Wave Sequences

An Introduction to Wave Sequences

Much of my research involves algebraic explorations of the Boolean lattice space and their cosmological interpretations. However, there are a number of other areas that are of interest because their contrast with some of the characteristics of lattice change combines with representing natural forms of transformation.

Boolean transitions through the lattice space essentially involve lines in a hexagram switching from yin to yang or from yang to yin; individual lines changing polarity. This is a simple quantitative energy transformation. There are many other ways in which yin and yang may interact. In the following pages I shall investigate how waves of yin and yang can move through each other in various patterns. The idea for this type of movement is implicit in some of the traditional ideas in the Yi (for example, Ascending has the idea of the two yang lines rising up from the base position).

Note that wave sequences are really the dynamic animation of rotation groups.

Defining Cyclic Wave Functions

The Boolean lattice is defined by a partial ordering relation that defines up and down. In contrast, wave sequences are defined by a function that defines next and previous.  The main function of interest is a simple cyclic transformation, but other functions are possible too.

Invariant Cyclic Waves

The hexagrams defining the basic polarization ( and ) are invariant under the wave function. Rotating a uniform energy makes no difference; this means that applying the wave function to these hexagrams produces no change. Invarient waves are a special case of coherent wave sequences.

Coherent Cyclic Wave Sequences

Coherent wave sequences, especially the linear variety, are closely related to Billy Culver's Polar Diffusion Lattice and a proper comparison of the two ideas will be explored at a later date. For the moment, note that the hexagrams in the wave sequences appear as elements in chains in Culver's lattice.

First a simple definition: a wave is coherent if the body of yang passing through the yin moves as a single block durings its passage. We shall consider coherent waves of different magnitudes:

• One Yang Line - this wave arises when the function is seeded with .
  
  
• Two Yang Lines - this wave arises when the function is seeded with .
  
  
• Three Yang Lines - this wave arises when the function is seeded with .
  
  
• Four Yang Lines - this wave arises when the function is seeded with .
  
  
• Five Yang Lines - this wave arises when the function is seeded with .

It is interesting that all coherent waves have a periodicity of 6.

The hexagrams in these waves compose the First Chorand Sphere, with the waves themselves making up the latitudinal parallels of the structure.

Dispersed Cyclic Wave Sequences

Whilst coherent waves are usefully grouped according to the number of yang lines in the wave, this is not the case with dispersed waves. Instead, they are better grouped according to their periodicity.

• Periodicity Two
  
  
• Periodicity Three
  
  
• Periodicity Six

Other Wave Sequences

Probably the most well known form of wave motion in the Yijing is formed by the seasonal sequence of hexagrams.  This is described here.