Accepted Manuscript

Title: Numerical quantity affects time estimation in thesuprasecond range

Author: <ce:author id="aut0005"> Masamichi J.Hayashi<ce:author id="aut0010"> Aino Valli<ce:authorid="aut0015"> Synnove Carlson

PII: S0304-3940(13)00248-6DOI: http://dx.doi.org/doi:10.1016/j.neulet.2013.02.054Reference: NSL 29639

To appear in: Neuroscience Letters

Received date: 18-9-2012Revised date: 20-2-2013Accepted date: 21-2-2013

Please cite this article as: M.J. Hayashi, A. Valli, S. Carlson, Numerical quantityaffects time estimation in the suprasecond range, Neuroscience Letters (2013),http://dx.doi.org/10.1016/j.neulet.2013.02.054

This is a PDF file of an unedited manuscript that has been accepted for publication.As a service to our customers we are providing this early version of the manuscript.The manuscript will undergo copyediting, typesetting, and review of the resulting proofbefore it is published in its final form. Please note that during the production processerrors may be discovered which could affect the content, and all legal disclaimers thatapply to the journal pertain.

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Highlights (3 to 5 bullet points, maximum 85 char, incl space, per bullet point):

*Numerical information influences time estimation in the suprasecond range.

*The influence of numerosity on time estimation was observed only in females.

*Our study suggests a common representation for suprasecond intervals and numerosity.

*Degree of interconnectivity in parietal cortex may explain the gender differences.

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Numerical quantity affects time estimation in the suprasecond

range

Masamichi J. Hayashi a, b, *, Aino Valli a, c, Synnöve Carlson a, d, e

a Institute of Biomedicine, Physiology, University of Helsinki, Helsinki 00014, Finland;

b Institute of Cognitive Neuroscience, University College London, London WC1N 3AR, UK;

c Aalto University School of Electrical Engineering, Espoo 00076, Finland;

d Brain Research Unit, O. V. Lounasmaa Laboratory, Aalto University School of Science, Espoo 00076,

Finland;

e Medical School, University of Tampere, Tampere 33014, Finland;

* Corresponding author: Masamichi J. Hayashi, PhD

Institute of Biomedicine, Physiology, PO Box 63, 00014 University of Helsinki, Finland; Tel: +358 9

191 25285; Fax: +358 9 191 25302; Email: mjhgml@gmail.com

Email addresses: mjhgml@gmail.com (M.J. Hayashi), aino.valli@aalto.fi (A. Valli),

syncarls@cc.helsinki.fi (S. Carlson)

Abbreviation: IPC, intraparietal cortex; ATOM, A Theory Of Magnitude

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Abstract

Of stimuli differing in the magnitude of their numerical information, the one with the larger

numerosity is perceived to last longer than that with the smaller numerosity. This numerosity-time

interaction is proposed to be due to a shared neural representation for numerical magnitude and time

intervals in the parietal cortex. Neuroimaging studies of temporal processing suggest that subsecond

and suprasecond intervals could be mediated by distinct neural substrates. However, whether the

numerosity-time interaction occurs independently of the time intervals used in the tasks remains

unknown. Here we show that numerical information interacts with time estimation in the suprasecond

range in females, but not in males. Our results suggest that the numerical magnitude and suprasecond

intervals have shared representations in the human brain, but the associative strength between these

dimensions might be different between males and females.

Key words: time perception; quantity; numerosity; magnitude system; sex differences

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1. Introduction

Judgments of time intervals are often susceptible to interferences from seemingly irrelevant

stimulus properties such as speed of motion [1], temporal frequency [8], size [17], luminance [23],

stimulus sequence and repetition [7, 18]. In addition to these simple features of stimuli, recent

behavioral studies have shown that duration judgments are also influenced by irrelevant numerical

magnitude information in the stimulus. Typically, a stimulus that contains information of larger

numerosity is judged to last longer than a stimulus containing information of smaller numerosity.

However, it has been pointed out that the numerosity-time interaction in categorical duration

discrimination tasks (e.g., longer versus shorter judgment) [4, 16, 23] could solely be explained by a

decision bias as a result of conflicting (or congruent) more-versus-less categorical information

between time and numerosity dimensions [3, 5, 6] rather than distortion of subjective passage of time.

