Abstract
Subitizing (enumerating four or fewer objects) and estimation (enumerating five or more objects) are two rapid enumeration processes. The relationship between them remains undetermined, especially in tactile modality. The present study used a double enumeration paradigm to assess switch costs. In this paradigm, participants were required to enumerate two sequentially presented arrays of tactile stimuli, each with a set size either within or outside of a predetermined subitizing range. When enumeration process switched between subitizing and estimation, participants’ response to the second array showed a higher error rate and worse precision, relative to no processing switch conditions. Meanwhile, the switch costs exhibited an asymmetry pattern - the switch from estimation to subitizing gave rise to a worse precision than the switch from subitizing to estimation did. During a switch from subitizing to estimation, the switch costs nearly vanished, since subitizing had already mobilized both approximate number representation system (ANS) and object individuation (OI). The switch costs also disappeared when inter-stimulus intervals (ISIs) between the two arrays were extended (i.e., preparation effect). Our results supported “dual component hypothesis” that subitizing activated OI and ANS processes while estimation only activated ANS, corresponding with evidence from visual modality. Taken together, the present findings suggest that tactile subitizing mobilizes both OI and ANS processes, and non-symbol number representation is modality-independent.
Similar content being viewed by others
Data Availability
All data are available at https://osf.io/ksjcu/.
Notes
In each ANOVA of each experiment, the Bonferroni correction for multiple comparisons was used in post-hoc tests. Whenever the Sphericity assumption was violated, we applied the Greenhouse-Geisser correction in each ANOVA
References
Amedi, A. (2002). Convergence of Visual and Tactile Shape Processing in the Human Lateral Occipital Complex. Cerebral Cortex, 12(11), 1202–1212. https://doi.org/10.1093/cercor/12.11.1202
Amedi, A., Malach, R., Hendler, T., Peled, S., & Zohary, E. (2001). Visuo-haptic object-related activation in the ventral visual pathway. Nature Neuroscience, 4(3), 324–330. https://doi.org/10.1038/85201
Anobile, G., Arrighi, R., & Burr, D. C. (2019). Simultaneous and sequential subitizing are separate systems, and neither predicts math abilities. Journal of Experimental Child Psychology, 178, 86–103. https://doi.org/10.1016/j.jecp.2018.09.017
Anobile, G., Arrighi, R., Castaldi, E., & Burr, D. C. (2021). A Sensorimotor Numerosity System. Trends in Cognitive Sciences, 25(1), 24–36. https://doi.org/10.1016/j.tics.2020.10.009
Anobile, G., Arrighi, R., Togoli, I., & Burr, D. C. (2016a). A shared numerical representation for action and perception. ELife, 5, e16161. https://doi.org/10.7554/eLife.16161
Anobile, G., Cicchini, G. M., & Burr, D. C. (2016b). Number As a Primary Perceptual Attribute: A Review. Perception, 45(1–2), 5–31. https://doi.org/10.1177/0301006615602599
Anobile, G., Turi, M., Cicchini, G. M., & Burr, D. C. (2012). The effects of cross-sensory attentional demand on subitizing and on mapping number onto space. Vision Research, 74, 102–109. https://doi.org/10.1016/j.visres.2012.06.005
Arrighi, R., Togoli, I., & Burr, D. C. (2014). A generalized sense of number. Proceedings of the Royal Society B: Biological Sciences, 281(1797), 20141791. https://doi.org/10.1098/rspb.2014.1791
Arrington, C. M., & Logan, G. D. (2004). The cost of a voluntary task switch. Psychological Science, 15(9), 610–615. https://doi.org/10.1111/j.0956-7976.2004.00728.x
