go to Brief Introduction & Summary below.

TABLE OF CONTENT | |
---|---|

Section 1 | Introduction, Observations, & Summary |

Section 2 | 'I-CHING' Basics |

Section 3 | Hexagrams as Life Situations |

Section 4 | Consultation with the Lords Above |

Section 5 | The { ICG Hexagram Placement Scheme } |

Section 6 | { Combinatorial Mathematics } in the 'I-CHING' |

Section 7 | The { Parity of '4' } in the 'I-CHING' & { Non-parity } |

Section 8 | Determinants, Magic Squares, & Multiplication Tables |

Section 9 | The { 'Tao' of the 'I' } & the { ICG Game } ( updated 2006-4-11 ) |

Section 10 | Concluding Remarks |

1st EPILOG ( dated 2005-2-23 ) | Thoughts on the Tetrahedra |

The 'I-CHING' is the ancient Chinese { Book of CHANGE } , dating back to more than 4,000 years ago.

Our key observations here are :

### CHANGE is the essence of TIME .

### CHANGE is the essence of DISTANCE / Physical Dimensions.

( See Section 1 for an analogy. )

The { ICG Approach } is a mathematical / combinatorics approach to the 'I-CHING ' :

- the { Parity-of-'4' } in a { 3-Dimensional Space } is exhibited by the 4 cross-diagonals of a cube :
- they are all equal in length , and
- they intersect one-another at the same angle .

( This arises from the { Trigram Placement Scheme according to WEN WANG } . See Section 2 & Section 5 )

- This { Parity-of-'4' } concept is carried thru onto the { ICG Hexagram Placement Scheme } for the 64 Hexagrams, in Section 5 , with :
- the { X-Axis } , { Y-Axis } , & { Z-Axis } all being { modulo 4 } based ,
so that continuity is achieved on an 'ad-infinitum' basis . ( 4 x 4 x 4 = 64 ) .

- the { X-Axis } , { Y-Axis } , & { Z-Axis } all being { modulo 4 } based ,
- Probability Calculations in Section 6 , arising from the traditional { Ceremony with the 50 sticks } in a { Consultation with the Lords above } , are also { modulo 4 } based, and this also brings us onto numbers of the order of { 1 / 2^64 } , very fine numbers indeed for more than 4,000 years ago.
Whether there is a hint here onto { C.H.A.O.S. } is beyond the author's current scope.

- The { Reverse } process , i.e. reading a Hexagram up-side-down , in Section 7 , then bring us onto the mechanics of { Non-parity } arising from a pure { Parity-of-'4' } , with :
- the Hexagrams on the { X-Z planes } at { Y = 0 modulo 4 } & { Y = 2 modulo 4 }
behaving markedly different from :

- the Hexagrams on the { X-Z planes } at { Y = 1 modulo 4 } & { Y = 3 modulo 4 } .

And further { Non-parity } refinements are also present on these { X-Z planes } .

- the Hexagrams on the { X-Z planes } at { Y = 0 modulo 4 } & { Y = 2 modulo 4 }
- Our final observations / proposals here are : ( Section 9 & Section 10 )
- { Structured CHANGE } are more likely to achieve the desired results .
- The mathematics of the 'I-CHING' may well be an alternative way to describe nature .

( Three Body Problem / Characteristics of Numbers / Matrix & Linear Algebra / 'I-CHING' )