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]

Contents

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

Later research on short-term memory and working memory revealed that memory span is not a constant even when measured in a number of chunks. The number of chunks a human can recall immediately after presentation depends on the category of chunks used (e.g., span is around seven for digits, around six for letters, and around five for words), and even on features of the chunks within a category. Chunking is used by the brain's short-term memory as a method for keeping groups of information accessible for easy recall. It functions and works best as labels that one is already familiar with—the incorporation of new information into a label that is already well rehearsed into one's long-term memory. These chunks must store the information in such a way that they can be disassembled into the necessary data. [8]

The storage capacity is dependent on the information being stored. For instance, span is lower for long words than it is for short words. In general, memory span for verbal contents (digits, letters, words, etc.) strongly depends on the time it takes to speak the contents aloud. Some researchers have therefore proposed that the limited capacity of short-term memory for verbal material is not a "magic number" but rather a "magic spell," i.e. a period of time. [9] Baddeley used this finding to postulate that one component of his model of working memory, the 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", [13] 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 1988 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 1985 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. Autism expert Daniel Tammet has suggested, however, 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 at Brunel University London 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

Related Research Articles

Long-term memory (LTM) is the stage of the Atkinson–Shiffrin memory model in which informative knowledge is held indefinitely. It is defined in contrast to sensory memory, the initial stage, and short-term or working memory, the second stage, which persists for about 18 to 30 seconds. LTM is grouped into two categories known as explicit memory and implicit memory. Explicit memory is broken down into episodic and semantic memory, while implicit memory includes procedural memory and emotional conditioning.

Short-term memory is the capacity for holding a small amount of information in an active, readily available state for a short interval. For example, short-term memory holds a phone number that has just been recited. The duration of short-term memory is estimated to be on the order of seconds. The commonly cited capacity of 7 items, found in Miller's Law, has been superseded by 4±1 items. In contrast, long-term memory holds information indefinitely.

Working memory is a cognitive system with a limited capacity that can hold information temporarily. It is important for reasoning and the guidance of decision-making and behavior. Working memory is often used synonymously with short-term memory, but some theorists consider the two forms of memory distinct, assuming that working memory allows for the manipulation of stored information, whereas short-term memory only refers to the short-term storage of information. Working memory is a theoretical concept central to cognitive psychology, neuropsychology, and neuroscience.

<span class="mw-page-title-main">George Armitage Miller</span> American psychologist (1920–2012)

George Armitage Miller was an American psychologist who was one of the founders of cognitive psychology, and more broadly, of cognitive science. He also contributed to the birth of psycholinguistics. Miller wrote several books and directed the development of WordNet, an online word-linkage database usable by computer programs. He authored the paper, "The Magical Number Seven, Plus or Minus Two," in which he observed that many different experimental findings considered together reveal the presence of an average limit of seven for human short-term memory capacity. This paper is frequently cited by psychologists and in the wider culture. Miller won numerous awards, including the National Medal of Science.

The Atkinson–Shiffrin model is a model of memory proposed in 1968 by Richard Atkinson and Richard Shiffrin. The model asserts that human memory has three separate components:

  1. a sensory register, where sensory information enters memory,
  2. a short-term store, also called working memory or short-term memory, which receives and holds input from both the sensory register and the long-term store, and
  3. a long-term store, where information which has been rehearsed in the short-term store is held indefinitely.

In the study of vision, visual short-term memory (VSTM) is one of three broad memory systems including iconic memory and long-term memory. VSTM is a type of short-term memory, but one limited to information within the visual domain.

In cognitive psychology, chunking is a process by which small individual pieces of a set of information are bound together to create a meaningful whole later on in memory. The chunks, by which the information is grouped, are meant to improve short-term retention of the material, thus bypassing the limited capacity of working memory and allowing the working memory to be more efficient. A chunk is a collection of basic units that are strongly associated with one another, and have been grouped together and stored in a person's memory. These chunks can be retrieved easily due to their coherent grouping. It is believed that individuals create higher-order cognitive representations of the items within the chunk. The items are more easily remembered as a group than as the individual items themselves. These chunks can be highly subjective because they rely on an individual's perceptions and past experiences, which are linked to the information set. The size of the chunks generally ranges from two to six items but often differs based on language and culture.