To examine whether numerical information influences time estimation at the perceptual level, Chang

et al. [3] used a time reproduction task that aimed to minimize the role of categorical decisions. The

results showed that participants tended to estimate the larger numerical magnitude to last longer,

which resulted in longer time reproduction. The authors suggested that this result reflected modulation

of subjective passage of time by numerosity information at the perceptual level due to shared

representations for time intervals and numerical magnitude, in line with A Theory Of Magnitude

(ATOM) [21] suggesting a common neural representation for time, space and quantity in the

intraparietal cortex (IPC).

Although Chang et al.’s study demonstrates that numerical magnitude influences time

estimation, the generality of this phenomenon is unclear. For example, since the numerosity-time

interaction with a time reproduction task has so far been tested only in the range of subsecond

intervals (≤ 1 s), it is not known whether such interaction occurs also in the range of suprasecond

intervals (> 1 s). A growing body of neuroimaging studies of temporal processing suggests that

temporal processing of subsecond and suprasecond intervals rely on partially overlapping but distinct

neural networks [12, 22]. These studies suggest that the occurrence of the numerosity-time interaction

might depend on stimulus time intervals that carry numerical values.

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In addition to the limited knowledge about time intervals, there is little information about

possible gender differences in the numerosity-time interaction. The parietal cortex, where the general

magnitude system is supposed to be located, has been reported to show structural differences between

the sexes, and these findings were linked with sex differences in visuo-spatial performance [11].

Despite these findings, possible behavioral sex differences in the interactions between the magnitude

dimensions consisting of the common metrics (i.e., time, space and quantity) have rarely been

addressed. To our knowledge, there is only one behavioral study reporting sex differences in the

spatial representation of numerosity [2]. Specifically, this study showed sex differences in the degree

of spatial numerical association of response code (SNARC), numerical distance effect and linear

acuity in number-line estimation. Authors concluded that these findings reflect sex differences either in

the acuity of the representation or in the reliance on the spatial representation of number in the mental

number-line. The study indicates a potential gender difference in the magnitude system. It is, however,

unclear whether the interaction of other combinations of magnitude dimensions that form the common

metrics in ATOM (i.e., interaction between numerosity and time, and between space and time) also

show some behavioral sex differences.

In the present study, we examined whether the magnitude of numerical quantity influences

suprasecond time estimation, and whether there are any sex differences in the degree of the interaction.

To address these questions, we used a time reproduction task with non-symbolic numerical dot arrays.

2. Material and methods

In total, 44 healthy, right-handed adults (22 males and 22 females) participated in the

experiments. The male and female participants were randomly assigned into two groups (Group A and

B, each group consisting of 11 males and 11 females). There were no statistically significant

differences between sexes with respect to age and years of education in both groups (Table S1). All

participants gave a written informed consent. The experiments were approved by the Ethics

Committee of the Hospital District of Helsinki and Uusimaa.

We employed a time reproduction task involving numerosity-time interaction (Fig. 1A) [5].

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The task was to estimate the duration of a visual stimulus containing numerical information (dot

arrays) and to reproduce the duration by holding down the spacebar with the right index finger after

the stimulus had disappeared. The dot arrays contained 1, 4, 7 or 10 dots and the stimulus durations

were 1.5, 1.8, 2.1, 2.4 or 2.7 s. Group A received dot arrays in which the size of the dots was the same

across the dot arrays (Fig. 1B, Stim A). Group B received dot arrays in which the total area of the dots

in each dot array was adjusted to be equal across different numerical magnitudes (Fig. 1B, Stim B).

These two different formats of dot arrays were used in order to control the factors of total area of the

dots and size of each dot that correlated with the increasing numerical magnitude. Participants were

instructed to fixate their eyes at the center of the screen, to ignore task irrelevant stimulus features (e.g.,

location of the dots), and not to “count” during the estimation and reproduction of the time intervals.

Each participant completed 300 trials after performing 10 practice trials.

[Insert Fig. 1 here]

The dot arrays were generated by an automated program developed by Dehaene and

colleagues [19]. The spatial positions of the dots placed within a gray circle (approximately 6 degrees)

were randomized. The stimuli were presented at the center of a cathode-ray-tube monitor running at

100 Hz. Participants put their chins on a chin rest positioned at a distance of 62 cm from the monitor.

The computer keyboard was located between the monitor and the chin rest. Psychtoolbox

(http://psychtoolbox.org) implemented on MATLAB software (Mathworks) was used to run the

stimuli.

