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THE MAGICAL NUMBER 7 PLUS OR MINUS 2

   George Armitage Miller once famously complained: “My problem is that I have been persecuted by an integer(整数). For seven years this number has followed me around”. So begins his now famous article The Magical Number Seven, Plus or Minus Two: Some Limits on our Capacity for Processing Information. He goes on: “There is… some pattern governing its appearances.

  Either there really is something unusual about the number or I am suffering from delusions of persecution”. Despite the whimsical nature of his title and introduction, Miller had a serious intent, and the article was to become a landmark of cognitive psychology and the study of working memory (the ability to remember and use pieces of information for a limited amount of time).

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The persistence with which this number plagues me is far more than a random accident.
                    George Armitage Miller

  Miller’s paper was published in The Psychological Review in 1956, when behaviourism was being superseded by the new cognitive psychology. This fresh approach – which Miller wholeheartedly embraced – focused on the study of mental processes, such as memory and attention.

  At the same time, advances in computer science had brought the idea of artificial intelligence closer to reality, and while mathematicians, such as Alan Turing, were comparing computer processing with the human brain, cognitive psychologists were engaged in the converse: they looked to the computer as a possible model for explaining the workings of the human brain. Mental processes were being described in terms of information processing.

"The process of memorizing may be simply the formation of chunks… until there are few enough chunks so that we can recall all the items."
                George Armitage Miller

   Miller’s main interest was in the field of psycholinguistics, stemming from his work during World War II on speech perception, which formed the basis for his doctoral thesis. This led him to take an interest in the growing field of communications, which in turn introduced him to information theory. He was particularly inspired by Claude Shannon, a leading figure in communications, who was investigating effective ways of turning messages into electronic signals.

  Shannon’s communication model, which involved translating ideas into codes made up of “bits”, underpins all digital communication. Miller was inspired to look at mental processes in a similar way, and to establish the ground rules for the modern field of psycholinguistics in his 1951 book, Language and Communication.

"The kind of linguistic recoding that people do seems to me to be the very lifeblood of the thought processes."
                  George Armitage Miller

Seven categories

   Miller took Shannon’s method of measuring nformation and his idea of “channel capacity” (the amount of information that can be processed by a system) and applied it to the model of short-term memory as an information processor. This was when he began to be “persecuted” by the recurrence and possible significance of the number seven; “sometimes a little larger and sometimes a little smaller than usual, but never changing so much as to be unrecognizable”.

  The first instance of the “magical” number came from experiments to determine the span of absolute judgment – how accurately we can distinguish a number of different stimuli. In one experiment cited in Miller’s paper, the physicist and acoustic specialist Irwin Pollack played a number of different musical tones to participants, who were then asked to assign a number to each tone.

   When up to around seven different tones were played, the subjects had no difficulty in accurately assigning numbers to each of them, but above seven (give or take one or two), the results deteriorated dramatically. In another experiment, by Kaufman, Lord, et al, in 1949, researchers flashed varying numbers of coloured dots on to a screen in front of participants.

   When there were fewer than seven dots, participants could accurately number them; when there were more than seven, participants were only able to estimate the number of dots. This suggests that the span of attention is limited to around six, and caused Miller to wonder whether the same basic process might be involved in both the span of absolute judgment and the span of attention.

  The tones and dots in these experiments are what Miller calls “unidimensional stimuli” (objects that differ from one another in only one respect); but what interested Miller is the amount of information in speech and language we can effectively process, and items such as words are “multidimensional stimuli”. He looks to later studies by Pollack in which the simple tones were replaced by tones that varied in six ways (such as pitch, duration, volume, and location).

  Surprisingly, despite the apparently larger amount of information, the results still pointed to a differential limit of seven, plus or minus two. The difference is that as more variables are added, accuracy slightly decreases. Miller claims this allows us to make “relatively crude judgments of several things simultaneously”.

  It may explain how we are able to recognize and distinguish such complex things as spoken words and people’s faces, without having to process the individual sounds or features. Miller sees the human mind as a communication system: as the input information increases, the amount transmitted to the brain also increases initially, before levelling off at an individual’s “channel capacity”.

   Miller then took this idea of channel capacity a stage further, applying it to the model of short-term memory. William James first proposed the notion of short-term memory, and it had long been an accepted part of the model of the brain as an information processor, coming between the sensory input of information and long-term memory. Hermann Ebbinghaus and Wilhelm Wundt had even suggested that short-term memory had a capacity limited to around seven items (seven, again).