<span class="mw-page-title-main">Baddeley's model of working memory</span> Model of human memory

Baddeley's model of working memory is a model of human memory proposed by Alan Baddeley and Graham Hitch in 1974, in an attempt to present a more accurate model of primary memory. Working memory splits primary memory into multiple components, rather than considering it to be a single, unified construct.

<span class="mw-page-title-main">Alan Baddeley</span> British psychologist (born 1934)

Alan David Baddeley CBE FRS is a British psychologist. He is known for his research on memory and for developing the three-component model of working memory. He is a professor of psychology at the University of York.

Information processing theory is the approach to the study of cognitive development evolved out of the American experimental tradition in psychology. Developmental psychologists who adopt the information processing perspective account for mental development in terms of maturational changes in basic components of a child's mind. The theory is based on the idea that humans process the information they receive, rather than merely responding to stimuli. This perspective uses an analogy to consider how the mind works like a computer. In this way, the mind functions like a biological computer responsible for analyzing information from the environment. According to the standard information-processing model for mental development, the mind's machinery includes attention mechanisms for bringing information in, working memory for actively manipulating information, and long-term memory for passively holding information so that it can be used in the future. This theory addresses how as children grow, their brains likewise mature, leading to advances in their ability to process and respond to the information they received through their senses. The theory emphasizes a continuous pattern of development, in contrast with cognitive-developmental theorists such as Jean Piaget's theory of cognitive development that thought development occurs in stages at a time.

<span class="mw-page-title-main">Memory and aging</span> Aspect of senescence

Age-related memory loss, sometimes described as "normal aging", is qualitatively different from memory loss associated with types of dementia such as Alzheimer's disease, and is believed to have a different brain mechanism.

Memory has the ability to encode, store and recall information. Memories give an organism the capability to learn and adapt from previous experiences as well as build relationships. Encoding allows a perceived item of use or interest to be converted into a construct that can be stored within the brain and recalled later from long-term memory. Working memory stores information for immediate use or manipulation, which is aided through hooking onto previously archived items already present in the long-term memory of an individual.

In psychology and neuroscience, memory span is the longest list of items that a person can repeat back in correct order immediately after presentation on 50% of all trials. Items may include words, numbers, or letters. The task is known as digit span when numbers are used. Memory span is a common measure of working memory and short-term memory. It is also a component of cognitive ability tests such as the WAIS. Backward memory span is a more challenging variation which involves recalling items in reverse order.

In mental memory, storage is one of three fundamental stages along with encoding and retrieval. Memory is the process of storing and recalling information that was previously acquired. Storing refers to the process of placing newly acquired information into memory, which is modified in the brain for easier storage. Encoding this information makes the process of retrieval easier for the brain where it can be recalled and brought into conscious thinking. Modern memory psychology differentiates between the two distinct types of memory storage: short-term memory and long-term memory. Several models of memory have been proposed over the past century, some of them suggesting different relationships between short- and long-term memory to account for different ways of storing memory.

CHREST is a symbolic cognitive architecture based on the concepts of limited attention, limited short-term memories, and chunking. The architecture takes into low-level aspects of cognition such as reference perception, long and short-term memory stores, and methodology of problem-solving and high-level aspects such as the use of strategies. Learning, which is essential in the architecture, is modelled as the development of a network of nodes (chunks) which are connected in various ways. This can be contrasted with Soar and ACT-R, two other cognitive architectures, which use productions for representing knowledge. CHREST has often been used to model learning using large corpora of stimuli representative of the domain, such as chess games for the simulation of chess expertise or child-directed speech for the simulation of children's development of language. In this respect, the simulations carried out with CHREST have a flavour closer to those carried out with connectionist models than with traditional symbolic models.

The modality effect is a term used in experimental psychology, most often in the fields dealing with memory and learning, to refer to how learner performance depends on the presentation mode of studied items.

