THE MAGICAL NUMBER THREE-PLUS OR MINUS ZERO

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Abstract
Research by Miller (1956) and Simon (1974) shed light on limitations of human beings in carrying out various operations on information. Both authors concluded that the span of immediate recall of people is in the range between five and nine. Simon concluding that it is closer to five than to nine. Both authors approached the issues through results of experimentation on human subjects, and neither connected any of the work to ideas from mathematical logic having to do with the organization of information. Although this prior work was of considerable significance, its full significance will never be recognized until it is possible to relate it to human performance in such society-steering roles as those filled by powerful managers, designers of large systems, and public opinion makers, for the purpose of improving significantly the quality of what they do. The work of Simon and Miller is reinterpreted here from the perspective of mathematical logic, with special emphasis on means of structuring information using the lattice as the organizing unit. Two different types of lattice are examined, and their connection to human capacity to integrate information and make decisions is interpreted in the light of the work of Simon and Miller. It is concluded that there are substantive reasons for viewing three as the magical number, especially in system design theory.

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