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:
Supply (+) Demand = Z(1)
- Quantum Mechanics:
Wave (+) Particle = Z(2)
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)
Syntactical (+) Semantical = Z(12)
Convergence (+) Causation = Z(13)
- Nervous System:
Sympathetic (+) ParaSympathetic = Z(14)