Skip to main content
SpringerLink
Log in

Cross-dimensional magnitude interaction is modulated by representational noise: evidence from space–time interaction

  • Original Article
  • Published:
Psychological Research Aims and scope Submit manuscript

Abstract

Magnitudes along different dimensions (e.g., space and time) tend to interact with each other in perception, with some magnitude dimensions more susceptible to cross-dimensional interference than others. What causes such asymmetries in cross-dimensional magnitude interaction is being debated. The current study investigated whether the representational noise of magnitudes modulates the (a)symmetry in space–time interaction. In three experiments using different formats of length, we showed that dynamic unfilled lengths resulted in a higher representational noise than either static unfilled length or static filled length. Correspondingly, we observed that the time-on-space effect was larger for dynamic unfilled lengths than for static unfilled length or static filled length (and it did not differ between the latter two). Further correlational analyses showed that the susceptibility of a target dimension to the influence of a concurrent dimension increased as a function of participants’ representational noise in the target dimension (e.g., the noisier length representations, the larger the time-on-space effect). In all, our study showed that the representational noise of space and time modulates the way the two dimensions interact. These findings suggest that cross-dimensional magnitude interactions arise as a result of memory interference, with noisier magnitudes being more prone to being nudged by concurrent magnitudes in other dimensions. Such memory interference can be seen as a result of Bayesian inference with correlated priors between magnitude dimensions.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4

Similar content being viewed by others

Data statement

The datasets generated during and/or analyzed during the current study are publicly available in Open Science Framework (https://osf.io/8pvsr/).

Notes

  1. A power analysis (using the "pwr" package in R) on the space-on-time effect in Casasanto and Boroditsky (2008) (with the effect size averaged across experiments) showed that to reach a power of 0.80 at α = 0.05 with two predictors in a multiple regression design requires a minimum of 6 data cells. The design in this and the following experiments (with 25 data cells), thus, clearly exceeds this minimum.

  2. It seems that reproduced durations were the longest in Experiment 3 (where the stimulus duration was defined as the time interval between the two bars) and second longest in Experiment 1. It is likely that more attention was needed to process unfilled lengths in both Experiments 3 and 1, leading to longer apparent durations (e.g., Zakay & Block, 1995); in addition, participants might have inadvertently timed the stimulus duration from the onset of the first vertical bar to the offset of the second vertical bar, hence leading to longer apparent duration. It should be noted that these possible confounds changed the intercept (i.e., longer reproductions across all stimulus durations/lengths) but would have little impact on the slopes (e.g., how reproduced durations changed as a function of stimulus length), which the current paper is interested in.

  3. One might be puzzled by the null difference here given that stimulus duration significantly affected length reproduction in Experiment 2 but not in Experiment 1. Note the effect size being not significantly different between the two experiments simply indicates that the difference in the effect sizes is not large enough to be statistically detectable or meaningful; this finding does not mean that the effect was similarly present or absent in both experiments (i.e., it is still possible that the effect was statistically present in one experiment but not in the other in individual analyses); therefore, the null difference here does not contradict the results from the individual experiments.

References

  • Agrillo, C., Ranpura, A., & Butterworth, B. (2010). Time and numerosity estimation are independent: Behavioral evidence for two different systems using a conflict paradigm. Cognitive Neuroscience, 1, 96–101.

    Article  PubMed  Google Scholar 

  • Alais, D., & Burr, D. (2004). The ventriloquist effect results from near-optimal bimodal integration. Current Biology, 14(3), 257–262.

    Article  PubMed  Google Scholar 

  • Allan, L. G. (1979). The perception of time. Perception & Psychophysics, 26(5), 340–354.

    Article  Google Scholar 

  • Amadeo, M. B., Campus, C., & Gori, M. (2019). Time attracts auditory space representation during development. Behavioural Brain Research, 376, 112185.

    Article  PubMed  Google Scholar 

  • Barbaree, H. E., & Mewhort, D. J. K. (1994). The effects of the z-score transformation on measures of relative erectile response strength: A re-appraisal. Behaviour Research and Therapy, 32(5), 547–558.

    Article  PubMed  Google Scholar 

  • Besner, D., & Coltheart, M. (1979). Ideographic and alphabetic processing in skilled reading of English. Neuropsychologia, 17(5), 467–472.

    Article  PubMed  Google Scholar 

  • Bonn, C. D., & Cantlon, J. F. (2017). Spontaneous, modality-general abstraction of a ratio scale. Cognition, 169, 36–45.

    Article  PubMed  PubMed Central  Google Scholar 

  • Boroditsky, L. (2000). Metaphoric Structuring: Understanding time through spatial metaphors. Cognition, 75, 1–28.