Attout, L., Noël, M.-P., Vossius, L., & Rousselle, L. (2017). Evidence of the impact of visuo-spatial processing on magnitude representation in 22q11.2 microdeletion syndrome. Neuropsychologia, 99, 296–305. https://doi.org/10.1016/j.neuropsychologia.2017.03.023
Blakemore, C., & Campbell, F. W. (1969). On the existence of neurones in the human visual system selectively sensitive to the orientation and size of retinal images. The Journal of Physiology, 203(1), 237–260. https://doi.org/10.1113/jphysiol.1969.sp008862
Brysbaert, M., & Stevens, M. (2018). Power Analysis and Effect Size in Mixed Effects Models: A Tutorial. Journal of Cognition, 1(1), 9. https://doi.org/10.5334/joc.10
Burr, D. C., Anobile, G., & Arrighi, R. (2018). Psychophysical evidence for the number sense. Philosophical Transactions of the Royal Society B: Biological Sciences, 373(1740), 20170045. https://doi.org/10.1098/rstb.2017.0045
Burr, D., & Ross, J. (2008). A Visual Sense of Number. Current Biology, 18(6), 425–428. https://doi.org/10.1016/j.cub.2008.02.052
Burr, D. C., Turi, M., & Anobile, G. (2010). Subitizing but not estimation of numerosity requires attentional resources. Journal of Vision, 10(6), 20–20. https://doi.org/10.1167/10.6.20
Cai, Y., Hofstetter, S., van Dijk, J., Zuiderbaan, W., van der Zwaag, W., Harvey, B. M., & Dumoulin, S. O. (2021). Topographic numerosity maps cover subitizing and estimation ranges. Nature Communications, 12(1), 3374. https://doi.org/10.1038/s41467-021-23785-7
Cheng, X., Lin, C., Lou, C., Zhang, W., Han, Y., Ding, X., & Fan, Z. (2021). Small numerosity advantage for sequential enumeration on RSVP stimuli: An object individuation-based account. Psychological Research, 85(2), 734–763. https://doi.org/10.1007/s00426-019-01264-5
Chesney, D. L., & Haladjian, H. H. (2011). Evidence for a shared mechanism used in multiple-object tracking and subitizing. Attention Perception & Psychophysics, 73(8), 2457–2480. https://doi.org/10.3758/s13414-011-0204-9
Cicchini, G. M., Anobile, G., & Burr, D. C. (2016). Spontaneous perception of numerosity in humans. Nature Communications, 7(1), 12536. https://doi.org/10.1038/ncomms12536
Cohen, Z. Z., Aisenberg, D., & Henik, A. (2018a). The effects of training on tactile enumeration. Psychological Research, 82(3), 468–487. https://doi.org/10.1007/s00426-016-0835-5
Cohen, Z. Z., Arend, I., Yuen, K., Naparstek, S., Gliksman, Y., Veksler, R., & Henik, A. (2018b). Tactile enumeration: A case study of acalculia. Brain and Cognition, 127, 60–71. https://doi.org/10.1016/j.bandc.2018.10.001
Cohen, Z. Z., & Henik, A. (2016). Effects of Numerosity Range on Tactile and Visual Enumeration. Perception, 45(1–2), 83–98. https://doi.org/10.1177/0301006615614662
Dehaene, S., & Changeux, J. P. (1993). Development of elementary numerical abilities: A neuronal model. Journal of Cognitive Neuroscience, 5, 390–407. https://doi.org/10.1162/jocn.1993.5.4.390
de Hevia, M. D., & Spelke, E. S. (2010). Number-Space Mapping in Human Infants. Psychological Science, 21(5), 653–660. https://doi.org/10.1177/0956797610366091
DeWind, N. K., Adams, G. K., Platt, M. L., & Brannon, E. M. (2015). Modeling the approximate number system to quantify the contribution of visual stimulus features. Cognition, 142, 247–265. https://doi.org/10.1016/j.cognition.2015.05.016
Eger, E., Sterzer, P., Russ, M. O., Giraud, A.-L., & Kleinschmidt, A. (2003). A Supramodal Number Representation in Human Intraparietal Cortex. Neuron, 37(4), 719–726. https://doi.org/10.1016/S0896-6273(03)00036-9
