Further Reading:
https://en.wikipedia.org/wiki/Quark
https://en.wikipedia.org/wiki/Eightfold_way_(physics)
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Category Archives: fourfolds
Build Your Atomic Habits
In Atomic Habits, author James Clear describes the behavior of making and breaking habits in four stages:
- Cue:
To increase a habit, make its cue obvious
To decrease a habit, make its cue invisible - Craving:
To increase a habit, make its craving attractive
To decrease a habit, make its craving offputting - Response:
To increase a habit, make its response easy
To decrease a habit, make its response hard - Reward:
To increase a habit, make its reward satisfying
To decrease a habit, make its reward unfulfilling
Further Reading:
James Clear / Atomic Habits: An Easy & Proven Way to Build Good Habits & Break Bad Ones
https://aliabdaal.com/book-notes/atomic-habits-summary/
Atomic Habits: An Easy & Proven Way to Build Good Habits & Break Bad Ones
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Et in Arcadia Ego
Further Reading:
https://en.wikipedia.org/wiki/Et_in_Arcadia_ego
https://en.wikipedia.org/wiki/Et_in_Arcadia_ego_(Guercino)
https://en.wikipedia.org/wiki/Memento_mori
https://en.wikipedia.org/wiki/Mono_no_aware
https://en.wikipedia.org/wiki/Sic_transit_gloria_mundi
https://en.wikipedia.org/wiki/Vanitas
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Surrounded by Idiots
Here’s another modern-day take on the Four Temperaments, a popular book series by Thomas Erikson called “Surrounded by Idiots.” After the original which is subtitled “The Four Types of Human Behavior and How to Effectively Communicate with Each in Business (and in Life),” he has written sequels titled “Surrounded by Narcissists,” “… by Psychopaths,” “… by Bad Bosses,” and “… by Setbacks”.
I have found a simple chart explaining his original four types using a two-by-two matrix of introvert vs. extrovert and task or issue-oriented vs. relation-oriented, and a review I read indicates that the DISC Theory of personality is the main influence for the author (and which is also related to humorism.)
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- Red: Extrovert and Task/Issue-oriented
- Yellow: Extrovert and Relation-oriented
- Blue: Introvert and Tasks/Issue-oriented
- Green: Introvert and Relation-oriented
Notably the cover art for the series uses four colors for the different types of people: Red, Yellow, Green, and Blue. These colors are sometimes also used by others to denote the Four Temperaments. These four colors are often used for other classification schemes, and even for corporate logos. Also, these four colors are the set union of the three primary colors of light and the (traditional) three primary pigments.
Further Reading:
Thomas Erikson: Surrounded by Idiots
https://www.businessinsider.com/guides/learning/surrounded-by-idiots-book-review
https://en.wikipedia.org/wiki/Humorism
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The Four-Drive Theory
The Four-Drive Theory of Lawrence and Nohria of the Harvard Business School is a popular model for the motivations of employees within a work environment. They list four drives which need to be in balance for worker happiness and productivity:
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- Drive to Acquire
- Drive to Bond
- Drive to Learn
- Drive to Defend
Further Reading:
Paul R. Lawrence, Nitin Nohria / Driven: how human nature shapes our choices
http://changingminds.org/explanations/needs/lawrence_nohria.htm
https://blogresellerprofits.com/2020/02/14/four-drive-model-theory/
Images for Four Drive Theory:
https://www.google.com/search?q=four+drive+theory&tbm=isch
Also:
http://changingminds.org/explanations/needs/needs.htm
https://en.wikipedia.org/wiki/Four_Fs_(evolution)
https://en.wikipedia.org/wiki/Leadership
(Where’s a Wikipedia Page?)
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The Diamond Approach Design Method
Again, I have taken a diagram and bent it into my preferred vision. At least the original figures have isosceles right triangles to begin with. However, they were in a left-to-right sequence (ordered by time) instead of a cycle as I have done. On many diagrams of the diamond approach there are indeed loops that return the user to positions earlier in the sequence so I don’t feel too bad.
The steps that are part of the diamond approach are reminiscent of other learning cycles, such as that of Kolb. The original left-to-right sequence emphasizes the order, as well as showing that steps may be divergent or convergent (analytic or synthetic) in their methods. Instead I have denoted divergence by arrows facing away from each other and convergence by arrows facing towards each other.
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- Discover (divergent)
- Define (convergent)
- Develop (divergent)
- Deliver (convergent)
The main creator of the Diamond Approach is A. H. Almaas, who has written many books on spirituality or esoteric subjects such as the Enneagram. Being a skeptical sort, I have no idea if the notions and methods in these books are worth your time, but the goals indeed sound laudable. How do they differ from psychoanalysis, psychotherapy, or other techniques to improve mental health? Further reading may be required before you pay for classes and retreats.
Further Reading:
https://www.diamondapproach.org/home
https://www.diamondapproach.org/almaas
https://en.wikipedia.org/wiki/A._H._Almaas
https://www.google.com/search?q=the+diamond+approach+design+method&tbm=isch
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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.
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- 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:
Disciplines, Fields, and Virtues: The Full Stoic System in One Neat Package
Images of Logics, Ethics, Physics:
https://www.google.com/search?q=logics+physics+ethics&tbm=isch
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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:
https://en.wikipedia.org/wiki/Law_of_excluded_middle
https://en.wikipedia.org/wiki/Law_of_noncontradiction
https://plato.stanford.edu/entries/logic-classical/
https://plato.stanford.edu/entries/logic-intuitionistic/
https://plato.stanford.edu/entries/logic-linear/
Pete Wolfendale / Essay on Transcendental Realism
(at PhilPapers)
https://plato.stanford.edu/entries/contradiction/
https://ncatlab.org/nlab/show/paraconsistent+logic
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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:
https://en.wikipedia.org/wiki/Claude_Fayette_Bragdon
https://www.gutenberg.org/ebooks/author/4128
https://theosophy.wiki/en/Claude_Fayette_Bragdon
https://rbscp.lib.rochester.edu/bragdon-family-papers-claude-bragdon-architectural-drawings
https://rbscp.lib.rochester.edu/3514
https://bauarchitecture.com/research.loshuworldofwonderous.shtml
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!
https://reelrundown.com/animation/Anime-Philosophy-1-Melancholy-of-Haruhi-Suzumiya
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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
or
- 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/
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Equivalent Exchange 