Category Archives: eightfolds

The Gnostic Ogdoad

ChatGPT said:

The Gnostic Ogdoad is a group of eight divine beings or emanations that were central to certain Gnostic cosmologies. The divisions of the Gnostic Ogdoad vary depending on the specific Gnostic system, but generally, they consist of four pairs of male and female aeons, or divine beings.

Here is one example of the divisions of the Gnostic Ogdoad [note: some of my Greek names at right are different. See refs. below.]:

  1. Barbelo and Bythos: Barbelo represents the divine feminine aspect of the highest deity, while Bythos represents the divine masculine aspect. Together, they represent the ultimate unity and transcendence of the divine.
  2. Nous and Aletheia: Nous represents divine mind or wisdom, while Aletheia represents truth. Together, they represent the intellectual and rational aspects of the divine.
  3. Logos and Zoe: Logos represents divine word or speech, while Zoe represents life. Together, they represent the creative and life-giving aspects of the divine.
  4. Anthropos and Ecclesia: Anthropos represents the divine human or perfect man, while Ecclesia represents the divine assembly or church. Together, they represent the human and social aspects of the divine.

It’s important to note that different Gnostic systems may have different variations or interpretations of the Ogdoad, and some may not include all eight divine beings.

Further Reading (not by ChatGPT):

Previously I wrote about a different, earlier Ogdoad:

The Ogdoad: Unity of Eight Gods



The Ancient and the Modern

In the past, I’ve created several diagrams juxtaposing pairs of fourfolds, for example

So here’s another, The Four Classical Elements and Space-Time-Energy-Matter.

I asked ChatGPT to look at this association: “Please write a short essay comparing and contrasting the classical four elements of air, fire, earth, and water with the modern scientific foursome of space, energy, matter, and time.”

The concept of the classical four elements of air, fire, earth, and water has been a fundamental aspect of ancient philosophy for thousands of years. This idea, which was first proposed by the ancient Greek philosopher Empedocles, held that these four elements were the building blocks of the universe and were responsible for all natural phenomena.

In contrast, the modern scientific foursome of space, energy, matter, and time provides a more comprehensive and rigorous explanation of the nature of the universe. Space refers to the three-dimensional continuum in which all matter exists, and it provides the framework for the movements of objects. Energy refers to the capacity of a system to perform work and is responsible for all physical and chemical processes. Matter refers to any physical substance, including solid, liquid, and gas. Time, on the other hand, is a fundamental aspect of the universe that allows for the measurement of the duration of events and the progression of physical processes.

One key difference between the classical and modern concepts of the elements is that the classical elements were thought to have qualities and personalities, while the modern elements are purely physical and mathematical constructs. The classical elements were thought to interact with each other in specific ways to produce the natural world, while the modern elements interact according to the laws of physics and chemistry.

Another difference is that the classical elements were limited to four, while the modern elements form a much more complex and nuanced picture of the universe. This difference reflects the advancement of human knowledge and understanding of the natural world over time.

In conclusion, the classical four elements of air, fire, earth, and water have played an important role in shaping human thought and culture. However, the modern scientific foursome of space, energy, matter, and time provides a more comprehensive and scientifically rigorous explanation of the universe and its workings. Both concepts have contributed to our understanding of the world, and they continue to play a role in shaping our ideas about the nature of reality.

Not quite enough, so I replied “Thank you, that’s pretty good. However, please say more about how air is like space, how fire is like energy, how earth is like matter, and how water is like time.”

Certainly! Let me expand on the similarities between the classical elements and the modern scientific elements:

1. Air and space: Both air and space are often thought of as being intangible and difficult to define. They both provide the framework for other physical phenomena, such as the movements of objects in space or the flow of air currents. Additionally, both air and space have the ability to contain other elements or substances, such as the gases that make up air or the stars and planets that exist within space.

2. Fire and energy: Fire is often associated with heat and light, and it can be both destructive and transformative. Energy also has the ability to transform physical systems, such as through chemical reactions or the transfer of heat. Furthermore, fire can be seen as a form of energy that is released through combustion, and it can be harnessed for practical purposes, such as cooking food or heating homes.

3. Earth and matter: Earth is often thought of as being solid and unchanging, while matter is the physical substance that makes up the universe. Earth provides a foundation for other physical phenomena, such as the growth of plants or the construction of buildings. Similarly, matter provides the building blocks for physical systems, such as the atoms and molecules that make up the substances in our world.

4. Water and time: Water is often thought of as being cyclical and constantly changing, such as through the phases of the tides or the flow of rivers. Time is also cyclical and constantly changing, as it moves forward and allows for the progression of physical processes and the measurement of the duration of events. Furthermore, just as water can shape the physical world through erosion and the formation of land masses, time shapes the physical world through its influence on the progression of physical processes.

In conclusion, there are certainly similarities between the classical four elements of air, fire, earth, and water, and the modern scientific foursome of space, energy, matter, and time. These similarities reflect the continuity of human thought and understanding of the natural world, and they demonstrate the ongoing influence of ancient ideas in shaping our modern understanding of the universe.


The Main Sequence of Star Types

I will scan your star charts.

— Nomad, from Star Trek “The Changeling”

While reading “Entering Space” by Robert Zubrin, I chanced upon the subject of stellar classification. The Morgan-Keenan system goes from O-type, the hottest, to M-type, the coolest (Red dwarfs). Our own sun, Sol, is an example of a G-type star, which are on the cool side yet still hot and bright. Later, other types have been added, for example White Dwarfs are known as D-types. If humankind will someday journey to remote stars, it’s best to memorize this handy list!

The Morgan-Keenan system is as follows:

  • O-type
  • B-type
  • A-type
  • F-type
  • G-type
  • K-type
  • M-type

This is sometimes remembered by the mnemonic “O be a fine gal/guy, kiss me.”

Further Reading:



The Millennial Project: colonizing the galaxy in eight easy steps

The eight “easy” steps of the Millennial Project (MP) are:

  • Foundation (Institutions to promote MP)
  • Aquarius (Colonize and utilize Earth’s oceans)
  • Bifrost (To low Earth orbit and outer space)
  • Asgard (Build a large space station)
  • Avalon (Colonize and utilize the Moon)
  • Elysium (Colonize Mars)
  • Solaria (Colonize the Solar System)
  • Galactia (Then on to the Milky Way)

Further Reading:

Marshall T. Savage / The Millennial Project

Robert Zubrin / Entering Space: creating a space-faring civilization

Robert Zubrin / The Case for Mars

Carl Sagan / Pale Blue Dot: a vision of the human future in space

MP reminds me a bit of Olaf Stapledon:


Linear Logic and the Four Elements

Here is an alignment between two of my favorite topics, the four operators of linear logic and the four elements.

I’ve been wanting to create this eight-fold for a while, and so here it is. I think it looks rather nice.

At this point I should present my reasons for this symbolic amalgam, but I leave it up to you, dear reader.

However, I will write the names of the symbols starting with the upper left and going widdershins…

  • Fire / With
  • Earth / Plus
  • Water / Times
  • Air / Par

[*5.188, *11.26, *13.82]


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:




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:






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


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 Eight Legged Essay

Further Reading: