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Goldenality


        Harmony is a relationship that doesn't limit itself within any confined system. It is a quality that extends itself limitlessly within whatever boundaries are imposed upon it. In music, one could have two notes and through the use of the formula for finding their harmonic mean, a third note could be found whose pitch would be in harmony with the other two. But this doesn't guarantee harmony among the first two notes. They might be discordant with one another. This analogy is a perfect example as to what happens when two lovers, who are ill matched, produce a child. The child will be in harmony with both parents to the degree that both parents are in harmony with each other. That is how the harmonic mean works. That is how family creation works. So, how does nature ensure harmony among all of its preexisting customers? It sets up a standard on each planet before that planet produces life. It doesn't matter too much what standard is chosen. There are many standards nature has to choose from. But once a standard is chosen, all life on a planet abides by that harmonic standard, for it knows no other. If organisms who are already established within their harmonic system were to arrive to a planet of a vastly different harmony, then the two life forms would not conflict, but they would be unintelligible to one another. Life on various planets doesn't respond, favorably or unfavorably, to any standard other than its native one unless the foreign standard shares similar characteristics with the native. Since differing standards would be, by definition, uniquely generated, all characteristics would not be shared between them, making similarity and harmonic appreciation limited. Even elements of discord need to be shared in order to make any sense of them.

        On our planet we have been exhibiting two standards within our "developed" countries. The reason for this can only be one: individuals residing within such countries come equiped with the expectation of a standard which is foreign to this planet. Such individuals can respond to both the native standard on Earth and the foreign standard from their "lost world". Persons native to Earth might only respond to Earth's standard for the most part. Although no rational explanation can be found to authenticate this social trait among us, a deeply personal explanation can be found by posing another question: is there any other factor, other than environment and genes, that influences the developing individual? There is. It is called point of view. Unfortunately, our points of view are largely identified with our organs of perception making objective recognition of the origin to our perspective largely inaccurate and befuddled with self-doubts. Does point of view originate within a sense of perception or organ of mentation (the mind), or does point of view originate from our soul beyond mind and lent out to these "extensions of vision"? How would we find this out? And what value would we gain from such proof? It would explain why old (relatively more advanced) souls have a predilection for engaging in two standards of harmony while young souls native to Earth orient themselves largely to just one. [Emulation complicates matters slightly.] Despite the body's orientation to just one standard under which it is born, one's point of view takes in a much larger framework. If point of view incorporates the memories of previous lives lived on planets built from foreign standards, then point of view can't help but enjoy both systems of harmony. Such is the heritage of many persons living in developed countries. Their heritage harks back to another planet called Maldek, where the standard there was foreign to our own here on Earth. Earth's standard is the Golden Ratio, while Maldek's standard is the Pell Ratio. Which standard shall hold sway on any given planet? The native one, or else the foreign one.   ;-)   If human relations extend beyond developed countries, then the native one is the best to use for it would be globally understood and appreciated. But within developed countries, there may be a tendency to exhibit physical, mental, and emotional behavior framed along guidelines set forth by either standard: foreign or native born. This cannot be helped, nor should it be prevented.

The Golden Section

A---C-----B

The line AB is cut in extreme and mean ratio at C since
AB : CB = CB : AC = Phi

 

The Golden Section

  1. Let AB be the given straight line.
  2. Draw BD = AB ÷ 2 perpendicular to AB.
  3. Join AD.
  4. With center D, radius DB, draw an arc cutting DA at E.
  5. With center A, radius AE, draw an arc cutting AB at C.
  6. Then C is the golden section of AB.
  7. AB = 1       BD = 1/2
  8. AD2 = AB2 + BD2
  9. AD2 = 12 + (1/2)2
  10. AD = ± Ö(5/4)
  11. AD = (± Ö5)/2
  12. ED = BD
  13. AC = AD – BD
  14. AC = (± Ö5)/2 – 1/2
  15. AC = (-1 ± Ö5) / 2
  16. AC = 0.618033989..... and -1.618033989.....

Click here for an alternate way to make this Golden Section

        Modularity is a key concept to goldenality: that a smaller replica of a larger unit can be constructed with internal proportions identical to the larger unit. The Golden Ratio exhibits this quality extensively in nature, geometry, and mathematics. The Pell Ratio exhibits this quality a bit furtively --- mostly in geometry. But there is another side to archetyping a planet. Aspects of Deity also need to be exhibited in a planet's aesthetic system. The Golden Ratio does a superb job of exhibiting physical properties of harmony while the Pell Ratio exemplifies more of Deity's qualities. [More on this later....] So, aesthetic systems specialize in benefits that are unique to their planet's living systems.
 
 
Next Lesson: How to find infinitely various types of a mean (average) from among innumerable values.
 
References:
A mathematically thorough overview of The Golden Ratio.
A more poetic sketch of examples of what makes the Golden Ratio golden.
A terse definition of the Golden Mean by Euclid.

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Monday, 16 August 2004 15:30:00 MST [an error occurred while processing this directive]