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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 is a 1956 paper by the cognitive psychologist George A. Miller. In it Miller showed a number of remarkable coincidences between the channel capacity of a number of human cognitive and perceptual tasks. In each case, the effective channel capacity is equivalent to between 5 and 9 equally-weighted error-less choices: on average, about 2.5 bits of information. Miller hypothesized that these may all be due to some common but unknown underlying mechanism.

The concept of this limit is illustrated by imagining the patterns on the faces of a die. It is easy for many people to visualise each of the six faces. Now imagine seven dots, eight dots, nine dots, ten dots, and so on. At some point it becomes impossible to visualise the dots as a single pattern (a process known as subitising), and one thinks of, say, eight as two groups of four. The upper limit of your visualisation of a number represented as dots is your subitising limit for that exercise.

The film Rain Man, starring Dustin Hoffman, portrayed a fictitious autistic savant, who was able to visualise the number represented by an entire box of toothpicks spilled on the floor. A similar feat was clinically 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.

The term hrair limit was used by Ed Yourdon in his Modern Structured Analysis (Prentice Hall, 1979) to mean the maximum number of subroutines that should be called from the main program, again set at between 5 and 9. The limit is not there because the computer will become confused if it is exceeded, but rather because the programmer will. (The term hrair is from the novel Watership Down; in Lapine, the word hrair is used for any number greater than four.)

It is particularly advantageous for computer programmers to have a high attention limit because their effectiveness is enhanced if they don't get confused too often. Each time a programmer gets confused, either through grappling with a problem that has not been adequately analysed to take account of the programmer's typical attention limit, or even due to a simple interruption like answering the phone, it has been estimated (by Gerry Weinberg) to cost the project on which the programmer is engaged at least half an hour of lost time.

In organisation theory the limit has a similar meaning: the maximum number of projects that one can be involved in simultaneously before chaos starts to ensue.

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