Scales and Correlative Thought

Two excerpts from The Book of Changes: Yijing, Word by Word

Copyright © 2009, Bradford Hatcher, free PDF download at 

Introduction to Scales

Excerpt from The Book of Changes: Yijing, Word by Word, Volume 1, pp. 444-449

    Scales, in the sense of the word used in music, may have been a part of our

cultural thinking nearly as long as numbers. Warren S. McCulloch, who pioneered

work in neural net theory and learned that up to six “things” can be perceived by

these nets without language and counting, was fond of the question: “What is a

number, that a man may know it, and a man, that he may know a number?” The

answer for several millenia was just “big magic,” a formulation which has tended

to disappoint some of us. Around the world, as far as our tribes had spread, there

came a time within each group when numbers were given symbols or names. When

they were, for each new number N, there were suddenly not only N things to

count: there was also now a universe which could be divided into N kinds of

things. This problem was usually taken up first by the local wizard or shaman.

    Any continuous spectrum, such as that of visible light, sound vibration or

the human experience, can be divided by any whole integer, resulting in a scale.

This does not mean that this division will make enough sense to hold human

attention - there needs also to be a resonance (called ying in the Yi) in the human

psyche, as well as enough simplicity for the scale to be remembered. When there is,

the scale survives in our lore. For example, in the light spectrum, certain divisions

“feel” more natural. The scale of two divides light into warm and cool colors. Two

scales of three may be used: the additive or light primaries (red, yellow and blue)

and the subtractive (magenta, cyan and yellow). Two scales of four are also

apparent: the printer's black, magenta, cyan and yellow and the human eyeball's

black (rods) and red, green and blue (cones). But six, not five, is the next most

logical division. Attempts to assign colors to the Wu Xing or Five Agents had to

omit the color of the sky. With sound, the spectrum “divides itself” into specific

ranges by laws of physics, at the doublings of vibration frequencies in physical

objects such as taut strings. The further divisions within these ranges may seem

more arbitrary. That these ranges are called octaves reflects only one of these: the

pentatonic and the chromatic scales are two of many other options. But it is a

resonance within our own aesthetic sensitivities, and thus an accord with the

neural substratum and physical structures of these senses, which gives a particular

scale longevity in our cultures and languages.

    Scales which survive do so when they both cover a spectrum well enough

to describe a full class or category of experience and resonate well enough within

our beings that we may use them to communicate these experiences and so create

mutual understanding. Seeing scales in terms of their longevity in human culture

may tend to prejudice us against the newer but ultimately viable ones, but the

uphill struggle to acceptance may also be seen as a good thing, as it is in science.

The human mind, particularly when it is seeking the security of belief, can extract

significance from nearly any white noise or set of random events. Many of these

can survive for quite a while though, as with the belief that there is meaning in the

random assignment of decimal calendar dates to our days (numerology), or in the

random sequencing of the letters of the various alphabets (gematria). A criterion to

judge the practical worth of this significance, such as its utility or effectiveness in

communication, should be part of our mental apparatus here. The gods of ancient

Greece, who each had their well-defined dominions over the various aspects of

human existence, survived not because they were immortal, but because of the

unusual clarity of this domain definition and its resonance with the mortals who

kept them alive. The relevant spectrum here was the broader range of human

experience. The discipline of psychology attempts to accomplish a similar scaling

with its terminologies, to cover the ranges of human behaviors, emotions, defense

mechanisms, intelligences and so forth. But in its pretensions about being the

science of behavior, psychology often forgets that it, too, is behavior, and perhaps

ultimately, a languaging behavior, not so unlike the development of the Yijing.

    The Yijing, like its counterparts in the west, is founded upon a handful of

these time-tested scales and upon their resonance in the human psyche. The

fourteen smaller diagrams, which both coexist with and constitute the Yijing’s

sixty-four Hexagrams or Ba Gua, are rooted in the three Scales of Two, Four and

Eight. Before charting the scope of the meanings of these fourteen, a short

discussion of these scales is in order; of other scales which are buried more deeply

in the body of Yi lore; and of a few of the many scales which were left out.

