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

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

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Section XXIII - Understanding Physical [ Quasi 24-Symmetry ] - Phase III

Summary for the Section :

• In this Section , we shall bring-in the [ TRUDEAU Colors-to-Numbers Conversion Scheme ] ,
  • and apply it to the [ 24 QSM-Configurations --- Canandian Rockies Series ] ,
    • with interesting results .

  We shall also list-out our findings from computer-aided analysis ,

  • on the [ Fu-Hei / ASCENDING combination ] for the conversion to the [ 8-colors sequences ] .

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Bringing-in the [ TRUDEAU Colors-to-Numbers Conversion Scheme ] :

• Let us now bring-in the [ TRUDEAU Colors-to-Numbers Conversion Scheme ] , as follows :

  Color #1	Color #2	Color #3	Color #4	Color #5	Color #6	Color #7	Color #8
  ***********	***********	***********	***********	***********	***********	***********	***********
  RED	MAGENTA	ORANGE	GREEN	BLUE	CYAN	YELLOW	PURPLE

  And the essense of the [ TRUDEAU Colors-to-Numbers Conversion Scheme ] is that :

  • it enabled us to convert [ Pattern RYAN ] to the [ 1-2-3-4-5-6-7-8 Base Structural Pattern ] ,
    • as shown in the diagram on-the-right below .

    

  And we do recognize that this [ Base Structural Pattern ] is in fact :

  • the [ Base Structural Pattern ] in { Row 1 , Column 1 } of the [ 24 Base Structural Patterns ] from Section III .

  

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Bringing-in the 2 matching sets of [ 8-colors sequence ] form the last Section :

• Let us now bring-in again the 2 matching [ sets-of-24 ] at the [ 8-colors sequences ] level , from the last Section :

  

• Let us now bring-in the [ TRUDEAU Colors-to-Numbers Conversion Scheme ] , as follows :

  Color #1	Color #2	Color #3	Color #4	Color #5	Color #6	Color #7	Color #8
  ***********	***********	***********	***********	***********	***********	***********	***********
  RED	MAGENTA	ORANGE	GREEN	BLUE	CYAN	YELLOW	PURPLE

  • and apply it to both diagrams immediately above .

• We then arrive at this set of 2 diagrams for the [ 8-numbers strings ] , below :

  

  • And we do recognize that both of these diagrams are exact replicas of the [ 24 Base Structural Patterns ] from Section III .

• This then is the irrevocable evidence we needed , to show that :
  • the [ 24 Base Structural Patterns ] from Section III is indeed the correct [ set-of-24 ] to use ,
    • to quantify the [ Structural Mapping relations ] ;
      • when the conversion to the [ 8-colors sequences ] is done via the [ Fu-Hei / ASCENDING combination ] .

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Using Computer-aided Analysis :

• Let us set up , at this point , the procedure for the computer-aided analysis here .

  First , we recap the course-of-action thus far in the current 3 Sections :

  • Step One :
    • We start-off with [ Configuration Mount Robson ] , and :
      • do the [ 2-notch rotations ] to arrive at the [ 24 QSM-Configurations --- Canadian Rockies Series ] .

  • Step Two :
    • We do the conversion to the [ 8-colors Sequences ] on the [ 24 QSM-Configurations ] ,
      • via the [ Fu-Hei / ASCENDING combination ] .

  • Step Three :
    • We derived [ Pattern RYAN ] ,
      • via applying the [ Fu-Hei / ASCENDING combination ] on [ Configuration Mount Robson ] .

    

  • Step Four :
    • We derived the [ TRUDEAU Colors-to-Numbers Conversion Scheme ] ,
      • via using a [ reverse procedure ] on the conversion to the [ 1-2-3-4-5-6-7-8 Base Structural Pattern ] :

      

  • Step Five :
    • We apply the [ TRUDEAU Colors-to-Numbers Conversion Scheme ] to the set-of-24 [ 8-colors sequences ]
      • to arrive at the set-of-24 [ 8-numbers strings ] .

  And this final set-of-24 [ 8-numbers strings ] in [ Step Five ] will always match the [ 24 Base Structural Patterns ] from Section III .

• Quite obviously ,
  • we can replace [ Configuration Mount Robson ] in [ Step One ] above

    with any other [ configuration ] from the [ Reduced Set of 5,040 configurations ] ,

    • and go thru analysis procedure above up-to [ Step Five ] .

  And in fact we were able to so on a computer and confirm that :

  • the [ 24 Base Structural Patterns ] in Section III is indeed the correct [ set-of 24 ] to use ,
    • to quantify the [ Structural Mapping relations ] ;
      • when the conversion to the [ 8-colors sequences ] is done via the [ Fu-Hei / ASCENDING combination ] .

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The Obvious Question :

• The obvious question to ask , at this point , is :
  • What would happen if we were to :
    • stick with the [ Fu-Hei Scheme of Fixed-Positions ] but vary the [ Read-Off Order ] .

    Would we then come up with different sets-of-24 [ 8-colors sequences ] and [ 8-numbers strings ] ,

    • spotting entirely different [ Structural Mapping relations ] .

• This is indeed an intriguing question ,
  • and we shall provide a more in-depth look at the subject matter in Part VII of this paper ,
    • when we look at the issue of [ Physical Symmetry vs. Logical Symmetry ] .

• But let us first take a quick look at the [ quasi sub-symmetric sets ] to be found within the set of [ 24 QSM-Configurations ] , next .

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go to the next section : Section XXIV - Physical [ Tri-Symmetric Sets ] within the [ 24 QSM-Configurations ]

go to the last section : Section XXII - Understanding Physical [ Quasi 24-Symmetry ] - Phase II

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

Original dated 2011-3-06