Wuli, I am interested in your alegory between ethics and harmony...
here is an equation that fits some of that metaphore, maybe!...
"It is clear that increasing the interest in problem of harmony and golden section in modern science has found its reflection in modern philosophy in form of new original philosophical concepts. The Byelorussian philosopher Eduard Soroko who advanced in the 80th the highly interesting concept of "structural harmony of systems" developed one of the similar concepts. This concept and the "Law of Structural Harmony of Systems" following from it rightfully can be considered as one of the greatest philosophical achievements of the 20th century.
Soroko's main idea is to consider real systems since "dialectical point of view". As is well known any natural object can be presented as the dialectical unity of the two opposite sides A and B. This dialectical connection may be expressed in the following form:
A + B = U (universum). (1)
The equality of (1) is the most general expression of the so-called conservation law.
Here A and B are distinctions inside of the unity, logically non-crossing classes or substratum states of any whole. There exists the only condition that A and B should be measured with the same measure and be by members of the ratio underlying inside the unity.
The examples of (1) may be probability and improbability of events, mass and energy, nucleus of atom and its envelope, substance and field, anode and cathode, animals and plants, spirit and material origin in the value system, profit and cost price, etc.
The expression of (1) may be reduced to the following normalized form:
`A +`B = 1, (2)
where `A and `B are the relative "weights" of the parts A and B forming some unity.
The partial case of (1) is the "law of information conservation":
I + H = log N, (3)
where I is the information quantity and H is the entropy of the system having N states.
The normalized form of law (3) is the following:
R +`H = 1, (4)
where is the relative redundancy, is the relative entropy.
Let's consider the process of system self-organization. This one is reduced to the passage of the system into some "harmonious" state called the state of the thermodynamic equilibrium. There exists some correlation or proportion between the sides A and B of the dialectical contradiction of (1) in the state of the thermodynamic equilibrium. This correlation has a strictly regular character and is a cause of the system stability. Soroko turns to the principle of multiple relations to find a character of connection between A and B in the state of the thermodynamic equilibrium. This principle is well known in chemistry as "Dalton's law" and in crystallography as the "law of rational parameters".
Soroko advances the hypothesis that the principle of multiple relations is the general principle of the Universe. That is why there exists in accordance with this principle the following correlation between the components R and R è`H in the equality of (4):
log R = (s + 1) log`H (5)
or
log`H = (s + 1) log R. (6)
The expressions of (5), (6) may be represented in the exponential form:
R = (`H )s+1; (7)
`H = Rs+1, (8)
where the number s is called the range of multiplicity and takes the following values: 0, 1, 2, 3, ... .
Inserting the expressions of (7), (8) into the equality of (4) we get the following algebraic equations respectively:
(`H )s+1 +`H - 1 = 0; (9)
Rs+1 - R - 1 = 0. (10)
Marking in y the variables `H and R in the equations of (9), (10) we get the following algebraic equation:
ys+1 + y - 1 = 0. (11)
Let's introduce the new variable for the equation of (11). Inserting the expression of into (11) we get the following algebraic equation:
xs+1 - xs - 1 = 0. (12)
We can see that the latter equation coincides with the algebraic equation of the golden p-proprtion. The real root of the equation of (11) is inverse value to the golden p-proportion, i.e.
(13)
where ts is the root of the equation of (12).
In accordance with Soroko's concept, the roots of the equation of (11), which is equivalent to the equation of (13), expresses the law of the structural harmony of systems.
Summing up Soroko had formulated the following "Law of Structural Harmony of Systems":
"Generalized golden sections are invariants, which allow natural systems in process of their self-organization to find harmonious structure, stationary regime of their existence, structural and functional stability".
What peculiarity has "Soroko's Law"? Starting since Phyphagor the scientists were connected the concept of a Harmony with the only golden proportion "Soroko's Law" claimed that the harmonies state corresponding to the classical golden proportion is no only for the same system. "Soroko's Law" allows an infinite number of the "harmonies" states corresponding to the numbers ts or the inverse numbers (s = 1, 2, 3, ...), which are the real roots of the general algebraic equations of (11), (12)."