    The Scale of One, or the pantheistic Unity of the mystics, received its fullest

development later, in the Song dynasty, in the Yijing-based, metaphysical

speculations of Shao Yong, Zhou Dunyi, Cheng Yi and Zhu Xi. Like the Qabalists,

with their En, No-thing, En Sof, The Limitless, and En Sof Or, The Limitless Light,

they used three names: Wu, No-thing, Wu Ji, The Ultimate No-thing, and Tai Ji,

The Supreme Ultimate. The third of these, which back in the Han was called Tai Yi,

The Supreme Unity, was expressed in the familiar Taiji Tu, the enduring diagram

made famous by Zhou Dunyi, which depicts Yin and Yang as complements within

a circle, or as belonging together in a greater whole.

    The Scale of Two, polarity or dichotomy, takes many forms, and it is very

important to note that not all possible pairs fit into the Rou and Gang (Yin and

Yang) system of classification. The Yijing’s Scale of Two is called either Er Yao,

The Two Lines, Er Chi, The Two Essences, or Liang Yi, The Two Powers. This

particular set of pairs is concerned with matched complements and not with paired

antagonists or all-or-none dichotomies. For instance, later in this chapter, in

excerpting glosses from the fifth and sixth Wings (the Xi Ci Zhuan) to illustrate

how the these authors thought of Rou and Gang, I had to be careful not to mislead

by including such pairs as Unfortunate and Fortunate (Xiong and Ji), Wrong and

Right (Shi and De) and Death and Life (Si and Sheng). While it is obvious that

that these pairs belong together in dyadic relationships, they do not bear the same

kind of relationship to each other that Rou and Gang do. We do not want to

encourage overly simplistic thinking here: we humans have suffered much over the

centuries from mistaken dualisms (man is to woman as superior is to inferior; us is to

them as good is to evil, caucasian is to negro as light is to darkness). The dualisms

which occur in the Yi are not concerned with “moral” judgments, even when they

contrast superior with inferior or strong with weak. The complementary Scale of

Two also plays an important role in the structure of the Hexagrams or Gua. See

Dimensions, under Ban Xiang, the Half Images (Zhen and Hui Ba Gua). There is

also more discussion of dichotomy in Dimensions, under Gua Ming, the Hexagram


    The Scale of Three, as found in most cultures, will tend to take two forms,

which may be called Synchronic or Spatial and Diachronic or Temporal. The first,

or spatial, places an equally important mediating or equilibrating force between

two opposites. In the body of Yi commentary, and Chinese culture generally, these

are the San Cai, The Three Powers: of Heaven (Tian), Humanity (Ren) and Earth

(Di). In the structure of the Hexagrams or Gua, these are the San Wei, the Three

Places or Dignities. See Dimensions, under San Cai. The second or temporal kind

of triplicity places the present (Jin) between past (Wang) and future (Lai), or more

accurately, some way of looking at the present between ways of looking at past

and future. This kind of triplicity, which of course concerns Change, is at the heart

of the way the Book of Changes is used, and is discussed implicitly in Dimensions,

under Gua Bian, or the Hexagram Changes. The temporal triplicity also appears in

the Zhouyi text at 18.0 and 57.5 (Zhi Gua 18.0), where it concerns the getting of

fresh perspectives on time and change. Finally, the positions of the three lines in

the Ba Gua, especially as conceived of as a family, appear to have meanings

associated with a temporal triplicity. The bottom line might be seen as Beginning

(Zhen simply goes, while Xun is ready to go, given the right opportunity). The

middle line could be While Going (Kan concentrates and integrates, while Li

appreciates and differentiates). The top line could be After Going (Gen simply

stops, while Dui will have some satisfaction first).

    The Scale of Four, or Quadruplicity, is nearly universal in human cultures.

