CONSTRAINT ANALYSIS OF MANY-DIMENSIONAL RELATIONS.
Technical rept. no. 2,
ILLINOIS UNIV URBANA ELECTRICAL ENGINEERING RESEARCH LAB
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As part of an attempt to apply information theory to the internal activities of large systems, a preliminary study was made of the simplifications possible when the data about the linkage between variables was merely whether the linkage was zero or non-zero. The study thus became a study of how to simplify an n-ary relation. Relations between large numbers of variables are often not as complex as they seem, for they are often constructed from simpler sub-relations, and retain something of their simplicity. The idea is here treated rigorously, and a method is developed for detecting and measuring the degree of essential simplicity. The individual relation is made to generate a sequence of progressively simpler relations where it comes in the sequence determines and measures its degree of essential simplicity. The method may be useful when one wishes to consider relations or systems that, while involving very large numbers of variables, retain some simplicity derived from the sub-relations that formed them. Author