To quantify the degree of contribution of stimulus duration and numerosity to the reproduced

duration, we computed non-parametric partial correlations between the reproduced duration and

physical stimulus duration, and between the reproduced duration and numerical magnitude. In this

analysis, we treated variables of non-interest (i.e., “numerical magnitude” for calculating partial

correlations between the reproduced duration and physical stimulus duration, and “stimulus duration”

for calculating partial correlations between the reproduced duration and numerical magnitude) as

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covariates. Non-parametric correlations were used because they allowed us to capture a monotonic

increase (or decrease) even if the relationship was nonlinear. A positive effect of stimulus duration (i.e.,

a positive partial correlation between stimulus duration and reproduced duration) would indicate that

the participant adjusted response durations according to the physical duration of the stimuli, and a

positive effect of numerosity (i.e., a positive partial correlation between numerical magnitude and

reproduced duration) would indicate that the reproduced durations were systematically increasing with

increasing numerical magnitude. These values were individually computed, and then used as the input

data in the statistical analysis. One sample two-tailed t-test was used to test statistical significance. The

gender differences of these effects were tested using two-way ANOVAs.

Although the partial correlation analysis quantifies the systematic influence of stimulus

duration and numerosity on duration reproduction, it does not yield information about the actual

reproduced duration and the extent of influences of numerical magnitudes on time reproduction for

each level of stimulus duration. For a close scrutiny of the data in regard with the actual reproduced

duration, we computed the mean reproduced duration for each level of stimulus duration by

categorizing the conditions of numerical magnitude into small (1 and 4) and large (7 and 10). The

reproduced durations were tested using a three-way mixed-design ANOVA. Degree of freedom was

corrected using Greenhouse-Geisser estimates of sphericity when Mauchly’s test indicated that the

assumption of sphericity had been violated.

3. Results

The results showed that the physical stimulus duration had a significant positive effect on

time reproduction in both groups (Group A (Stim A), t (21) = 19.21, p < .001, Cohen’s d = 4.095;

Group B (Stim B), t (21) = 23.37, p < .001, Cohen’s d = 4.984) (Fig. 2A), indicating that participants

increased their response duration according to the increase of stimulus duration. The most important

finding was that numerical information had also a significant positive effect on time reproduction in

both groups, indicating that participants reproduced a longer duration when a larger number of dots

was presented (Group A (Stim A), t (21) = 3.27, p = .004, Cohen’s d = .698; Group B (Stim B), t (21) =

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2.25, p = .035, Cohen’s d = .479) (Fig. 2B)

[Insert Fig. 2 here]

To determine whether the effect of stimulus duration and numerosity on duration

reproduction were different between stimulus sets and sexes, we further separated the values of partial

correlation coefficients on the basis of sex, and performed a 2 (stimulus set) x 2 (sex) two-way

ANOVA for the effect of duration and the effect of numerosity on duration reproduction. The results

for the effect of stimulus duration on reproduced duration showed that neither the main effect of sex

(η2 = .036) nor stimulus set (η2 = .008), nor an interaction (sex x stimulus set, η2 = .020) was

significant (p > .05). In contrast, the degree of influence of numerosity on time reproduction was

significantly different between males and females: numerosity influenced females’ time reproduction

more than males’ (F (1, 40) = 4.92, p = .032, η2 = .109) (Fig. 2C). Neither the main effect of stimulus

set (η2 = .001) nor the interaction between stimulus set and sex (η2 = .006) was significant (p > .05),

ruling out the possibility that an increase of the total area of dots with the increase of numerosity in

Stim A could solely explain our findings. The significant sex difference was not eliminated even when

the age and years of education of the participants were controlled. Finally, one-sample t-tests showed a

significant positive effect of numerosity on time reproduction in females (t (21) = 3.73, p = .001,

Cohen’s d = .796) but not in males (p > .05, Cohen’s d = .290), indicating a sex specificity of the

numerosity effect. Together, our results showed that presentation of task-irrelevant numerical

information influenced suprasecond time estimation. The magnitude of the interaction was asymmetric

between the sexes; numerical magnitude influenced time estimation in females but not in males.