This is best known in the west as the four Greek elements: fire, water, air and earth;

in the realm of human experience as father, mother, son and daughter; in our need

to grow food as summer, winter, spring and autumn; and in our need to remain

oriented as south, north, east and west. As cultures began to communicate, a

lasting cross-fertilization began, with long lists of attributes accruing to these four

groups of meanings. But often, due to cultural differences and to differing sets of

shared associations, there is not a similar universality in what goes into each of the

four categories. As such, there is no perfect system of translation between all of

these culturally-based systems. Often there is at least one set which can be truly

annoying. The most vexing of these are pointed out in the pages of the Si Xiang,

the four two-line figures, by underlined notes. The word si, four, does not appear in

the Zhouyi text, but fang, the word used for direction, also means square. The

Scale of Four was very much alive at the time (it is used in the Shujing) and it is

implied here in the Zhouyi wherever time and season (shi) are mentioned.

    The Scale of Five takes two typical forms: the Pentagram (with five points

equidistant, also called the Seal of Solomon) and the Mandala (the four directions

plus a center). In the west, the former is more common: a “fifth essence,” or quint-

essence, as spirit or aether, was added to the four elements to make the pentagram

(the star pointed upward for purposes of transcendence, or downward for the

purposes of manifestation). The mandala is more common in Asian cultures. This

uses the terms of the Wu Xing, The Five Movements or States of Change: Fire

(Huo), Water (Shui), Metal (Jin), Wood (Mu) and Earth (Tu). Earth takes the

central position in the mandala when this form is used. While the Wu Xing formula

is very ancient, dating back at least to the Early Zhou dynasty, it really has no

home base in the Yijing. Many of the Han dynasty scholars tried to integrate the

two. In the Song, integrations appeared in diagrams which look strikingly like the

Qabalah’s much later “Tree of Life” diagram, but this is too far down history’s

road. More relevant to our purposes here is that the first four of the Wu Xing (less

Earth) were also used as names for the Si Xiang or The Four Emblems. This fact

should be remembered when using these as names for the four. I have also made

this omission of the central element in the Wai Guang segment at the Si Xiang, or

Four Emblems, when drawing comparisons with the Indian Tattwas, the Wisdoms

of Tibet and the Buddhist Khandas.

    Only one Scale of Six is developed in the Yi, found in the structure of the

Hexagrams or Gua. Each of the six line places (Yao Wei) is assigned a number of

meanings, loci within “the time,” and characteristics (Yao De) when occupied by

the different kinds of lines. These are discussed in more detail in Dimensions. In the

west, Scales of Six are depicted in the more familiar form of the Hexagram (adopted

fairly recently by the Jews and there called the Star or Shield of David, Magen

David) with two sets of three shown interlaced and interrelated. But the similarities

between this and the Gua structure end here. In the Hermetic traditions, the six

places are assigned grammatical subjects. In the Yi, the six places take the role of

prepositions, much like the positions in a Tarot spread or the Houses in Astrology.

A nearly forgotten ancient Chinese Scale of Six is found in the Shujing as the Six

Treasuries or Storehouses (Liu Fu): constituted by Grain or Seed, (Gu) plus the

more familiar Fire, Water, Metal, Wood and Earth. This could have been a precursor

to the Wu Xing before Gu was dropped out. This is an interesting scale to ponder:

these six, between them, have just about everything necessary to build an ancient

civilization. Without grain for textiles, let alone agriculture, the five would not be


    Scales of Seven and Nine do not appear in the Yi, although they coexisted

in Chinese culture. The numbers seven and nine (qi and jiu) occur here in both

numerical and metaphorical uses. Seven implies a cycle of return (perhaps from

seven days for a week or a phase of the Moon), and nine, an exhaustive process

covering a range of possibilities (such as climbing up the nine hills at 51.2).

