Duality Theory and TRIZ

This issue commences a cycle of publications devoted to investigation of the role of duality in problem solving (and thinking on the whole). The cycle opens with a paper of 1974 that broke the ground.

One of the shortcomings of the paper was that it did not define duality formally but built upon the fuzzy philosophical definition:

The author later realized that philosophical schools vary both by the list of opposites they study and by properties they attribute to them. Some assume that all opposites are mutually convertible: good can turn into evil, dark can turn into light, etc. Others, e.g. Taoism, assume that they are not convertible, but each has a piece of the other inside. Still others assume that they are neither convertible nor share any pieces of each other. Still others assume that the opposites are merged in everything. Etc.

The list of important opposites vary wildly too. Some assume that the mother of all opposites is "male - female" dichotomy. Others concentrate on "heavenly vs earthly", "good vs evil" and other ethical opposites. Still others focus on more mundane opposites such as energy and mass, form and substance, time and space, ideas and realities, hidden and showing, abstract and concrete, etc.

Views on interaction between opposites vary too. Some assume that there is always a conflict between opposites. For them dualism and conflict/contradiction are synonymous. Others assume that opposites just co-exist in everything.

To further complicate the situation, philosophical definitions of duality are quite different from those in precise sciences. For example, various branches of mathematics define their own very specific types of duality and have specific duality theories of these types. There is no general definition of mathematical duality or general theory of mathematical duality in mathematics.

The upcoming publications will try to clean up this mess and propose a unified theory of duality, which would generalize all hitherto known concepts of duality and include them as particular cases. A formal definition of duality will be given that would apply to all hitherto known types of duality (to the degree of their fuzziness, of course). Technological/technical dualities will be introduced and studied. The theory of technological dualities will be applied to TRIZ.