The Magical Number Seven, Plus or Minus Two

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Miller's article[edit]


The second cognitive limitation Miller discusses is memory span. Memory span refers to the longest list of items (e.g., digits, letters, words) that a person can repeat back in correct order on 50% of trials immediately after presentation. Miller observed that memory span of young adults is approximately seven items. He noticed that memory span is approximately the same for stimuli with vastly different amount of information—for instance, binary digits have 1 bit each; decimal digits have 3.32 bits each; words have about 10 bits each. Miller concluded that memory span is not limited in terms of bits but rather in terms of chunks. A chunk is the largest meaningful unit in the presented material that the person recognizes—thus, what counts as a chunk depends on the knowledge of the person being tested. For instance, a word is a single chunk for a speaker of the language but is many chunks for someone who is totally unfamiliar with the language and sees the word as a collection of phonetic segments.

Miller recognized that the correspondence between the limits of one-dimensional absolute judgment and of short-term memory span was only a coincidence, because only the first limit, not the second, can be characterized in information-theoretic terms (i.e., as a roughly constant number of bits). Therefore, there is nothing "magical" about the number seven, and Miller used the expression only rhetorically. Nevertheless, the idea of a "magical number 7" inspired much theorizing, rigorous and less rigorous, about the capacity limits of human cognition. Nonetheless, the number seven constitutes a useful heuristic, reminding us that lists that are much longer than that become significantly harder to remember and process simultaneously.




Other cognitive numeric limits[edit]

Cowan also noted a number of other limits of cognition that point to a "magical number four",[10] and different from Miller, he argued that this correspondence is no coincidence. One other process that seems to be limited at about four elements is subitizing, the rapid enumeration of small numbers of objects. When a number of objects are flashed briefly, their number can be determined very quickly, at a glance, when the number does not exceed the subitizing limit, which is about four objects. Larger numbers of objects must be counted, which is a slower process. The film Rain Man portrayed an autistic savant, who was able to rapidly determine the number of toothpicks from an entire box spilled on the floor, apparently subitizing a much larger number than four objects. A similar feat was informally observed by neuropsychologist Oliver Sacks and reported in his book The Man Who Mistook His Wife for a Hat. Therefore, one might suppose that this limit is an arbitrary limit imposed by our cognition rather than necessarily being a physical limit. (On the other hand, autism expert Daniel Tammet has suggested that the children Sacks observed may have pre-counted the matches in the box.[15]). There is also evidence that even four chunks is a high estimate: Gobet and Clarkson conducted an experiment and found that over half of the memory recall conditions yielded only about two chunks. Research also shows that the size, rather than the number, of chunks that are stored in short-term memory is what allows for enhanced memory in individuals.[16][original research?]

See also[edit]


  1. ^ Miller, G. A. (1956). "The magical number seven, plus or minus two: Some limits on our capacity for processing information". Psychological Review. 63 (2): 81–97. doi:10.1037/h0043158. PMID 13310704. 
  2. ^ Gorenflo, Daniel; McConnell, James (1991). "The Most Frequently Cited Journal Articles and Authors in Introductory Psychology Textbooks". Teaching of Psychology. 18: 8–12. doi:10.1207/s15328023top1801_2. 
  3. ^ Kintsch, Walter; Cacioppo, John T. (1994). "Introduction to the 100th anniversary issue of the Psychological Review" (PDF). Psychological Review. 101 (2): 195–9. doi:10.1037/0033-295X.101.2.195. 
  4. ^ Garfield, Eugene (1985). "The Articles most cited in the SCI from 1961 to 1982. 7. Another 100 Citation Classics: The Watson-Crick Double Helix has its turn" (PDF). Essays of an Information Scientist: 1985, Ghost writing and other essays. Philadelphia: ISI Press. pp. 187–96. ISBN 978-0-89495-000-1. 
  5. ^ Shiffrin, Richard; Robert Nosofsky (April 1994). "Seven plus or minus two: A commentary on capacity limitations.". Psychological Review. 2. 101 (Centennial): 357–361. doi:10.1037/0033-295X.101.2.357. Retrieved 23 April 2012. 
  6. ^ Schweickert, Richard; Boruff, Brian (1986). "Short-term memory capacity: Magic number or magic spell?". Journal of Experimental Psychology: Learning, Memory, and Cognition. 12 (3): 419–25. doi:10.1037/0278-7393.12.3.419. 
  7. ^ Baddeley, A (1992). "Working memory". Science. 255 (5044): 556–9. doi:10.1126/science.1736359. PMID 1736359. 
  10. ^ a b Cowan, Nelson (2001). "The magical number 4 in short-term memory: A reconsideration of mental storage capacity". Behavioral and Brain Sciences. 24 (1): 87–114; discussion 114–85. doi:10.1017/S0140525X01003922. PMID 11515286. 
  11. ^ Tarnow, Eugen (2010). "There is no capacity limited buffer in the Murdock (1962) free recall data". Cognitive Neurodynamics. 4 (4): 395–7. doi:10.1007/s11571-010-9108-y. PMC 2974097Freely accessible. PMID 22132047. 
  12. ^ Murdock, Bennett B. (1962). "The serial position effect of free recall". View Table of Contents and Online First Publication Journal of Experimental Psychology. 64 (5): 482–8. doi:10.1037/h0045106. 
  13. ^ Bays, P. M.; Husain, M. (2008). "Dynamic shifts of limited working memory resources in human vision". Science. 321: 851–854. doi:10.1126/science.1158023. 
  14. ^ Ma, W. J.; Husain, M.; Bays, P. M. (2014). "Changing concepts of working memory". Nature Neuroscience. 17 (3): 347–356. doi:10.1038/nn.3655. 
  15. ^ Wilson, Peter (31 January 2009). "A savvy savant finds his voice". The Australian. Retrieved 10 November 2014. 
  16. ^ Gobet, Fernand; Gary Clarkson (November 2004). "Chunks in memory: Evidence for the magical number four . . . or is it two?". Memory. 12 (6): 732–747. doi:10.1080/09658210344000530. 

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