    The Scale of Eight is represented only by the Ba Gua, the eight three-line

diagrams. Despite the assertions made in the legendary history of the Yi that the Ba

Gua came down from ancient times, to be later combined into the sixty-four Gua,

there is as yet no strong evidence of this either in the early literature or among the

Shang dynasty Oracle or Dragon Bones. There is only the assumption that an

elemental concept (Ba Gua) must precede a compound one (Gua). But, as the text

of the Da Xiang, or Overall Image, makes delightfully clear, there is no better way

to decipher the meaning of a Hexagram text than by analyzing the relationship

between its two constituent Ba Gua. It appears unlikely that the sets of meanings

and connotations of the Ba Gua were very fully developed at the time the Zhouyi

was written. Elemental images such as water, wood and shock will appear in the

text where they might be expected. There are also certain preponderances of ideas

which occur with statistical significance in the Chong Gua, those Hexagrams

composed of three-line figures doubled (e.g. words for seems or likeness in Gua

30). Because there is neither an external reference nor an explicit internal reference

to the Ba Gua in the Zhouyi, the modernists insist that they did not exist yet. This

is another fallacy - a lot of elements and dimensions are never explicitly mentioned.

And it completely ignores another statistically significant phenomenon: there

exists a very intriguing plethora of Chinese reiteratives in the Chong Gua. These

are doubled words such as xi xi, e e, su su, suo suo and jue jue in Gua 51. There is

also the phrase Xi Kan, repeated crisis, as the Gua Ming for Gua 29. (William

deFancourt also develops this line of thinking in his "Some Thoughts on the Eight

Trigrams," in Oracle 1.4). There will be more be said on other aspects of this subject

under History.

    The Scales of Ten, Twelve, Sixteen and Forty, as I have used them in the

Wai Guang segments throughout, do not occur as such in the Yijing. These are,

however, drawn along “natural” lines, or “grain,” which occur within the Yijing’s

inherent geometry and the attributes of its elements. The first clue that this might

be a meaningful exercise came when I grafted Crowley’s assignment of sixteen of

the Gua to the sixteen Court Cards of the Tarot onto the Xian Tian arrangement of

the Gua and saw the bilaterally symmetrical pattern. Crowley also began to make

the connections between the Ba Gua, the Qabalah’s Sepiroth and Astrology’s

Planets. But he never saw the system as complete as it is presented here. See

Dimensions, Figures 31 through 34, and a few of the Index Keys at the end of the


    The Scale of Ten holds an important place in Chinese culture, in the form of

the Shi Gan Tian, or The Ten Celestial Stems, but this is not developed in the Yi.

Also, an ancient ten-day week is mentioned in the Zhouyi at 55.1.

    The Scale of Twelve, in the form of the Shi Er Di Zhi, or The Twelve Earthly

Branches, appears in an interesting reference in the Zhouyi (at 19.0) to what are

known as The Sovereign Gua of the Twelve Moons, hinting that the assignments

of twelve of the Gua to something at least like the Twelve Branches had already

been made by the end of the Early Zhou. This scale is also discussed and graphed

in the Dimensions chapter.

    The Scale of Sixteen appears in two forms, both of which are embedded

within the structures of the Hexagram or Gua. The first is in the occurrence of the

Trigrams or Ba Gua in either the lower (Zhen Gua) or the upper (Hui Gua) places,

where they are interpreted differently: the first as a convergent or subjective force

or sense within, and the latter as a divergent or objective force or sense without.

See Dimensions, under Ban Gua, The Half Images, and the segment on Zhen and

Hui Gua in the text for each of the Trigrams or Ba Gua below. The second is in the

function of sixteen of the Hexagrams or Gua as Nuclear Hexagrams (Hu Gua), see

Dimensions, under Hu Gua.

    Two Scales of Twenty-Eight appear. The first is in the form of the Qian Gua

or Inverse pairs of the diagrams. See Dimensions, under Qian Gua and Figure 4.

The second is the set of Jiao Gua or Reverse pairs, in which the Trigrams or Ba

Gua switch places. The eight Hexagrams or Gua formed by doubled Trigrams (the

Chong Gua) are left out. See Dimensions under Jiao Gua and Figure 6. Twentyeight

also occurs in Chinese astrology, in the Twenty-eight Lunar Mansions,

which was added to the Yijing lore during the Han dynasty.

    Two Scales of Thirty-Two also show up in these paired Gua dimensions.

