A Mathematical Study of the Dynamics of Conscious Acquiring of Knowledge through Reading and Cramming and the Process of Losing Information from the Brain by Natural Forgetting of Facts

ABSTRACT

We model the conscious learning process of human brain with a dynamical equation (cramming dynamics) by considering both the data entry and loss of data simultaneously. We show the analytical solution of the differential equation in some special cases. We define some indexes like memory index, merit index, utilization index etc. Using them we can measure the corresponding memory functions. Applications of this model have also been discussed. More general numerical and analytical results are also presented at the end.

We model the conscious learning process of human brain with a dynamical equation (cramming dynamics) by considering both the data entry and loss of data simultaneously. We show the analytical solution of the differential equation in some special cases. We define some indexes like memory index, merit index, utilization index etc. Using them we can measure the corresponding memory functions. Applications of this model have also been discussed. More general numerical and analytical results are also presented at the end.

KEYWORDS

Switching Function, Cramming Dynamics, Memory Index, Merit index, Utilization Index, Relative Performance Index

Switching Function, Cramming Dynamics, Memory Index, Merit index, Utilization Index, Relative Performance Index

Cite this paper

Roy, S. & Majumdar, P. (2010). A Mathematical Study of the Dynamics of Conscious Acquiring of Knowledge through Reading and Cramming and the Process of Losing Information from the Brain by Natural Forgetting of Facts.*Psychology, 1,* 252-260. doi: 10.4236/psych.2010.14034.

Roy, S. & Majumdar, P. (2010). A Mathematical Study of the Dynamics of Conscious Acquiring of Knowledge through Reading and Cramming and the Process of Losing Information from the Brain by Natural Forgetting of Facts.

References

[1] H. Ebbinghaus, “Memory: A Contribution to Experimental Psychology,” translated by H. A. Ruger and C. E. Bussenius, published by Teachers College, Columbia University, New York City, 1913.

[2] H. Eichenbaum, “Conscious Awareness, Memory and the Hippocampus,” Nature Neuroscience, Vol. 2, No. 9, 1999, pp. 775-776.

[3] F. Benfenati, “Synaptic Plasticity and the Neurobiology of Learning and Memory,” Acta Biomed, Vol. 78, Suppl. 1, 2007, pp. 58-66.

[4] H. F. Crovitz and H. Schiffman, “Ferquency of Episodic Memories as a Function of their Age,” Bulletin of the Psychonomic Society, Vol. 4, No. 5B, 1974, pp. 517-518.

[5] R. B. Anderson and R. D. Tweney, “Artifactual Power Curves in Forgetting,” Memory and Cognition, Vol. 25, No. 5, 1997, pp. 724-730.

[6] J. T. Wixted and E. B. Ebbesen, “Genuine Power Curves in Forgetting: A Quantitative Analysis of Individual Subject Forgetting Functions,” Memory and Cognition, Vol. 25, No. 5, 1997, pp. 731-739.

[7] J. Metcalfe, “Recognition Failure and the Composite Memory Trace in Charm,” Psychological Review, Vol. 98, No. 4, 1991, pp. 529-553.

[8] M. Chappell and M. S. Humphreys, “An Auto-Associative Neural Network for Sparse Representations: Analysis and Application to Models of Recognition and Cued Recall,” Psychological Review, Vol. 101, No. 1, 1994, pp. 103-128.

[9] M. S. Humphreys, J. D. Bain and R. Pike, “Different ways to Cue a Coherent Memory System: A Theory for Episodic, Semantic and Procedural Tasks,” Psychological Review, Vol. 96, No. 2, 1989, pp. 208-233.

[10] D. L. Hintzman, “Judgments of Frequency and Recognition Memory in a Multiple-Trace Memory Model,” Psychological Review, Vol. 95, No. 4, 1988, pp. 528-551.

[11] J. J. Hopfield, “Neural Networks and Physical Systems with Emergent Collective Computational Abilities,” Proceedings of the National Academy of Sciences, Vol. 79, No. 8, 1982, pp. 2554-2558.

[12] S. Sikstrom, “Power Function Forgetting Curves as an Emergent Property of Biologically Plausible Neural Network Models,” International Journal of Psychology, Vol. 34, No. 5-6, 1999, 460-464.

[13] I. I. Stepanov and C. I. Abramson, “A New Mathematical Model for Assessment of Memorization Dynamics,” The Spanish Journal of Psychology, Vol. 8, No. 2, 2005, pp. 142-156.

[1] H. Ebbinghaus, “Memory: A Contribution to Experimental Psychology,” translated by H. A. Ruger and C. E. Bussenius, published by Teachers College, Columbia University, New York City, 1913.

[2] H. Eichenbaum, “Conscious Awareness, Memory and the Hippocampus,” Nature Neuroscience, Vol. 2, No. 9, 1999, pp. 775-776.

[3] F. Benfenati, “Synaptic Plasticity and the Neurobiology of Learning and Memory,” Acta Biomed, Vol. 78, Suppl. 1, 2007, pp. 58-66.

[4] H. F. Crovitz and H. Schiffman, “Ferquency of Episodic Memories as a Function of their Age,” Bulletin of the Psychonomic Society, Vol. 4, No. 5B, 1974, pp. 517-518.

[5] R. B. Anderson and R. D. Tweney, “Artifactual Power Curves in Forgetting,” Memory and Cognition, Vol. 25, No. 5, 1997, pp. 724-730.

[6] J. T. Wixted and E. B. Ebbesen, “Genuine Power Curves in Forgetting: A Quantitative Analysis of Individual Subject Forgetting Functions,” Memory and Cognition, Vol. 25, No. 5, 1997, pp. 731-739.

[7] J. Metcalfe, “Recognition Failure and the Composite Memory Trace in Charm,” Psychological Review, Vol. 98, No. 4, 1991, pp. 529-553.

[8] M. Chappell and M. S. Humphreys, “An Auto-Associative Neural Network for Sparse Representations: Analysis and Application to Models of Recognition and Cued Recall,” Psychological Review, Vol. 101, No. 1, 1994, pp. 103-128.

[9] M. S. Humphreys, J. D. Bain and R. Pike, “Different ways to Cue a Coherent Memory System: A Theory for Episodic, Semantic and Procedural Tasks,” Psychological Review, Vol. 96, No. 2, 1989, pp. 208-233.

[10] D. L. Hintzman, “Judgments of Frequency and Recognition Memory in a Multiple-Trace Memory Model,” Psychological Review, Vol. 95, No. 4, 1988, pp. 528-551.

[11] J. J. Hopfield, “Neural Networks and Physical Systems with Emergent Collective Computational Abilities,” Proceedings of the National Academy of Sciences, Vol. 79, No. 8, 1982, pp. 2554-2558.

[12] S. Sikstrom, “Power Function Forgetting Curves as an Emergent Property of Biologically Plausible Neural Network Models,” International Journal of Psychology, Vol. 34, No. 5-6, 1999, 460-464.

[13] I. I. Stepanov and C. I. Abramson, “A New Mathematical Model for Assessment of Memorization Dynamics,” The Spanish Journal of Psychology, Vol. 8, No. 2, 2005, pp. 142-156.