Attention, Perception, & Psychophysics

, Volume 79, Issue 3, pp 833–840 | Cite as

Individual differences in long-range time representation

  • Camila S. Agostino
  • Marcelo S. Caetano
  • Fuat Balci
  • Peter M. E. Claessens
  • Yossi Zana
Article

Abstract

On the basis of experimental data, long-range time representation has been proposed to follow a highly compressed power function, which has been hypothesized to explain the time inconsistency found in financial discount rate preferences. The aim of this study was to evaluate how well linear and power function models explain empirical data from individual participants tested in different procedural settings. The line paradigm was used in five different procedural variations with 35 adult participants. Data aggregated over the participants showed that fitted linear functions explained more than 98% of the variance in all procedures. A linear regression fit also outperformed a power model fit for the aggregated data. An individual-participant-based analysis showed better fits of a linear model to the data of 14 participants; better fits of a power function with an exponent β > 1 to the data of 12 participants; and better fits of a power function with β < 1 to the data of the remaining nine participants. Of the 35 volunteers, the null hypothesis β = 1 was rejected for 20. The dispersion of the individual β values was approximated well by a normal distribution. These results suggest that, on average, humans perceive long-range time intervals not in a highly compressed, biased manner, but rather in a linear pattern. However, individuals differ considerably in their subjective time scales. This contribution sheds new light on the average and individual psychophysical functions of long-range time representation, and suggests that any attribution of deviation from exponential discount rates in intertemporal choice to the compressed nature of subjective time must entail the characterization of subjective time on an individual-participant basis.

