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The duality principle by Sabah E. Karam

(excerpted from http://www.posttool.com/cisna/dual.html

The preceding remarks imply that it is impossible to establish a unifying conceptual model from which we can view all the scientific disciplines. Some would argue that we have to seek convergence beyond the domain of Science itself. The arguments against successfully producing a unified model are strong. My argument is that the Quranic verse 51:49 is a clear principle which can be applied to, not only, the scientific disciplines, but also, to the social and behavioral sciences. This principle I shall call "the duality principle." It characterizes several of the laws and operations found in almost all areas of study labeled as science. It is also a principle observed in the humanities. Terms like complementary, dialectical, opposite or inverse are sometimes used to connote the idea of dualness. They are sometimes two opposing forces, two operations or two characteristics. They can be observed functioning alone in a given phenomenon but, often times, can be distinguished and separated and labeled with their distinct properties. Other times the two 'forces' act in unison and cannot be separated. Many times the duality principle can be identified immediately by the very terms that are used to define them, e.g. action and reaction, particle and anti-particle, inhaling and exhaling. In general, however, terms that are in a dual relationship cannot be identified without knowing the Science behind their definitions. For example; chlorophyll-hemoglobin, electron-proton, evaporation-condensation stand in a dual relationship with each other but their descriptive terms do not disclose that relationship!

In mathematics, called the queen of the sciences, all 'operators' and 'operations' do not exist except 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 come to mind immediately as dual operations. The calculus is nothing more than the application of two dual operators that, in fact, are inverses of each other, viz. integration and differentiation. In physics, action and reaction, positive and negative charges, particle and wave theories are known as dual and/or complementary principles. In economics, supply and demand, profit and loss are connected in a dualistic manner. In biology the functions of chlorophyll and hemoglobin, inhaling and exhaling, muscle contraction and extension, osteoblasts and osteoclasts, lymphatic and myeloid elements are known to have opposite functions. In philosophy and political Science the concepts of liberalism and conservatism and thesis vs. antithesis (Hegelianism) are dialectical or opposites and also fall into the dual category. In chemistry, the theory of Lavoisier that every definite compound consists of two parts having opposite electrical activity was the basis for Jacob Berzelius' dualistic formulas (Melhado, 1981). In a book on the philosophy of language, a linguist (Eco, 1984) describes duality as a structure from which language derives its meaning. Mind and matter, 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 called "the Poet of Duality" (Shoaf, 1985), 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.

Using the Quranic verse 51:49 as the basis of the duality principle and as a common measure of the social, mathematical, the natural sciences and the humanities will greatly simplify and unify the structure from which we view all human knowledge. We should consider duality as an axiom of the world in which we live. Our study of the respective instances of duality in language, biology, poetry, physics, music, economics, psychology, mathematics, political science, geology, history, chemistry and in all the other well-defined disciplines will give us a view of the world which is more simplified, organized, unified and "scientific." This will make it possible to accommodate the humanities and view the "human problems in their fullness from several perspectives." The general reign of order within science and the humanities may well be founded in this principle.

Islamic elementary and high schools can establish a science curriculum based on the duality principle. The principle can be introduced at early stages in the educational process. If we teach the principle in the beginning school levels and identify those activities in our lives to which duality applies we can then extend the principle to the more subtle dualistic relationships which exist in mathematics, science, language and ultimately to all the other disciplines. Inhaling and exhaling, the waking and sleeping states, night and day, hot and cold are activities and observable facts that every one of us, consciously or unconsciously, witness daily. The extension of these observations to those which have observed in the natural and social sciences can thus be handled in a natural way. Before students begin studying the theories of any scientific discipline, they should be presented with the structure of duality and how it applies to us daily in the world in which they live.

Recall the, sometimes heated, debate over whether light was a particle or whether it was a wave. The debate ended, after many decades, in the full acceptance of the dual nature of light. Light is both a wave and a particle. Modern day physicists no longer argue about the complementary characteristic of matter and energy, they accept duality. Associated with every force is a (theorized) particle. Gravity is a force. Its dual, a particle called the graviton, has not been, and may never be, discovered. The strong force which binds the protons together in the nucleus of every atom is called the gluon. The gluon's existence has not been demonstrated experimentally. Its theoretical existence is accepted, however, as is the theoretical existence of every particle which has a 'force' associated with it. What has been adopted here is, in fact, the duality principle described in the Quran. In physics this theory is called 'supersymmetry.' This theory has lead to a more advanced theory, still being developed, which is being dubbed the TOE (Theory of Everything). TOE is based on a concept called dual-spaces which depends on the theory of supersymmetry. For a summary of the ideas behind dual spaces you can read several articles on TOE and the Mathematics of Duality in several past issues of Scientific American www.sciam.com including http://www.sciam.com/1999/1299issue/1299weinberg.html.

A corollary to the Duality Principle applies to Einstein's unsuccessful search for a "unified field" which would unite general relativity, his own theory of space-time and gravitation, with Maxwell's theory of electromagnetism. The contemporary effort, called the Grand Unified Theory (GUT), is a continuation of Einstein's efforts and has produced a proliferation of models. According to the Duality Principle, if a unified force were found that united the strong, weak, electromagnetic and gravitational forces then a complementary force, a dual force, would also be discovered!

References

Popper, K. R. (1974). Studies in the Philosophy of Biology. University of California Press, Berkeley, CA, 259-284.

Godel, K. (1962 translation). On Formally Undecidable Propositions of Principia Mathematica and Related Systems. New York Basic Books.

Hurd, P. D. (1992). Closing the Educational Gaps between Science, Technology, and Society. Bull. Sci. Tech. Soc., Vol. 12, 127-135.

Santilli, R. M. (1978). Lie-Admissible Approach to the Hadronic Structure. Volume 1. Hadronic Press. Nonantum, MA, 1-30.

Eco, U. (1984). Semiotics and the Philosophy of Language. Indiana University Press. Bloomington, IN.

Melhado, E. M. (1981). Jacob Berzelius, The Emergence of his Chemical System. The University of Wisconsin Press. Madison, WI.

Shoaf, R. A. (1985). Milton, Poet of Duality: A Study of Semiosis in the Poetry and the Prose. Yale University Press. New Haven, CT, 1-10.


 

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