In the I Ching there are traditionally 4096 states reflecting 212 static forms (yes/no) or 46
dynamic forms (yes/no and changing yes/no). Thus in 4096 states there are only 64 'perfect' forms when viewed from
the 6 changing line perspective, thus an 'unchanging' hexagram is rare, 64 in 4096 = 1 in 64.
In each hexagram there are 63 possible changing states, one static state (no line changes) and so a lot of room for commentary on change! The traditional perspective focused on the six dichotomies (the exponential in 46) as individual units and commented on those lines changing rather than comment on all possible combinations (see my example page that covers the full order in stepping 'up' a hexagram)
The six lines of a hexagram are, in themselves, foundational, reflecting changes in levels and so act as snapshots of distinct changes that reflect both change as transformation but also of transcendence - see below for comments on transformation and transcendence - the lines as such reflect 'walking through' a hexagram using recursion where each 'level' (and so line) increases the range of possible qualities by a power of 2.
Thus the hexagram is the 'whole', line 1 changes give us two possibles. Line 2 changes give us four, line 3 eight etc etc you can build a tree-diagram of this development that will end-up with a sequence of 64 hexagrams - the changing line patterns for the hexagram under analysis. Note what this process naturally does, it reflects the movement from generic qualities (general) to high detail (the particular), a movement traditionally commented upon as movement from 'worker' to 'sage', from 'raw' to 'refined'.
As you move 'up' a hexagram so you move towards a full set of 64 hexagrams reflected in the WHOLE of the hexagram under consideration where the ordering etc reflects sources of analogies to describe expressions of the hexagram under consideration in different contexts. At the bottom there are only two hexagrams applicable to the set, they are 'raw', 'undifferentiated', 'approximations'. As you step through the process of development so all hexagrams emerge but in a specific order reflecting the overall differences in the hexagram under consideration, the hexagram's 'code' if you like, its DNA strand that determines the range of expressions etc., that make the hexagram 'unique'.
When we move to the level of dodecagrams, 212, which is what is compressed into the changing lines of 46, we deal with all possible combinations of change where each combination is a distinct, commentable, expression, this is a high-precision perspective. IOW the 'traditional' I Ching needs filling-out in the context of line change text where multiples apply. (Harmen and LiSe are working on an ancient text that seems to cover comments on the 4096. My own focus is on the patterns behind expressions and so a little more abstract and long term in development (for specific application to the IC see the still-developing page ))
The ICPlus material notes that, given the dodecagram focus, so a hexagram with changing lines in fact reflects a unique form, a static form, where the change in a hexagram is an expression of a quality 'inbetween' what the hexagram is and what it is interpreted as becoming. By this I mean that, for example, if hexagram 01 has changing lines 2 and 4 then this does not necessarily mean hexagram 01 is changing into hexagram 37 but more so is 'half way there' and that point reflects hexagram 01 'shape shifting' but not 'changing'. It is like you putting on very different clothes such that people see the clothes as the expression but at the core is still you. If I move to the dodecagram level I will find a specific dodecagram, no changing lines etc, that will reflect the meaning of '01 with 2 and 4 changing' and it will NOT be the dodecagram that reflects hexagram 37.
Note that, in recursion of yin/yang each level of symbol derivation reflects a PARTS perspective to the previous level as a WHOLE. Thus the static dodecagrams are the parts, more detail, of the WHOLES that are the changing hexagrams. In turn the static hexagrams are the PARTS, more detail, of the WHOLES that are the changing trigrams. In turn the static trigrams are the PARTS, more detail, of the WHOLE that is T'ai Chi. In principle we could make the dodecagrams 'dynamic', giving them changing lines, and so derive all of their parts, but that would give us over 16+million states to deal with! No need, we can learn 4096 states and that is enough for 'day to day' activity!
