HyC Adventures
The Poetics of Perception
Meta-Fours

 

 

Meta-Fours

 

Hyatt Carter

 

 

Along with three and seven, four is a richly symbolic and mythic number that seems to turn up all over the place: four elements, four seasons, four directions, four dimensions (in our universe), DNA and RNA both have four bases . . . the list is long.

 

My fascination with the number four began many years ago with the study of James Joyce’s Finnegans Wake, a meanderthalltale wherein four plays a central role both structurally and thematically. Joyce would have been quick to notice a sexual innuendo in the previous sentence and, indeed, my continuing meditations on the numerous (and numinous) epiphanies of the number four may be thought of as foreplay . . . or four-play!

 

The number “four” figures prominently and frequently in our conceptual models, with Ken Wilber’s Four Quadrants as a salient example. Mandalas, wherein four symbolic objects are symmetrically placed, are enduring religious icons that express truth, beauty, goodness . . . and unity—if one may add “unity” to the traditional axiological trinity, thus making it a quaternity.

 

In light of all this, it seems safe to say that there is something deeply archetypal about the number “four.”

 

Michael Denton, in his excellent book Nature’s Destiny, even gives it a divine twist: “It has often been said that God is a mathematician; on the evidence of molecular biology we might add that He is keen on the number four.”

 

So pervasive a principle, and one that even enjoys divine sanction, deserves a name. And so I hereby christen these epiphanies of the number four as Meta-Fours—a play on the word “metaphor” and also the sense (or nonsense) of—A man’s reach should exceed his grasp or what’s a meta- for?

 

I’ll coin another word: Tetralogian.

 

Tetralogian plays on the word “theologian,” but whereas the theologian has as his field of expertise the nature of God, and things divine, the tetralogian looks into fourfold things, and the nature of Quad.

 

What about Tetragasms?

 

Tetragasms are what the Tetralogian enjoys during fourfold epiphanies.

 

Here is a quote from C. G. Jung on what he calls the “quaternity principle,” which gives me grounds for believing that my enchantment with the number four is not entirely trivial, or should I say quadrivial?

 

“The oldest mandala drawing known to me is a paleolithic ‘sun-wheel,’ recently discovered in Rhodesia. It, too, is based on the quaternary principle. Things reaching so far back into human history naturally touch upon the deepest layers of the unconscious, and can have a powerful effect on it even when our conscious language proves itself to be quite impotent.

 

“Such things cannot be thought up but must grow again from the forgotten depths if they are to express the supreme insights of consciousness and the loftiest intuitions of the spirit, and in this way fuse the uniqueness of present-day consciousness with the age-old past of life.” — Jung on Active Imagination, edited by Joan Chodorow

 

Meta-Fours are enshrined on the back of every dollar bill and you will find them if you contemplate the stars in the Great Seal. As Joseph Campbell observes in his book, The Inner Reaches of Outer Space:

 

“In the radiant disk above the American bald eagle’s head, the stars of the original 13 states are composed to form a Solomon’s seal symbolic of the union of soul and body, spirit and matter. Each of the interlaced equilateral triangles, one upward turned, the other downward, is a Pythagorean tetraktys, or ‘perfect triangle of fourness,’ of nine points, four to a side, enclosing a tenth representing the generative center (‘still point of the turning world’) out of which the others derive their force.

 

“The upward triangle is of spiritual, the downward pointing, of physical energy. Thus interlaced, the two rep­resent the physical world recognized as informed by the spiritual.”

 

 

 


 

 

Several friends share my interest in Meta-Fours and we have an ongoing game of coming up with puns, or word play, that involve the number 4. Here are four examples:

 

 1. May the fours be with you!

 2. Tour de Fours

 3. A Mighty Fourtress Is Our Quad

 

Jung, a quadratic thinker who favored four over the number three, and therefore a Quaternity over the Trinity, would surely have liked the fourth example:

 

 4. You can’t see the fourest for the threes.

 

 

A Sampling of

Meta-Fours

 

Four is the model of wholeness and completion. The examples from physics suggesting totality or completeness are most impressive: the four dimensions of space-time, the four basic forces underlying all interactions, the four components needed for a complete quantum relativistic description of the electron, and from the primitive sciences, the four basic elements: earth, air, fire, and water.

