A Study in Synthesis

July 13, 2017

An early work (1934) in the study of fourfolds is James H. Cousins’ “A Study in Synthesis”, which is available for downloading at the link below.

Cousins’ key fourfold is

  • Intuition
  • Cognition
  • Emotion
  • Action

which is similar to Jung’s psychological types except Action replaces Sensation.

Each fourth also has two movements as follows:

  • Intuition: Illumination / Inspiration
  • Cognition: Contemplation / Observation
  • Emotion: Aspiration / Creation
  • Action: Organization / Execution

Cousins was an influence to Patrick Geddes, renowned as a town planner, who had several fourfolds of his own.

Further Reading:

James H. Cousins / A Study in Synthesis









Human Stupidity

July 9, 2017

I’ve crossed enough paths to know that one in four people are rock stupid.

— Shadow Moon, from television’s American Gods

Here’s a rather pessimistic take on humankind.

An economist at UC Berkeley sorted people into four groups based upon their proclivities for gain or loss, for themselves and for others. This leads to four groups:

  • Intelligent: Gain for themselves and gain for others
  • Bandits: Gain for themselves and loss for others
  • Helpless: Loss for themselves and gain for others
  • Stupid: Loss for themselves and loss for others

In fact, Professor Cipolla thought the greatest threat to humanity was stupidity, and developed five laws for the foolish.

At first, I considered gain and loss in purely economic terms, but then realized gain and loss should also include the creation and improvement of information and knowledge.

Further Reading:

The five universal laws of human stupidity




Popper’s Three Worlds Made Four

July 5, 2017

Philosopher Sir Karl Popper divided the ontology of all that is into three parts:

World 1: The physical world, the world of physical objects and events, including biological entities.

World 2: Subjective reality, the world of mental objects and events, that occur in (individual) minds.

World 3: Objective knowledge, the world of all products of thought, that may be physical or not.

Instead of physical or mental monism, or the dualism of mind and matter, Popper suggested a pluralism (triplism?) consisting of three worlds. All the elements of each of these worlds, Popper argued, can be said to exist.

One could say that each higher world requires the world below it in order to exist: World 1 < World 2 < World 3. That is, World 2 is emergent or supervenient on World 1, and World 3 is emergent or supervenient on World 2. In addition, these worlds interact with each other.

There is no necessary evaluation of the “truth” of the elements of World 3. There are many products of thought that exist in World 3 that are indeed false. But Popper spends much time talking about the quality of World 3 objects that give credence to their existence. That is, the “objective” goodness or quality of a product makes that product more real.

I suggest that the introduction of another world is necessary for a proper division and understanding of Popper’s Three Worlds. Let’s call it

World 4: Normative values, the world of all intersubjective evaluations.

Indeed, Popper argues that the objective value of certain objects in World 3 gives credibility to the notion that there are such World 3 objects, and not just World 2 instances within minds.

World 4 could serve as a mediator between World 2 and World 3. Popper states that people can evaluate the World 3 products of the mind within their own subjectivities, but it seems to me that they must be trained or lead to appreciate the “objective” greatness of these products. They do not happen in a vacuum, so perhaps a better description would be that they have an “intersubjective” value.

Why would a person discount the well accepted scientific theories of evolution or climate change just because they don’t fit with his other beliefs?

Why would a person destroy ancient sculptures of timeless beauty just because it offends his religious beliefs?

Such cognitive biases could easily block a person from accepting some objective knowledge that conflicts with their values. Certainly the biases exist in the subjective mind, but are learned and maintained in the intersubjective cultural milieu.

A takeaway fourfold for you is presented on the right.

  • Substantive
  • Subjective
  • Objective
  • Normative

Further Reading:

Karl Popper / Three Worlds. The Tanner Lecture on Human Values, delivered at the University of Michigan, 1978




Sean Carrol / The Big Picture: On the Origins of Life, Meaning, and the Universe Itself

Manfred Eigen, Ruthild Winkler / Laws of the Game: how the principles of nature govern chance

[*8.134, *10.6]


Edward T. Hall’s Map of Time

May 14, 2017

Quite by accident, I ran across anthropologist Edward T. Hall’s Map of Time in his book “The Dance of Life: the other dimension of time”. In it, he shows a mandala of different notions of time which tries to answer the question, “what is time”? The mandala consists of eight (or nine) different notions of time, organized as a fourfold of duals:

  • Physical / Metaphysical
  • Micro / Sync
  • Biological / Personal
  • Profane/ Sacred

In addition, there are four duals of attributes:

  • Group / Individual
  • Cultural / Physical
  • Conscious/ Unconscious
  • Low Context / High Context

So that the different times have these attributes:

  • Physical: Low Context, Conscious, Physical, Group
  • Metaphysical: Low Context, Conscious, Cultural, Group
  • Micro: High Context, Unconscious, Cultural, Individual
  • Sync: High Context, Unconscious, Physical, Individual
  • Biological: Low Context, Unconscious, Physical, Group
  • Personal: Low Context, Unconscious, Physical, Individual
  • Profane: High Context, Conscious, Cultural, Individual
  • Sacred: High Context, Conscious, Cultural, Group

And the different attributes belong to these notions of time:

  • Physical: Physical, Biological, Personal, Sync
  • Cultural: Metaphysical, Sacred, Profane, Micro
  • Group: Biological, Physical, Metaphysical, Sacred
  • Individual: Profane, Micro, Sync, Personal
  • Conscious: Physical, Metaphysical, Sacred, Profane
  • Unconscious: Micro, Sync, Personal, Biological
  • Low Context: Personal, Biological, Physical, Metaphysical
  • High Context: Sacred, Profane, Micro, Sync

The ninth notion of time is a synthesis of all eight which he calls meta-time.

Further Reading:






The Eight Worldly Winds

March 28, 2017

This fourfold of duals from Buddhism lists the hopes and fears that bind us to the world and our culture. They are known as the eight worldly winds, concerns, or dharmas. Both hopes and fears, wanting and not wanting, can be seen as negative.

  • Hope for Pleasure and Fear of Pain
  • Hope for Gain and Fear of Loss
  • Hope for Praise and Fear of Blame
  • Hope for Prestige and Fear of Disgrace

Further Reading:








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.