In recursion each level of analysis gives us finer details of the WHOLE that is T'ai Chi but we also layer our meanings, we reduce chunk size to manage things better as we learn - we instinctively impose a hierarchy of part-whole relationships across each level. In engineering a ratio of 2:1 in context-to-text reflects a good operational relationship, it is like all of the parts that are 'you', all parts working semi-autonomously but also as a distributed system, summed to make 'you'.
In the tradition of yin/yang etc so the mentioned 2:1 ratio is reflected in the notion of T'ai Chi (the undifferentiate whole) breaking down into its parts - yin and yang. As long as you can see yin/yang you are NOT explicitly seeing the WHOLE - which is what consciousness has to deal with in that our consciousness-nature is parts oriented and so cannot explicitly see the species-nature instincts, the ultimate WHOLES used to interact with reality. The form of these instincts is always IMPLIED through the use of words etc and as a consequence of experiencing context pushing one's buttons - and so the "Why did I do/say THAT!!??" as your consciousness tries to understand what is going on when you respond instinctively/intuitively as a species member to a stimulus.
These subtle differences in issues of change reflect what appears to be fundamentals in our neurocognitive processes, we can (a) transform and so 'shape shift' where our core is maintained but our exterior changes depending on context or (b) we transcend, which means our core changes - we do move from 01 to 37 rather than express qualities of 37 over a core of 01. IOW we require modes of interpretation that cover both transforming and transcending.
The (a) reflects phase transitions, it is like a cup of water in solid form, ice, that is heated - it becomes liquid and then steam but only the expression has changed, it is still 'water'. This is biased to being 'mechanistic' in that reversal is allowed, I can drop back to the 'ground' state. (this gets into concepts of scalars, magnitudes, cardinal numbers)
The (b) reflects true change as raw materials (flour, sugar etc) into a cake, where once produced it cannot be reversed. This is explicitly thermodynamic, no reversals. (this gets into concepts of vectors and ordinality. Combine (a) and (b) moves us into the realm of tensors, complex matrices dynamics, the 'arrow of time' etc etc)
The main differences are in the modes of interpretation where, moving from the bottom line of a hexagram to the top line reflects a passage through 64 possible states. The QUALITY of the states, focused on the context of 'refinement' and so 'worker' (base line) to 'sage' (top line), adds nuances to interpretations of change, BUT we can also consider the hexagram as a WHOLE that shape-shifts and so complex patterns of line changes other than the single-line change focus we see in the traditional IC material.
There is more to all of this in that the comments on a changing line deal with an anomoly to the unchanging form, the idealist form. Thus, for example, an unchanging hexagram 01 reflects an ideal form of 'pure' yangness. Changing line 1 reflects (a) a transformation process of an aspect of hex 01 being brought-out, the issues of 'different clothes, same core', or (b) a transcendence process of hex 01 changing into 44.
The (a) format reflects an exaggeration of hex 01 where aspects of 44 are reflected in the interpretation, the transformation is heading in the direction of expressions we categorise as '44'. Thus for hex 01 the line comment is a warning about being seduced by the yang power and emerging too early in development. The line comment as such is not about the change TO 44 but about the 'shape-shifting' development of hex 01 described by analogy to 44.
Another example, in hexagram 23 (mountain over earth) the second line change is related to hexagram 04 (mountain over water)
23.2 - "To avoid any conflict, agreement is made on those parts to be removed."
Hexagram 04 covers containment (water) within which is applied a sense of discernment (mountain in top position) and the generic properties of 04 (to put on a mask, a social 'filter', education-as-socialisation) are reflected in this line comment of 23.2 where what elements of the 'bed', the metaphor used in hexagram 23 to reflect our belief systems, what we 'rest' upon, are to be removed is discussed, there is a focus on quality control and the avoidance of 'something' - IOW we exclude, keep out, something - the conflict (which is what the water trigram focuses upon, containment doubled gives us control) and the discernment reflect the keeping of a quality part of the original mask that was our belief systems prior to our 'pruning' (which is what 23 is about in the context of 'stripping').