Nelson Cowan is the Curators' Distinguished Professor of Psychological Sciences at the University of Missouri. He specializes in working memory, the small amount of information held in mind and used for language processing and various kinds of problem solving. To overcome conceptual difficulties that arise for models of information processing in which different functions occur in separate boxes, Cowan proposed a more organically organized "embedded processes" model. Within it, representations held in working memory comprise an activated subset of the representations held in long-term memory, with a smaller subset held in a more integrated form in the current focus of attention. Other work has been on the developmental growth of working memory capacity and the scientific method. His work, funded by the National Institutes of Health since 1984, has been cited over 41,000 times according to Google Scholar. The work has resulted in over 250 peer-reviewed articles, over 60 book chapters, 2 sole-authored books, and 4 edited volumes.

Working memory training is intended to improve a person's working memory. Working memory is a central intellectual faculty, linked to IQ, ageing, and mental health. It has been claimed that working memory training programs are effective means, both for treating specific medical conditions associated with working memory deficit, as and for general increase in cognitive capacity among healthy neurotypical adults.

<span class="mw-page-title-main">Memory</span> Faculty of mind to store and retrieve data

Memory is the faculty of the mind by which data or information is encoded, stored, and retrieved when needed. It is the retention of information over time for the purpose of influencing future action. If past events could not be remembered, it would be impossible for language, relationships, or personal identity to develop. Memory loss is usually described as forgetfulness or amnesia.

Broadbent's filter model is an early selection theory of attention.

References

  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. CiteSeerX   10.1.1.308.8071 . doi:10.1037/h0043158. hdl:11858/00-001M-0000-002C-4646-B. PMID   13310704. S2CID   15654531.
  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. S2CID   145217739.
  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. Archived from the original (PDF) on March 3, 2016.
  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. ↑ "Miller's Law". changingminds.org. Retrieved November 8, 2018.
  6. ↑ Boag, Simon; Brakel, Linda A. W.; Talvitie, Vesa (November 8, 2018). Philosophy, Science, and Psychoanalysis: A Critical Meeting. Karnac Books. ISBN   978-1-78049-189-9 . Retrieved November 8, 2018– via Google Books.
  7. ↑ Talvitie, Vesa (November 8, 2018). The Foundations of Psychoanalytic Theories: Project for a Scientific Enough Psychoanalysis. Karnac Books. ISBN   978-1-85575-817-9 . Retrieved November 8, 2018– via Google Books.
  8. ↑ 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. PMID   8022968.
  9. ↑ 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. PMID   2942626.
  10. ↑ Baddeley, Alan (1992). "Working memory". Science. 255 (5044): 556–9. Bibcode:1992Sci...255..556B. doi:10.1126/science.1736359. PMID   1736359.
  11. ↑ Baddeley, Alan (2000). "The episodic buffer: a new component of working memory?". Trends in Cognitive Sciences. 4 (11): 417–23. doi: 10.1016/S1364-6613(00)01538-2 . PMID   11058819. S2CID   14333234.
  12. ↑ Hulme, Charles; Roodenrys, Steven; Brown, Gordon; Mercer, Robin (1995). "The role of long-term memory mechanisms in memory span". British Journal of Psychology. 86 (4): 527–36. doi:10.1111/j.2044-8295.1995.tb02570.x.
  13. 1 2 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.
  14. ↑ 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   2974097 . PMID   22132047.
  15. ↑ Murdock, Bennett B. (1962). "The serial position effect of free recall". Journal of Experimental Psychology. 64 (5): 482–8. doi:10.1037/h0045106.
  16. ↑ Bays, P. M.; Husain, M. (2008). "Dynamic shifts of limited working memory resources in human vision". Science. 321 (5890): 851–854. Bibcode:2008Sci...321..851B. doi:10.1126/science.1158023. PMC   2532743 . PMID   18687968.
  17. ↑ 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. PMC   4159388 . 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. ↑ 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. PMID   15724362. S2CID   13445985.
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