Principle of Duality - A philosophical View
For Science the duality principle takes different forms for different schema of Science. To list a few,
To memorize and recapitulate the Boolean duality principle “one part may be obtained from the other if the binary operators and the identity elements are interchanged�.
Stating that every algebraic expression deducible from the postulates of Boolean algebra remains valid if the operators and the identity elements are interchanged. Further the identity element is the inverse of its own.
To put forward the duality principle of Geometry, “All the propositions in projective geometry occur in dual pairs which have the property that, starting from either proposition of a pair, the other can be immediately inferred by interchanging the parts played by the words "point" and "line." A similar duality exists for reciprocation�.
In mathematics, often called the queen of the sciences, all 'operators' and 'operations' are studied only in a dual relationship. One rarely learns an operation in mathematics without also learning its inverse operation. Addition and subtraction, multiplication and division, raising to a power and taking roots, the distributive law and factoring, all come to mind immediately as examples of dual operations. Calculus is nothing more than the study of two dual operators that are, in fact, inverses of each other, viz. integration and differentiation.
In physics, action and reaction, positive and negative charges, and particle and wave theories are known as dual and/or complementary principles. To hark back, the heated debate over whether light was to be classified as a particle or a wave. After many decades the debate finally ended with the full acceptance of the dual nature of light. Scientists acknowledged, over three quarters of a century years ago, that light has both a wave and a particle nature.
In chemistry, Lavoisier’s theory that every definite compound consists of two parts having opposite electrical activity was the basis for Jacob Berzelius' dualistic formulas
In biology the functions of chlorophyll and hemoglobin, inhaling and exhaling, muscle contraction and extension, anabolic and catabolic, lymphatic and myeloid elements are known to have opposite functions.
In economics, supply and demand, and profit and loss are connected in a dualistic manner.
In philosophy and political science the concepts of liberalism and conservatism, thesis and antithesis (Hegelianism) are dialectical, or opposites, and also fall into the dual category.
In a book on the philosophy of language, the linguist Eco U., describes duality as a structure from which language derives its meaning. Life and death, mind and matter (dualism of Descartes), space and time, subsistent forms and spacio-temporal objects, subjective ideas and objective reality, good and evil, yin and yang, the list is endless.
In the humanities John Milton is referred to as the “Poet of Duality", because of his focus on the concepts of good and evil and the ultimate paired destiny to which mankind will be delegated, heaven or hell.
Terms like complementary, dialectical, opposite or inverse are sometimes used to indicate the idea of dualism. Dualism is often times used to refer to two opposing forces, two operations or two characteristics. The dual pairs might be observed functioning alone in a given phenomenon but more frequently, can be distinguished, separated and labeled with their distinct properties.
The Philosophy so far has been neat and clean in defining the stark nature of the duality principle.
If there is Good, there is bad; if there is truth there is lie; if there is beauty there is ugly; if there is heaven there is hell. Thus the postulates of philosophy remain consistent in defining the elements and their inverse in a way that the element beholds its meaning only for the true fact that there is an existential inverse element to it, or to put in another way the inverse element exists only for the very fact the elementary elements exist, for the knowledge of good alone can play the role in defining what evil is. The philosophy connives the world about the darker and lighter faces of the elements.
To state the duality principle of Philosophy, "And all things have we created in pairs in order that we may reflect on it." Philosophy asserts that every equal has a counter unequal as of the equal. The equal rests upon the unequal and vice versa.
To march a step ahead, it’s the Jurisprudence of Philosophy that acclaims that if you are to the world, the world is for you; and if you are not to this world, the world is not for you. It is ultimately you who see this world, for what the world is to see to you. Thence it is you who define the world and wherefore define yourself to the World.
posted by Sameer G Kulkarni @ 5/27/2005 09:14:00 AM
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