To further investigate whether the influence of numerical magnitude on reproduced duration

occurred similarly across the different stimulus duration conditions, we computed the reproduced

durations for each stimulus duration by dividing the magnitude of numerosity into small (1 and 4) and

large (7 and 10) sets (Fig. 3A and 3B). The plots of the differences in reproduced durations between

large and small numerosity conditions are shown in Figure 3C. The results of 2 (stimulus set) x 2

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(numerical magnitude) x 5 (stimulus duration) three-way mixed-design ANOVA showed that

participants in Group A reproduced longer durations than those in Group B (main effect of stimulus set,

F (1, 42) = 4.74, p = .035, η2 = .101). The reproduced durations increased monotonically with

increasing stimulus duration (main effect of stimulus duration, F (1.36, 57.25) = 369.07, p < .001, η2

= .867), a replicate of the results of the partial correlation analysis (Fig. 2A). More importantly,

participants reproduced significantly longer durations when the numerical magnitude was large than

when it was small (main effect of numerical magnitude, F (1, 42) = 11.76, p = .001, η2 = .004). This

result confirmed the initial finding of the partial correlation analysis that showed a significant positive

effect of numerosity on duration reproduction (Fig. 2B). Finally, our results also showed an interaction

of numerical magnitude and stimulus duration (numerical magnitude x stimulus duration, F (3.21,

134.81) = 4.62, p = .003, η2 = .002), whereas other interactions were not significant (p > .05, stimulus

set x stimulus duration, η2 = .003; stimulus set x numerical magnitude, η2 < .001; stimulus set x

numerical magnitude x stimulus duration, η2 < .001). The post-hoc analysis revealed that time

estimation of a larger numerosity resulted in longer time reproduction when the stimulus duration was

1.8 s (F (1, 210) = 10.83, p = .001, r = .96), 2.1 s (F (1, 210) = 22.68, p < .001, r = .98) and 2.7 s (F (1,

210) = 5.04, p = .026, r = .91). In the other two stimulus duration conditions, the difference of

reproduced durations did not reach statistical significance (p > .05, 1.5 s, r = .30; 2.4 s, r = .81),

although the mean reproduced durations in these conditions were longer when a larger numerosity was

presented (Fig. 3C). These results together indicate that numerical magnitude influences time

estimation across different levels of stimulus durations.

[Insert Fig. 3 here]

4. Discussion

The present study showed that time estimation in the suprasecond range was influenced by

numerosity information presented by dot arrays. The finding of the influence of numerical magnitude

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on time estimation is consistent with previous reports of numerosity-time interaction in tasks involving

subsecond [3, 5, 16, 23] and suprasecond intervals [4]. However, because most of these studies used

categorical discrimination tasks [4, 16, 23], their results may reflect decision bias as a result of

conflicting (or congruent) more-versus-less categorical information between time and numerosity

dimensions [3, 5, 6]. In contrast to these previous studies, we minimized the role of categorical

decisions by employing a time reproduction task, and found that the presentation of numerical

information influences suprasecond time estimation. This result extends the previous finding that

numerosity-time interaction occurs in time reproduction tasks involving subsecond intervals [3, 5] to

tasks employing suprasecond intervals.

The significant influence of numerosity on time estimation suggests that the neural

representations of time intervals and numerical magnitude are shared in the human brain. This

suggestion receives support from several previous behavioral studies. Meck and Church (1983)

proposed a mode-control model, which suggests that numerosity and temporal processing are

mediated by the same internal mechanism [14]. They demonstrated that rats were equally sensitive to

the discrimination of number of auditory stimuli and the duration of the auditory signals. Importantly,

this study also showed that the effect of duration discrimination training was spontaneously transferred

to number discrimination. A similar transfer effect was recently found in preverbal 9-month-old infants

[13], suggesting that an abstract common magnitude representation between numerosity and time

exists from early age on in humans.

Our finding of numerosity-time interaction in the suprasecond range is in line with the results

of an earlier study using time intervals within the subsecond range [3, 5]. Based on these results, we

suggest that the numerosity-time interactions in these different ranges of time intervals could be

mediated by a common neural mechanism, probably by a common magnitude system in the IPC.

However, it is also important to note that, while the representation of numerosity in the IPC has been

well established [15], it is still inconclusive whether the subsecond and suprasecond time intervals are

both represented in the IPC [12, 22]. Our study does not completely rule out the possibility that the

numerosity-time interactions in the subsecond and suprasecond range are mediated by separate neural

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mechanisms but with a similar behavioral outcome. Brain areas involved in temporal processing might

not only depend on the duration range but also on other task characteristics [12]. Therefore, in addition

to studies of temporal processing, direct physiological measurements during numerosity-time

interaction in subsecond and suprasecond range would be necessary for the determination of their

neural bases.

