## 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)