 

At the same time, in the psyche, four is the symbol of unity and completion—of a person’s striving for wholeness. Indeed, as von Franz says, “Jung devoted practically the whole of his life’s work to demonstrating the vast psychological significance of the number four. . . .”

 

Roger S. Jones, a research physicist and author of Physics as Metaphor, points out that the major task of his book is to explore “the four foundation concepts of physics: space, time, matter, and number.” He also refers to them as the four cardinal metaphors.

 

 

 

 

The four modes of evolution:

 

 Cosmogenesis

traces the origin and evolution of the physical universe;

 

 phylogenesis,

the evolutionary development of plant and animal species;

 

 ontogenesis,

the life cycle of a single organism or individual.

 

 Microgenesis

traces the developmental steps that lead to a single thought, feeling, or perception within the individual.

 

 

 

 

Wolfgang Pauli, the Noble laureate physicist, was great pals with Carl Jung, so it should come as no surprise that he was an aficionado of the fourfold. In one of his dreams, Pauli saw an image that came to be known as Pauli’s world clock. Note how the number four figures in this image:

 



 
 

 

 

 

As John Sanford reminds us in the following quote, the cross embodies the fourfold theme:

 

“The cross is in Christian imagery a mandala—a fourfold, concentric shape. The arms of Christ outstretched on it symbolize the whole of creation being embraced by Christ while the place where the four arms of the cross join is the Center. There are, of course, many mandalas found in the religions all over the world, suggesting, as Jung has shown, that everywhere life strives for wholeness and completion. There are also many other religions in which the symbol of the cross plays an important role, as Jung has also shown in his many writings. But the Christian cross is a little different, because it is fixed into the ground. The reason that one of the extensions of the cross is longer than the others is because it is grounded. This fixedness in the ground of the Christian cross relates to its rootedness in human life. Mystically speaking, we are the ground in which the mystery of the cross is to be grounded. Then and then only does the mystery become realized. When a person goes through the mysterion, the mystical initiation into the hidden significance of the cross, then the cross has become real, that is has been grounded in actual human existence.” (Mystical Christianity)

 

 

 

 

John Sanford on the number four:

 

“Jung does not invent the symbol of the Quaternity for wholeness, but is able to show that it comes up spontaneously in the symbols of the unconscious in order to represent the whole state. Wholeness, therefore, seems to have a four-fold structure, since the four appears over and over as a highly important number symbolic of the foundation for totality. Thus we have the Four Gospels in Christian lore, the importance of the number four in American Indian ritual, the four directions of the compass, the four corners of the square, the four functions of the psyche, and many other manifestations of the number four as a number that includes all that belongs to a total state.”

 

 

 

 

“The Fourfold Path of Jesus,” an essay in my book, Thinking Is the Best Way to Travel, discusses four intertwinings of a fourfold theme:

 

1) Jesus with his four ways of Heart, Soul, Mind, and Strength.

2) Jung’s four functions: Feeling, Intuition, Thinking, and Sensation.

3) The four disciplines of Yoga: Bhakti, Rajah, Jnana, and Karma.

4) Creation Spirituality’s four paths: positive, negative, creative, and transformative

 

 

 

 

Another elegant insight from the Buddhist tradition shows how pervasive are the secret workings of silence. The sacred syllable OM is said to be made up of four elements: oohuuhmmm: representing birth, life, “death,” and these three enclosed by the fourth element: the creative silence out of and back into which it unceasingly comes and goes.

 

 

 

 

An innovation by Charles Hartshorne has to do with the following question, How can we think adequately about the idea of God and the relation between God and the world until we know all the options? It was not until after his 90th birthday, after many years of reflection, that he finally solved to his satisfaction the arrangement of a 16-fold matrix that presents an exhaustive list of the formal options for thinking about God and the world—in terms of permutations of contrasting pairs such as necessity and contingency.