    Article  PubMed  Google Scholar 

  • Boroditsky, L., & Ramscar, M. (2002). The roles of body and mind in abstract thought. Psychological Science, 13, 185–189.

    Article  PubMed  Google Scholar 

  • Bottini, R., & Casasanto, D. (2013). Space and time in the child’s mind: metaphoric or ATOMic? Frontiers in Psychology, 4, 803.

    Article  PubMed  PubMed Central  Google Scholar 

  • Bottini, R., Crepaldi, D., Casasanto, D., Crollen, V., & Collignon, O. (2015). Space and time in the sighted and blind. Cognition, 141, 67–72.

    Article  PubMed  Google Scholar 

  • Bottini, R., Guarino, C., & Casasanto, D. (2013). Space is special: A domain-specific mapping between time and nontemporal magnitude. In M. Knauff, M. Pauen, N. Sebanz, & I. Wachsmuth (Eds.), Proceedings of the 35th annual conference of the cognitive science society (pp. 233–238). Austin, TX: Cognitive Science Society.

  • Bueti, D., & Walsh, V. (2009). The parietal cortex and the representation of time, space, number and other magnitudes. Philosophical Transactions of the Royal Society B: Biological Sciences, 364, 1831–1840.

    Article  Google Scholar 

  • Cai, Z. G., & Connell, L. (2015). Space–time interdependence: Evidence against asymmetric mapping between time and space. Cognition, 136, 268–281.

    Article  PubMed  Google Scholar 

  • Cai, Z. G., & Connell, L. (2016). On magnitudes in memory: An internal clock account of space–time interaction. Acta Psychologica, 168, 1–11.

    Article  PubMed  Google Scholar 

  • Cai, Z. G., Connell, L., & Holler, J. (2013). Time does not flow without language: Spatial distance affects temporal duration regardless of movement or direction. Psychonomic Bulletin & Review, 20, 973–980.

    Article  Google Scholar 

  • Cai, Z. G., & Wang, R. (2014). Numerical magnitude affects temporal memories but not time encoding. PLoS ONE, 9, e83159.

    Article  PubMed  PubMed Central  Google Scholar 

  • Cai, Z. G., Wang, R., Shen, M., & Speekenbrink, M. (2018). Cross-dimensional magnitude interactions arise from memory interference. Cognitive psychology, 106, 21–42.

    Article  PubMed  Google Scholar 

  • Cai, Z. G., Wu, L., & Wang, R. (2020). Cross-dimensional magnitude interactions reflect statistical correlations among physical dimensions: Evidence from space-time interaction. https://osf.io/spmzj/.

  • Cappelletti, M., Freeman, E. D., & Cipolotti, L. (2009). Dissociations and interactions between time, numerosity and space processing. Neuropsychologia, 47, 2732–2748.

    Article  PubMed  PubMed Central  Google Scholar 

  • Casasanto, D., & Boroditsky, L. (2008). Time in the mind: Using space to think about time. Cognition, 106, 579–593.

    Article  PubMed  Google Scholar 

  • Casasanto, D., & Bottini, R. (2014). Mirror reading can reverse the flow of time. Journal of Experimental Psychology: General, 143(2), 473.

    Article  Google Scholar 

  • Casasanto, D., Fotakopoulou, O., & Boroditsky, L. (2010). Space and time in the child’s mind: Evidence for a cross-dimensional asymmetry. Cognitive Science, 34, 387–405.

    Article  PubMed  Google Scholar 

  • Chang, A. Y. C., Tzeng, O. J. L., Hung, D. L., & Wu, D. H. (2011). Big time is not always long numerical magnitude automatically affects time reproduction. Psychological Science, 22, 1567–1573.

    Article  PubMed  Google Scholar 

  • Cicchini, G. M., Arrighi, R., Cecchetti, L., Giusti, M., & Burr, D. C. (2012). Optimal encoding of interval timing in expert percussionists. Journal of Neuroscience, 32(3), 1056–1060.

    Article  PubMed  Google Scholar 

  • de Hevia, M. D., Girelli, L., & Vallar, G. (2006). Numbers and space: A cognitive illusion? Experimental Brain Research, 168(1–2), 254–264.

    Article  Google Scholar 

  • de Hevia, M. D., & Spelke, E. S. (2009). Spontaneous mapping of number and space in adults and young children. Cognition, 110(2), 198–207.

    Article  PubMed  Google Scholar 

  • DeLong, A. J. (1981). Phenomenological space-time: Toward an experiential relativity. Science, 213, 681–683.

