**PAPER 4**

*In this Paper I investigate how from the sheer and mere Observation and Experiment one evolves – through the Principles enunciated in the Paper – to the equivalence : identity of this Observation and Experiment of the scientists and the methodology of Proportion that I use as the tool of discovery in my works.*

I

EMPIRICAL OBSERVATION:EXPERIMENT

The Empirical Fact

The Empirical Quality

The Empirical Proportion

Quality as the Aggregatum of Facts:Quantities

Proportion as the Aggregatum of Quality.

II OUR WORKS AS THE OBSERVATION:EXPERIMENT OF EMPIRICAL PROPORTIONS

III VERIFICATION

MATHEMATICAL EQUIVALENCE AS IN EQUIVALENCE TO PROPORTION

IV

V

OUR WORKS AND THEIR EMPIRICAL VERIFICATION

In the mass universe all proportions are proportional to each other

Phaemonon:Quantity:Fact [A] Phaenomenon:Quantity:Fact [B] [C] [D]

To

Quality [AQ]

To

Proportion [AP]

A X A = AQ

And

AQ X Constant X =

BQ X Constant X

Proportion :

Quality A X constant X = Quality B X constant X

EMPIRICAL OBSERVATION:EXPERIMENT

The Empirical Fact

The Empirical Quality

The Empirical Proportion

Quality as the Aggregatum of Facts:Quantities

Proportion as the Aggregatum of Quality.

*0f how we observe:describe Empirical Proportion in the same mode as Empirical Quality and Empirical Quality in the same mode as Empirical Fact:Quantity.**Syllogistic Equivalence of Empirical Proportion; Empirical Quality and Empirical Fact.**0f the Empirical Fact ---> Empirical Quality ---> Empirical Proportion Cycle**Of the Vice-versa of this Cycle.**0f the Principle (Principle 0f Empirical Equivalence) that Empirical Fact:Quantity; Empirical Quality and Empirical Proportion are Equivalent to Each Other In Terms 0f the Principle 0f Equivalence:Identity**0f how in this Cycle the Observation 0f One of the Three Links [Empirical Fact; Empirical Quantity; Empirical Proportion] is the Observation of the Other Links (as by the Principle 0f Empirical Equivalence q.v. supra]**0f How the Principle of Empirical Equivalence q.v. occurs:progressess as in to all our Empirical Observations:Experiments.*II OUR WORKS AS THE OBSERVATION:EXPERIMENT OF EMPIRICAL PROPORTIONS

*Our Works as the Assertions:Enunciations:Statements 0f Principle(s)**Of the Enunciation 0f All and Any 0f These Principles (apart from the Assertions themselves) as Proportions (Direct-Inverse)**0f How All These Proportions are Empirical Proportions.*III VERIFICATION

*0f how the Observation:experiment 0f Empirical Proportion is the Observation:Experiment 0f Empirical Quality and the Observation:Experiment 0f Empirical Quality is the 0bservation:Experiment 0f Empirical Fact :Quantity**0f How in Verification q.v.the Agreement:Equivalence:Transformation of One Link (of the Empirical Proportion Cycle) as in the Other Link(s) (of the Same Cycle) is Observed:Experimented**0f How this Verification Itself Is Executed (0ccurs:Progressess) as By Empirical Observation:experiment.**0f the Empirical Transformation 0f One Link (q.v. Above) (of the Empirical Proportion Cycle) as in to the Other (Link)**0f How this Empirical Transformation Occurs:Progressess as accordant to these Three Principles :**A - Principle that Empirical Fact:Quantity is transformed as into Empirical Quality as by the Operation:Occurrence:Progression 0f The Relative Laws (e = mc2 and/or 0ther Laws - if any -)**B – Principle that Proportion is Quality AQ (Quantity A X A) X Constant X = Quality BQ (Quantity B X B) X Constant X**C – Principle that Proportion and Mathematical Equation:Equivalence q.v. are Equivalent:Identities in terms of the Principle 0f Equivalence:Identity q.v*MATHEMATICAL EQUIVALENCE AS IN EQUIVALENCE TO PROPORTION

*Mathematical Equivalence can be arithmetical, algebraic, geometrical or other equivalent type:mode.**0f how we choose the Algebraic Equation as 0ur Expression of Mathematical Equivalence*IV

*0f HowTherefore as from All and Any Observation:Experiment 0f All and Any Empirical Fact:Quantity we arrive (as by the Relative Empirical Transformation) to the Relative Empirical Proportion(s).**And Vice-Versa*V

OUR WORKS AND THEIR EMPIRICAL VERIFICATION

*0f How all the Proportions as in to our Works are Verifiable by the Tool:Method 0f Mathematical Equivalence 0f The Relative Quantities to the Relative Qualities (as per the Relative Principles:Equations q.v. Above) and (In Turn) 0f The Relative Qualities To The Relative Proportions (as per the Relative Principles:Equations q.v. Above)*In the mass universe all proportions are proportional to each other

*Therefore and accordingly all Equations of the Tool:Method of Mathematical Equivalence supra q.v. are proportional to each other**Therefore and accordingly All Packets of Quantities and All Qualities multiplied by their respective constant (X) are also proportional to each other*Phaemonon:Quantity:Fact [A] Phaenomenon:Quantity:Fact [B] [C] [D]

To

Quality [AQ]

To

Proportion [AP]

A X A = AQ

And

AQ X Constant X =

BQ X Constant X

Proportion :

Quality A X constant X = Quality B X constant X