The first is the thirty-two Gua pairs which form the meaningful part of the Hou

Tian (Later Heaven) or Wen Wang (King Wen) Sequence, the chapter numbers

most familiar to readers. These are the twenty-eight Qian Gua or Inverse pairs

above, plus the four opposite pairs which are symmetrical and so have no inverse.

See Dimensions, under Gua Xu and Figures 3 and 27. The second scale is that of

the thirty-two Pang Tong Gua pairs, the Opposites. See Dimensions, under Pang

Tong Gua and Figure 5.

Correlative Thought

Excerpt from The Book of Changes: Yijing, Word by Word, Volume 2, pp. 4-7

    There are a number of ways to view the role of superstructure in analyzing the Yijing.

Joseph Needham, in Science and Civilization in China, Vol. 2, summarized early thought

about what he called correlative thinking (at p. 331):

    A number of modern students, H. Wilhelm, Eberhard, Jablonski, and above all Granet,

have named the kind of thinking with which we have here to do ‘coordinative thinking’ or

‘associative thinking.’ This intuitive-associative system has its own causality and its own

logic. It is ... a characteristic thought form of its own. H. Wilhelm contrasts it with the

‘subordinative’ thinking of European science, which laid such emphasis on external

causation. In coordinative thinking, conceptions are not subsumed under one another, but

placed side by side in a pattern, and things influence one another not by acts of mechanical

causation, but by a kind of ‘inductance’ ... . The key word in Chinese thought is Order and

above all Pattern (and, if I may whisper it for the first time, Organism). The symbolic

correlations or correspondences all formed part of one colossal pattern. Things behaved in

particular ways not necessarily because of prior actions or impulsions of other things, but

because their position in the ever-moving cyclical universe was such that they were endowed

with intrinsic natures which made that behavior inevitable for them. If they did not behave in

those particular ways they would lose their relational positions in the whole (which made

them what they were), and turn into something other than themselves. They were thus parts

in existential dependence upon the whole world-organism. And they reacted upon one

another not so much by mechanical impulsion or causation as by a kind of mysterious

resonance. [pp. 280-281]

    The more abstract the explanations became the more the system as a whole assumed

the character of a repository of concepts, to which all concrete phenomena in Nature could

be referred. [p. 310]

    [Citing Eitel]: There is underlying these diagrams a recognition of the truth that things

are groups of relations ... . Causation is here represented as imminent change ... in the

activity of which divergence and direction are inherent. [p. 325]

    [With regard to scientific thought]: the elaborated symbolic system of the Book of

Changes was almost from the start a mischievous handicap. It tempted those who were

interested in Nature to rest in explanations which were no explanations at all. The Book of

Changes was a system for pigeon-holing novelty and then doing nothing more about it. Its

universal system of symbolism constituted a stupendous filing system. It led to a stylization

of concepts almost analogous to the stylizations which have in some ages occurred in art

forms, and which finally prevented painters from looking at Nature at all. [p. 336]

    [Developing a cultural analog]: The Book of Changes might almost be said to have

constituted an organization for ‘routing ideas through the right channels to the right

departments.’ ... Perhaps the entire system of organismic thinking was in one sense the

mirror image of Chinese bureaucratic society. Not only the tremendous filing system of the

[Yijing], but also the symbolic correlations in the stratified matrix world might be so

described. Both human society and the picture of Nature involved a system of coordinates, a

tabulation framework, a stratified matrix in which everything had its position, connected by

the ‘proper channels’ with everything else. [p. 337-8]

In his doctoral thesis, George Fendos, adds a few more pieces:

    [Summarizing “Analogy, Mysticism and the Structure of Culture,” Current

Anthropology, Apr, 1983]: Sheldon Klein “sees the hexagrams of the [Yijing] as part of a

metasystem for generating relational data base structures that supplies the rules for

qualifying abstract images and guides the computation of metaphors. The rules consist of

equivalence sets of abstract and concrete terms that are markers of classification categories

covering the whole range of traditional Chinese world knowledge. ... [R]ules are encoded in

this system as analogical operators that relate situational state descriptions and allow for

quick response.” [p. 118]

    [Of the XCZ]: Organism refers to a vital whole the properties and functions of which

are determined not only by the properties and relations of its individual parts (mechanical

view), but by the character of the whole which they compose and by the relations of the

parts to the whole. The philosophy of organism entails an analogy wherein properties and

relations within an entity not a vital whole are seen as correlating to those in an organism .... 

