Dualities Span the Academic Disciplines

Duality principles, theorems, and models can be found in the natural, social, and life sciences. In philosophy and the humanities dual-ness is often treated as a dualism.

Dualism & Duality Models Span the Scientific and Non-Scientific Disciplines

Examples of Paired-Terms for Dualistic Relationship

In many cases it is not immediately obvious that paired terms are dualistically related.

Action-Reaction
Biotic-Abiotic

Examples of Terms for Non-Obvious Dualistic Relationship

Notable exceptions are words that are antonyms, polar opposites, or negations of each other.

Activation - Inhibition
Agency- Structure

Examples Of Words Implying A Dualistic Relationship

Below is a non-exhaustive list of WORDS, listed in alphabetical order, that describe properties suggesting a trade-offs or interplay between dualing pairs. In scientific and non-scientific nomenclature many words incorporate a notion of dual or paired.

Psychology

In Social Psychology the Reflective-Impulsive Model is duality model. Three major advantages of dual-system models are (a) their integrative power, (b) their foundation in well-established constructs of cognition and neuroscience; and (c) the ease with which they can explain the interplay of judgments and nonjudgmental processes. Dual-system models in the cognitive sciences that are versatile tools which have integrated existing findings and stimulate new research in social cognition.

In Cognitive Psychology a duality arises naturally from the distinct roles played by a referent and a probe in comparative judgment. Current ongoing investigations are attempting to explain how reference duality and referential duality are dualistic themselves. Dual-system models, referred to above, explain social cognition and behavior as a joint function of two interconnected mental faculties, each operating according to different principles. Paired terms such as: reflective-impulsive (reflective-reflexive), propositional-associative, systematic-heuristic, and intentional-unintentional are found in social cognitive studies.

The Dialogical Self is a new theoretical construct in psychology that requires analysis and thinking in dualities. Dualities are considered "systemic units of two opposites that are mutually related by functional dynamic relations."

Valsiner, J. (2005). Scaffolding within the structure of Dialogical Self: Hierarchical dynamics of semiotic mediation. New Ideas in Psychology, 23(3), pp. 197-206.

Physics

Electricity and magnetism are fields having properties dualistically paired. They include:

Permittivity - Permeability
Piezoelectricity - Magnetostriction;
Ferroelectric - Ferromagnetic Materials
Electrets - Permanent Magnets
Faraday - effect Is Dual of the Kerr-effect.
Voltage - Current
Parallel - Serial Circuits
Impedance - Admittance
Reactance - Susceptance
Short Circuit - Open Circuit
Time Domain - Frequency Domain

Differential equations developed for DC circuits can be applied to AC circuit analysis by replacing the real numbers with complex numbers.

Biology

In Molecular Biology, code-duality refers to the fact that living systems always form a unity of two coded and interacting messages, the analog coded message of the organism itself and its re-description in the digital code of DNA. As analog codes the organisms recognize and interact with each other in the ecological space, giving rise to a horizontal semiotic system (the ecological hierarchy), while as digital codes they (after eventual recombination through meiosis and fertilization in sexually reproducing species) are passively carried forward in time between generations. This of course is the process responsible for nature's vertical semiotic system, the genealogical hierarchy.

Economics

Duality Theory of production is a dual model that imposes a number of simplifying assumptions regarding economic production technologies, including dual concavity/convexity assumptions.

Convexity is a significant concept in recovering technology information from economic models; cost functions are considered concave and profit functions are regarded as being convex.

Computer Science

In the Computational Sciences programming techniques are based on the concept of an "object" which is a data structure encapsulated with a set of routines that operate on the data. In object-oriented (OO) paradigms an object has a dual characteristic: state and behavior. The following table depicts some of the dualistic categories used in the software engineering dichotomies.

Digital - Analog

Synchronous - Asynchronous

Hierarchical - Flat

Distributed - Central-processing

Sequential - Parallel

Static - Dynamic

Top Down - Bottom Up

Goal Oriented - Process Oriented

Explicit - Implicit

Goal Oriented - Process Oriented

Active - Passive

Predictable - Statistical

Mathematics

In mathematics, duality has a variety of seemingly unrelated meanings. Some examples: (1) De Morgan's Laws. (2) Dualities transform, translate or map, mathematical structures in one theory into mathematical structures in another theory. (2) Given any valid theorem in plane projective geometry, interchanging the roles of point and line results in a equally valid theorem. (3) In category theory, the objects of one theory are mapped into objects of another theory and the structure-preserving mappings between objects in the first theory are transformed into mappings in the second theory, but with direction of the arrows reversed. For an incomplete list of all versions of duality in mathematics see:

http://en.wikipedia.org/wiki/Category:Duality_theories

String Theory is the only known approach to resolving the Grand Unification Theory (GUT)** problem that is at the core of modern physics: the incompatibility of quantum mechanics and gravity. The most important physical principles, gauge theory and general relativity, are predicted by string theory. Superstring theories are related by duality transformations known as T duality and S duality. These two dualities yield mathematical results showing that quantities of large (R) and small (1/R) distance are essentially the same. The theory incorporates the strong and weak couplings required in theories of classical mechanics and quantum physics.

