International Encyclopedia of Systems and Cybernetics

"The relation between two series such as for every part of one series there is a corresponding part in the other series and no part of either series is without a corresponding part in the other".

J. FEIBLEMAN and J.W. FRIEND add to their definition that the correlation can be: "one-many; one-one; many-one, many-many" (1969, p.33). Any relation implies one or another of these types of correlation.

The existence of correlations constitutes the base for homeomorphies and isomorphies. For example, any integrated system possesses a boundary (its contact subsystem with its environment) and, in the above meaning, there is a functional and structural correlation between the boundary and some internal subsystems as well as with some parts of the environment. In the realm of models, isomorphies signal correlations between similar aspects of otherwise different systems.

Correlation is also understood as the permanence of interrelations within a system, a condition basic for its stability, i.e. a co-variance of some significant processes. S. DINER writes accordingly: "The reduction of correlation between more and more distant points on a trajectory is in fact the fundamental mark of the appearance of a random character. This is basically deterministic chaos" (1992, p.351). De-correlation implies thus a kind of memory loss of its initial conditions by the system.

There is a critical distance for correlation, which depends on the field's parameters. This implies that interactions become negligible beyond some specific limit – which does not necessarily means inexistant, if D. BOHM's implicate order idea is accepted.

Correlations frequently are significant clues for the study of systems.

Correlations can be causal, complementary, parallel or reciprocal. In such cases, they are generally obvious… but not necessarily very clearly and well understood. Neither are their evolution in time precisely established. Growth phenomena for instance can be of quite different kinds, reflecting diverse types of correlations.

A particular, but very interesting case is the association that can be created, or at least supposed or attempted, between two statistical series related to different sequences of events.

A certain parallelism or similarity between such series can be significant, but not necessarily so: the correlation between smoking and lungs cancer was widely and protractedly discussed before the cause-effect relation became well established and generally recognized.

In any case correlations between two processes can be a consequence of a common causal link with a third process.

The study of correlations is a quite developed part of statistical analysis and includes frequency distribution, time series analysis, linear and non linear trends, theory of sampling, graphs, matrixes and tables, coefficients of reliability, etc.

Correlation as a forecasting tool

Correlation in time with some seemingly or possibly related developments in technically connected fields is an important forecasting tool. For example, the use of micro-electronics in the construction of radio sets was a significant technical novelty whose impact on the radio sets industry could be more or less predicted by perceptive industrialists in the field… and ruin the business of the others.

I.G. BLOOR states: "The correlation technique attemps to put a value on the strength of any relationship producing a so-called "correlation coefficient" in the range of + 1 to -1. The stronger correlation is +1." (1987, p.7). When practically possible, correlation calculation would be very useful.