In the present study, we used non-symbolic dot arrays, while a previous study on

numerosity-time interaction employing time reproduction used symbolic numbers [3]. The similar

influence of symbolic and non-symbolic nuumerosity on time estimation suggests that time estimation

interacts with numerical magnitude irrespective of the notation of the numerical information. This idea

agrees with a previous functional magnetic resonance imaging adaptation study reporting a

notation-independent representation of numerical magnitude (Arabic digits, number words and dot

arrays) in the human IPC [20]. These studies together suggest that the neural representation of time

intervals may overlap with the notation-independent numerosity representation.

We showed that the numerosity-time interaction was present even when the total area of the

dot arrays was controlled. This result rules out the possibility that the increase of the total area of the

dot array, which correlated with the increase of the numerical magnitude in Stim A (Fig. 1B), would

solely explain the observed influence on time. A limitation of our study is that some of the other

parameters, such as the total contour length of dots and the spatial extent of dots, correlated with the

increase of the number of dots, thus, these parameters could have influenced time estimation.

In addition to the novel finding that numerosity-time interaction occurs within the suprasecond

range, the present results also suggest a gender difference such that numerosity influences time

estimation in females but not in males. One potential biological basis that mediates the gender

difference is the degree of interconnectivity between neural populations that represent numerosity and

time. It has been suggested that one possible mechanism of the numerosity-time interaction is that

numerosity and time are both represented in the IPC but by different neural populations, and the

interaction emerges as the result of their close connections [3, 5]. If this is the case, the greater influence

of numerosity on time estimation in females could be explained by the greater interconnectivity between

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these neural populations. This explanation is supported by a previous study that investigated gender

differences in brain structure and brain activity during arithmetic tasks [10]. The study showed that, in

the IPC, the regional gray-matter volume, which may reflect underlying synaptogenesis and dendritic

arborization [9], was larger in females than in males. Moreover, the region where the gray-matter

volume difference between the genders was observed overlapped with the region that showed gender

differences in the activity during numerical processing. This study suggests that sex differences in the

influence of numerosity on time estimation could be explained by the degree of connectivity between

neural populations that represent time and numerosity in the IPC.

Finally, it is important to note that, although we showed that the factors of age and education

were not relevant to the observed sex differences, gender differences in some other cognitive abilities

may possibly explain the present results [2]. Studies addressing other cognitive skills could further

elucidate the source of the sex difference in the numerosity-time interaction.

5. Conclusion

The present study demonstrated that numerical information, presented by a non-symbolic dot

array, influences time estimation in the suprasecond time range. This result provides evidence that

suprasecond intervals and numerical magnitude have shared neural representations. However, the

influence of numerical information on the time estimation was observed only in females, suggesting

that the genders differ from each other regarding the strength of the association between numerosity

and time. Taken together, the present results extend previous findings of numerosity-time interaction in

subsecond time estimation to the suprasecond time range, and shed light on the sex difference in the

organization of the general processing system of magnitude.

Acknowledgements

This study was supported by Brain Research at Aalto University and University of Helsinki

postdoctoral program (MJH), Researcher Exchange Program between the Academy of Finland and

Japan Society for the Promotion of Science (MJH), the Academy of Finland National Centers of

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Excellence Program 2006–2011 (SC) and the aivoAALTO project of the Aalto University (SC and

AV).

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Figure Legends

Fig. 1. Stimulus sequence and sets of dot arrays. (A) The stimulus sequence. After the presentation of a

gray circle, a dot array was presented either for 1.5, 1.8, 2.1, 2.4 or 2.7 s. After the dot array stimulus

had disappeared, participants reproduced the duration. (B) The visual dot arrays. Four different

numerical magnitudes of dot arrays (1, 4, 7 and 10 dots) shown in two different formats were used.

Fig. 2. Results of the partial correlation analysis. (A) Mean partial correlation coefficients between the

reproduced duration and physical stimulus duration, and (B) between the reproduced duration and

numerical magnitude. (C) Sex differences in the mean partial correlation coefficients between the

reproduced duration and numerical magnitude. Black bars correspond to Stim A and white bars

correspond to Stim B. All error bars denote SEM. * p < .05, ** p < .01, *** p < .001.

Fig. 3. Plots of reproduced durations for each stimulus duration. Mean reproduced durations when

numerical magnitude was presented using (A) Stim A, and (B) Stim B. Black bars indicate the mean

reproduced duration in small numerosity (1 and 4) conditions, and white bars in large numerosity (7

and 10) conditions. (C) Mean differences in reproduced durations between large and small numerosity

conditions (large-small) for Stim A (black bars) and Stim B (white bars). All error bars denote SEM.

