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 the term '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.

EXAMPLES OF EACH TYPE:

  • 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:
    Convergence (+) Causation = Z(13)

  • Nervous System:
    Sympathetic (+) ParaSympathetic = Z(14)