On 8-Colors Combinatorics and [ Quasi 24-Symmetry ]

by Frank C. Fung ( 1st published in March, 2011. )

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Section XXX - Revisiting the Concept of [ QI ] and [ OU ] ( / )

Summary for the Section :

• In this Section , we shall revisit the Concept of [ QI ] and [ OU ] :
  • with an application here on the Half-on-Half rotations of the [ 8-Colors Cube ] .

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The Concept of [ QI ] and [ OU ] :

• The concept of { [ QI ] vs. [ OU ] } is a ancient and traditional Chinese concept :
  • 

  and this concept was previously brought up in the author's other paper ,

  • An Approcah to the I-CHING , back in 2004 .

• Let us recall briefly the meaning of [ QI ] and [ OU ] :
  • [ QI ] usually carries the following meanings :
    • Extra-ordinary , special and unusual ;

    • Surprised and astonished ;

    • Singular , the odd-one-out , or unattached ;

    • Odd as in odd-and-even ;

  • [ OU ] usually carries the following meanings :
    • Ordinary , plain and nothing-unusual ;

    • Calm and smooth , bound-to-happen in the usual course of events ;

    • Plural , paired , or in-a-group ;

    • Even as in odd-and-even ;

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Classifying [ CHANGE ] in terms of [ QI ] and [ OU ] :

• In the context of the [ Half-on-Half Rotations ] of our [ 8-Colors Cube ] :
  • We may now classify the [ changes ] into two (2) categories :
    • The [ 1-notch rotations ] and the [ 3-notch rotations ] are classified as [ QI-Changes ] ; and

    • The [ 2-notch rotations ] are classified as [ OU-Changes ] .

• Two Scenarios here :

  Scenario ONE :

  • If we permit rotations in all six (6) Axial-Directions :
    • we would be looking at the Global Set of 40,320 configurations .

      ( see Section XXVII for details . )

    And :

    • the [ OU-Changes ] will only permit us to move-around in a restricted set of [ 96 configurations ] .

    And as such ,

    • the Global Set of [ 40,320 configurations ] can now be divided into :
      • 420 sets of [ 96 QSM-Configurations ] .

  • And the [ QI-Changes ] will move us from set to set , i.e. :
    • from one set of [ 96 QSM-Conifgurations ] to another set of [ 96 QSM-Configurations ] .

  Scenario TWO :

  • If we permit rotations in the [ -X / -Y / -Z Axial-Directions ] :
    • we would be looking at the Reduced Set of 5,040 configurations .

      ( see Section XXVIII for details . )

    And :

    • the [ OU-Changes ] will only permit us to move-around in a restricted set of [ 24 configurations ] .

  

  And as such ,

  • the Reduced Set of [ 5,040 configurations ] can now be divided into :
    • 210 sets of [ 24 QSM-Configurations ] .
  • And the [ QI-Changes ] will move us from set to set , i.e. :
    • from one set of [ 24 QSM-Configurations ] to another set of [ 24 QSM-Configurations ] .

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The Key Point Here :

• While we started out with the same basic maneuver for both the [ QI-Changes ] and the [ OU-Changes ] ,
  • namely the [ 1-notch ( 90-degrees ) rotation ] ;

  the result of the [ QI-Changes ] and the [ OU-Changes ] are distinctly different .

• Thus , we must always keep our eyes open to identify the different types of [ changes ] .

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go to the next section : Section XXXI - The [ 6-elements loops ] for the Single Rolls

go to the last section : Section XXIX - Basic Combinatorics of [ 8-Colors Circular-Rings ]

return to the 8-Colors Combinatorics / Quasi 24-Symmetry HomePage

Original dated 2011-3-06