Abstract
This paper presents a mathematical analysis of magical numbers on human memory span. This analysis shows that, if memory is hierarchically organized, (1) the optimal chunk size of human short-term memory (STM) may be 7.34… ± 1.74 … for an exhaustive search strategy and 3.59 … ± 0.49 … for a self-terminating search strategy. Furthermore, it is shown how the optimal form of memory may change in a trade-off between memory organization cost and searching cost (or time). Comparing the theoretical estimates with previous empirical estimates, it is shown that limitations of human STM capacity may be related to the efficiency of design. It is also shown that the coding system of deoxyribonucleic acid (DNA) may be interpreted as a means of efficient information retrieval as in human STM.
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