**It is important to note that if DUALITY is regarded as an AXIOM of existence then (1) if a force, unifying gravity and light, is discovered then a dual force exists which is complementary to it or (2) it is impossible, experimentally but not theoretically, to prove GUT!

Psychobiology

"Converging evidence from studies of human subjectsand animal
models suggests that experiences across the life span can exert persistent changes in gene expression and behaviour … The dynamic yet stable nature of these heritable epigenetic marks implies the potential for phenotypic plasticity in response to environmental cues …"

Champagne, F.A. (2010a) Epigenetic influence of social experiences across the lifespan. Developmental Psychobiology 52(4): 299-311.

Champagne, F.A. (2010b) Early adversity and developmental outcomes: Interaction between genetics, epigenetics and social experiences across the lifespan. Perspectives on Psychological Science 5(5): 564-574.

SYMBOLICALLY WRITTEN USING

THE NOTATION OF THIS WEBSITE:

NATURE (+) NURTURE = Z

GENOTYPE (+) PHENOTYPE = Z

Duality In Geometry

Interchanging point and line in a valid geometric statement yields an equally valid statement.
(1a) Two non-parallel lines determine a point
(1b) Two non-coincident points determine a line.
(2a) Two triangles are in perspective from a point if they are in perspective from a line;
(2b) Two triangles are in perspective from a line if they are in perspective from a point. (Desargues Duality, 1639)

Duality materializes in almost every area of mathematics. Among mathematicians, however, there is no single definition that unifies all known notions of duality.

Modern origins of duality and dualism: 17th century

DESARGUES (1639) Duality (1639),

DESCARTES Dualism (1641).

20th Century Versions in Epistemology and Linguistics

BENTLEY & DEWEY Distinctions (1949),

J. DERRIDA Différance (1967).

Duality in Education, History of Science & Philosophy

The American educator-philosopher John Dewey (1859-1952) in an early paper questioned whether logic was a dualistic science.

Dewey, J. (1890). Is logic a dualistic science? Open Court, III: 2040-2043.

Dewey later admits to a belief in "epistemological dualism" acknowledging a "numerical duality in perception, namely, the difference between time and place" in the following paper.

Dewey, J. (1917). Duality and Dualism. The Journal of Philosophy, Psychology and Scientific Methods, 14(18 ), pp. 491-493.

Stable URL: http://www.jstor.org/stable/2940462

Although they were opposed to "crude dualisms" John Dewey and Arthur Bentley collaborated in producing a treatise on epistemology. It a 1949 book, The Knowing and the Known, they identified almost 100 dualistic relationships which they called DISTINCTIONS. The full text of the book can be found at the following link:

http://www.aier.org/aier/otherpublications/KnowingKr

The Poet Robert Frost declares "I AM A DUALIST!"

Robert Frost (1874-1963), the poet, was but affirmed his philosophical support for dualism when "I am a dualist"in a private letter, called snail mail today, in 1959.

In the Summer 2008 issue of Modern Age review of the book

Robert Frost: The Poet as Philosopher by Peter J. Stanlis. Foreword by Timothy Steele (Wilmington, DE: ISI Books, 2007). 452 pp.

J.F. Desmond summarizes Frost's position saying: "Dualism for Frost meant that all reality is comprised of matter and mind, or as he preferred, matter and spirit; as opposed to a monism that sees reality comprised of one element, spiritual or material. In contrast to Platonism's pure idealism on the one hand, and simple materialism on the other, Frost believed with Aristotle that matter and spirit were equally real and that all reality consisted of 'things in pairs ordained to everlasting opposition.' "

Arthur O. Lovejoy (1873 - 1962) founded the field known as the "history of ideas" in the 1936 book: The Great Chain of Being: A Study of the History of an Idea (1936). Harvard University Press.

In his 1930 book "The Revolt against Dualism: An Inquiry concerning the Existence of Ideas Lovejoy writes in the Preface:

"The principal purpose of this volume is not to present a private
and original speculation, but to show, through a critical survey
of the reflection of the greater part of a generation of philosophers
in America and Great Britain upon two [monism and dualism] important philosophical issues, that certain conclusions with respect to those issues have thereby been definitely established.

_

(θ θ ) Thema-Antithema Duality

Gerald Holton, Mallinckrodt Professor of physics and Professor of the History of Science (Emeritus) at Harvard University, has identified many dualities in the form of thema-antithema. Examples: discreetness-continuum, projection-retrojection, evolution-devolution. Holton emphasizes that one of the most important characteristics of a thematic hypothesis is that it is not subject to verification or falsification.

