Probability Theory Predicts That Chunking into Groups of Three or Four Items Increases the Short-Term Memory Capacity

Short-term memory allows individuals to recall stimuli, such as numbers or words, for several seconds to several minutes without rehearsal. Although the capacity of short-term memory is considered to be 7 ± 2 items, this can be increased through a process called chunking. For example, in Japan, 11-digit cellular phone numbers and 10-digit toll free numbers are chunked into three groups of three or four digits: 090-XXXX-XXXX and 0120-XXX-XXX, respectively. We use probability theory to predict that the most effective chunking involves groups of three or four items, such as in phone numbers. However, a 16-digit credit card number exceeds the capacity of short-term memory, even when chunked into groups of four digits, such as XXXX-XXXX-XXXX-XXXX. Based on these data, 16-digit credit card numbers should be sufficient for security purposes.

Keywords

Share and Cite:

Osaka, M. (2014) Probability Theory Predicts That Chunking into Groups of Three or Four Items Increases the Short-Term Memory Capacity. Applied Mathematics, 5, 1474-1484. doi: 10.4236/am.2014.510140.

Conflicts of Interest

The authors declare no conflicts of interest.

 [1] Miller, G.A. (1956) The Magical Number Seven plus or minus Two: Some Limits on Our Capacity for Processing Information. Psychological Review, 63, 81-97. http://dx.doi.org/10.1037/h0043158 [2] Cowan, N. (2001) The Magical Number 4 in Short-Term Memory: A Reconsideration of Mental Storage Capacity. Behavioral and Brain Sciences, 24, 87-114. http://dx.doi.org/10.1017/S0140525X01003922 [3] Baddely, A. (1994) The Magical Number Seven: Still Magic after All These Years. Psychological Review, 101, 353356. http://dx.doi.org/10.1037/0033-295X.101.2.353 [4] Nicolis, J.S. and Tsuda, I. (1985) Chaotic Dynamics of Information Processing: The “Magic Number Seven Plus-Minus Two” Revisited. Bulletin Mathematical Biology, 47, 343-365. [5] Satty, T.L. and Ozdemir, M.S. (2003) Why the Magic Number Seven plus or minus Two. Mathematical and Computer Modelling, 38, 233-244. http://dx.doi.org/10.1016/S0895-7177(03)90083-5 [6] Blom, G., Holst, L. and Sandell, D. (1991) Problems and Snapshots from the World of Probability. Springer-Verlag, New York.