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References

[1] S.W. Brown, Time, change, and motion: the effects of stimulus movement on temporal

perception, Percept Psychophys 57 (1995) 105-116.

[2] R. Bull, A.A. Cleland, T. Mitchell, Sex Differences in the Spatial Representation of Number, J

Exp Psychol Gen (2012).

[3] A.Y. Chang, O.J. Tzeng, D.L. Hung, D.H. Wu, Big time is not always long: numerical

magnitude automatically affects time reproduction, Psychol Sci 22 (2011) 1567-1573.

[4] V. Dormal, X. Seron, M. Pesenti, Numerosity-duration interference: a Stroop experiment, Acta

Psychol (Amst) 121 (2006) 109-124.

[5] M.J. Hayashi, R. Kanai, H.C. Tanabe, Y. Yoshida, S. Carlson, V. Walsh, N. Sadato, Interaction

of Numerosity and Time in Prefrontal and Parietal Cortex, J Neurosci 33 (2013) 883-893.

[6] R.B. Ivry, J.E. Schlerf, Dedicated and intrinsic models of time perception, Trends Cogn Sci 12

(2008) 273-280.

[7] A. Johnston, D.H. Arnold, S. Nishida, Spatially localized distortions of event time, Curr Biol

16 (2006) 472-479.

[8] R. Kanai, C.L. Paffen, H. Hogendoorn, F.A. Verstraten, Time dilation in dynamic visual

display, J Vis 6 (2006) 1421-1430.

[9] R. Kanai, G. Rees, The structural basis of inter-individual differences in human behaviour and

cognition, Nat Rev Neurosci 12 (2011) 231-242.

[10] K. Keller, V. Menon, Gender differences in the functional and structural neuroanatomy of

mathematical cognition, Neuroimage 47 (2009) 342-352.

[11] T. Koscik, D. O'Leary, D.J. Moser, N.C. Andreasen, P. Nopoulos, Sex differences in parietal

lobe morphology: relationship to mental rotation performance, Brain Cogn 69 (2009) 451-459.

[12] P.A. Lewis, R.C. Miall, Remembering the time: a continuous clock, Trends Cogn Sci 10

(2006) 401-406.

[13] S.F. Lourenco, M.R. Longo, General magnitude representation in human infants, Psychol Sci

21 (2010) 873-881.

[14] W.H. Meck, R.M. Church, A mode control model of counting and timing processes, J Exp

Psychol Anim Behav Process 9 (1983) 320-334.

[15] A. Nieder, S. Dehaene, Representation of number in the brain, Annu Rev Neurosci 32 (2009)

185-208.

[16] M. Oliveri, C. Vicario, S. Salerno, G. Koch, P. Turriziani, R. Mangano, G. Chillemi, C.

Caltagirone, Perceiving numbers alters time perception, Neurosci Lett 438 (2008) 308-311.

[17] F. Ono, J. Kawahara, The subjective size of visual stimuli affects the perceived duration of

their presentation., Percept Psychophys 69 (2007) 952-957.

[18] V. Pariyadath, D.M. Eagleman, Brief subjective durations contract with repetition, J Vis 8

(2008) 11.11-16.

[19] M. Piazza, V. Izard, P. Pinel, D. Le Bihan, S. Dehaene, Tuning curves for approximate

numerosity in the human intraparietal sulcus, Neuron 44 (2004) 547-555.

[20] M. Piazza, P. Pinel, D. Le Bihan, S. Dehaene, A magnitude code common to numerosities and

Page 16 of 19

Accep

ted

Man

uscr

ipt

Hayashi et al. 16/16

number symbols in human intraparietal cortex, Neuron 53 (2007) 293-305.

[21] V. Walsh, A theory of magnitude: common cortical metrics of time, space and quantity, Trends

Cogn Sci 7 (2003) 483-488.

[22] M. Wiener, P. Turkeltaub, H. Coslett, The image of time: a voxel-wise meta-analysis,

Neuroimage 49 (2010) 1728-1740.

[23] B. Xuan, D. Zhang, S. He, X. Chen, Larger stimuli are judged to last longer, J Vis 7 (2007)

2.1-5.

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Stim A

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Rep

rod

uced

du

rati

on

(s) Small (1 and 4)

Large (7 and 10)

1.5 1.8 2.1 2.4 2.7

0

20

40

60

80

100

Stimulus duration (s)

Dif

fere

nce in

rep

rod

uced

du

rati

on

s (

ms) Stim A

Stim B

C

Figure3