The Eight Trigrams of the Bagua

March 26, 2017

What can be said of the Eight Trigrams of Taoist cosmology, also known as the Bagua, that hasn’t already been said on ten thousand other web sites? Here I show the trigrams and their duals together in an arrangement that places one or two of them at a site of the four elements.

When considering the binary values of the trigrams, this arrangement is reminiscent of my Marriage of Opposites, Part 2. In doing this each link between them represents a common value for a trigram line. For example between Heaven / Earth and Water / Fire the 2nd line is yang for both Heaven and Water, and the 2nd line is yin for both Earth and Fire. Opposite this link is its reverse: the 2nd line is yin for both Thunder and Mountain, and yang for both Wind and Lake. All six links have this quality.

Two smaller diagrams show the common English names as well as the corresponding attributes of the trigrams. Interestingly, if Heaven and Wind are considered Air, Lake is considered Water, Mountain is considered Earth, and Thunder is considered Fire, then you have each element mentioned twice, once above and once below, and a crossed loop of pairs: Air / Earth, Fire / Air, Water / Fire, Earth / Water, and then back to Air / Earth. Nice!

Further Reading:

[*9.234, *9.235]


The Ogdoad: Unity of Eight Gods

March 24, 2017

Here’s a notable fourfold of dualities: the Ogdoad, or eightfold of deities. I usually don’t stray into ancient mythology but this cosmological system evidently led the Greeks to their idea of the four elements. These paired male and female deities were personifications of certain metaphysical concepts and their opposites.

  • Amun and Amaunet: The Hidden and its opposite
  • Nun and Naunet: The Abyss or primeval waters and its oppositional heaven
  • Kuk and Kauket: The Darkness and its opposite
  • Huh and Hauthet: The Boundless and its opposite

Some even conjecture that the word ANKH was formed from the initial sounds of these four or eight deities.

Further Reading:



The Four Dichotomies of the MBTI

March 17, 2017

In the Myer-Briggs Type Indicator, there are four pairs of opposites which sort personalities into sixteen different types. These four pairs of opposites are:

  • Extroversion vs. Introversion (E, I)
  • Sensing vs. Intuition (S, N)
  • Thinking vs. Feeling (T, F)
  • Judging vs. Perceiving (J, P)

The codes for these sixteen types are formed by listing one choice per opposite (E,I), (S,N), (T,F), and (J,P), written ESTJ, for example. Interestingly, four special subsets xNTx, xNFx, xSxJ, xSxP, (usually written NT, NF, SJ, SP), are aligned to the four personality temperaments by David Keirsey.

Sensing vs. Intuition and Thinking vs. Feeling are quite similar to the fourfold of Jung’s Psychological Types: Sensation, Intuition, Thinking, and Feeling. Also in Jung’s theory Intuition and Sensation are considered Perceiving, and Thinking and Feeling and considered Judging. However, there are significant differences in the two theories.

Further Reading:

Images for MBTI Dichotomies:

[*9.228, *9.229]


Robert Plutchik’s Emotions

March 8, 2017

Robert Plutchik devised a schema for eight basic emotions, divided into four pairs of opposites. Each of these also has a weaker and a stronger version (but not shown here).

  • Trust vs. Disgust
  • Joy vs. Sadness
  • Fear vs. Anger
  • Surprise vs. Anticipation

In addition, emotions called dyads can be built by non-opposed combinations of the basic emotions, and each of these twelve dyads has a reverse or opposite emotion, making 24 total. Between any two opposite pairs, two dyads may be considered covariant, and the other two may be considered contravariant. So for the two pairs of opposites A + A’ and B + B’, we have covariant A*B and A’*B’, which are opposite, say C and C’, and contravariant A*B’ and A’*B, which are also opposite, say D and D’. These four dyads are labeled in the diagram as C:C’::D:D’, which I hope is not too confusing.

  • [L:R] Love (Joy * Trust) : Remorse (Sadness * Disgust)
  • [S:M] Sentimentality (Trust * Sadness) : Morbidness (Joy * Disgust)
  • [G:E] Guilt (Joy * Fear) : Envy (Sadness * Anger)
  • [D:Pr] Despair (Fear * Sadness) : Pride (Joy * Anger)
  • [C:C] Curiosity (Trust * Surprise) : Cynicism (Disgust * Anticipation)
  • [U:H] Unbelief (Surprise * Disgust) : Hope (Trust * Anticipation)
  • [A:A] Awe (Fear * Surprise) : Aggression (Anger * Anticipation)
  • [O:A] Outrage (Surprise * Anger) : Anxiety (Fear * Anticipation)
  • [D:P] Delight (Joy * Surprise) : Pessimism (Sadness * Anticipation)
  • [D:O] Disappointment (Surprise * Sadness) : Optimism (Joy * Anticipation)
  • [S:C] Submission (Trust * Fear) : Contempt (Disgust * Anger)
  • [S:D] Shame (Fear * Disgust) : Dominance (Trust * Anger)

Further Reading:

[*9.224, *9.225, *9.230, *9.231]


The Marriage of Opposites, Part 2

February 21, 2017

sq_menageMy last post made me realize that I had written about six-fold things several times before. The first time was about Richard McKeon’s Aspects of Knowing, the second was about Vaughn Pratt’s Duality of Information and Time, and now we have Edward de Bono’s Six Thinking Hats.

For each of these schema, three pairs of opposites can be shown on the edges of a tetrahedron. I have previously written about the Alchemical Marriage of Opposites, where I imagined two pairs of opposites being in a fourfold. With this new common design, I see that three pairs of opposites can label the vertices of a tetrahedron. In fact, this may be at least as common as double dualities, and I have found several triple dualities to write about in the near future.