 

Hartshorne’s Matrix:


  I II III IV
1.  N.n  C.n  NC.n  O.n
2.  N.c  C.c  NC.c  O.c
3.  N.cn  C.cn  NC.cn  O.cn
4.  N.o  C.o  NC.o  O.o


Key to Interpretation:

I. God is wholly necessary

II. God is wholly contingent

III. God is diversely necessary and contingent.

IV. God is impossible or has no modal status.

 

1. World is wholly necessary.

2. World is wholly contingent.

3. World is diversely necessary and contingent.

4. World is impossible or has no modal status.

 

 

 

 

Maxwell’s Four Equations: 

 

 cL × E = – (δB / δt)

 cL × B = – (δE / δt)

 L · B = 0

 L · B = 0

 

 “In these equations, E stands for the electric field, B stands for the magnetic field, and c, the velocity of light, stands for a combination of electric and magnetic quantities that can be measured on a lab bench. Note here the symmetry of E and B. Never mind the incomprehensible doodles; for our purposes it’s not important to explain the workings of these equations. The point is, this is the scientific summons: ‘Let there be light!’” [ from The God Particle by Leon Lederman ]

 

 

 

 

The Four Quantum Numbers

 

It was once thought that it took three numbers, three quantum numbers, to locate an electron within an atom.

 

But Wolfgang Pauli decisively showed that it takes not three, but four quantum numbers to do the job. This insight led to Pauli’s discovery of what he came to call the “exclusion principle,” a discovery for which he was awarded the Nobel Prize for physics in 1945.

 

The four quantum numbers are named:

 

Principal QN, Angular Momentum QN, Magnetic QN, Spin QN

 

For a discussion of the Four Quantum Numbers, see the essay, “A Quartet of Quantum Numbers,” in my book, Some Little Night Musings.

 

 

 

 

The four levels of interpretation or meaning in a text:

 

 1. literal

 2. formal

 3. mythical

 4. anagogic

 

In the Jewish tradition, these are called:

 

 1. Pashat

 2. Remez

 3. Derash

 4. Sod

 

And in the Vedic tradition:

 

 1. Vaikri (gross)

 2. Madhyama (subtle)

 3. Pashyanti (causal)

 4. Para (ultimate)

 

 

 

 

The ending of a poem by William Blake:

 

 Now I a fourfold vision see,

 And a fourfold vision is given to me;

 Tis fourfold in my supreme delight

 And threefold in soft Beulah’s night

 And twofold always. May God us keep

 From Single vision and Newton’s sleep!

 

 

 

 

Note how Thomas Moore uses the four elements to characterize the mythical figure, Narcissus:

 

The ancient story of Narcissus, as told in the Metamorphoses of the Roman writer Ovid, is not just a simple story of a boy falling in love with himself. It has many subtle, telling details. Ovid tells us, for instance, that Narcissus was the son of a river god and a nymph. In mythology, parentage can often be taken as holding poetic truths. Apparently there is something essentially liquid or watery about Narcissus, and by extension, about our own narcissism. When we are narcissistic, we are not on solid ground (earth) or thinking clearly (air) or caught up in passion (fire). Somehow, if we follow the myth, we are dreamlike, fluid, not clearly formed, more immersed in a stream of fantasy than secure in a firm identity. [Care of the Soul, 57]

 

 

 

 

Deriving from quad-, “four” and via, “way or road,” quadrivial is a Joycean word that Jung would have appreciated since both writers were, like fours truly, aficionados of what I call Meta-Fours. The word brings to mind a crossroads, four roads that intersect and lead in four different directions. Pointing also in four directions, and with the same symbolic suggestiveness, is the Greek letter chi, whether in its lower- ( χ ) or upper-case form (X).