   Miller believed that what he called working memory had a capacity that corresponded to the limits of absolute judgment and span of attention. An experiment into the span of attention presented participants with random patterns of dots flashed on a screen for a fraction of a second. Participants instantly recognized the number if there were fewer than seven.

Bits and chunks

   In terms of our ability to process information, if working memory is limited to about seven elements, there is a potential bottleneck(瓶颈) restricting the amount that can be put into long-term memory. But Miller suggested that there was more to the correspondence than just the number seven, no matter how magical it appeared. The multidimensional stimuli of previous experiments could be seen as composed of several “bits” of related information, but treated as a single item.

   Miller believed that by the same principle, working memory organizes “bits” of information into “chunks”, to overcome the informational bottleneck caused by our limited spans of absolute judgment and short-term memory. A chunk is not, however, just an arbitrary grouping, but an encoding of bits into a meaningful unit; for example, a string of 21 letters represents 21 bits of information, but if this can be broken down into a sequence of three-letter words, it becomes seven chunks.

  Chunking is dependent on our ability to find patterns and relationships in the bits of information. To someone who does not speak the same language, the seven words might be meaningless, and would not constitute seven chunks, but 21 bits. Miller’s theory was backed up by earlier experiments by other psychologists. In 1954, Sidney Smith conducted experiments in memorizing a sequence of binary digits – a meaningless string of ones and zeroes to anyone unfamiliar with the binary system.

  Smith broke the series down into chunks, at first into pairs of digits, and then into groups of three, four, and five, and then “recoded” them by translating the binary chunks into decimal numbers: 01 became 1, 10 became 2, and so on. He found that by using this system it was possible to memorize and accurately reproduce a string of 40 digits or more, as long as the number of chunks was limited to the span of working memory.

   As an aid to memorizing large amounts of information, chunking and recoding is an obvious boon, but it is more than a mnemonic(记忆的) trick. Miller pointed out that this form of recoding is an “extremely powerful weapon for increasing the amount of information we can deal with”. It effectively stretches the informational bottleneck.

   Miller’s theory of chunking says that by building up or breaking down long streams of numbers or letters into memorable chunks, we increase the amount of information we can hold in working memory.Binary code is a way of recoding information into ever-more tightly packed parcels (through multi-base arithmetic). Miller claims our chunking process operates in a similar way.

The study of memory

   Miller himself moved away from the subject of memory in his later research, but his theory prompted others to examine it in more detail. Donald Broadbent argued that the real figure for working memory is probably less than seven, and this was later confirmed in experiments by Nelson Cowan, who found it to be around four chunks, depending on the length and complexity of the chunks, and the age of the subject.

   In the conclusion to his paper, Miller is dismissive of the significance of the number that originally prompted it. He concludes by saying: “Perhaps there is something deep and profound behind all these sevens… but I suspect that it is only a pernicious, Pythagorean coincidence”.

MORE TO KNOW…

APPROACH : Memory studies

BEFORE

  1885 Hermann Ebbinghaus publishes his pioneering book Memory: A Contribution to Experimental Psychology.
  1890 William James makes the distinction between primary (short-term) and secondary (long-term) memory in The Principles of Psychology.
  1950 Mathematician Alan Turing’s test suggests that a computer can be considered a thinking machine.

AFTER

  1972 Endel Tulving makes the distinction between semantic(语义的) and episodic memory.
   2001 Daniel Schacter proposes a list of the different ways we misremember in The Seven Sins of Memory.

GEORGE ARMITAGE MILLER

George Armitage Miller, born in West Virginia, USA graduated from the University of Alabama in 1941 with an MA in speech pathology(病理学), and went to Harvard to study for a PhD in psychology in Stanley Smith Stevens’ Psychoacoustic Laboratory, with Jerome Bruner and Gordon Allport. World War II was then at its height, and the laboratory was called upon to help with military tasks such as radio jamming. In 1951, Miller left Harvard for Massachusetts Institute of Technology (MIT), then returned to Harvard in 1955, where he worked closely with Noam Chomsky. In 1960, he co-founded the Harvard Center for Cognitive Studies. He later worked as a professor of psychology at Rockefeller University, New York, and Princeton University. In 1991, he was awarded the National Medal of Science.

Key works

1951 Language and Communication
1956 The Magical Number Seven, Plus or Minus Two
1960 Plans and the Structure of Behavior (with Eugene Galanter and Karl Pribram)