Hexagram Spectrums

Copyright © 2006 C. J. Lofting

Since the I Ching is a 'whole' and the hexagrams are derived from the 'cutting' of that whole into layers of yin/yang giving the resulting order of hexagrams (the 'binary' sequence) so the hexagrams form a spectrum. This is a property of part/whole dynamics and is repeated WITHIN each hexagram in that each is considered as a whole and we can extract its harmonics. But in what form are these hexagram harmonics? The I Ching is a form of language in that the categories in it describe 'all there is' from a universals perspective and local context then grounds and colours the perspective. Being a language, and being derived from self-referencing of yin/yang so it can describe anything and that includes itself. Thus the harmonics of a hexagram are described by analogy to members of the set of all hexagrams.

The manner in which we extract the spectrum of a hexagram is through using a method that is used in the brain for extracting parts from a whole. This is described elsewhere as the XOR or Exclusive OR method. With this method we can extract from any hexagram its unique, full, spectrum in the form of analogies to each of the 64 hexagrams where the harmonic is identified as the X-ness of a hexagram where X-ness means the characteristics of a particular hexagram, X, expressed THROUGH some other serving as context. For example, hexagram 27 has a character that focuses on infrastructure, a skeletal form ready for filling. It comes with a warning about the need to be discerning regarding what we take-in, what we put into our 'mouth'.

If we take hexagram 27 and XOR it with hexagram 01 we get hexagram 28. Hexagram 28 represents excess, too full, too much 'yang' where 28 is the source of analogy in describing the 27-ness of hexagram 01. We can do this for ALL hexagrams and so derive the harmonics of each hexagram. These are summarised in this page where we list the X-ness of a hexagram Y and with that the hexagram Z that describes by analogy the expression of that harmonic X in/through Y. The following table shows the method:

The XOR operator works where, given x and y as line values (0 = yin, 1 = yang) we create a third representation based on rules derived from this 'truth' table:

X	Y	X XOR Y
0	0	0
0	1	1
1	0	1
1	1	0

Thus, XOR-ing hexagram 27 with hexagram 01 gives us hexagram 28:

Hexagram 27	Hexagram 01	27 XOR 01 = Result - Hexagram 28
(line 6) 1	1	0
(line 5) 0	1	1
(line 4) 0	1	1
(line 3) 0	1	1
(line 2) 0	1	1
(line 1) 1	1	0

Put ANY hexagram in the first column and the XOR process will describe, by reference to some other hexagram, the expression of that first hexagram 'through' the middle hexagram - and so an expression of a part. - and so the 27-ness of 01 is described by analogy to the generic qualities of hexagram 28. This is NOT a property of the I Ching, it is a property of the methodology used to create the I Ching, self-referencing, aka recursion.

The method allows us to extract general descriptions of a hexagram using the I Ching itself where the ability to do this is due to the self-referencing that creates the I Ching. What is of interest here is that the harmonics are not just properties, they also include methods where the manner in which a hexagram ideally begins and ceases is described in the spectrum. The issue here is that this method applied to the category of a hexagram but not its singular form. In other words the traits of a member of the species will favour those with that trait in focusing on a goal of some sort that is associated with the trait, not the individual.

Thus the description covers the nature of all events described by hexagram X NOT necessarily the singular event of an individual since the trait spans the life time of all of the individuals that have it and so can the goal of that trait (the individual can die, be distracted etc and so never achieve the goal, but others like that individual, and so with the same traits WILL achieve the trait goal (Which, BTW, can span decades)). For more on this see the section on history in the paper "Language of the Vague" (pdf file). Note there are also some interesting concepts that come to mind when we realise that the same methodology is used in the creation of RNA and DNA codons. In other words the sequences we 'see' contain a lot more than we currently have imagined.

Summary of the Spectrums

These are in the form of links to spectrum-focused pages, one for each hexagram. These will be 'refined' as the work continues. Just click on the number to get the spectrum page. On the spectrum page the order of the harmonics is listed using the traditional I Ching numbers. This is followed by a cross reference of the particular hexagram and its expression through all of the others.