The Magical Number Seven, Plus or Minus Two

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"The Magical Number Seven, Plus or Minus Two: Some Limits on Our Capacity for Processing Information"[1] is one of the most highly cited papers in psychology.[2][3][4] It was written by the cognitive psychologist George A. Miller of Harvard University's Department of Psychology and published in 1956 in Psychological Review. It is often interpreted to argue that the number of objects an average human can hold in short-term memory is 7 ± 2. This has occasionally been referred to as Miller's law.[5][6][7]

Miller's article

In his article, Miller discussed a coincidence between the limits of one-dimensional absolute judgment and the limits of short-term memory. In a one-dimensional absolute-judgment task, a person is presented with a number of stimuli that vary on one dimension (e.g., 10 different tones varying only in pitch) and responds to each stimulus with a corresponding response (learned before). Performance is nearly perfect up to five or six different stimuli but declines as the number of different stimuli increases. The task can be described as one of information transmission: The input consists of one out of n possible stimuli, and the output consists of one out of n responses. The information contained in the input can be determined by the number of binary decisions that need to be made to arrive at the selected stimulus, and the same holds for the response. Therefore, people's maximum performance on a one-dimensional absolute judgment can be characterized as an information channel capacity with approximately 2 to 3 bits of information, which corresponds to the ability to distinguish between four and eight alternatives.

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 the correct order on 50% of trials immediately after the presentation. Miller observed that the memory span of young adults is approximately seven items. He noticed that memory span is approximately the same for stimuli with vastly different amounts 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. 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.

The "magical number 7" and working memory capacity

See also: Working memory § Capacity

Later research on

phonological loop, is capable of holding around 2 seconds of sound.[10][11] However, the limit of short-term memory cannot easily be characterized as a constant "magic spell" either, because memory span also depends on other factors besides speaking duration. For instance, span depends on the lexical status of the contents (i.e., whether the contents are words known to the person or not).[12] Several other factors also affect a person's measured span, and therefore it is difficult to pin down the capacity of short-term or working memory to a number of chunks. Nonetheless, Cowan has proposed that working memory has a capacity of about four chunks in young adults (and less in children and older adults).[13]

Tarnow finds that in a classic experiment typically argued as supporting a 4 item buffer by Murdock, there is in fact no evidence for such and thus the "magical number", at least in the Murdock experiment, is 1.[14][15] Other prominent theories of short-term memory capacity argue against measuring capacity in terms of a fixed number of elements.[16][17]

Other cognitive numeric limits

Cowan also noted a number of other limits of cognition that point to a "magical number four",

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.)[18] 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.[19] 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.[original research?
]

See also

References

  1. S2CID 15654531
    .
  2. S2CID 145217739
    .
  3. doi:10.1037/0033-295X.101.2.195. Archived from the original
    (PDF) on March 3, 2016.
  4. ISBN 978-0-89495-000-1
    .
  5. ^ "Miller's Law". changingminds.org. Retrieved November 8, 2018.
  6. ISBN 978-1-78049-189-9
    . Retrieved November 8, 2018 – via Google Books.
  7. ISBN 978-1-85575-817-9
    . Retrieved November 8, 2018 – via Google Books.
  8. PMID 8022968
    .
  9. PMID 2942626
    .
  10. PMID 1736359
    .
  11. S2CID 14333234
    .
  12. doi:10.1111/j.2044-8295.1995.tb02570.x
    .
  13. ^
    PMID 11515286
    .
  14. PMID 22132047
    .
  15. doi:10.1037/h0045106
    .
  16. PMID 18687968
    .
  17. PMID 24569831
    .
  18. ^ Wilson, Peter (January 31, 2009). "A savvy savant finds his voice". www.theaustralian.news.com.au. The Australian. Retrieved November 10, 2014.
  19. S2CID 13445985
    .

External links
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