Neuroscience and Behavioral Physiology

, Volume 46, Issue 2, pp 168–177 | Cite as

A Mathematical Model of Mental Time

  • A. V. Glasko
  • L. G. Sadykhova

Working from the concepts espoused by Ernst Mach and a previously developed mathematical theory of mental processes, we have introduced mathematical definitions of the duration of mental time intervals, initially for the perception (experiencing) of an individual event, and then for the general case, i.e., for the perception (experiencing) of sequences of events. The relationship between mental time and the duration of the corresponding interval of physical time was studied. The link between mental time and the perception of time was addressed (for two cases: “long” and “short” intervals). Theoretical formulas are compared with the results of experimental measurements. Process time is defined, and this can be employed in particular as a measure of work. The time reversal effect described in Mach’s works is analyzed and modeled.


mental time perception of time attention consciousness depth of impression fascination diligence process time time reversal 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Belen’kaya, L. Ya., “On the question of the perception of time duration and its impairments,” in: Studies in the Psychology of Perception, Nauka, Moscow, Leningrad (1984), pp. 342–360.Google Scholar
  2. 2.
    Borozdina, L. V. and Spiridonova, I. A., “Developmental changes in a subject’s time transpective,” Psikhol. Zh., No. 2, 40–50 (1998).Google Scholar
  3. 3.
    Budiyanskii, N. F., Effects of the Motivation Factor on the Perception of Time in Activity: Auth. Abstr. Mast. Thesis Psychol. Sci., Odessa (1984).Google Scholar
  4. 4.
    Cottle, T. J., Perceiving Time. A Psychological Investigation with Men and Women, New York (1976).Google Scholar
  5. 5.
    Gareev, E. M., “Methods of assessing subjective time in humans,” in: The Time Factor in the Functional Organization of Living Systems, JL (1980), pp. 128–131.Google Scholar
  6. 6.
    Gareev, E. M., Intercentral Interactions of the Neocortex on Assessment of Time and its Psychophysiological Patterns: Auth. Abstr. Mast. Thesis Psychol. Sci., Ufa (1987).Google Scholar
  7. 7.
    Glasko, A. V., “A model of the dynamics of attention during the process of perception,” Zh. Vyssh. Nerv. Deyat., 58, No. 6, 738–754 (2008a).Google Scholar
  8. 8.
    Glasko, A. V., “Attention as a dynamic invariant,” Obozr. Prikl. Prom. Mat., 13, No. 4, 624–625 (2006).Google Scholar
  9. 9.
    Glasko, A. V., “Perception of musical melodies,” Obozr. Prikl. Prom. Mat., 15, No. 2, 278–279 (2008b).Google Scholar
  10. 10.
    Glasko, A. V., “Synthesis of a Pavlov induction law and the Stevens psychophysical law in a dynamic equation describing the process of perception,” AIS’05, CAD-2005, Intellectual Systems, Intellectual SAPR: Proc. Int. Conf., Fizmatlit, Moscow (2005b), Vol. 2, pp. 166–174.Google Scholar
  11. 11.
    Glasko, A. V., “The question of time reversal in heat conduction equations,” in: Irreversible Processes in Nature and Technology: Proc. 3rd All-Russ. Conf., Bauman MGTU, Moscow (2005a), pp. 130–131.Google Scholar
  12. 12.
    Glasko, A. V., “The Stevens psychophysical law, evoked potential amplitudes, and the dynamics of attention…,” in: Psychophysics Today, V. N. Nosenko and I. G. Skotnikova (eds.), IP RAN, Moscow (2007), pp. 136–143.Google Scholar
  13. 13.
    Hume, D., Works in Two Volumes [Russian translation], Mysl, Moscow (1996), Vol. 1.Google Scholar
  14. 14.
    Kant I., Critique of Pure Reason [Russian translation], Mysl, Moscow (1994).Google Scholar
  15. 15.
    Kovalev, V. I., The Category of Time in Psychology (the personal aspect)… The Category of Materialist Dialectics, Nauka, Moscow (1988), pp. 216–230.Google Scholar
  16. 16.
    Kovalkin, S. S., Towards an Experimental Basis for a Model of Perception, Bauman MGTU, Moscow (2007).Google Scholar
  17. 17.
    Mach, E., Analysis of Feelings and the Relationship of the Physical to the Mental [Russian translation], Territ. Budush., Moscow (2005).Google Scholar
  18. 18.
    Mitchell, C. T. and Davis, R., “The perception of time in scale model environments,” Perception, 16, No. 1, 5–16 (1987).PubMedCrossRefGoogle Scholar
  19. 19.
    Mitina, L. M., “Effects of stimulus intensity on assessments and measurements of time intervals of different durations,” Vopr. Psikhol., No. 1, 64–73 (1977).Google Scholar
  20. 20.
    Mizyak, V. G., Dynamics of the Amplitude of Auditory and Visual Evoked Potentials as a Consequence of the Dynamics of Attention during the Perception of an External Stimulus, Bauman MGTU, Moscow (2007).Google Scholar
  21. 21.
    Moskvin, V. A. and Popovich, V. V., “Neuropsychological aspects of studies of time perception in healthy subjects…,” in: 1st Int. Conf. in Memory of A. R. Luriya: Coll. Reports, E. D. Khomskaya and T. V. Akhutina (eds.), RPO, Moscow (1998), pp. 160–166.Google Scholar
  22. 22.
    Näätänen, R., Attention and Brain Function, Izd. MGU, Moscow (1998).Google Scholar
  23. 23.
    Pakhno, I. V., The Experience of Time in Crisis Situations: Auth. Abstr. Mast. Thesis Psychol. Sci., Khabarovsk (2004).Google Scholar
  24. 24.
    Pod’yacheva, T. N., Bukreeva, N. A., and Volchek, E. E., “Studies of the relationship between perception of time and age in humans,” Vestn. Samar. Gos. Univ., No. 1, 30–39 (2006).Google Scholar
  25. 25.
    Rubinshtein, S. L., Basic General Psychology, Piter, St. Petersburg (2002).Google Scholar
  26. 26.
    Ryzhukhin, A. V., Specifi c Features of the Perception of Time by Adolescents with Asocial Behavior: Auth. Abstr. Mast. Thesis Psychol. Sci., Moscow (2011).Google Scholar
  27. 27.
    Tsukanov, B. I., “Characteristics of the perception of time in mentally retarded pupils,” Defektologiya, No. 3, 28–33 (1990).Google Scholar
  28. 28.
    Vcherashnii, A. E., Solution of a Dynamic Model of the Process of Perception of an External Stimulus and the Stevens Psychophysical Law, Bauman MGTU, Moscow (2006).Google Scholar
  29. 29.
    Voronenko, I. N., Characteristics of the Reproduction of Time Segments and Intervals by Students with Different Types of Autonomic Regulation and Levels of Anxiety: Auth. Abstr. Mast. Thesis Psychol. Sci., Stavropol State Univ., Stavropol (2005).Google Scholar
  30. 30.
    Woodrow, G., “Time perception,” in: The Handbook of Experimental Psychology [Russian translation], S. S. Stevens (ed.), IL, Moscow (1963), pp. 859–875.Google Scholar
  31. 31.
    Zakay, D., The Impact of Time Perception Processes on Decision Making Under Time Stress, in: Time Pressure and Stress in Human Judgment and Decision Making, O. Svenson and A. J. Maule (eds.), Plenum Press, New York, London (1993), pp. 59–72.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Department of Higher Mathematics, Department of Sociology and Culture StudiesBauman Moscow State Technical UniversityMoscowRussia

Personalised recommendations