 

Which brings to mind a word that begins with chi

 

 

 

 

Chiasmus is a rhetorical figure that reverses the terms of the two clauses that make up a sentence, or a part of a sentence. You “cross” the terms by reversing their order. For example, in his “Ode to a Grecian Urn,” John Keats ends the poem with two lines that begin with a chiasmus:

 

 "Beauty is truth, truth beauty," — that is all

 Ye know on earth, and all ye need to know.

 

A tetralogical analysis reveals a fourfold structure that can be “crossed” as follows:

 

 truth       beauty

      χ

 beauty      truth

 

This entitles chiasmus to privileged membership in Meta-Fours.

 

For more on chiasmus, not only as a rhetorical figure but also, and more importantly, as a figure of thought, see the Chiasmus Page on this site.

 

 

     

     

 

 

The Fourfold Constant

 

While I use the term Meta-Fours, my friend David Spooner, a fellow tetralogian who hails from Scotland, speaks in terms of the Fourfold Constant. A sampling compiled by David:

 

Classes of compounds essential to life are 4 in number—nucleic acids, proteins, lipids and carbohydrates.

 

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The building blocks of life are four: carbon, nitrogen, oxygen, phosphorous.

 

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Hemoglobin is formed from 4 amino acids.

 

■□

 

The cerebrum of the human brain has 4 paired and major lobes of its own, and under this forebrain the remainder is similarly of 4 parts.

 

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There have been 4 major stages in the evolution of Homo sapiens:

 

 i) various Australopithecus

 ii) Homo habilis

 iii) Homo erectus

 iv) Homo sapiens

 

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The four orders of higher insects are the only ones with perfect metamorphosis—Lepidoptera, Coleoptera (beetles), Hymenoptera (ants, bees and wasps) and Diptera (two-winged flies, mosquitoes etc.).

 

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And, returning to the world of physics, in that concrete bunker between Cherbourg and Paris, an apparently entirely new form of nuclear matter has been formed. Tetraneutrons have been created, clusters of neutrons bound together in fours. It is hypothesized that tetraneutrons could be the nuclei of ‘element zero,’ an element without a proton currently missing from the periodic table.

 

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In the beginning, Indo-European language shows the centrality of the number four in origins. Its roots suggest that it was a base-4 language in which the fundamental number was 4, arising most probably from our mineral- and chemical-built digits. So counting worked on the principle of 4 + 1, 4 + 2 and so forth. The word for 8 in proto-Indo-European consists of a double form of the word for 4, that is 4 + 4. Then in leaping to the word ‘nine’ a root seems to be ‘new’ as in German neu and neun, Italian nove (new) and nuove (nine), French neuf (nine and new).

 

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The earliest number symbolism occurred in Babylon, and the zikkyrats varied in numbers of stages between 4 and 7. The Babylonian system had 4 directions, lunar phases, winds, seasons, watches of the day and night, 4 elements, humours and cardinal virtues.

 

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Almost all peoples of antiquity possessed a name for the Deity composed of four letters. Among Gnostics, the Supreme Being was denoted by the number 4, and in the Acts of Thomas when passing through the fourth gate the initiate is referred to as a “body released by a pentad.”

 

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The Hebrew Tetragrammaton, or 4-lettered mystery, is the name of the Creative Power. It includes the past, present and future forms of the verb ‘to be’, and was revered as a symbol of the immutable I AM. Jehovah is INVH.

 

■□

 

The centrality of the number 4 is not as mystical as may appear at first sight. Apart from 2, all prime numbers are odd. There are those that are 1 less than a multiple of 4: 3, 7, 11 and 19; and those that are 1 more than multiple of 4: 5, 13, 17.

 

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The Pythagoreans, said Nicomachus, call the number 4 “the greatest miracle,” “a God after another manner,” “a manifold divinity,” the “fountain of Nature” and its “key bearer.”

 

■□

 

 

For some amazing fourfold patterns that David has found in great works of music and literature, see the essay “Meta-Fours à la David Spooner” in my book, Some Little Night Musings.

 

You can visit David’s website online at:

 

http://members.authorsguild.net/davidspooner/index.htm

 

 

     

     

 

 

A Logic of Tetrads

 

Another friend who is an aficionado of fours, though with a different emphasis than my eclectic approach, is Ben Udell, with whom I have enjoyed exchanging emails for several years now.