Keywords

Time representation Line paradigm Time discounting Psychophysics 

References

  1. Allan, L. G. (1983). Magnitude estimation of temporal intervals. Perception & Psychophysics, 33, 29–42. doi: 10.3758/BF03205863 CrossRefGoogle Scholar
  2. Balci, F., & Gallistel, C. R. (2006). Cross-domain transfer of quantitative discriminations: Is it all a matter of proportion? Psychonomic Bulletin & Review, 13, 636–642. doi: 10.3758/BF03193974 CrossRefGoogle Scholar
  3. Dasgupta, P., & Maskin, E. (2005). Uncertainty and hyperbolic discounting. American Economic Review, 95, 1290–1299. doi: 10.1257/0002828054825637 CrossRefGoogle Scholar
  4. Di Luca, M., & Rhodes, D. (2016). Optimal perceived timing: Integrating sensory information with dynamically updated expectations. Scientific Reports, 6, 28563. doi: 10.1038/srep28563 CrossRefPubMedPubMedCentralGoogle Scholar
  5. Eisler, H. (1976). Experiments on subjective duration 1868–1975: A collection of power function exponents. Psychological Bulletin, 83, 1154–1171. doi: 10.1037/0033-2909.83.6.1154 CrossRefPubMedGoogle Scholar
  6. Estes, W. K. (1956). The problem of inference from curves based on group data. Psychological Bulletin, 53, 134–140. doi: 10.1037/h0045156 CrossRefPubMedGoogle Scholar
  7. Frederick, S., Loewenstein, G. F., & O’Donoghue, T. (2002). Time discounting and time preference: A critical review. Journal of Economic Literature, 40, 351–401. doi: 10.1257/002205102320161311 CrossRefGoogle Scholar
  8. Gallistel, C. R., Fairhurst, S., & Balsam, P. (2004). The learning curve: Implications of a quantitative analysis. Proceedings of the National Academy of Sciences, 101, 13124–13131. doi: 10.1073/pnas.0404965101 CrossRefGoogle Scholar
  9. Gallistel, C. R., & Gelman, R. (1992). Preverbal and verbal counting and computation. Cognition, 44, 48–74. doi: 10.1016/0010-0277(92)90050-R CrossRefGoogle Scholar
  10. Glicksohn, J., & Hadad, Y. (2012). Sex differences in time production revisited. Journal of Individual Differences, 33, 35–42. doi: 10.1027/1614-0001/a000059 CrossRefGoogle Scholar
  11. Green, L., & Myerson, J. (2004). A discounting framework for choice with delayed and probabilistic rewards. Psychological Bulletin, 130, 769–792. doi: 10.1037/0033-2909.130.5.769 CrossRefPubMedPubMedCentralGoogle Scholar
  12. Grondin, S. (2010). Timing and time perception: A review of recent behavioral and neuroscience findings and theoretical directions. Attention, Perception, & Psychophysics, 72, 561–582. doi: 10.3758/APP.72.3.561 CrossRefGoogle Scholar
  13. Grondin, S., & Laflamme, V. (2015). Stevens’s law for time: A direct comparison of prospective and retrospective judgments. Attention, Perception, & Psychophysics, 77, 1044–1051. doi: 10.3758/s13414-015-0914-5 CrossRefGoogle Scholar
  14. Han, R., & Takahashi, T. (2012). Psychophysics of time perception and valuation in temporal discounting of gain and loss. Physica A, 391, 6568–6576. doi: 10.1016/j.physa.2012.07.012 CrossRefGoogle Scholar
  15. Kass, R. E., & Raftery, A. E. (1995). Bayes factors. Journal of the American Statistical Association, 90, 773–795. doi: 10.1080/01621459.1995.10476572 CrossRefGoogle Scholar
  16. Kim, B. K., & Zauberman, G. (2009). Perception of anticipatory time in temporal discounting. Journal of Neuroscience, Psychology, and Economics, 2, 91–101. doi: 10.1037/a0017686 CrossRefGoogle Scholar
  17. Kim, B. K., & Zauberman, G. (2013). Can Victoria’s Secret change the future? A subjective time perception account of sexual-cue effects on impatience. Journal of Experimental Psychology: General, 142, 328–335. doi: 10.1037/a0028954 CrossRefGoogle Scholar
  18. Lucci, C. R. (2013). Time, self, and intertemporal choice. Frontiers in Neuroscience, 7, 40. doi: 10.3389/fnins.2013.00040 CrossRefPubMedPubMedCentralGoogle Scholar
  19. Matthews, W. J., & Meck, W. H. (2016). Temporal cognition: Connecting subjective time to perception, attention, and memory. Psychological Bulletin, 142, 865–907. doi: 10.1037/bul0000045 CrossRefPubMedGoogle Scholar
  20. Pinheiro, J., Bates, D., DebRoy, S., Sarkar, D., EISPACK authors, Heisterkamp, S., & Van Willigen, B. (2016). nlme: Linear and nonlinear mixed effects models (R package version 3.1-125). Retrieved from http://CRAN.R-project.org/package=nlme
  21. Ray, D., & Bossaerts, P. (2011). Positive temporal dependence of the biological clock implies hyperbolic discounting. Frontiers in Neuroscience, 5, 2. doi: 10.3389/fnins.2011.00002 CrossRefPubMedPubMedCentralGoogle Scholar
  22. Samuelson, P. A. (1937). A note on measurement of utility. Review of Economic Studies, 4, 155–161.CrossRefGoogle Scholar
  23. Sheather, S. J., & Jones, M. C. (1991). A reliable data-based bandwidth selection method for kernel density estimation. Journal of the Royal Statistical Society, Series B, 53, 683–690. doi: 10.2307/2345597 Google Scholar
  24. Shi, Z., Church, R. M., & Meck, W. H. (2013). Bayesian optimization of time perception. Trends in Cognitive Sciences, 17, 556–564. doi: 10.1016/j.tics.2013.09.009 CrossRefPubMedGoogle Scholar
  25. Sozou, P. D. (1998). On hyperbolic discounting and uncertain hazard rates. Proceedings of the Royal Society B, 265, 2015–2020. doi: 10.1098/rspb.1998.0534 CrossRefPubMedCentralGoogle Scholar
  26. Stevens, S. S. (1957). On the psychophysical law. Psychological Review, 64, 153–181. doi: 10.1037/h0046162 CrossRefPubMedGoogle Scholar
  27. Stevens, S. S. (1961). To honor Fechner and repeal his law. Science, 133, 80–86. doi: 10.1126/science.133.3446.80 CrossRefPubMedGoogle Scholar
  28. Takahashi, T., Oono, H., & Radford, M. H. (2008). Psychophysics of time perception and intertemporal choice models. Physica A, 387, 2066–2074. doi: 10.1016/j.physa.2007.11.047 CrossRefGoogle Scholar
  29. Walsh, V. (2003). A theory of magnitude: Common cortical metrics of time, space and quantity. Trends in Cognitive Sciences, 7, 483–488. doi: 10.1016/j.tics.2003.09.002 CrossRefPubMedGoogle Scholar
  30. Wearden, J. H., & Jones, L. A. (2007). Is the growth of subjective time in humans a linear or nonlinear function of real time? Quarterly Journal of Experimental Psychology, 60, 1289–1302. doi: 10.1080/17470210600971576 CrossRefGoogle Scholar
  31. Wittmann, M. (2009). The inner experience of time. Philosophical Transactions of the Royal Society B, 364, 1955–1967. doi: 10.1098/rstb.2009.0003 CrossRefGoogle Scholar
  32. Wittmann, M., & Paulus, M. P. (2008). Decision making, impulsivity and time perception. Trends in Cognitive Sciences, 12, 7–12. doi: 10.1016/j.tics.2007.10.004 CrossRefPubMedGoogle Scholar
  33. Zauberman, G., Kim, B. K., Malkoc, S. L., & Bettan, J. R. (2009). Discounting time and time discounting: Subjective time perception and intertemporal preferences. Journal of Marketing Research, 46, 543–556. doi: 10.1509/jmkr.46.4.543 CrossRefGoogle Scholar

Copyright information

© The Psychonomic Society, Inc. 2017

Authors and Affiliations

  1. 1.Federal University of ABCSão Bernardo do CampoBrazil
  2. 2.Koç UniversityİstanbulTurkey

Personalised recommendations