Another example, in hexagram 49 (lake over fire) the third line change is related to hexagram 17 (lake over thunder)
"Exposed to danger one faces adverse testing times. Only when revolutionary words have three times been encountered are things in accord." [Put in too much energy, immature start. Let the word get around first]."
Hexagram 17 deals with establishing a belief system, something to follow, be it a person or an idea. Hex 49 deals with revolutions/revelations and that is the context. The changing line three elicits an exaggeration and so a warning about being too hasty in asserting the 'new' belief as we do in revolutions, we need to let the word get around, let it sink in, give it time to germinate and sprout (the base trigram in this change is now thunder and so a focus on the 'new', the 'sudden' etc etc - each 'change' reflects an exaggeration of some aspect of the whole that is 49 where that aspect is describable through analogy to the hexagram that would emerge if the change was completed together with the generic properties of the associated trigrams)
Given these patterns, we can derive composite line change comments where, for example, changing lines 1, 2, and 5 of hexagram 01 reflect an exaggeration of aspects of 01 that make it look like 56 (fire over mountain). Since change is taking us AWAY from the hexagram so an exaggerations interpretation comes as a warning, we are 'drifting' away from where we should be, so some form of comment is applicable re loyalty (56) being an exaggerated format of singlemindedness (01). perhaps being TOO self-involved, to loyal to oneself and so open to delusions perhaps?
On the other hand, a full change reflects a 'transcendence' and so a core change, perhaps from the rigid singlemindedness in faith in oneself to becoming loyal to another/others?
Change as exaggeration is usually a no-no in that you are becoming unbalanced, distorting things. This can be useful short term but long term it is usually not a good idea, the focus in transformation is on adapting to a context not changing context. Thus these sorts of comments need to give warnings but be open to allowing 'small' exaggerations ;-) For example, when the first chill of winter comes (in autumn) we 'instinctively' start to grow winter coats. This is 'instinctive', driven by the context and usually not noticed. When spring comes we 'instinctively' start to molt. These are short-term, cyclic, 'reversible' processes that allow flexibility in adapting to the context and so 'local' exaggerations where 'normal services' are resummed as soon as possible, we drop-back to a 'ground state' to conserve energy overall. As such they are 'exaggerations' in adapting to extremes in temperature etc., but exaggerations that do not influence our generic core sense of self, IOW these exaggerations are actions of 'shape shifting'.
Change as transcendence is usually a plus, in that a static or 'threatening' context needs to be escaped. That said, the warning is in the fact that sometimes we wish to escape by stepping backwards, we back away saying 'anything but THIS!!' and that can make us step off the edge of cliff if not careful and so into a context that is 'worse' that what we left ;-) Thus transcendences are best 'seeked' in looking forwards (gets into the 'grass is greener' concept as well ;-)). Thus one benefits from finding some place to go prior to departure, delay the gratification a little. That said, there can be times when immediate gratification is required! Thats where learning the I Ching can help in intuitively selecting a 'good' place to back-in to (e.g. if Northern hemisphere and its autumn then back-away 'south', going north means moving into the cold!)
Change-by-Transcendence being irreversible means we need to be wary of these forms of change, e.g. I dont want to invent something that ensures I keep my winter coat on 'forever'! - There is no going back here, there is always a loss of innocense but also a movement to being possibly 'wiser' , or possibly more 'corrupted' ;-) There is the ability to 'start again', be 'born again' - common themes in decribing moments of transcendence.
I think you can see from these how we need to be careful about the questions we pose in using the I Ching to flesh-out properties and methods of the situation, and I think you can see how some of the existing IC material needs 'refinement' ;-) - or perhaps it is just our methods of interpretation that need refinement where we can flesh-out more from what is currently there, increased power of resolution.