In algebraic notation this triple marriage of opposites yields:

(A + A’)(B + B’)(C + C’) = (ABC + A’B’C’) + (AB’C’ + A’BC) + (A’BC’ + AB’C) + (A’B’C + ABC’)

I might even call this diagram a “Ménage of Opposites”, but ménage of course merely means household. Appropriate, nonetheless.


This diagram also represents four pairs of opposites.



The Six Thinking Hats of Edward de Bono

February 20, 2017


I know what you’re thinking (and not necessarily because I’m wearing a colored hat): this is about six things and not four. But wait, notice how the six thinking styles form three pairs of opposites:

Creative (Green) pairs with Process (Blue)

Positive (Yellow) pairs with Negative (Black)

Facts (White) pairs with Emotion (Read)

Then the three pairs of opposites can be arranged into a tetrahedron, where the opposite edges are the three pairs. A tetrahedron has four vertices and four faces, where each vertex is the opposite of its opposite face.

The vertices are Creative + Positive + Emotion, Creative + Negative + Facts, Process + Positive + Facts, and Process + Negative + Emotion. The faces are Creative + Positive + Facts, Creative + Negative + Emotion, Process + Positive + Emotion, and Process + Negative + Facts.

The first link below lists the same opposites for the Six Hats as I found. And there are also a huge number of links out there devoted to the Six Thinking Hats, so I can’t list or summarize them all, or even a small portion.

Further Reading:

Edward de Bono / Six Thinking Hats

… and many more.



Graham Wallas: The Four Stages of Creativity

February 16, 2017

sq_creative_stagesGraham Wallas devised a fourfold for stages of creativity:

  • Preparation
  • Incubation
  • Illumination
  • Verification

From the “Art of Thought” description on Amazon:

“The first in time I shall call Preparation, the stage during which the problem was ‘investigated … in all directions’; the second is the stage during which he was not consciously thinking about the problem, which I shall call Incubation; the third, consisting of the appearance of the ‘happy idea’ together with the psychological events which immediately preceded and accompanied that appearance, I shall call Illumination. And I shall add a fourth stage, of Verification …”

Further Reading:

Turning ideas into reality: the four stages of creativity

Graham Wallas / The Art of Thought

Albert Rothenberg, Carl R. Husman, eds. / The Creativity Question

[*9.198, *9.199]


Neon Genesis Evangelion Rebuilt

January 30, 2017

sq_evangelionThe final movie of this tetralogy has been named:

  • Evangelion 1.0: You Are (Not) Alone
  • Evangelion 2.0: You Can (Not) Advance
  • Evangelion 3.0: You Can (Not) Redo
  • Evangelion 4.0: You Will (Not) Happen

Alternative facts are (not) fun!


Seen post-post:



The Four Master Tropes

January 26, 2017

sq_four_tropes4My post on analogy brought another fourfold to mind, one with metaphor and its analogs.

Kenneth Burke wrote about the Four Master Tropes of “figurative” or “poetic” rhetoric: metaphor, metonymy, synecdoche, and irony. He also proposed “literal” or “realistic” versions, respectively: perspective, reduction, representation, and dialectic, and expounded on the correspondence.sq_four_tropes2

Giambattista Vico, who wrote “The New Science”, is usually credited with initially listing these four tropes, but he may have had inspiration from others. Hayden White, who wrote “Metahistory”, was inspired by Burke’s Tropes and proposed that it formed a syncretism with other fourfolds such as political ideologies, Pepper’s world views, and Frye’s literary emplotments.


Frank J. D’Angelo / The Four Master Tropes: Analogues of Development, Rhetoric Review, Vol. 11, No. 1. (Autumn, 1992), pp. 91-107.

Kenneth Burke / Four Master Tropes, The Kenyon Review Vol 3, No 4 (1941) pp. 421-438

Also see:

[*3.172, *4.15, *4.27, *9.182]


Four Futures after Capitalism

January 23, 2017

sq_four_futuresAs conservative capitalism whips itself into an ecstasy of fevered apoplexy over the change in political climate, it is fun to step back and imagine what might transpire after capitalism’s eventual passing. To offer help, Peter Frase has written the excellent and cautionary “Four Futures: life after capitalism”.

Frase gives us four idealized futures blocked out by a matrix of two variables each ranging over two possibilities: 1) the structure of the social environment being either egalitarian or hierarchical, and 2) the resources of the natural environment being either scarce or abundant. What’s nice about the descriptions of these futures are the ample examples from science fiction media: TV, movies, novels, etc.

One assumption over all four futures is that, given sufficient resources of material and energy, technology, automation, and robotics will improve to the extent that human work as we know it will eventually be made unnecessary. Another is that climate change is real and will demand solutions and amelioration or it will only get much worse. And a big take home message is that the rich and powerful are in a much better position to benefit from ignoring climate change than you and me.

What will happen to the common person when their labor is superfluous? Not detailed are the possibilities if even the humans at the top are deemed unnecessary and the machines revolt. In order of diminishing happiness for most of us:

  • Communism: Egalitarian Abundance
  • Rentism: Hierarchical Abundance
  • Socialism: Egalitarian Scarcity
  • Exterminism: Hierarchical Scarcity

The cover has a nice iconography for the futures: a conveyor belt on a 3D printer assembly line shows a glass of wine for Communism (Cheers!), a key hole for Rentism, a watering can for Socialism, and a skull for Exterminism (Ouch!).


Peter Frase / Four Futures: life after capitalism

Some better reviews than mine:


There’s a similar fourfold of futures I forgot I mentioned in my article on Trompenaars, although fragmentation-coherence is used instead of scarcity-abundance, and there is a more positive spin:

Also, Frase has a blog that can be found at:

[*9.82, *9.190, *9.191]