    Article  PubMed  Google Scholar 

  • Dormal, V., Andres, M., & Pesenti, M. (2008). Dissociation of numerosity and duration processing in the left intraparietal sulcus: A transcranial magnetic stimulation study. Cortex, 44, 462–469.

    Article  PubMed  Google Scholar 

  • Dormal, V., & Pesenti, M. (2013). Processing numerosity, length and duration in a three-dimensional Stroop-like task: Towards a gradient of processing automaticity? Psychological Research Psychologische Forschung, 77, 116–127.

    Article  Google Scholar 

  • Dormal, V., Seron, X., & Pesenti, M. (2006). Numerosity-duration interference: A Stroop experiment. Acta Psychologica, 121, 109–124.

    Article  PubMed  Google Scholar 

  • Droit-Volet, S., Clément, A., & Fayol, M. (2003). Time and number discrimination in a bisection task with a sequence of stimuli: A developmental approach. Journal of Experimental Child Psychology, 84, 63–76.

    Article  PubMed  Google Scholar 

  • Droit-Volet, S., Clément, A., & Fayol, M. (2008). Time, number and length: Similarities and differences in discrimination in adults and children. The Quarterly Journal of Experimental Psychology, 61(12), 1827–1846.

    Article  PubMed  Google Scholar 

  • Ernst, M. O., & Banks, M. S. (2002). Humans integrate visual and haptic information in a statistically optimal fashion. Nature, 415(6870), 429–433.

    Article  PubMed  Google Scholar 

  • Fischer, M. H. (2001). Number processing induces spatial performance biases. Neurology, 57(5), 822–826.

    Article  PubMed  Google Scholar 

  • Gallistel, C. R., & Gelman, R. (2000). Non-verbal numerical cognition: From reals to integers. Trends in Cognitive Sciences, 4, 59–65.

    Article  PubMed  Google Scholar 

  • Girelli, L., Lucangeli, D., & Butterworth, B. (2000). The development of automaticity in accessing number magnitude. Journal of Experimental Child Psychology, 76(2), 104–122.

    Article  PubMed  Google Scholar 

  • Grondin, S. (2010). Timing and time perception: A review of recent behavioral and neuroscience findings and theoretical directions. Attention, Perception, & Psychophysics, 72(3), 561–582.

    Article  Google Scholar 

  • Henik, A., & Tzelgov, J. (1982). Is three greater than five: The relation between physical and semantic size in comparison tasks. Memory & Cognition, 10(4), 389–395.

    Article  Google Scholar 

  • Hurewitz, F., Gelman, R., & Schnitzer, B. (2006). Sometimes area counts more than number. Proceedings of the National Academy of Sciences, 103, 19599–19604.

    Article  Google Scholar 

  • Javadi, A. H., & Aichelburg, C. (2012). When time and numerosity interfere: The longer the more, and the more the longer. PLoS ONE, 7(7), e41496.

    Article  PubMed  PubMed Central  Google Scholar 

  • Jazayeri, M., & Shadlen, M. N. (2010). Temporal context calibrates interval timing. Nature Neuroscience, 13, 1020–1026.

    Article  PubMed  PubMed Central  Google Scholar 

  • Kaufmann, L., Koppelstaetter, F., Delazer, M., Siedentopf, C., Rhomberg, P., Golaszewski, S., et al. (2005). Neural correlates of distance and congruity effects in a numerical Stroop task: an event-related fMRI study. Neuroimage, 25(3), 888–898.

    Article  PubMed  Google Scholar 

  • Kranjec, A., Lehet, M., Woods, A. J., & Chatterjee, A. (2019). Time is not more abstract than space in sound. Frontier in Psychology, 10, 48.

    Article  Google Scholar 

  • Lakoff, G., & Johnson, M. (1980). Metaphors we live by. Chicago and London: The University of Chicago Press.

    Google Scholar 

  • Lakoff, G., & Johnson, M. (1999). Philosophy in the flesh: The embodied mind and its challenge to western thought. Chicago: University of Chicago Press.

    Google Scholar 

  • Lambrechts, A., Walsh, V., & van Wassenhove, V. (2013). Evidence accumulation in the magnitude system. PLoS ONE, 8, e82122.

    Article  PubMed  PubMed Central  Google Scholar 

  • Leibovich, T., Katzin, N., Harel, M., & Henik, A. (2017). From “sense of number” to “sense of magnitude”: The role of continuous magnitudes in numerical cognition. Behavioral and Brain Sciences, 40, e164.

    Article  Google Scholar 

  • Lourenco, S. F., Ayzenberg, V., & Lyu, J. (2016). A general magnitude system in human adults: Evidence from a subliminal priming paradigm. Cortex, 81, 93–103.

