Chapter XX

Correspondence Theory & Method

We can define correspondence as a measure of the degree, direction and manner that two different systems or sets of points respond in a similar ways to similar kinds of stimuli. The similarity of two systems or sets is not just analogical in character, nor is it directly causal, rather they can be said to be of a complementary nature. Complementariness of relationship, or the degree of interdependence, is the basis for correspondence between systems. We can further distinguish between general or theoretical, natural, logical or hypothetical or mechanical or experimental correspondence depending upon the relational terms that we identify, the analytical dimensions that these terms frame, and the standards of comparative measurement that we adopt as evidence for these dimensional frames of reference.

Correspondence is a general term that I have adopted for the systematic identification of relationships and relational patterngs that cooccur and recur in complex systems and chaotic super sets. Correspondence is related statistically to the correlation coefficient, or a general measure of how to comparable sets "move together" or are similar or dissimilar, but it moves beyond correlation and intercorrelational analysis in permitting us to specify deterministic directions and unequal equilibria in relational patterns that we can observe, and thereby to predict in a general way, or to state an "expectation" of likelihood of behavior given such and such conditional constraints. We may say that two similar sets of relationships that occur in parallel fashion with two different and independent sets or systems, correspond with one another, even upon different analytical levels of integrative articulation, because they coexist within the same relativisitic framework in which similar kinds of mechanical principles are said to be operating. Thus, we understand that two different cultures correspond to one another, even if the patterning of either cultures is very different, if both these cultures articulate in certain ways consistent relationships that correspond. Similarly, we can state the same kind of correspondence for two different kinds of living systems that operate in similar ways but in different ecological systems. Thus we observe in the natural biotic world many examples of parallelism and convergence between completely independent systems, in large part because the framework under which both sets of systems are operating correspond to one another in basic ways. Correspondence theory and method becomes therefore a systematic approach to handling very large systems in a manner that permits us to speak in simplified terms that realistically represent the meta-system of which the real systems that we observe are construed as examples or demonstrations.

Correspondence between complex systems or super sets is not the kind of one-to-one correspondence that is generally associated with this term. What can be called complex correspondence is a measure of the degree to which the profiles and landscape of systems resemble one another, especially along certain dimensions of analysis. Two very different kinds of systems may exhibit near perfect correspondence along a single or limited set of dimensions that are not otherwise obvious to observation unless analysis along those dimensions are systematically made. We may say that the correspondence of two systems is not direct correspondence, which implies a kind of analogy of relationship, but are abductively mediated as being similar results of similar kinds of eidetic structures operating upon different sets of data points.

Complex correspondence can be said therefore to be indirect correspondence, and to be implicit to a system. Evidence for such correspondence may be obvious to the naked eye or presented to raw experience, but this evidence will appear incomplete and only partial in nature. Complex correspondence is therefore also never, or at least, very rarely, perfect correspondence.

Another way of looking at the problem of correspondence is to ask ourselves to what degree do two systems or things correspond to one another, versus some other or alternate system by which both might be compared. In a sense, it gives us a way of comparing systematically apples and oranges.

The basis for correspondence theory is the presupposition that all things and all systems in nature and in reality are indirectly related to one another. Independence of systems becomes relative to the frameworks that we specify for such systems, and only coincidental or contemporaneous systems that coccur can be said to be relatively independent. For such a hypothesis of independence to be made, we must determine that the two systems are spatially separated in such a manner that, at least upon the level of analysis we identify, no significant interactions are taking place between the two systems. If we were comparing the size, shape and weight of two large objects of mass, we might speculate that such systems may be relatively independent of one another in terms of their chemical composition, but we would be hard pressed to prove that the two systems were not interacting with one another in a gravitational sense. If we are examining two different archaeological sites that are widely space in time and place, and yet we find remarkable patterns of correspondence between them, we would be hard pressed to say whether or not the sites were somehow "related" in a chronological way or whether they just exhibit a kind of independent correspondence within similar kinds of frameworks.

Relationships in corresponding systems can be said to be structured in similar ways.

The basis of determining correspondence between two unrelated systems is what can be called the identification of complementarity that relates the two systems to one another. Complementarity of design or relational patterning between two independent systems can be said to be the measure of the degree of holistic integration achieved by these two systems.

Determining systematic correspondence between two or more complex systems or supersets was an impossibility before the advent of digital and analog computing, and with the increasing power and efficiency of mechanical computing, the capacity to establish in a systematic manner correspondence between different kinds of systems has increased many fold.

Dimensional sets allow the conversion and relation between different components.

Dimensionless sets

The kind of correspondence that we are speaking about is in a basic sense quantitative correspondence, and this is by definition non-qualitative. Qualitative correspondence between systems can only be achieved in broadly or loosely descriptive terms, or alternatively in theoretical and rational terms, depending upon the similarities of property or framework of two different systems that we are comparing. Qualitative correspondence works best upon a very basic level of description and upon a very general level of theoretical abstraction, but we cannot depend upon this form of correspondence alone without the evidentiary support of quantitative forms of correspondence. Usually, with quantitative correspondence of complex systems, numerous variables along multiple dimensions are systematically compared for relationship and degree of similarity between the two systems. We can specify that two sets of complex variables will show a significant correlational pattern of similarity or contrast, if the two sets of variables correspond in a complementary manner to one another. In other words, both sets of variables are governed by similar principles or general frames of reference.