Category Archives: eightfolds

The Eight Legged Essay

Further Reading:




The Four Elements of Thinking

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



Maxwell Relations

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:

Thermodynamics and the Four Thermodynamic Potentials

[*12.194, *12.195]


John Buridan’s Octagon of Opposition

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.

  • ∀ S are P
  • ∃ S are P
  • ∀ S are ¬ P
  • ∃ S are ¬ P

Next I show a fourfold of modal operators and their equivalents. The modern modal symbols are (meaning Necessarily) and or ◊ (meaning Possibly).

  • P ≡ ¬ ◊ ¬ P
  • ◊ P ≡ ¬ ¬ P
  • ¬ P ≡ ◊ ¬ P
  • ¬ ◊ P ≡ ¬ P


Further Reading:

The Art of the Syllogism

Click to access Demey_DWMC2015_Buridan_Avicenna_slides.pdf

Click to access Buridan_Octagon.pdf

Click to access hughes-buridan.pdf





Humankind, Unbound

Many books detail how we are our own worst enemy, how we are too smart for our own good, or not smart enough in the right way. This one traces the origin and evolution of eight technologies that make us who we are today, for better or worse.

  • Fire
  • Tools (incl. Digging tools, Weapons)
  • Language (incl. Writing, Music, Art, Symbolic Communication, Ethnicity, Culture)
  • Clothing
  • Shelter
  • Farming (Agriculture, Husbandry)
  • Machines (incl. Ships, the Wheel, and on to Precision Machinery)
  • Computers

Instead of having two technologies, “Clothing” and “Shelter,” Currier combines them, and lists “technologies of interaction” which includes writing, water-craft, the wheel, etc.

Can we overcome the myriad conflicts that threaten our survival? Please check back in a hundred years to see how we’re doing! It’s not very long, compared to how far we’ve come.

Further Reading:

Richard L. Currier / Unbound: how eight technologies made us human, transformed society, and brought the world to the brink

Some reviews:

Book Summary: “Unbound: How Eight Technologies Made Us Human” by Richard L. Currier

Click to access Volume8-Number1-Article7.pdf





I’ve written a few times about relating two different fourfolds and juxtaposing or comparing them in one eightfold diagram. A normal analogy is usually written as A:B::C:D, which means A is to B as C is to D. So if you have two such fourfolds, one way to write it as an eightfold is A:B::C:D:::E:F::G:H. I think a good name for this is a hyper-analogy. I couldn’t really find anything of merit about this concept, but perhaps it goes by another name.

I’m not sure what diagram arrangement shows this the best. Some ideas are 1) A-D are arranged vertically (as well as E-H) and both are arranged horizontally (side-by-side), or 2) A-D are the triangles pointing down, and E-H are the triangles pointing up. Or, 3) A-B can be the upper left and C-D the lower right squares, and E-H can be the upper right and lower left squares. Or, one can use the radial eightfold schema, and have 4) A-D are the triangles on the inside, E-H are the triangles on the outside (or vice-versa).

For example, here I show the Four Causes combined with my Structure-Function. Also, please examine my Eightfold Metaphysics, which combines Space-Time-Matter-Energy with Structure-Function. Additionally, another I like is the one for Tanabata, which relates the astronomical with the symbolized. I could go on and on, and probably will.

Further Reading:



The Tao of Thoth

Ethan Indigo Smith’s recent book, “The Tao of Thoth,” is a companion to a previous book of his I reviewed, “The Matrix of Four“. But instead of dwelling on fourfolds from ancient and esoteric sources, this book’s appeal to me is mainly for eightfolds. The sources are again traditional and occult, and indeed the title’s constituents come from ancient Asian and Egyptian cultures. Smith encourages us to contemplate these venerable concepts to reclaim simplicity in our lives and move away from any unnecessary complexity of modern life.

Certainly Smith is legitimate in critiquing present-day institutions and mentalities that valorize profit and consumption over ecological and humanitarian well-being. Can we learn from ancient cultural precepts and use them to heal the earth as a whole as well as enhance the health of our own lives, our descendants lives, and that of our follows? We seem to be avoiding the simple fact that current lifestyles are unsustainable for the earth and even harmful to our own psyche.

The first chapter introduces us to the Taiji, or Yin Yang, as well as the Tao of Asian study. The “Tao of Thoth” is also introduced and seems to be the relationship between the Taiji and the Tenets of Thoth (also referred to as Thoth Energy). Several claims are then made as to their separate and related simplicity and applicability. The next two chapters deal with this so-called Thoth Energy and the Taiji in more detail.

In Chapter 1 the Egyptian god Thoth is described in some detail, and his connection to gods in other mythologies, both Eastern and Western. The term Thoth Energy seems to describe the principles conceptualized by his attributes. That these principles are found in separate traditions is indicative our common humanity, rather than cultural approbation (maybe except for continuity between the Egyptian (Thoth), Greek (Hermes), and Roman (Mercury) gods). Next the Eight Trigrams of the Bagua and the eight deities of the Ogdoad are discussed.

A list of the Seven Tenets of Thoth close the chapter: Mentalism, Correspondence, Vibration, Polarity, Rhythm, Cause and Effect, Gender, and their relationship to the Tao. Hermetic and occult principles are often associated with individual self-development and not social coherence common to institutions. These tenets are the Seven Hermetic Principles mentioned in Chapter II of the Kybalion. Hermeticism is also deeply connected with Alchemic principles.