In the [Yijing] the analogy at work implies that the nature and processes operating in the

[Yijing] are the same as those operating in the real world. [p. 185]

    Gerald Swanson [The Great Treatise: Commentary Tradition to the Book of Changes,

PhD Thesis, Univ. of WA, 1974] asserts that the doctrine of macrosm / microsm [sic] is

only one of four forms of argument from analogy in the [XCZ]. The other three are social-

political, technological, vitalistic. [p. 278]

    The above lays the groundwork for what I will term the linguistic model (note that I do

not use the term analogy). The fourteen Xiao Gua can behave as combinatory radicals, as

vocabulary elements or as subjects, following rules of lexemics. The sixty four Gua are

combinations of subject and adverbial predicate. The sets of two, three and six Places (Wei)

are transitive prepositional predicates. The dimensional rules for the quasi-algebraic

combination of symbols constitute the morphology. The operations of change are a syntax.

The sum of the valid Xiang Shu dimensions within the superstructure itself (which defines

the parts of speech) is the Yijing’s grammar. The Yi Li aspects are vocabulary elements, and

are the dimensions most subject to change (but not elimination) by accretion and deletion.

And yet the structure of the system as a whole holds the changes in vocabulary in check.

The vocabulary elements, being finite in number and “defined” in contrast with each

other’s boundaries within the context of larger geometrical patterns (parts of speech), are all

subordinate to the larger structures. This function was hinted at in a comment on the

“compare counterparts” sections in Xiao Gua, the Small Symbols Thus is the summed

vocabulary development herein more akin to a thesaurus or a taxonomy than a dictionary.

The Xiang Shu elements, in contrast, change by invention and discovery according to

implicit structural and mathematical rules.

    This last comment is important. And here an analogy to DNA is appropriate. It is this

set of rules which allows the Dragon to travel in Time, to undergo the multitude of changes

made by commentators and scribes and even self-correct the corresponding multitude of

errors. The Yijing’s structure is its negative entropy, its means of self-rectification and

continuance (heng) regardless of the non-viable mutations and freaks (which our atomic era

is so full of). The book can introduce itself to archaeologists. It can carry itself through both

overgrowth and overpruning.

    Perhaps our unfamiliarity with the language model stems from comparison with our

more familiar spoken languages, which tend to develop more spontaneously and to develop

grammatical structures which are largely subliminal until studied in retrospect. But there

exists a number of close examples of other, consciously designed languages which also tend

to exhibit finitude of vocabulary, economy of structure and mathematical symmetry. The

most familiar of these is mathematics itself. Chemistry, with its periodic table of elements, is

another. Music is such a language. And so too are the Yijing’s distant cousins: Qabalah,

Tarot, Astrology, Alchemy, etc. to which the linguistic model (to this scowler at least) is

vastly more appropriate (and more useful in counseling) than the metaphysical models.

    It is within the individual patterns, usually as matrix grids which chart the dimensions

(morphology) of each part of speech, where lies the dimension of Correlative Thought

which Needham, Shchutskii, Fendos and others speak of. The dimensions of the matrix

grids are the Numbers, the Shu of Xiang Shu, the Scales discussed at some length in Xiao

Gua, the Small Symbols. For example, the Signs of western Astrology are in part or in one

dimension functions of the multiplication of the Three Qualities (Cardinal, Fixed and

Mutable) by the Four Elements (Fire, Earth, Air and Water) so that each of the twelve

represents a unique combination in this matrix and all combinations are exhausted. The

eight-by-eight Ba Gong grids of the Yi’s Xian Tian and other, more original arrangements

are similarly exhaustive matrices. These grids are used as templates, which we then

superimpose onto the subjects of our various investigations, or whatever we would like to

think of as reality. Think now of Carl Jung’s “mission of psychology” to map and reclaim

territory from the unconscious mind. The grid has become the system of latitudes and

longitudes with which we chart this terrain and draw our maps. We also have choices here

in the grids we use. We need only to substitute scales to see yet another aspect of the

terrain, much as geology maps give us one kind of data and topographic maps another. Or,

more suited to our mental dimension, the same equation in analytic geometry can often be

graphed using either rectangular or polar coordinates and this process will offer quite

different pictures of our object of inquiry. This also helps to remind us that the map is a tool

and not the terrain.