Faul, F., Erdfelder, E., Lang, A.-G., & Buchner, A. (2007). G*Power 3: A flexible statistical power analysis program for the social, behavioral, and biomedical sciences. Behavior Research Methods, 39, 175–191. https://doi.org/10.3758/BF03193146
Feigenson, L., Dehaene, S., & Spelke, E. (2004). Core systems of number. Trends in Cognitive Sciences, 8(7), 307–314. https://doi.org/10.1016/j.tics.2004.05.002
Fischer, J., & Whitney, D. (2014). Serial dependence in visual perception. Nature Neuroscience, 17(5), 738–743. https://doi.org/10.1038/nn.3689
Fornaciai, M., & Park, J. (2017). Distinct Neural Signatures for Very Small and Very Large Numerosities. Frontiers in Human Neuroscience, 11. https://doi.org/10.3389/fnhum.2017.00021
Fornaciai, M., & Park, J. (2018). Serial dependence in numerosity perception. Journal of Vision, 18(9), 15. https://doi.org/10.1167/18.9.15
Fornaciai, M., & Park, J. (2020). Neural Dynamics of Serial Dependence in Numerosity Perception. Journal of Cognitive Neuroscience, 32(1), 141–154. https://doi.org/10.1162/jocn_a_01474
Fornaciai, M., & Park, J. (2021). Decoding of EEG Signals Shows No Evidence of a Neural Signature for Subitizing in Sequential Numerosity. Journal of Cognitive Neuroscience, 1–15. https://doi.org/10.1162/jocn_a_01734
Gallace, A., Tan, H. Z., & Spence, C. (2006). Numerosity Judgments for Tactile Stimuli Distributed over the Body Surface. Perception, 35(2), 247–266. https://doi.org/10.1068/p5380
Gallace, A., Tan, H. Z., & Spence, C. (2008). Can Tactile Stimuli Be Subitised? An Unresolved Controversy within the Literature on Numerosity Judgments. Perception, 37(5), 782–800. https://doi.org/10.1068/p5767
Gallistel, C. R., & Gelman, R. (1991). Subitizing: The preverbal counting process. In F. Craik, W. Kessen, & A. Ortony (Eds.), Thoughts memories and emotions: Essays in honor of George Mandler (pp. 65–81). Erlbaum.
Gallistel, C. R., & Gelman, R. (1992). Preverbal and verbal counting and computation. Cognition, 44, 43–74. https://doi.org/10.1016/0010-0277(92)90050-R
Graham, B., & Lavric, A. (2021). Preparing to switch languages versus preparing to switch tasks: Which is more effective? Journal of Experimental Psychology: General. https://doi.org/10.1037/xge0001027
Hochman, S., Cohen, Z. Z., Ben-Shachar, M. S., & Henik, A. (2020). Tactile Enumeration and Embodied Numerosity Among the Deaf. Cognitive Science, 44(8). https://doi.org/10.1111/cogs.12880
Hofstetter, S., Cai, Y., Harvey, B. M., & Dumoulin, S. O. (2021). Topographic maps representing haptic numerosity reveals distinct sensory representations in supramodal networks. Nature Communications, 12(1), 221. https://doi.org/10.1038/s41467-020-20567-5
Katzin, N., Cohen, Z. Z., & Henik, A. (2019). If it looks, sounds, or feels like subitizing, is it subitizing? A modulated definition of subitizing. Psychonomic Bulletin & Review, 26(3), 790–797. https://doi.org/10.3758/s13423-018-1556-0
Kaufman, E. L., Lord, M. W., Reese, T. W., & Volkmann, J. (1949). The Discrimination of Visual Number. The American Journal of Psychology, 62(4), 498. https://doi.org/10.2307/1418556
Kleiner, M. B., Brainard, D. H., & Pelli, D. G. (2007). What’s new in Psychtoolbox-3? Perception, 36(2), 301–307. https://doi.org/10.1068/v070821
Knops, A., Piazza, M., Sengupta, R., Eger, E., & Melcher, D. (2014). A Shared, Flexible Neural Map Architecture Reflects Capacity Limits in Both Visual Short-Term Memory and Enumeration. Journal of Neuroscience, 34(30), 9857–9866. https://doi.org/10.1523/JNEUROSCI.2758-13.2014
Logan, G. D., & Gordon, R. D. (2001). Executive control of visual attention in dual-task situations. Psychological Review, 108(2), 393–434. https://doi.org/10.1037/0033-295X.108.2.393
