All posts by Martin K. Jones

The Three Pillars of Stoicism

The Four Cardinal Virtues of Wisdom, Justice, Temperance, and Courage are often linked to the “Three Pillars” of Stoicism: Logics, Ethics, and Physics. Logics and rational thought enables the virtue of (practical) wisdom to produce intelligent assent or rejection. Ethics and moral strivings condition the virtue of justice (and courage) to inform proper action or non-action. Physics and natural constraints temper the virtue of courage (and temperance) by proportionate or bounded desire or aversion.

    • Logics (Rational Domain): Assent for (practical) Wisdom
    • Physics (Natural Domain): Desire for Courage and Temperance (restraint)
    • Ethics (Moral Domain): Action for Justice

Note the mismatch between Four Cardinal Virtues and the Three Pillars. Some add Metaphysics to get Four Pillars, although what domain does it inform? (Supernatural? Speculative? Philosophical?) Also note my use of the term “Logics”. If the British can use the term “Maths” then I can certainly use “Logics,” because logic can now come in many different formulations.

Further Reading:

The Highest Good: An Introduction To The 4 Stoic Virtues

Disciplines, Fields, and Virtues: The Full Stoic System in One Neat Package


The Spheres of Human Understanding

The Four Cardinal Virtues

Images of Logic, Ethics, Physics:



The Endless of Sandman

The Endless are merely patterns. The Endless are ideas. The Endless are wave functions. The Endless are repeating motifs. The Endless are echoes of darkness, and nothing more… And even our existences are brief and bounded. None of us will last longer than this version of the Universe.

Destruction of the Endless

The Endless are:

    • Destiny
    • Death
    • Dream
    • Destruction
    • Desire
    • Despair
    • Delirium

Further Reading:




Linear Logic and the Laws of Excluded Middle and Noncontradiction

If LEM is the Law of Excluded Middle and LNC is the Law of Non-contradiction then

  • Classical Logic preserves both LEM and LNC
  • Intuitionistic Logic preserves LNC, but rejects LEM
  • Co-Intuitionistic Logic preserves LEM, but rejects LNC
  • Linear Logic broadly preserves neither, but narrowly preserves and rejects them with its pairs of conjunctive and disjunctive logical operators

Above is shown the four operators of Linear Logic and the statements for their preservation and rejection of LEM and LNC.

Further Reading:

Pete Wolfendale / Essay on Transcendental Realism
(at PhilPapers)





Charles Howard Hinton

Another early author of note about the fourth dimension, Charles Howard Hinton, invented the terms “Ana” and “Kata” to denote the two movements along a fourth-dimensional direction. He was also the inventor of the term “tesseract” for a four-dimensional cube.

Further Reading:






Four-Dimensional Vistas

The Fourth Dimension has been an interest of mine since I was a child. I’m not sure when I first heard about it, but I still have my coverless copy of “Geometry of 4 Dimensions” by Henry Parker Manning that I bought in a used book store. (I wonder why it hasn’t ever been reissued by Dover?) Maybe I heard about the fourth dimension in some science fiction TV movie, or in some mathematical survey book like “Mathematical Snapshots” or “Mathematics and the Imagination”.

Once I tried to explain to my best friend about my newly discovered insight how a hypercube could be folded up in four-dimensional space from its so-called three-dimensional net consisting of eight cubes, just as a regular three-dimensional cube could be folded up from its two-dimensional net of six squares. This 3D net somewhat resembling a cross is famously seen in Dali’s “Crucifixion (Corpus Hypercubus),” although I probably didn’t refer to this painting in my explanation.

I’m not sure who came up with the take-away message from my exposition, but it remains clear in my memory that the “junk in the middle” of the hypercube was a piece of the fourth dimension, just as the faces of a cube enclose a piece of our normal third dimension.

I recently came across Claude Fayette Bragdon, architect, author, draughtsman, stage designer, and mystic. At first I was interested in his drawings found on-line. His book “Four-Dimensional Vistas” started off with a good if overly wordy introduction to the concept of the fourth dimension. But then he suggests that many esoteric concepts such as the meaning of dreams, reincarnation, past-life regression, prognostication, ESP, etc. could possibly be explained by higher dimensional space or even higher dimensional time.