    Article  PubMed  Google Scholar 

  • Lourenco, S. F., & Longo, M. R. (2010). General magnitude representation in human infants. Psychological Science, 21(6), 873–881.

    Article  PubMed  Google Scholar 

  • Lourenco, S. F., & Longo, M. R. (2011). Origins and development of generalized magnitude representation. In S. Dehaene & E. M. Brannon (Eds.), Space, time and number in the brain: Searching for the foundations of mathematical thought (pp. 225–244). London: Elsevier.

    Chapter  Google Scholar 

  • Magnani, B., Oliveri, M., & Frassinetti, F. (2014). Exploring the reciprocal modulation of time and space in dancers and non-dancers. Experimental Brain Research, 232, 3191.

    Article  PubMed  Google Scholar 

  • Manyam, V. J. (1986). A psychophysical measure of visual and kinaesthetic spatial discriminative abilities of adults and children. Perception, 15(3), 313-324.3199.

    Article  PubMed  Google Scholar 

  • Martin, B., Wiener, M., & van Wassenhove, V. (2017). A Bayesian perspective on accumulation in the magnitude system. Scientific Reports, 7, 1–14.

    Article  Google Scholar 

  • McGurk, H., & MacDonald, J. (1976). Hearing lips and seeing voices. Nature, 264, 746–748.

    Article  PubMed  Google Scholar 

  • Meck, W. H., & Church, R. M. (1983). A mode control model of counting and timing processes. Journal of Experimental Psychology: Animal Behavior Processes, 9, 320–334.

    PubMed  Google Scholar 

  • Merritt, D. J., Casasanto, D., & Brannon, E. M. (2010). Do monkeys think in metaphors? Representations of space and time in monkeys and humans. Cognition, 117, 191–202.

    Article  PubMed  PubMed Central  Google Scholar 

  • Moon, J. A., Fincham, J. M., Betts, S., & Anderson, J. R. (2015). End effects and cross-dimensional interference in identification of time and length: Evidence for a common memory mechanism. Cognitive, Affective, & Behavioral Neuroscience, 15, 680–695.

    Article  Google Scholar 

  • Nicholls, M. E., Lew, M., Loetscher, T., & Yates, M. J. (2011). The importance of response type to the relationship between temporal order and numerical magnitude. Attention, Perception, & Psychophysics, 73, 1604–1613.

    Article  Google Scholar 

  • O’Brien, R. M. (2007). A caution regarding rules of thumb for variance inflation factors. Quality & Quantity, 41(5), 673–690.

    Article  Google Scholar 

  • Oliveri, M., Vicario, C. M., Salerno, S., Koch, G., Turriziani, P., Mangano, R., et al. (2008). Perceiving numbers alters time perception. Neuroscience Letters, 438, 308–311.

    Article  PubMed  Google Scholar 

  • Petzschner, F. H., Glasauer, S., & Stephan, K. E. (2015). A Bayesian perspective on magnitude estimation. Trends in Cognitive Sciences, 19, 285–293.

    Article  PubMed  Google Scholar 

  • Pufall, P. B., & Shaw, R. E. (1972). Precocious thoughts on number: The long and the short of it. Developmental Psychology, 7(1), 62.

    Article  Google Scholar 

  • Rammsayer, T. H., & Verner, M. (2015). Larger visual stimuli are perceived to last longer from time to time: The internal clock is not affected by nontemporal visual stimulus size. Journal of Vision, 15, 5.

    Article  PubMed  Google Scholar 

  • Riemer, M., Diersch, N., Bublatzky, F., & Wolbers, T. (2016). Space, time, and numbers in the right posterior parietal cortex: Differences between response code associations and congruency effects. NeuroImage, 129, 72–79.

    Article  PubMed  Google Scholar 

  • Schlichting, N., de Jong, R., & van Rijn, H. (2018). Robustness of individual differences in temporal interference effects. PLoS ONE, 13(8), e0202345.

    Article  PubMed  PubMed Central  Google Scholar 

  • Schultz, L. M., & Petersik, J. T. (1994). Visual-haptic relations in a two-dimensional size-matching task. Perceptual and Motor Skills, 78(2), 395–402.

    Article  PubMed  Google Scholar 

  • Schulze-Bonsel, K., Feltgen, N., Burau, H., Hansen, L., & Bach, M. (2006). Visual acuities “hand motion” and “counting fingers” can be quantified with the Freiburg visual acuity test. Investigative Ophthalmology & Visual Science, 47(3), 1236–1240.