Mayr, U., & Kliegl, R. (2000). Task-set switching and long-term memory retrieval. Journal of Experimental Psychology Learning Memory & Cognition, 26(5), 1124–1140. https://doi.org/10.1037/0278-7393.26.5.1124
Meiran, N. (1996). Reconfiguration of processing mode prior to task performance. Journal of Experimental Psychology Learning Memory & Cognition, 22(6), 1423–1442. https://doi.org/10.1037/0278-7393.22.6.1423
Monsell, S. (2003). Task switching. Trends in Cognitive Sciences, 7(3), 134–140. https://doi.org/10.1016/S1364-6613(03)00028-7
Monsell, S., & Mizon, G. A. (2006). Can the task-cuing paradigm measure an endogenous task-set reconfiguration process? Journal of Experimental Psychology: Human Perception and Performance, 32(3), 493–516. https://doi.org/10.1037/0096-1523.32.3.493
Nieder, A. (2012). Supramodal numerosity selectivity of neurons in primate prefrontal and posterior parietal cortices. Proceedings of the National Academy of Sciences, 109(29), 11860–11865. https://doi.org/10.1073/pnas.1204580109
Nieder, A. (2016). The neuronal code for number. Nature Reviews Neuroscience, 17(6), 366–382. https://doi.org/10.1038/nrn.2016.40
Nieder, A. (2017). Magnitude Codes for Cross-Modal Working Memory in the Primate Frontal Association Cortex. Frontiers in Neuroscience, 11. https://doi.org/10.3389/fnins.2017.00202
Nieder, A., & Dehaene, S. (2009). Representation of Number in the Brain. Annual Review of Neuroscience, 32(1), 185–208. https://doi.org/10.1146/annurev.neuro.051508.135550
Piazza, M., De Feo, V., Panzeri, S., & Dehaene, S. (2018). Learning to focus on number. Cognition, 181, 35–45. https://doi.org/10.1016/j.cognition.2018.07.011
Piazza, M., Fumarola, A., Chinello, A., & Melcher, D. (2011). Subitizing reflects visuo-spatial object individuation capacity. Cognition, 121(1), 147–153. https://doi.org/10.1016/j.cognition.2011.05.007
Piazza, M., Mechelli, A., Price, C. J., & Butterworth, B. (2006). Exact and approximate judgements of visual and auditory numerosity: An fMRI study. Brain Research, 1106(1), 177–188. https://doi.org/10.1016/j.brainres.2006.05.104
Pietrini, P., Furey, M. L., Ricciardi, E., Gobbini, M. I., Wu, W.-H. C., Cohen, L., Guazzelli, M., & Haxby, J. V. (2004). Beyond sensory images: Object-based representation in the human ventral pathway. Proceedings of the National Academy of Sciences, 101(15), 5658–5663. https://doi.org/10.1073/pnas.0400707101
Pomè, A., Anobile, G., Cicchini, G. M., Scabia, A., & Burr, D. C. (2019). Higher attentional costs for numerosity estimation at high densities. Attention, Perception, & Psychophysics, 81(8), 2604–2611. https://doi.org/10.3758/s13414-019-01831-3
Revkin, S. K., Piazza, M., Izard, V., Cohen, L., & Dehaene, S. (2008). Does Subitizing Reflect Numerical Estimation? Psychological Science, 19(6), 607–614. https://doi.org/10.1111/j.1467-9280.2008.02130.x
Riggs, K. J., Ferrand, L., Lancelin, D., Fryziel, L., Dumur, G., & Simpson, A. (2006). Subitizing in Tactile Perception. Psychological Science, 17(4), 271–272. https://doi.org/10.1111/j.1467-9280.2006.01696.x
Rogers, R. D., & Monsell, S. (1995). Costs of a predictible switch between simple cognitive tasks. Journal of Experimental Psychology, 124(2), 207. https://doi.org/10.1037/0096-3445.124.2.207
Sathian, K., & Zangaladze, A. (2002). Feeling with the mind's eye: Contribution of visual cortex to tactile perception. Behavioural Brain Research, 135(1–2), 127–132. https://doi.org/10.1016/S0166-4328(02)00141-9
Sengupta, R., Bapiraju, S., & Melcher, D. (2017). Big and small numbers: Empirical support for a single, flexible mechanism for numerosity perception. Attention, Perception, & Psychophysics, 79(1), 253–266. https://doi.org/10.3758/s13414-016-1221-5
