Triangle and Tetrahedron

 

Carbon, the basic element of life, takes this shape. 

Depth psychology demonstrates many complementary images and functions.  Empirically observed, a dream with a turning to the left signifies going towards the unconscious, toward the right toward consciousness.  Coincidence?

Two triangles, each with 3 vertices and three edges (6 of each altogether) merge to form a tetrahedron with only 4 vertices but still 6 edges.

How do we geometrically reconcile triangulation with Carl Jung’s functions that are psychological opposites, which requires opposing pairs laid out on a square?  How do we reconcile trinity with quaternity?

Tetrahedrons and a Stable Cube

The triangle is reconciled with the square in the stable cube.  Two tetrahedrons with a common center stabilize a cube.

Each face of the cube has one diagonal from one tetrahedron and one from the other.

The square and the two tetrahedrons have a common center point.

See Synergetics, by R. Buckminster Fuller, pages 7-8.

We can now deal with opposites on the side of a cube.  Can we represent the psychological functions on the cube?

Linus Pauling showed that metals have this kind of structure.  See Utopia or Oblivion, by R. Buckminster Fuller, page 102.

Metals conduct electricity. Our brain and body conduct psychic energy.  Is this more than a coincidence? Does our psyche have this balanced structure?  Let us assume so and see if it makes any sense.

Star of David, Tetrahedrons, and Cube

The Star of David may be considered a special view of the two tetrahedrons in the stable cube.  It is the view from one of the cube’s vertices.  Since this cube vertex is in the center of the star, it and its opposite vertex, which is also in the center, do not participate in the formation of the star.  However, the cube is still there along with the two tetrahedrons. 

If you look from one of the vertices of the cube, and look in upon it, it is easy to ignore your own position in the pattern.   It is also easy to “purify” the image and ignore the far point in the center.

The Star of David becomes a cube with eight vertices when the center point is included and all 6 points of the star are connected directly to each of the other 5 points.

Each vertex of the cube is also a vertex of one of the tetrahedrons.  From Figures 1 and 2, you can see that from this point a tetrahedron looks like a triangle.

Flat representations of reality often distort and obscure as much as clarify.  This case shows that even the center can represent two (or more) points. If the ego’s (or Head Brain’s) dominant function is the nearer of the two center points of the star, then we can say the dominant function can be represented by one of the vertices of the cube.  What does the far point, the opposite vertex of the cube, represent?

Psychological Functions on the Cube

On the upper half of the cube are the extroverted functions.  The lower half of the cube represents introversion.

There are eight vertices on the cube, one for each of Jung’s eight functions.

The shaded sides are the only two sides that can represent the types.  They have their auxiliary second function on the other end of their vertical edge, and their opposite, least preferred function farthest away on the side’s diagonal.

The extroverted and introverted form of each function (for example F_I and F_E) are on the farthest point away from each other on the cube, across the “long” diagonal that would run through the center of the cube.

Figure 12 is another view of the cube in Figure 11, from either the N_E or N_I vertex.  Intuition is now in the center, both the introverted and extroverted vertices.

To answer the question posed earlier, the far center point, or opposite vertex, is the same function in its opposite attitude.

Psychological Types on the Cube

The cube in Figure 14 shows how an ISFP and ENTP are placed at the vertex of their dominant function.  The vectors connect the four Head Brain functions in their proper order and attitude.

The cube in Figure 15 has the eight SF and NT types.

The cube in Figure 16 is necessary to show the ST and NF types.  This isomer cube reverses the F and T points in relation to the S and N.  This is consistent with two functions being possible as the auxiliary.

Functions 5 - 8 on the Cube

There are eight functions, but only four are assigned to a type by Jung and the MBTI.  Where are the remaining four functions, functions 5-8, for each type?

So far as consciousness and the Head Brain is concerned, they appear quite absent.  The unconscious, however, contains all the opposites, so it must contain these functions.  Also, a law of nature says that an imbalance in one place results in a complementary opposite imbalance elsewhere.  Do we have a clue from the placement of the functions on the cube?

