Duality Science Academy

Baltimore, MD

Text/Voice 443-267-8885

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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.

### 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 animalmodels suggests that experiencesacross 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., 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.

Champagne

SYMBOLICALLY WRITTEN USINGTHE NOTATION OF THIS WEBSITE:

**NATURE**(+)**NURTURE**=**Z****GENOTYPE**(+)**PHENOTYPE**=**Z**

DUALITY in GEOMETRYInterchanging 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 apointif they are in perspective from aline;(2b) Two triangles are in perspective from alineif they are in perspective from apoint. (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.

http://mathworld.wolfram.com/DesarguesTheorem.html

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),**

**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/KnowingKnown/KnowingKnownFullText.pdf

**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 Philosopherby 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.' "

See: http://www.isi.org/journals/modern_age.html

**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

*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."

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 discrete

calculus statistics

analog computers digital computers

ontology epistemology

category theory set theory

relativity theory quantum mechanics

field theory particle physics

topology algebra

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Duality Science Academy

Baltimore, MD

Text/Voice 443-267-8885

sabah