Even though I initially found many of these hypotheses too far-fetched for my tastes, I still found some interesting ideas to mull over in this little book.

Further Reading:

The art of Claude Fayette Bragdon, 1866–1946

Claude Fayette Bragdon / Four-Dimensional Vistas (1930)

Claude Fayette Bragdon / The Beautiful Necessity (1910)

Claude Fayette Bragdon / Architecture and Democracy (1918)

For my gratuitous anime tie-in, Bragdon’s world-view suddenly reminds me of the anime character  Haruhi Suzumiya, who wished for her aliens, time-travelers, and ESPers so much that she willed them into being. If only she had known about the fourth dimension!

[*3.139, *12.121, *13.50]



Sixteen Emotions

Emotions are also often divided into sixteen different types instead of the eight we saw in The Circumplex Model of Affect. The Geneva Emotion Wheel (1.0) used the same Valence and Arousal axes and produced the following 16 emotions:

(Circular Order) Anger, Contempt, Disgust, Envy, Guilt, Shame, Fear, Sadness, Surprise, Interest, Hope, Relief, Satisfaction, Joy, Elation, Pride

(Alphabetized) Anger, Contempt, Disgust, Elation, Envy, Fear, Guilt, Hope, Interest, Joy, Pride, Relief, Sadness, Satisfaction, Shame, Surprise

(But an updated GEW Version 3.0 has 20 emotions in a circle on Valence and Control axes. See below for details.)

Another study used a Deep Neural Network on a training set of emotional facial expressions. They used the algorithm to track instances of 16 facial expressions one tends to associate with amusement, anger, awe, concentration, confusion, contempt, contentment, desire, disappointment, doubt, elation, interest, pain, sadness, surprise and triumph. (See below for details.)

Further Reading:

Deep Neural Network Study:

GEW (Geneva Emotion Wheel, Version 1.0)

GEW Version 3.0, with 20 emotions on a Valence and Control wheel with 2 options per emotion (in Circular Order):

Irritation, Anger
Contempt, Scorn
Disgust, Repulsion
Envy, Jealousy
Disappointment, Regret

Guilt, Remorse
Embarrassment, Shame
Worry, Fear
Sadness, Despair
Pity, Compassion

Longing, Nostalgia
Astonishment, Surprise
Feeling Disburdened, Relief
Wonderment, Feeling Awe
Tenderness, Feeling Love

Enjoyment, Pleasure
Happiness, Joy
Pride, Elation
Amusement, Laughter
Involvement, Interest

There are also several Classroom Charts available for Teachers and Students, for example (both in Alphabetical order):

Angry, Bored, Confused, Curious, Disappointed, Embarrassed, Excited, Grumpy, Happy, Nervous, Proud, Sad, Scared, Shy, Silly, Surprised

Angry, Afraid, Bored, Embarrassed, Excited, Guilty, Happy, Hopeful, Loved, Jealous, Proud, Sad, Shy, Sorry, Surprised, Tired

Images for Sixteen Emotions:


The Circumplex Model of Affect

James Russell developed a circumplex model of emotion, not to be confused with the interpersonal circumplex. (There are a variety of circumplex models for various subjects, since they are merely circular and continuously scaled in nature.)

This model is also called Emotional Valence and Arousal, where Valence ranges from Negative to Positive (or Unpleasant to Pleasant) and Arousal ranges from Low to High (or Mild to Intense). We get the fourfold partitions of

  • Mildly Unpleasant
  • Mildly Pleasant
  • Intensely Unpleasant
  • Intensely Pleasant


  • Low & Negative
  • Low & Positive
  • High & Negative
  • High & Positive

There are several way to discretize this circumplex into eight parts, but here is one from Russell (1980).

  • Aroused
  • Excited
  • Pleased
  • Contented
  • Sleepy
  • Depressed
  • Miserable
  • Distressed

Compare with the concept of Flow, where the variables are challenge and skill, instead of arousal and valence.

