## Newton's Third Law of Motion

Newton's 3rd Law asserts that forces always act in pairs. If object X exerts a force on object Y then object Y exerts an equal, but opposite, force on object X.

"Whenever a first body exerts a force F on a second body, the second body exerts a force −F on the first body. F and −F are equal in magnitude and opposite in direction."

This Law is also commonly stated in the form: Every action has an equal and opposite reaction.

Action = - Reaction
Which can be Rewritten as
Action + Reaction = 0
Action + Reaction = constant

## Conservation and Symmetry

A duality principle holds in Projective Geometry because we can state the fundamental axioms in terms of the interchangeable terms 'point' and 'line.' The axioms in two-dimensions cannot be proved but in three-dimensions they are theorems which are provable.

Noether's theorem, proved in 1915, allows physicists to identify conserved quantities from symmetries of the laws of nature. Time translation symmetry yields a conservation in energy; space translation symmetry yields a conservation of momentum; rotation symmetry yields a conservation of angular momentum.

Conservation and equilibrium conditions in physics and zero-sum properties in economic and game theory are expressed in the form of equations. In conservation systems

Potential Energy + Kinetc Energy = Constant

## Generalization Of Constant

The symbol (+) used in the following mathematical looking 'formulas' represents a generalized property of addition indicating the interaction and interdependency of the paired (dual) items summed in the equation.

Constant can have several meanings. Below I will use the symbol Z represent the numeric value 0 but also any of the following meanings:

• a numeric value (1), (7a), and (7b),
• an equilibrium point (3a), (6), and (9),
• a stability condition (8a) and (8b),
• a steady state condition (11),
• a homestasis condition in cells (13)
• an oscillatory dynamic balance.

• Economics:
Supply (+) Demand = Z(1)
• Quantum Mechanics:
Wave (+) Particle = Z(2)
• Biology:
Bone Resorption (+) Formation = Z(3a)
Hemoglobin (+) Chlorophyll = Z(3b)
• Newtonian Mechanics:
Action (+) Reaction = Z(4)
• General Relativity:
Push (+) Pull = Z(5)
• Microbial Infections:
Pathogenesis (+) Symbiosis = Z(6)
• Physics of Forces:
Kinetic (+) Potential Energy = Z(7a)
• Action (+) Reaction = Z(7b)Social Psychology:
Reflective (+) Reflexive = Z(8a)
Intentional (+) Unintentional = Z(8b)
• Structuration Theory:
Agency (+) Structure = Z(9)
• Theory of Evolution:
Nature (+) Nurture = Z(10)
• Molecular Biology:
Genotype (+) Phenotype = Z(11)
• Language:
Syntactical (+) Semantical = Z(12)
• Biosemiotics:
Semiotic Downward
Convergence(+)Causation = Z(13)
• Nervous System:
Sympathetic (+) ParaSympathetic = Z(14)

## 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)."