Chapter 2 discusses the Tao, Taiji (Yin Yang), and Taiji practice (Tai Chi). The Eight Layered Body is mentioned (the physical body, the chi body, the emotional body, mental body, psychic body, causal body, body of individuality, and the body of Tao). The next seven chapters deal with the seven hermetic principles which are hinted to align with Taoist principles as well, but do they do so in clear ways? Perhaps I need to study both the Kybalion and the Taiji in depth before I understand their connection.

And so briefly:

  • Chapter 3 (Mentalism) mentions The Eightfold Path.
  • Chapter 4 (Correspondence) mentions the Seven Minor Physical Planes (Chapter VIII of the Kybalion).
  • Chapter 5 (Vibration, Chapter IX of the Kybalion) mentions the Eight Limbs of Yoga.
  • Chapter 6 (Polarity, Chapter X of the Kybalion) mentions the Eight Energies or Gates of Taiji and the fourfold Known Knowns.
  • Chapter 7 (Rhythm, Chapter XI of the Kybalion) mentions the Bagua and Eight Taiji Principles.
  • Chapter 8 (Cause and Effect, Chapter XII of the Kybalion) mentions the Eight Auspicious Symbols of Buddhism.
  • Chapter 9 (Gender, Chapter XIII of the Kybalion, and Mental Gender, Chapter XIV) mentions the Eight Auspicious Offering Bowls and the Eight Secrets of the Tao Te Ching.
  • In Chapter 10, I am certainly glad that Smith rounded out the Seven Tenets to Eight with Patience. Mentioned are Chakras and the Spectrum of Light and the fourfold Wu Wei. In contrast, the last Chapter XV of the Kybalion deals with “Hermetic Axioms,” discussing several of the principles together.

After each chapter discussing a tenet, Smith suggests a Taiji or Taiji-inspired meditative practice that embraces a core concept: standing meditation, champion posture, shaking, arm swinging (Renunciation/Reintegration, Evaporation/Condensation), spiraling balance, pressurization, integrating Yin and Yang, walking.

It would be nice to have a bibliography and index included in this book, as many sources are mentioned and it would be convenient to have it as a quick reference. I must say that I didn’t find this short book as rewarding as “The Matrix of Four,” nevertheless, I found it worth reading and it piqued my interest for trying Tai Chi.

Further Reading:

Ethen Indigo Smith / The Tao of Thoth

The Three Initiates / The Kybalion

[*12.50, *12.51]




Who Do You Love?

Who do you love?
Who do you love?
Who do you love?
Who do you love?

— From Who Do You Love by Bo Diddley

The constituents of this list had pretty much congealed in my mind when I ran across information on the eight kinds of love. I thought that in this difficult time it might be useful to consider what is most important by examining all the people and all the things one can love as well as their myriad ramifications. Indeed, love may be the most considered and talked about emotion. Might one even say it is at the root of all of human action?

I know that in order to substantiate my claims I should justify these particular selections by comparing and contrasting them with each other, or to show their association to the eight kinds of love, and to do both would be a worthwhile effort. If I just show my diagram and my little list no one will think much of it. I could say I would return later but we all know how I tend to be distracted by the next bright shiny thing.

At the very least I could do some research, or do some hard thinking about why I’ve chosen these particular eight. I’m not sure if such diligence will reap any benefits but all one can do is try their best. So therefore I invite you to continue reading and perhaps you will be enlightened or perhaps you will be disappointed by what I say in the following analysis, if it even manages to appear at all.

I see that there are some modern analyses of love like Robert Sternberg’s Triangular Theory of Love, based on concepts of passion, intimacy, and commitment. This theory seems to be devoted to interpersonal relationships but maybe so is the Greek Eight types. But I’m thinking of love in a broader sense than just interpersonal, although maybe that doesn’t agree with certain definitions of love.

Love doesn’t have to reciprocated, of course, or directed towards another loving entity. For example, Agape is love of humanity in general, but humanity in general cannot return one’s love. One can also love negative things, like hate, or strife, or friction, and some even make a career out of it. But I’m going to leave that out for now. Alas, my interest has waned on this post and so I will have to try again at a later time.

  • Love of Self
  • Love of Leader
  • Love of Group
  • Love of Other
  • Love of Nature
  • Love of Ideas
  • Love of Gods
  • Love of Things

Further Reading:





The Eight Kinds of Love

There are several mentions of eight types of love purportedly discussed by the ancient Greeks, but I’m short on the actual references.

In no particular order:

  • Agape: unconditional love
  • Eros: romantic love
  • Philia: affectionate love
  • Philautia: self love
  • Storge: familiar love
  • Pragma: enduring love
  • Ludus: playful love
  • Mania: obsessive love

I had an earlier post on The Four Loves by C. S. Lewis, but now I see that he just left out half of them for some reason. Missing are Philautia, Pragma, Ludus, and Mania, which seem important, but since I haven’t read the book, I don’t know his reasons.

Further Reading:

8 Types of Love – Which One Are You?



The Eight Auspicious Symbols

Pause only for a moment to contemplate Ashtamangala, or the Eight Auspicious Symbols of Buddhism:

  • The Endless Knot
  • The Treasure Vase
  • The Lotus Flower
  • Two Golden Fish
  • The Fancy Parasol
  • The Conch Shell
  • The Victory Banner
  • The Dharma Wheel

Further Reading:

The Whitewater Rafter’s Guide to the 8 Auspicious Symbols of Buddhism