The first four functions are on one plane of the cube.  The remaining four are on the opposite side, apparently quite separate.  Since they are discarded polar opposites, it makes sense that they would have their seat of operation as far away as possible from the conscious attitude.  If it is possible, the logical place for them is somewhere outside the head, somewhere in the rest of our body.

Functions 5 - 8 are in the Gut Brain

It appears that the remaining functions lodge in what Remo Roth calls the Gut Brain.  They also align so that the “dismissed” aspect of each function “faces the other”.  S_E faces N_E, N_I  faces S_I, T_E faces  F_E, and F_I  faces  T_I.  For example, S_E, concerned with appreciating the rich uniqueness of each aspect of reality, dismisses the concern of N_E with possibilities that rely on seeing what is in common rather than unique. This alignment makes sense because it facilitates a complementary psyche. The Gut Brain is part of our instinctual make-up.

All this supports Remo Roth’s stress on the necessity of connecting to the Gut Brain for wholeness.

The Functions and the Tetrahedrons

The judging and perceiving functions in the ISFP Head Brain are on different diagonals on the cube’s face, and are on different tetrahedrons.    This makes sense.  Each of the preferred functions dominates a different tetrahedron.  The dominant F_I is on one tetrahedron while the auxiliary S_E is on the other. T_E is on the same tetrahedron as F_I, so consciousness in this tetrahedron is focused solely on judging.  This leaves the energy of both perceiving functions on this tetrahedron, S_I and N_E, available to the unconscious autonomous Gut Brain.  Similarly, consciousness in the other tetrahedron is focused solely on perceiving, S_E and N_I, leaving F_E and T_I available to the unconscious.

The ISFP Gut Brain is a complementary ESFJ with function order reversed.  F_E is as far away as possible from F_I.  F_E also strategically faces T_E, the Head Brain’s least conscious function.  This positions F_E to be the most activated compensatory function deep in the unconscious Gut Brain.  It is also positioned to have optimal affect contaminating T_E.  S_I similarly faces N_I.  This gives the Gut Brain the maximum influence over the less preferred conscious functions of T_E and N_I.

This hyperactivates and especially “contaminates” the shadow functions in the Head Brain.  Altogether, this intimate structure facilitates intimate communication between the ego and the unconscious.  Acting in harmony together creates a natural gyroscopic balance.

To the extent, however, that the ego is out of touch with the emanations from the Gut Brain, and instead tries to live its opinion by force (will power), instead of with a living dialogue with the unconscious, it sets up a tragic battle between the “Head Self” and the “Body Self”.

Where is your True Self?

The ego, the center of consciousness, or Head Self, is in the center of the Head Brain side of the cube.  Its position is an intellectual pole attitude.  The ego’s identification with its point of view eliminates, but only intellectually, the stress of living with our instincts.  The ego may quickly pay the price with some combination of neurotic behavior and battles with foes onto whom we have unwittingly projected our own inner conflict.

The ego in the center of the Head Brain side of the cube implies some conscious use of all four functions, not just the preferred.  This is correct.  The contamination occurs only in certain areas.  Intuitives can drive cars.

Our True Self is in the center of the cube and tetrahedrons, in what I call the Integral Self.  To find it we need to be able to sort out truth from falsehood, sincerity from duplicity, in ourselves and others.  The only true gyroscope in this process is a respectful attitude toward the communication from the unconscious, which includes the Gut Brain.

With the view from the ego or Head Brain, we cannot distinguish the Head Self and Body Self from the Integral Self.  The points coincide.  This is why we feel whole so long as our projections do not come back to haunt us.  But it is a latent neurotic situation.

The Self, to Jung, certainly meant the True Self, the Integral Self.  This is clear especially from his understanding of suffering.  The Head Self has difficulty with sacrifice and pursues “happiness”.  The Integral Self transforms us through a dynamic that includes great misery.

The transcendent function also appears to the ego to lodge at the crossroads of the four conscious functions.  But it also originates in the True Self, not on the Head Brain plane.

The Fourth Dimension - Wholeness

Jung’s Psychological Types’ conceptual framework is an incomplete three-dimensional scheme of preferences between equally possible opposites.  The ego can have either.

