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Challenge: Comprehending complexity and appropriateness

Metaphor Project


The appropriate global socio-economic mode of organization must necessarily be more complex than is accepted within any particular frame of reference. It is therefore more than probable that it cannot be fully comprehended within any single frame of reference.

1. Limitations of axiomatically defined systems

The probability is increased in the light of the classic study of axiomatic systems by Kurt Gödel (1931). Prior to this a climate of opinion existed among mathematicians in which it was tacitly assumed that each sector of mathematical thought can be supplied with a set of axioms sufficient for developing systematically the endless totality of true propositions about a given area of inquiry. Gödel demonstrated that no system can be comprehensible without being self-contradictory. In doing so he showed that it is impossible to establish the internal logical consistency of a very large class of deductive systems, unless principles of reasoning are adopted which are so complex that their internal consistency is as open to doubt as that of the systems themselves. (E Nagel et al. Gödels Proof, 1958)

Care should be taken in dismissing the relevance of such insights to the comprehension of social systems. A recent discussion of their relevance in the Financial Times concludes that although "he was concerned specifically with systems of symbols such as mathematics and other languages... experience indicates that the principle applies to organisational systems too. Its implications are particularly destructive for bureaucratic attempts at management. Their tendency is to lay down systematic rules intended to cover every eventuality and, when they don't, to lay down more rules supposed to close the loophole. Whilst Gödel's principle suggests that any such process is necessarily self-frustrating, almost all bureaucracies seem determined to believe otherwise." (Michael Dixon. The Common Laws of Organizational Stupidity, 4 Sept 1986).

This also suggests the merit of reflecting on the relationship between the political axioms in terms of which attempts are made to govern countries and groups of countries, especially to the extent that they are embodied in political slogans reflecting values which are "axiomatic". Such slogans presumably preclude consideration of modes of organization which are not built directly upon such axioms. But Gödel also showed that there is an endless number of true arithmetical statements which cannot be formally deduced from any given set of axioms by a closed set of rules of inference. The dramatic implications of this has just recently been demonstrated in the world of chess, traditionally referred to as the "Game of Kings" because of the manner in which it simulated the strategic problems of a leader. There are many axioms governing the different possibilities of winning in a chess endgame situation. To the considerable astonishment of the chess community, a very recent computer analysis of endgames has however demonstrated that there are many other ways of winning, unforeseen by such axioms, and in some cases inconsistent with them (K L Thompson, 1986).

2. Comprehension of appropriateness

Comprehending appropriateness might be illustrated by the problem of comprehending the nature of an n-dimensional object (e.g. a hypercube) whose elements represent factors in a mathematical model of a socio-economic system. Portions of the representation can be comprehended when they are represented as 2 or 3-dimensional diagrams of cross-sections of the n-dimensional structure. Integrating a set of such representations tends to be a task beyond the current abilities of the human mind.

It could be argued that it is not vital that the n-dimensional object be comprehensible in its entirety, provided the mathematical representation can be proved to be satisfactory. This is the case with the current use of hypercubes as the basis for the organization of new, and more efficient, forms of computer memory. Provided the product finally works, people do not feel that it is necessary to understand it in its entirety. The wiring diagram can be represented, even though it is meaningless to those making the sequence of connections between the parts. A similar argument is made concerning the lack of need for a driver to understand the engine.

This attitude is not however acceptable in the case of the presentation of some new mode of socio-economic organization, whether at the macro or the micro level. It is one thing for people to have confidence in leaders (or experts) who can claim to comprehend such a mode in its entirety, even though their followers do not. Most social innovations in the past have been implemented on this basis. It is quite another thing when the appropriate mode of organization cannot be fully comprehended by any leader (or expert), especially, as is the case at present, when the motivations of such elites are increasingly considered questionable.

3. Constraints on learning

The situation is further complicated by the learning dimension. If the appropriate mode were fully comprehensible, it would then exclude the possibility of a learning dimension. It would permit learning within that mode, but it could not render explicit (and would therefore probably preclude) learning beyond the framework imposed by that mode. It could not permit learning by which the framework itself would be challenged. It would thus be consistent with human development within a framework implemented at a particular historical moment, but opposed to human development arising from insights emerging subsequently. Such a mode would therefore be consistent with human development in a "minor" key but not with human development in a "major" key, namely development requiring paradigm shifts.

4. Constraints on social organization

A response to this situation is not to expect or require that the appropriate mode be comprehensible in its entirety to any one person or group. It could be expected that different people or groups would be capable of comprehending different features or processes of that mode and would then act to ensure their implementation. But, necessarily, such people or groups would then not comprehend the justification for the activities of other people or groups concerned with other features or processes.

5. Partial comprehension of contextual appropriateness

The socio-political situation would then be one in which:

The difficulty is that, in such a context of partial comprehension, no group (e.g. Group A) would be in a position to distinguish between: In such a situation, for the contextual mode to function appropriately, the groups would act in support or opposition to each other to provide a system of checks and balances that would permit human development to occur in the optimum manner. No group could effectively take a position within this context in support of the contextual mode. It would, because of the necessary partiality of its comprehension, quite validly be perceived as acting to further certain interests consistent with that partiality.

The challenge then is to explore ways of improving comprehension of fruitful patterns of interaction between groups and perspectives that of necessity must function in shifting coalitions in support and opposition to one another.

From Encyclopedia of World Problems and Human Potential

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