Tian, Y., & Chen, L. (2018). Cross-modal attention modulates tactile subitizing but not tactile numerosity estimation. Attention, Perception, & Psychophysics, 80(5), 1229–1239. https://doi.org/10.3758/s13414-018-1507-x
Togoli, I., & Arrighi, R. (2021). Evidence for an A-Modal Number Sense: Numerosity Adaptation Generalizes Across Visual, Auditory, and Tactile Stimuli. Frontiers in Human Neuroscience, 15, 713565. https://doi.org/10.3389/fnhum.2021.713565
Togoli, I., Marlair, C., Collignon, O., Arrighi, R., & Crollen, V. (2021). Tactile numerosity is coded in external space. Cortex, 134, 43–51. https://doi.org/10.1016/j.cortex.2020.10.008
Trick, L. M., & Pylyshyn, Z. W. (1994). Why are small and large numbers enumerated differently? A limited-capacity preattentive stage in vision. Psychological Review, 101(1), 80–102. https://doi.org/10.1037/0033-295X.101.1.80
Vetter, P., Butterworth, B., & Bahrami, B. (2008). Modulating Attentional Load Affects Numerosity Estimation: Evidence against a Pre-Attentive Subitizing Mechanism. PLoS ONE, 3(9), e3269. https://doi.org/10.1371/journal.pone.0003269
Whalen, J., Gallistel, C. R., & Gelman, R. (1999). Nonverbal Counting in Humans: The Psychophysics of Number Representation. Psychological Science, 10(2), 130–137. https://doi.org/10.1111/1467-9280.00120
Xu, F., & Spelke, E. S. (2000). Large number discrimination in 6-month-old infants. Cognition, 74(1), B1–B11. https://doi.org/10.1016/S0010-0277(99)00066-9
Xu, F., Spelke, E. S., & Goddard, S. (2005). Number sense in human infants. Developmental Science, 8(1), 88–101. https://doi.org/10.1111/j.1467-7687.2005.00395.x
Xu, Y. (2009). Distinctive Neural Mechanisms Supporting Visual Object Individuation and Identification. Journal of Cognitive Neuroscience, 21(3), 511–518. https://doi.org/10.1162/jocn.2008.21024
Acknowledgements
This work was supported by grants from the Natural Science Foundation of China (Grant No. 62061136001, 31861133012,11774379).
Funding
This study was funded by Natural Science Foundation of China (Grant No. 62061136001, 31861133012,11774379).
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Ethics Approval
All procedures performed in studies involving human participants were in accordance with the ethical standards of the institutional and/or national research committee and with the 1964 Helsinki declaration and its later amendments or comparable ethical standard
Conflicts of Interest
The authors declare that they have no conflict of interest.
Informed Consent
Informed consent was obtained from all individual participants included in the study.
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Significance Statement
Subitizing and estimation are two critical enumeration processes for non-symbol numbers enumeration. While the evidence from the visual and auditory modalities was sufficient, there were relatively fewer investigations on the switch costs between the them in tactile modality. Here we implemented non-symbol tactile enumeration tasks and revealed object individuation (OI) processes during the asymmetric transition for switch cost, and proved non-symbol numbers representation was on abstract level and modality-independent.
Supplementary Information
ESM 1
(DOCX 1205 kb)
Rights and permissions
About this article
Cite this article
Lou, C., Zeng, H. & Chen, L. Asymmetric switch cost between subitizing and estimation in tactile modality. Curr Psychol 42, 15141–15155 (2023). https://doi.org/10.1007/s12144-022-02858-w
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12144-022-02858-w