be taken as
evidence for an influence of the perception of numbers in the exogenous orienting of
attention.
Other studies have investigated the partial overlap between neuronal circuits
processing spatial cognition and numerical representations in the dorsal pathway (Fias
et al, 2001). For example, the inferior parietal areas (Chochon, Cohen, van de Moortele
& Dehaene, 1999; Dehaene, Piazza, Pinel, & Cohen, 2003; Pesenti Thioux, Seron & De
Volder, 2000; Pinel, Dehaene, Riviere, & LeBihan, 2001) have been shown to sustain
comparison tasks.
The experiments presented here have two goals. In the first two experiments we
want to further explore space-number relations. We will test the effect of shifts of
attention to
location
on a numerical process. The access to the number will be task-
relevant. The core representation of numbers will be accessed through a number
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Effects of attention to location
and motion on number processing
comparison task, where the effects of covert exogenous attention to irrelevant
lateralized visual stimuli will be examined. In the second experiment the effects of shifts
of attention generated by symbolic non predictive arrows on the same number
comparison task will be measured. The third, fourth and fifth experiments will evaluate
the effects of shifts of attention to
motion
on this comparison process and consequently,
the possible impact of motion stimuli on the core representation of numbers. If an effect
of these stimuli is found on number comparison, motion can be proposed as a
mechanism operating along the mental number line.
Specifically, in Experiment 1 we will manipulate the side of presentation of
lateralized visual stimuli that will precede the comparison on numbers higher or lower
than the reference number 5. While numbers lower than five should be easier to
compare after the capture of attention to the left, numbers higher than five should be
easier to compare after the capture of attention to the right. This outcome would favour
the view of the representation of numbers implying spatial attention components, that
are shared with those processes of attention implied in other spatial inputs. Differing
from Fischer et al. (2003), our experimental paradigm implies the capture of attention
by exogenous irrelevant stimuli and the response to a supposedly spatially arranged
endogenous mental number line. Moreover, the experiment will help in the
characterization of the comparison process; as we have indicated, such process would
imply access to the semantic representation of numbers (Dehaene & Cohen, 1995) that
would be related to space.
The second experiment has the same goal as the previous one, but, in this case,
instead of lateralized stimuli, non predictive symbolic stimuli will be used as cues to
numbers. Central arrows that point to the left or to the right will precede the
presentation of the target number where the same number comparison task has to be
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