"It is the interdisciplinary spread or sharing of such fundamental themata that has produced something like a scientific imagination shared by all scientists ..." (p.16)

Holton, G. (1988). Thematic Origins of Scientific Thought: Kepler to Einstein. Cambridge: Harvard Univ. Press.

Prof. Holton in a 1996 book (Einstein, History, and Other Passions) explains why there was a "rebellion against science at the end of the 20th century." It is reminiscent of the Lovejoy's 1930 book mentioned above. Lovejoy's book contrasted monism and dualism which he regarded as the foundation of the scientific method. Lovejoy labeled Monisms as being one of five "metaphysical pathos."

Duality concepts can be used to classify academic disciplines as being the study of continuous (infinite) or discrete (finite) varialbles.

Continuous

Calculus

Analog Computers

Ontology

Category Theory

Relativity Theory

Field Theory

Topology

Discrete

Statistics

Digital Computers

Epistemology

Set Theory

Quantum Mechanics

Particle Physics

Algebra

Genomics and Systems Biology

Examples of how the terms dual, duality, dualism, etc. are used in the sciences and humanities

Dual Pigment

Complementary structures and functions: hemoglobin and chlorophyll.

Dual Biological Functions for Internal Equilibrium

Bone homeostasis is maintained by a dynamic duality between bone resorption by osteoclasts and bone formation by osteoblasts.

Focal Point Theory Models for Dissecting Dynamic Duality Problems of Microbial Infections

http://www.ncbi.nlm.nih.gov/pmc/articles/PMC226697

Duality in Poetry

Shoaf, R. A. (1985). Milton, poet of duality : a study of semiosis in the poetry and the prose. Yale University Press, New Haven, CT

Stanlis, J. (2007). Robert Frost: The Poet as Philosopher (Foreword by Timothy Steele). Wilmington, DE: ISI Books.

Duality in Life

Duality is considered to be an axiom of life itself!

Rosen, R. (1991). Life Itself: A Comprehensive Inquiry into the Nature, Origin, and Fabrication of Life. NY: Columbia Univ. Press

Duality in String Theory

In 1919 Theodor Kaluza, a mathematician, solved Einstein's equations for general relativity using 5 dimensions and found that Maxwell's equations for electromagnetism emerged simultaneously. Kaluza suggested the introduction of a 5th dimension to Einstein who, after consulting with his colleagues, responded that the idea was impractical because physicists could not conduct experiments in five dimensions!

The various dualities discovered in string theory have led to numerous advances in quantum field theory (the exact solutions of some supersymmetric gauge theories), mathematics (Calabi-Yau mirror symmetry), and quantum gravity (the counting of black hole entropy). The essential meaning of duality, for string theorists, is a correspondence between apparently different theories that lead to the same physical results!

Kaluza, Theodor (1921). "Zum Unitätsproblem in der Physik". Sitzungsber. Preuss. Akad. Wiss. Berlin. (Math. Phys.), 966-972.

English Translation:

Sabbata, V. & Schmutzer, E. (1983). Unified field theories of more than 4 dimensions, Proceedings of the International School of Cosmology and Gravitation (Erice). Singapore: World Scientific.

Duality in Economics

Dualities in economic and social theories: agency and structure, the individual and society, mind and body, values and facts, and knowledge and practice.

Jackson, W. A. (1999). Dualism, duality and the complexity of economic institutions. International Journal of Social Economics, 26, 545-58.

Ecological Population Duality

Hutchinson, G.E. (1957). Concluding remarks. Cold Spring Harbor Symposia on Quantitative Biology. 22:415-427.

Quantitative Phytochemistry

Gottlieb, O.R. & M.R. Borin (1998). Evolution of angiosperms via modulation of antagonisms. Pythochemistry. 49 (1),1-15.

"Antagonistic pairs characterize such a wide range of physical, chemical, biological, and social systems that the concept of their modulation emerges as a fundamental mechanism of universal development (p. 13)".

Quantitative Chemo-Biology

Gottlieb, O.R. & M.R. Borin (2003). Quantitative chemo-biology: A chemical paradigm to understand biological phenomena. ARKIVOC 11, 356-365.

"Providing experimental evidence based on natural products, we then perceived the importance of dualistic systems in all phenomena. Some of these pairs were detected in the present work, e.g. shikimate/acetate pathways, gallic/caffeic acids, forest/cerrado, ecosystems/ecotones. Our results indicated that these dualistic systems, jointly with a wide range of physical, chemical, biological, and social systems, offer the ecological plasticity indispensable for adaptations to environmental changes. Thus, Quantitative Chemo-Biology reveals modulation of opposing features as the fundamental mechanism of evolutionary-ecology, and the concept should possess universal relevance. Antagonism is not only an evolutionary principle ruling angiosperms, but also operates in many universal systems, from molecules to universe. (p. 363)."