Archive for the ‘fourfolds’ Category

Free Four

July 11, 2018

One, two, free, four!

— Pink Floyd

There ain’t no such thing as a free lunch.

— Origin unknown

In the United States of America we celebrated freedom on July 4th. Here are four free or not so free things.

It is useful to consider Richard McKeon’s words on freedom from his Philosophic Semantics and Philosophic Inquiry:

The question, What is freedom? is one of the recurrent ambiguous questions of philosophy which has opened up new dimensions in contemporary thought and action. It is a significant question because the initial interpretation, “freedom is the absence of external impediments to action,” focuses attention on the need to remove the ambiguities of “absence”, “external”, “impediments”, and “actions” and the growing host of ambiguities in each clarifying statement. The semantic scheme constructed from the modes of thought sets forth, thus far (see chart p.253), three sets of determinations of the question, What is freedom? What is freedom in fact or interpretation, What things are free?; What is freedom in thought or method, What property do free things share?; What is freedom in being or principle, What are the grounds of the possibility or the actuality of freedom? The question takes on a vast scope of meanings under these distinctions; and since a complete interpretation of the question makes use of all four semantic headings, the number is increased by the number of possible combinations of the four. The indefinitely large number of possible meanings is the source of the richness of philosophic inquiry, for each interpretation may be used as the hypothesis for further investigation.

Further Reading:


Four Freedoms






The Eisenhower Matrix

July 7, 2018

What is important is seldom urgent and what is urgent is seldom important.

— Dwight Eisenhower, 34th President of the USA.

For your self improvement, here is a simple two by two matrix that can help you decide how to prioritize your “To Do” list. Sort everything into four groups, depending on whether it is important or not, and whether it is urgent or not:

  • Important & Urgent : Do First
  • Not Important & Urgent : Delegate
  • Important & Not Urgent : Do Later
  • Not Important & Not Urgent : Eliminate

Further Reading:

Other images of the Eisenhower Matrix:





Science, Technology, Engineering, and Mathematics

June 14, 2018

STEM: Science, Technology, Engineering, and Mathematics. We often hear that these areas of education and expertise are critical for the development of our modern society. To attract students to these fields, banners and logos are full of bright colors and crisp graphics. In comparison, above is my rather dull diagram. Not very enticing, is it?

Some are now adding Arts to the four, giving STEAM. I think the Arts are important of course, but fives don’t go with my oeuvre.

In addition, I give you a diagram with Chinese substituted for English (科學 技術 工程 數學).

Further Reading:,_technology,_engineering,_and_mathematics



Wan Shou Wu Jiang

June 10, 2018

While eating out the other day I noticed a melamine plate with an interesting fourfold arrangement of Chinese characters on it. After asking the waitress what they meant and she didn’t know, I decided to figure them out using “the internet”. I first tried to use a photo of one of the characters with Google translate, but that didn’t seem to work. Next I tried several “draw the character” websites like Mobilefish, but those are tricky and require you to draw the strokes of the character in the correct sequence. Finally, with some success I was able to determine that the characters “Wan Shou Wu Jiang” (wàn shòu wú jiāng or 萬壽無疆) mean “infinite long life”, and are on many Chinese tableware, both antique and everyday.

I have to say I think representing fourfolds with such tidy logograms is quite beautiful and I would enjoy seeing my diagrams translated into them.

Further Reading:万寿无疆-porcelains-since-the-late-qing-period/萬壽無疆&client=firefox-b-1&source=lnms&tbm=isch&sa=X&ved=0ahUKEwjNocTB-r3bAhVEoFMKHTWDBaEQ_AUICigB&biw=1480&bih=985



The Infinity Stones

April 16, 2018

Sure, why not? Here is a handy-dandy diagram for the six Infinity Stones appearing together soon in the latest Marvel/Disney extravaganza.

Further Reading:

Please compare to other fine six-folds in this blog, for example:




March 29, 2018

What happens when the fourfold of Noether’s Theorem is spliced together with the fourfold of Pauli-Jung? Both have Space-Time and Matter-Energy. The former has Conservation and Symmetry, and the latter has Causality and Synchronicity.

I had to remind myself that Conservation means consistency (of matter or energy) through time (and space), and Symmetry means consistency (of form) through space (and time), so in some sense they are dualistic.

Combined, one has the three axes of dual concepts, represented above.

Further Reading:



The Six Elements

March 26, 2018

What happens if one combines the four classical Greek (Western) elements with the five classical Chinese (Eastern) elements? Air is in the former and not the latter. Wood and metal are in the latter and not the former.

I’ve left out the Aether (the Fifth Element) of the West because I follow Empedocles, and I see that the five classical Japanese elements have those four and Void as well. But, I’m just looking at material and tangible elements.

One might consider Wood and Metal to be derivatives of Earth, but let’s consider them to be distinct for this exercise. So, maybe six elements!

Further Reading:



A General Theory of Value, Part 2

March 20, 2018

What is value?

