Category Archives: fourfolds

The Circumplex Model of Affect

February 15, 2022 Martin K. Jones 1 Comment

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:

https://en.wikipedia.org/wiki/Emotion_classification

https://en.wikipedia.org/wiki/Circumplex_model_of_group_tasks

https://www.google.com/search?channel=cus5&source=univ&tbm=isch&q=circumplex

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

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2367156/

Design for Emotion and Flow from Trevor van Gorp

fourfolds

Eugen Rosenstock-Huessy and His Cross of Reality

February 3, 2022 Martin K. Jones 1 Comment

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:

https://en.wikipedia.org/wiki/Eugen_Rosenstock-Huessy

https://plato.stanford.edu/entries/rosenstock-huessy/

Home

https://dartmouthalumnimagazine.com/articles/eugen-rosenstock-huessy

Fractured Paradigms

Trajective and Prejective in Rosenstock-Huessy’s “Cross of Reality”

Fourfold Vision Meets Cross of Reality

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

Click for PDF: Martin Zwick / Rosenstock’s “Cross of Reality,” A Space-Time Framework for Isomorphisms

Martin Zwick / Ideas and Graphs: the Tetrad of Activity
https://works.bepress.com/martin_zwick/216/

Click to access QUADRILATERAL%20TEACHING.pdf

Letters to the Third Millennium (Book Review)

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

[*13.44, *13.46]

fourfolds, Philosophy

The Passions of the Stoics

January 3, 2022 Martin K. Jones 4 Comments

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:

https://en.wikipedia.org/wiki/Stoic_passions

http://people.wku.edu/jan.garrett/stoipass.htm

https://en.wikipedia.org/wiki/On_Passions

https://immoderatestoic.com/blog/2013/4/2/stoic-emotionsall-three-of-them

https://en.wikipedia.org/wiki/Passions_(philosophy)

Stoic Ethics

https://en.wikipedia.org/wiki/Passion:_An_Essay_on_Personality

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anime, fourfolds

The Four Immeasurables

November 17, 2021 Martin K. Jones Leave a comment

May all beings have happiness and the causes of happiness.
May they be free of suffering and the causes of suffering.
May they never be separated from supreme joy beyond all sorrow.
May they abide in equanimity free from attachment and aversion.

— Buddhist Prayer

I’m currently watching a beautiful anime called “The Heike Story”, based on the Japanese Tale of the Heike. The central character is a child plagued with the ability to see visions (usually of death and destruction) of the future and remote events. She is anguished to witness these and is powerless to do anything about them, but finally (spoilers!) determines that she might ease her mind by praying for those involved.

This character is not portrayed as any sort of religious individual, so I wondered what kind of prayer might be appropriate for her. Searching for an “Atheist Prayer”, I quickly found the Buddhist Prayer above that might be something like she would say, that encodes the “Four Immeasurables” of Buddhist thought. This prayer is not offered to any god or gods, but just a wish and hope for those in mind and indeed for all sentient beings.

The Four Immeasurables of Buddhism are

Maitri: Loving kindness
Karuna: Compassion
Mudita: Sympathetic Joy
Upeksha: Equanimity

Further Reading:

https://iai.tv/articles/prayer-for-atheists-auid-1181

The Four Immeasurables

https://www.google.com/search?q=four+immeasurables&tbm=isch

https://en.wikipedia.org/wiki/The_Heike_Story

[*13.16]

eightfolds, fourfolds

The Four Elements of Thinking

October 10, 2021 Martin K. Jones Leave a comment

While searching for something else I chanced upon “The Four Elements of Thinking: Reasoning, Creativity, Synthesis, Evaluation” by Benjamin Cheung, Ph.D., published in 2019. Any book about the four classical elements being used as metaphors for other things is of personal interest, plus that the things being four aspects of thinking was immediately intriguing. Dr. Cheung divides thinking into the four aspects of the subtitle, plus he divides each aspect into four sub-aspects or skills as follows:

- Reasoning (Earth Thinking)
  - Evidence
  - Inductive Reasoning
  - Deductive Reasoning
  - Abductive Reasoning
- Creativity (Air Thinking)
  - Investigation
  - Incubation
  - Insight
  - Innovation
- Synthesis (Water Thinking)
  - Linking
  - Perspective
  - Synthesis
  - Pivots
- Evaluation (Fire Thinking)
  - Decisions
  - Judgments
  - Contingency Plans
  - Validation

Note his choice in assignment of the Classical Four Elements to each of these aspects of thinking. I would have assigned them differently: Reasoning to Fire, Creativity to Earth, Synthesis to Air, and Evaluation to Water. The price of the e-book is reasonable, so I may investigate the “thinking” behind his alignments by purchasing and reading further.

He also has an interesting book on collections of ideas which he arranges into a “periodic table,” which might be analogous to a more modern scientific elemental assignment. Additionally, he has had Kickstarters on playing or flash cards for both books, which is a notion somewhat dear to my heart (See A Game of Fourfolds).

I have mentioned thinking or thought often in this blog, and believe that poor thinking or irrational thinking is greatly to blame for many of our current ills. Blame can also be attributed to poor communication skills. The best thinking can be obscured by poor communication. What is the best theory of the linkage between thought and language?

Further Reading:

Benjamin Cheung, Ph. D. / The Four Elements of Thinking: Reasoning, Creativity, Synthesis, Evaluation

Link to Amazon

https://en.wikipedia.org/wiki/Language_and_thought

[*13.1]

eightfolds, fourfolds, Physics, Science

Maxwell Relations

September 25, 2021 Martin K. Jones Leave a comment

Maxwell Relations are commonly known as a set of four partial differential equations between four thermodynamic quantities or potentials: pressure (P), volume (V), temperature (T), and entropy (S). So for example the expression (∂T/∂V) |_S means the partial derivative of T with respect to V while keeping S constant.