Further Reading:

James Russell / A Circumplex Model of Affect, J. of Personality and Social Psychology 1980, Vol. 39, No. 6, 1161-1178

James A. Russell, Maria Lewicka, Toomas Niit / A Cross-Cultural Study of a Circumplex Model of Affect, J. of Personality and Social Psych. 1989, Vol. 57 No. 5, 848-856

Jonathan Posner, James A. Russell, Bradley S. Peterson / The circumplex model of affect: An integrative approach to affective neuroscience, cognitive development, and psychopathology
Dev. Psychopathol. 2005, 17(3), 715-734


Eugen Rosenstock-Huessy and His Cross of Reality

Imperative (prejective), conjunctive or optative (subjective), preterite or perfect (trajective), neutral indicative (objective) are grammatical necessities arising out of times and spaces.

— Eugen Rosenstock-Huessy

Further Reading:

Click for PDF:  Martin Zwick / Rosenstock-Huessy’s “Cross of Reality” and Systems Theory

Martin Zwick / Ideas and Graphs: the Tetrad of Activity

Click to access QUADRILATERAL%20TEACHING.pdf

Caryl Johnston / Grammar, Speech, Rhetoric, & the Fate of Humanity

[*13.44, *13.46]




Eight Days a Week

Eight days a week
Is not enough to show I care

— The Beatles

No, I’m not trying to convince you that we should all change to an eight-day week, and join all the other myriad and failed attempts at calendar reform. But just look at what we have in the Gregorian Calendar: seven day weeks, months of various sizes, days of the month falling willy-nilly on random week-days, and even extra days thrown into the calendar year because of day and solar year mismatch. And the moon’s phases also have conditioned the rough size of months, without helping to show us where they occur.

Instead I’m thinking about a change in calendar representation. It all started with the diagram above showing the days of the week and the sun, moon, and planets associated with them. Ordinary calendars show weeks as seven rectangles in a row for the days of the week labeled by the days of the month. But each day looks the same, except for their place in line along the row. It’s hard to remember the dates of each day, week after week.

Having some success using the non-circular diagram to help remember the Zodiac and their houses (which is pretty old anyway), I thought I might represent each week of Sunday through Saturday as an eight-fold with a blank, with the days of the week in specific places. Since months consist of 28 days or more, four eight-folds (E) could show the bulk of the days for each month (E1 through E4). Some days might come before the first Sunday (in E0), and some days might come after the last Saturday (in E5). Sometimes E1 and E4 may be short a few days as well.

For example, here is January 2022. By my nomenclature, E0 has just the 1st. E1 has the 2nd through the 8th, then E2 has 9-15, E3 has 16-22, E4 has 23-29, and E5 has 30-31.

Months may be joined end to end in a descending series, with four extra weeks (as Es) occurring here and there as need be. After all, for 7 day weeks, having 13 months of 28 days each would be ideal since 28*13 + 1 = 365. Why go to all this trouble when it is easier to look at a regular calendar? I think it is a bit easier to remember dates with this method, but I’m really just beginning with this idea. I’ll try to post a picture of February 2022 soon.

Further Reading:





The Passions of the Stoics

I will show you fear in a handful of dust.

— From “The Waste Land”, by T. S. Eliot

The Stoics divided the passions into four parts, consisting of a two by two matrix of “good” or “bad” emotions versus whether they occur during the present or while thinking about the future.

  • Delight (or Pleasure): present and good
  • Distress: present and bad
  • Desire (or Appetite) : future and good
  • Dread (or Fear): future and bad

To Stoics all these passions were actually harmful, in the sense that they are irrational and instead should be thoughtfully managed. Instead one should have Three Good Feelings and but not Three Not-as-Good Feelings:

  • Joy (chara) instead of Pleasure
  • Wish (or Hope) (boulesis) instead of Appetite
  • Care (eulabeia) instead of Fear

What about Distress and its Stoic version (which might even be Calm or Ease)? And what of emotions for past memories? They might be  Relief (past and “bad”) and  Regret (past and “good”).

Further Reading:

Stoic Ethics