In his unpublished book “A General Theory of Value”, architect Michael Benedikt argues for a information-theoretic account of value, defining value as follows:

The theory of value offered in this book revolves around three propositions: first, that positive value is attributed to that which preserves or creates more life; second, that “lifefulness” is characterized by a particular quantity and combination of complexity and organization; and third, that in the case of human societies and minds, achieving this optimal quantity and combination of complexity and organization depends on the quality and flow of information among people, and between people and their less-animate environment—plants, animals, buildings, places, things.

It is fascinating that the things that are alive and the products of these lives obtain the highest calculated value of “complexity and organization”.

In order to begin to quantify value, a measurement of the complexity and a measurement of the organization of an entity or system is required. It is worth noting that “not organized” does not mean “complex”, nor does “not complex” mean “organized”. Thus complexity and organization are independent of one another.

Above I have schematized Benedikt’s “Ω Plane”, which consists of two axes, organization and complexity, ranging from disorganized (chaotic) to organized, and simple to complex. “Δ Ω” is simply the measure of the increase in both complexity and organization, and points the way to “value”.

Generously, Benedikt has made his unpublished book available on his web site for all to read.

Further Reading:

Michael Benedikt / A General Theory of Value (unpublished)

A good resource for reading about information:

Also see Cesar Hidalgo’s excellent “Why Information Grows”.

Cesar Hidalgo / Why Information Grows: The Evolution of Order, from Atoms to Economies

[*7.132, *10.86]


A General Theory of Value

March 16, 2018

What is value?

In “A General Theory of Value”, philosopher Ralph Barton Perry argued for a naturalistic account of values, defining value as “any object of any interest.”

From 1946 to 1948, Perry gave a Gifford Lecture, which later was enlarged to became his book “Realms of Value”. The Gifford Lectures are purportedly about “natural theology”, but many normative subjects have been addressed in them.

Above I have diagrammed Perry’s eight “realms of value”, although I have changed morality to ethics. I have also paired them up to give a fourfold, which doesn’t seem too erroneous.

  • Custom and Art
  • Economics and Science
  • Politics and Law
  • Religion and Ethics

I’m disappointed that Knowledge is missing from his list, but I could eliminate some of his choices and rearrange a bit to make room for it.

Further Reading:

Ralph Barton Perry / A General Theory of Value: its meaning and basic principles construed in terms of interest

Ralph Barton Perry / Realms of Value (Gifford Lectures)

On this blog: The World Values Survey


Another “General Theory of Value” available on the web:

C. L. Sheng / A Utilitarian General Theory Of Value

[*10.74, *10.75]


The Glass Bead Game

March 6, 2018

No permanence is ours; we are a wave
That flows to fit whatever form it finds:
Through night or day, cathedral or the cave
We pass forever, craving form that binds.

― Hermann Hesse, The Glass Bead Game

“The Glass Bead Game”, also known as “Magister Ludi”, is the last full length book by German author Hermann Hesse. His works include many thoughtful and interesting stories, detailing the main character’s personal development and spiritual growth. Hesse won the Nobel Prize in Literature in 1946, and his books saw a resurgence of popularity in the 1960’s and 1970’s in the US.

“The Glass Bead Game” is special to me because it describes, although vaguely, a fictional game that is cultivated and played in a future idyllic setting of intellectual devotion, although the larger world is certainly a post-apocalyptic one. All human knowledge is the subject of the game, and the play somehow links mathematics, music, science, cosmology, history, poetry and literature and everything else accepted as higher learning for the imagined cultural time and place.

Is the book sexist because it describes the cloistered society of the game as being restricted to boys and men because of ability, or the idea that men are less distracted from intellectual pursuits without women around? The book is either a product of its time, or perhaps of the political setting in its fictional future. Interestingly, the main character, along with three other character’s lives shown in short stories said to be written by the main character himself, are easily associated with Carl Jung’s theory of psychological types. This is the meaning of the figure above.

Several individuals and groups have tried to imagine how the actual game or any “glass bead game” (GBG) could be played, and there are scattered links on the web, many broken over time and neglect. I agree that analogy and metaphorical thinking are key points to any GBG, as well as the other pillars of attributes nicely discussed in links below.

  • Analogy
  • Connection (or Affinity)
  • Cogitation (or Contemplation, Thought)
  • Formalism (or Rules)
  • Iconicity (or Representation)
  • Syncretism (or Objectivation, of Culture or Civilization)

(Some attributes have been substituted by thesaurus for word length.)

Further Reading:

Hermann Hesse / The Glass Bead Game

… For although in a certain sense and for light-minded persons non-existent things can be more easily and irresponsibly represented in words than existing things, for the serious and conscientious historian it is just the reverse. Nothing is harder, yet nothing is more necessary, than to speak of certain things whose existence is neither demonstrable nor probable. The very fact that serious and conscientious men treat them as existing things brings them a step closer to existence and to the possibility of being born.

[*8.138, *10.82]


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