Getting back to the change of line 1, hexagram 01, given the line comment about the CHANGE of line 1 (where this change of 1.1 is in fact a static dodecagram of the form 101111111111) we can work by implication to identify the influence or the identity of the characteristics of line 1 unchanging. How? by applying the opposite of 44, 24. IOW we can interpret the unchanging base line of 01 as having the meaning of the return of yang. This can give us a sequence through the hexagram of its expressions from base to top where the expressions are in the form of analogies to other hexagrams (since the I Ching describes 'all there is' so all descriptions are in the form of analogies to hexagrams etc) and the resulting sequence reflects the properties of the archetype that is 01, the nature of its unchanging lines.
Thus, a 'changing line' can also reflect not a change per se but an exaggeration of some form that shape-shifts the expression of the hexagram but not necessarily changes things, just distorts things. This act of distortion moves us into topological concepts where the WHOLE is distorted, never 'cut' such that any event, any exaggeration, can be expressed as an ordering of all of the hexagrams within the whole into a string from 'best fit' to 'worst fit'.
This ordering means, for example, that if given a hexagram that is the best fit so the worst fit will be its opposite. We can look-up a table of these relationships and derive the probable order of all of the other hexagrams, their relationship to the situation (see the still-developing pair matrices page )
Finally, in the ICPlus material there is a focus on the CAUSE of change in that, given the IC describes 'all there is', so all cause-effect relationships have to be describable using hexagrams. There is a pattern in the I Ching, brought-out in the study of the binary sequence, that shows meaning derivable from swapping the trigrams of a hexagram and the possible indication of this meaning as reflected in the nature of the context that changes a hexagram into another.
An example of this text-context dynamic: ANY hexagram changing into hexagram 44 is being influenced by a context reflecting the characteristics of hexagram 09 - the hexagram we get if we swap the trigrams of 44. This process reflects the PUSH nature of context on instincts, where generically it does not matter WHO/WHAT in particular is being pushed in that the push is at the species-member level where all instincts are the 'same' such that a push of 09 sets off the instinct leading into 44; LOCAL differences can influence this expression in particular, but in general the process is 'stimulus-response'. Thus, if I am in a context of 09, a focus on trying to be noticed by making small gains upon which to stand upon and so influence, that context will 'push' me to become focused on persuasion/seduction (characteristics of 44) to achieve my goals. This also works in reverse where a context of persuasion/seduction can force me to react by focusing on small 'conquests' to build-up a reputation as seducer/persuader and so become noticed and influencial!
My work in five-phase has led to my questioning the value of this from an objective perspective, in that the swapping method given can be 'skewed' to fit and so a subjective focus but not necessarily an objective focus. What I mean is that the context-text pairings stemming from swapping trigrams reflect 'best fit' conditions such that a context of hexagram 09 does not necessarily HAVE to force change into 44 (we can always fight the drive! ;-)). As you can see there is a lot of work to be done in fleshing all of this out in the context of basic meaning derivation, never mind just the IC!
The further consideration is to the properties that come from ordering hexagrams through
recursion of a 'basic' concept. Thus the binary sequence, that derived from recursuion of yin/yang and as such
the recursion of the concepts of integration/differentiation, will elicit PAIRS of hexagrams with each pair telling
us 'something' about relationships. The traditional sequence also reflects this pairing
and so its roots in recursion where the basic concept for the traditional sequence appears to be the differences
between properties of hexagram 01 (purity, individual, eternal) and hexagram 64 (mixed (purity of mixing), group,
When we form the binary sequence of the I Ching into a matrix out pops properties of matrices and especially of one particular type - we are dealing with isomorphism here - see the section at the end of the pairmatrix page titled "A Mathematics Aside".
Of note is the relationship of trigram swapping to complex number processes of a complex number and its conjugate. IOW to get a 'real' number I have to use the complex number and its conjugate. In the IC 'swapping' process this is reflected in trigram swapping in a hexagram - see the form of the matrix of the binary order of hexagrams. This is vague, abstract, stuff at the moment but I think worthy of development in that my work focuses on the derivation of meaning in general and so the isomorphisms across specialisations like the I Ching and Mathematics (also see this page for links to randomness through the Sierpinski gasket etc etc)