- (∂T/∂V) |_S = -(∂P/∂S) |_V
- (∂P/∂T) |_V = (∂S/∂V) |_T
- -(∂S/∂P) |_T = (∂V/∂T) |_P
- (∂V/∂S) |_P = (∂T/∂P) |_S

In my diagram above, the expressions that are equal are on either side of the common leg of adjacent isosceles right triangles.

Further Reading:

https://en.wikipedia.org/wiki/Maxwell_relations

Maxwell’s Relations (Part 1)

Maxwell’s Relations (Part 2)

Maxwell’s Relations (Part 3)

https://en.wikipedia.org/wiki/Thermodynamic_potential

Thermodynamics and the Four Thermodynamic Potentials

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Computation, fourfolds, linear logic, logic, Mathematics

Linear Process Algebra

August 27, 2021 Martin K. Jones Leave a comment

One of computer scientist and Professor Emeritus Vaughan Pratt’s most recent conference papers is on “linear process algebra,” which relates several of his previous interests on linear logic, Chu spaces, concurrent processes, events and states, etc.

The paper opens with a nice overview of computer science research primarily concerned with concurrent processes. Computation itself divides into the aspects of logical and algorithmic, formal methods into the logical and algebraic, concurrent computation into operational and denotational, and then the author gives a brief list of models of processes by a variety of mathematical structures until he comes to his theme of using Chu spaces.

As an example, he presents processes as Chu spaces over the set K, where K = { 0, T, 1, X}, with names and meanings :

0: Ready
T: Transition
1: Done
X: Cancelled

and then details four binary operations as working in Chu spaces over K:

P ; Q: Sequence
P + Q: Choice
P || Q: Concurrence
P ⊗ Q: Orthocurrence

Further Reading:

Vaughan Pratt / Linear Process Algebra

Click to access bhub.pdf

Click to access lpa.pdf

Click to access bud.pdf

https://www.researchgate.net/publication/2663060_Chu_Spaces_A_Model_Of_Concurrency

https://www.researchgate.net/publication/222310260_Types_as_Processes_via_Chu_spaces

https://en.wikipedia.org/wiki/Vaughan_Pratt

https://dblp.org/pid/p/VRPratt.html

[*12.122]

anime, fourfolds

Neon Genesis Evangelion Rebuilt, V2

August 19, 2021 Martin K. Jones Leave a comment

The fourth movie was finally made and finally shown! Thank you Hideaki Anno, for finishing your rebuild, and Amazon Prime, for letting us easily see all four.

Full of battles between giant robots and kaiju called angels, full of teenage, human, and non-human emotional struggles, and full of signature Evangelion nonsense, about midway I was getting a bit unhappy with it. But as it coming to a close I thought that this was indeed a good ending.

So what does “Thrice Upon a Time” mean? That this is the third ending? First for the series, second for the movies after the series, and thirdly for the rebuilt movies? And what does the designation “3.0+1.0” mean? Three movies plus one more?

Further Reading:

https://www.cnet.com/news/anime-epic-evangelion-gets-a-worthy-conclusion-heres-the-ending-explained/

https://www.indiewire.com/2021/08/evangelion-thrice-upon-a-time-review-1234658228/

https://www.polygon.com/22627444/watch-evangelion-franchise-amazon-netflix

https://en.wikipedia.org/wiki/Evangelion:_3.0%2B1.0_Thrice_Upon_a_Time

Neon Genesis Evangelion Rebuilt

fourfolds, Philosophy, Physics, Science

On the Death of a Giant

August 1, 2021 Martin K. Jones Leave a comment

Renowned physicist Steven Weinberg passed away recently. He was a giant in the world of physics and winner of the Nobel prize, advancing knowledge about the Standard Model and the unification of physical forces. He was also, famously, a materialist and atheist.

In his book “The Sophist”, Plato wrote (metaphorically?) about the battle of the gods and the giants. He related how the gods were friends of Platonic forms (perhaps being close to forms themselves) whereas the giants were materialists. Plato, being partial to forms, painted the giants as militant and unreasonable materialists, and the gods as a friendly and peaceful sort.

The Greek gods were friendly and peaceful? Perhaps the giants of the legend were the easy-going and reasonable sort, since the gods of the Greeks seemed the opposite. They say that history is rewritten by the victors.

Further Reading:

https://en.wikipedia.org/wiki/Steven_Weinberg

With Steven Weinberg’s death, physics loses a titan

https://www.scientificamerican.com/article/learning-to-live-in-steven-weinbergs-pointless-universe/

https://www.washingtonpost.com/local/obituaries/steven-weinberg-nobel-winning-physicist-who-united-principal-forces-of-nature-dies-at-88/2021/07/26/75d8d24a-ee31-11eb-bf80-e3877d9c5f06_story.html

A very nice article:

https://www.scottaaronson.com/blog/?p=5566

http://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.01.0172%3Atext%3DSoph.%3Apage%3D246

eightfolds, fourfolds, logic, Philosophy

John Buridan’s Octagon of Opposition

July 8, 2021 Martin K. Jones Leave a comment

Medieval logician John (or Jean) Buridan was a scholar of Aristotle, and wrote many works of commentary and elaboration on Aristotelian philosophy. Several items in logic and philosophy are tied to Buridan (such as Buridan’s Bridge and Buridan’s Ass) but he may now be more widely known for his Octagon which combines Aristotle’s Square of Opposition with a Square of Modality.

Below and to the right is a fourfold diagram of Aristotle’s Square of Opposition. The modern universal and existential (or particular) qualifiers are ∀ (meaning All) and ∃ (meaning Some), respectively. Also in these diagrams, ¬ means logical Not.