1. Attitude – two attitudes (introversion/extroversion)

2. Perception – two perceiving functions (S/N)

3. Judgment – two judging functions (F/T)

Adding the Head Brain/Gut Brain dimension creates the fourth dimension – Wholeness.  This is consistent with Bucky’s (Buckminster Fuller’s) tetrahedral framework.  However, the wholeness fourth dimension is not an ego preference.  It does not further define type.  The ego is always in the Head Brain - at that pole.

The missing fourth dimension provides the living connection to our instincts, to the objective ground of the collective unconscious.  We often experience a religious link.  However, “religion” is a loaded word; religious institutions fall victim to the Head Brain as easily as anything else.  The Head Self is similar to all other poles; it depreciates its opposite.  The psychic split is not just in the Head Brain (the ISFP Shadow absconding with T_E and N_I).  It is also a disconnection from the Gut Brain.  Attaining the connection with the Gut Brain requires an act of grace, a saving communication from the unconscious, followed by a free will Head Self sacrifice – acceptance of the other’s value, acceptance of a focal point outside itself.  Only this connects us to the World Soul.

The Projection Mess

The whole process would be quite simple and obvious if it didn’t involve the most self-deceiving of mechanisms – projection.  Sincerity, the desire to do good – any ideal – is a bugbear.  This is because projection falsifies our view of reality to the point where black can look white.  It deceives us thoroughly and happens beyond our control (except for a seemingly innocuous and private repression).  All we can do is get better at recognizing it after the fact when we are confronted.  This is an unavoidable struggle that we each must undertake.

At first we may not consciously recognize our shadow.  This is because our environment provides at least temporary support for an unbalanced worldview.  In a more or less pampered environment, the complementary images from the unconscious are easily projected onto others and so misinterpreted.  A sense of finality and the aggression instinct take over when there is no immediate counterforce to any misjudgment.  See Man and His Symbols (Jung et al.) page 172 for an excellent example by M-L von Franz of how the misinterpretation of a dream and inappropriate projection can lead to scapegoating others, and when this resonates collectively, to grave political confrontation.

This is normal.  Animals enjoy killing their prey, and are proud of it.  Nations still glorify their armed defenders of slogans that misdiagnose the problem.  But for mankind, it is the challenge of our times to prevent a global catastrophe.  As Remo Roth points out, at the beginning of the scientific revolution the Head Brain insights provided such success that modern man lost respect for the Gut Brain, losing connection to the World Soul.

In the struggle for survival, it is natural to discard what is not needed.  With societies, that has always meant discarding sympathy for competing societies or internal dissent.  Today we have reached the point where we must regain our social balance and confront collective projections that prevent wholeness. 

With the depreciation of the Gut Brain (as only subjective), the Integral Self is replaced by an artificial belief system that centers in the Head Self – a closed, self-deluding system.  These Head Self beliefs are unbalanced and arbitrary, and are mostly isms (i.e. nationalism, terrorism) that split the world into dangerous factions.  The telltale sign of any projection problem is the failure to confront the ignoble “enemy” in open, public debate where everyone can hear the complete argument, point and counterpoint, by each real person, unfiltered by anyone.  Only this minimizes the projections and unhealthy manipulation and alignment of the “public” within each group.

Harmony and Synchronicity

The achievement of attaining balance in the Integral Self, in the true center of the cube, could truly be called a sacred marriage, being the common center of two interlocked tetrahedrons.  It is also the apex of six conjoined pyramids, one to each side of the cube.

This ego journey is critical.  We are not a superfluous add-on in the universe.

When we are in the center of the cube, the Head Brain and Gut Brain are whole and in harmony.  At this point we are in harmony with the forces of the universe, as far as the unconscious reaches, which includes the World Soul.  At this point the psyche is participating in the harmony of the universe, and the intelligence in the universe may help us with synchronistic events – and miracles.

© 2004 John Gaboury

E-mail: John Gaboury at This email address is being protected from spambots. You need JavaScript enabled to view it.

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