    Article  Google Scholar 

  • Spence, C. (2009). Explaining the Colavita visual dominance effect. Progress in Brain Research, 176, 245–258.

    Article  PubMed  Google Scholar 

  • Srinivasan, M., & Carey, S. (2010). The long and the short of it: on the nature and origin of functional overlap between representations of space and time. Cognition, 116, 217–241.

    Article  PubMed  PubMed Central  Google Scholar 

  • Starr, A., & Brannon, E. M. (2016). Visuospatial working memory influences the interaction between space and time. Psychonomic Bulletin & Review, 23, 1839–1845.

    Article  Google Scholar 

  • Storch, D., & Zimmermann, E. (2019). The effect of space on subjective time is mediated by apparent velocity. Journal of Vision, 19(14), 19–19.

    Article  PubMed  Google Scholar 

  • Szűcs, D., & Soltész, F. (2007). Event-related potentials dissociate facilitation and interference effects in the numerical Stroop paradigm. Neuropsychologia, 45(14), 3190–3202.

    Article  PubMed  Google Scholar 

  • Thomas, E. A., & Cantor, N. E. (1975). On the duality of simultaneous time and size perception. Attention, Perception, & Psychophysics, 18(1), 44–48.

    Article  Google Scholar 

  • Thomas, E. A., & Cantor, N. E. (1976). Simultaneous time and size perception. Attention, Perception, & Psychophysics, 19(4), 353–360.

    Article  Google Scholar 

  • Trommershauser, J., Kording, K., & Landy, M. S. (Eds.). (2011). Sensory cue integration. Oxford: Oxford University Press.

    Google Scholar 

  • Walsh, V. (2003). A theory of magnitude: Common cortical metrics of time, space and quantity. Trends in Cognitive Sciences, 7, 483–488.

    Article  PubMed  Google Scholar 

  • Walsh, V. (2014). A theory of magnitude: The parts that sum to numbers. In R. C. Kadosh & A. Dowker (Eds.), The Oxford handbook of numerical cognition. Oxford: Oxford University Press.

    Google Scholar 

  • Wearden, J. H., Denovan, L., Fakhri, M., & Haworth, R. (1997). Scalar timing in temporal generalization in humans with longer stimulus durations. Journal of Experimental Psychology: Animal Behavior Processes, 23, 502–511.

    PubMed  Google Scholar 

  • Wehrman, J. J., Kaplan, D. M., & Sowman, P. F. (2020). Local context effects in the magnitude-duration illusion: Size but not numerical value sequentially alters perceived duration. Acta Psychologica, 204, 103016.

    Article  PubMed  Google Scholar 

  • Winter, B., Marghetis, T., & Matlock, T. (2015). Of magnitudes and metaphors: Explaining cognitive interactions between space, time, and number. Cortex, 64, 209–224.

    Article  PubMed  Google Scholar 

  • Xuan, B., Zhang, D., He, S., & Chen, X. (2007). Larger stimuli are judged to last longer. Journal of Vision, 7, 1–5.

    Article  PubMed  Google Scholar 

  • Zakay, D., & Block, R. A. (1995). An attentional-gate model of prospective time estimation. In M. Richelle, V. De Keyser, G. d’Ydewalle, & A. Vandierendonck (Eds.), Time and the dynamic control of behavior (pp. 167–178). Liège, Belgium: Universite de Liege.

    Google Scholar 

  • Zimmermann, E., & Cicchini, G. M. (2020). Temporal context affects interval timing at the perceptual level. Scientific Reports, 10(1), 1–10.

    Article  Google Scholar 

Download references

Acknowledgments

This work was supported by a CUHK-University of Manchester (UoM) Research Fund (Seed-corn Fund 2019) and a General Research Fund (14600220).

Author information

Authors and Affiliations

  1. Department of Linguistics and Modern Languages/Brain and Mind Institute, The Chinese University of Hong Kong, Leung Kau Kui Building, Shatin, New Territories, Hong Kong

    Zhenguang G. Cai

  2. Key Laboratory of Brain, Cognition and Education Sciences, Ministry of Education, & Guangdong Provincial Key Laboratory of Mental Health and Cognitive Science, Center for Studies of Psychological Application, School of Psychology, South China Normal University, Guangzhou, China

    Ruiming Wang

Authors
  1. Zhenguang G. Cai
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ruiming Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to Zhenguang G. Cai or Ruiming Wang.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Cai, Z.G., Wang, R. Cross-dimensional magnitude interaction is modulated by representational noise: evidence from space–time interaction. Psychological Research 86, 196–208 (2022). https://doi.org/10.1007/s00426-020-01472-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00426-020-01472-4

Search

Navigation