    Needham had few reservations about expressing the shortcomings of the Yijing’s

particular matrices when it came to the applied physical sciences: the Periodic Table was a

much more useful matrix for making things happen. But he was ultimately just pointing out

the error of the Chinese heirs to the Yijing in mistaking this document for a physical and

metaphysical model. He called these Xiang Shu busybodies mutationists. Others have said

numerologists. The picture changes completely when we look at the Yi as a philosophy and

a psychology and the subjects of investigation become the human mind, the human attitude

and the human experience.

    Recall now the Scales discussed in Xiao Gua, and that these Scales are tested across

time for both their relevance to and resonance with the human experience. They do not

survive if they fail these tests. It is these tested Scales which become the sides or the

dimensions of the matrix. These are developed prior to the matrix itself, and in their

development accrue associations or correspondences which span a wide range of fields of

inquiry. For example, the Greek Elements of Fire, Earth, Air and Water were correlated by

Carl Jung with his Intuiting, Sensing, Thinking and Feeling types, respectively. The Scales,

in other words, contain correlated and nested sets of analogs. The “chessboard” of the

matrix has just become three and four dimensional.

    When such a matrix is then superimposed upon a spectrum of accumulated life

experiences one begins to see that some of these little squares (more correctly, tessellated

cubes and hypercubes) are plenty full already, some are still relatively empty and some are

terra incognita, just begging to be explored and mapped out, or filled with invention if

necessary. The matrix has become a creative act as well as an exploratory aid. As said

before, although argument from analogy remains a logical fallacy, exploration and

investigation which makes fruitful use of analogy tends toward enrichment. The advent of

fractal geometry in chaos theory is beginning to make nested analogs both more promising

and more respectable. For example, if I want to understand why human governments tend

over generations to lose their sense of constitutional limits and overgrow their place into

parasitism, I can learn a great deal about this by investigating the smaller-scale behavior of

cancer cells in metastasis. This mode of thought was deftly demonstrated in Daniel

Goleman’s Vital Lies, Simple Truths: The Psychology of Self-Deception, and allowed his

theory to range from cellular to global scales of organization. This thought process may

have been first discussed by Herman Hesse in Magister Ludi or The Glass Bead Game.

Moving between disciplines with structural analogs is a key to interdisciplinary thinking.

    Three other aspects of Correlative or Matrix Thinking bear mention here:

    1) A matrix which is based upon scales intricate enough to contain a sequential order

or pattern of their own will tend to develop geometrical patterns of relationships between

spatially related elements within the matrix itself. The Ba Gong arrangement of the Xian

Tian is definitely one of these. In fact, every single Xiang Shu dimension discussed in this

section displays bilateral symmetry when plotted onto this grid. This property will be amply,

though not completely, demonstrated in the Patterns of the Xian Tian.

    2) A matrix has a mnemonic function. The “missing” content of a square may often

be deduced either from the content of the squares around it or by recourse to the higher

order of the structure which contains it (tertium non datur). This is akin to the matrix’s

creative function but it also applies to the recall of forgotten associations.

    3) A matrix gives simultaneous access to a number of concepts with a variety of

interrelationships: it offers choices within a single image. In the example of the Yijing as a

language of attitudes, the larger grid may be seen as a catalog or wardrobe of attitudes. If

being headstrong (Da Zhuang) is cautioned against, look across the grid to one of its

resonant partners, its Inverse, Distancing (Dun) and add some “big-picture” perspective to

the attitude.