 

Ben has a logical turn of mind which he may have inherited from his great uncle, the philosopher Charles Hartshorne, and with this turn of mind he shows how the fourfold makes “a recurrent logical pattern in philosophical issues.” The same pattern recurs in explanatory schemes as ancient as Aristotle’s four causes and as modern as the scientific method.

 

He also shows, with some elegant tables and graphics he has created, how a fourfold, or tetrastic, scheme of classification can shed revealing light on such subjects as logical psychology, modes of inference, requisites for beauty, elemental modes of the psyche, and a classification of the sciences and mathematics.

 

Let’s look at a simple example.

 

Aristotle’s four causes are:

 

 Efficient Cause

 Material Cause

 Final Cause

 Formal Cause

 

Ben renames, and rethinks, them as:

 

 Beginning

 Middle

 End (teleiosis)

 Check (entelechy)

 

Looking at this, you may be wondering why something comes after the end. In any quest, having arrived at the end, isn’t that all there is to it? Hardly. What if that end is somehow flawed, incomplete, or even illusory? This means that each end calls for some kind of checking or confirmation process. It is Ben’s claim that the importance of this crucial step can hardly be overstated.

 

To miss this, or undervalue it, or not see it for what it is, is a major oversight.

 

You can visit Ben’s website online at:

 

http://tetrast.blogspot.com/

 

 

     

     

 

 

Four for the Road

 

 

Lakoff and Nunez, in their book Where Mathematics Comes From (2000), argue that our understanding of arithmetic rests on four grounding metaphors:

 

 1. Arithmetic As Object Collection

 2. Arithmetic As Object Construction

 3. The Measuring Stick Metaphor

 4. Arithmetic As Motion Along a Path.

 

 

 

 

The “Wesleyan Quadrilateral,” a term coined by Albert Outler, names the methodology underlying John Wesley’s approach to theological reflection whereby our conclusions are grounded in four sources:

 

 1. Scripture

 2. Tradition

 3. Experience

 4. Reason

 

In The Book of Discipline of the United Methodist Church, the idea is stated as follows:

 

Wesley believed that the living core of the Christian faith was revealed in Scripture, illumined by tradition, vivified in personal experience, and confirmed by reason. Scripture, however, is primary, revealing the Word of God, so far as it is necessary for our salvation.

 

 

 

 

The Axiom of Maria Prophetess:

 

 One becomes two,

 two becomes three,

 and out of the third

 comes One as the fourth.

 

 

 

 

The fourfold idea finds a variety of expression in Ken Wilber’s thought—

 

 

Four different domains of reality:

 

 Physiosphere or material world

 Biosphere or the world of living things

 Noosphere or the realm of thought

 Theosphere or divine domain

 

Four stages in the cultural and individual development of the individual:

 

 1. preconventional

 2. conventional

 3. post-conventional

 4. “post-postconventional”           

 

Four Stages of Mysticism (with representative individuals):

 

 Nature Mysticism              Ralph Waldo Emerson

 Theistic Mysticism            Teresa of Avila

 Monistic Mysticism           Meister Eckhart

 Nondual Mysticism            Ramana Maharshi

 

Four major stages of transpersonal development: the psychic, the subtle, the causal, and the nondual.

 

Using Huston Smiths’ terminology, Wilber identifies four links in the Great Chain of Being: body, mind, soul, and spirit.

 

Finally, and foremost, the Four Quadrants:




 

 

 For an exploration and explication of the Four Quadrants, see my essay, “A Mandalic Model of Reality,” in the HyC Adventures section on this site.

 

 

 

 

Meta-Fours
Curves of Thought
Ken Wilber's Mandalic Model of Reality
Slender Gold: Emperor Huizong's Brush with Beauty
HCE in Finnegans Wake
The Happiness of Fish
Urrutia’s 1767 Map of Santa Fe
Evolution of the Word
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