The 3 Brains and the Enneagram create Four Core Relationships for each Type

Hornevian Brain Groups

Each Hornevian Group has a weakness that needs to be compensated.
Each Hornevian Group has a weakness that needs to be compensated.

Each Brain Talents Aids Survival

The Three Brains & Three Time Frames

Using my knowledge of Katherine Hurley's methods and her teachings of the Enneagram in the Healing Tradition and my knowledge of Neuropsychiatry, I examined the relationship between the Enneagram and the three separate brain structures of homosapiens:

1) The Old Brain/Reptilian Complex: Types 7. 8 and 3 representing Speed, Strength and Cunning; it is survival oriented, which means a "Future" Time Orientation.

2) Mammalian Brain or Paleomammalian Complex: Types 1, 2 and Type 6 representing Teaching the Right Ways, Nurturing and Loyalty; it is caring oriented, which means a "Present" Time Orientation

3) New Brain or NeoCortex: Types 4, 5 and 9 representing Originality, Knowledge and a Universal Perspective. It is information oriented, which means a "Past" Time Orientation, as you learn from past experiences and generations.

The Three Object Relation Groups

Understanding the Enneagram, Revised Ed.,Houghton Mifflin (2000), p. 318.
Understanding the Enneagram, Revised Ed.,Houghton Mifflin (2000), p. 318. | Source

Three Life Journeys

Types 7, 1 & 4 comprise both the FRUSTRATING OBJECT RELATION GROUP and THE PHYSICAL PLANE of a life's journey.

Types 8, 2 & 5 comprise both the REJECTING OBJECT RELATIONS GROUP and THE SPIRITUAL PLANE of a life's journey with its search for meaning through power, love and knowledge.

Types 3, 6 & 9 comprise the ACCEPTING OBJECT RELATIONS GROUP and THE MENTAL PLANE of life's journey.

The Best Chances for Survival by its nature requires intelligence and an Acceptance of the Reality of the Moment or STATUS QUO. One must adapt to thrive and succeed. Hence, the Mental Plane is a world of Interpersonal Gamesmanship.

TYPE 3 USES ITS INDIVIDUAL CUNNING AND CHARISMA. TYPE 6 USES THE ABILITIES, RESOURCES AND PROTECTION OF GROUPS. TYPE 9 USES ITS INTELLIGENCE TO AVOID CONFLICTS AND THE POWER OF DIPLOMACY TO OBTAIN ITS SURVIVAL.

The Enneagram Quad-Cubes are Visual Short Cuts

They point you in the direction of your MOST Neglected Time Frame. This area needs your effort and attention to develop into a working partner with your Core or Central Type (CT).

For Introspective Types (Types 4, 5 and 9), there is a need to develop Go Getter Types skills of Types 3, 8, and 7.

For Go Getter Types (8, 7 and 3), there is a need to develop the Networker Types skills of Types 6, 2 and 1.

Networker Types (Types 6, 2 and 1), need to develop the Introspective Types skills of Types 9, 5 and 4.

Myself as an example. QuadCube for Type 5

I am a Type 5, Knowledge Seeker, The Investigator, The Thinker or Observer. The matrix for Type 5 is to initially go towards Type 8, in direction of integration. Moving towards Type 2 is in the so-called direction of stress or disintegration is not needed. You don't need to work on the direction of stress. Shit happens and you will feel stressed. You will naturally seek the love and support of people who care for you. When stressed, you begin to unravel and will learn from the experience.

So, I suggest you move towards Type 8, then towards Type 3, your opposite type and your first step out of your Comfort Zone. Type 5's are "introspective types" according to Katherine Hurley and have difficulty initiating action. They are Thinkers, not Doers. It is their Achilles' heel. Types 8, 3 and 7 are "Doers", action types. You will get 80% of the results of working all the Enneagram Points by just focusing on your inherent weaknesses at Points 8, 3 & 7, the Go Getter Types.

Again, this is not the method advocated by Gurdjieff, but a short cut that I developed for myself, using my knowledge of Katherine Hurley's methods and teachings of the Enneagram in the Healing Tradition and my knowledge of the relationship between the 3 Enneagram Object Relations Groups and the three brains of man: 1) Reptilian Brain (Types 7. 8 and 3 representing Speed, Strength and Cunning; 2) Mammalian Brain ( Types 1, 2 and Type 6 representing Educating, Nurturing and Loyalty; and 3) New Brain/NeoCortex (Types 4, 5 and 9) representing Originality, Knowledge and a Universal Perspective.

Use together, you can create a 3 by 3 Personality Matrix Square that uses the 3 Object Relations Groups as rows and the 3 Hornevian Groups as columns.

The Quad-Cube for Enneagram Core Type 5

For each Core or Central Type (CT) from Type 1 through 9, you create a matrix with your Core Type in the Central Position of the Enneagram QuadCube and create a matrix with columns being the Hornevian Groups and the rows being the Object Relations Groups. The 3 most important Enneagram Points that you need to focus on appear in the "right" column automatically.

6__9__3
2__5__8
1__4__7

The number 5 is at the center of this Cube. Every column, row and diagonal that includes the number 5 corresponds to one of four special Groups associated with Type 5

the center row 2, 5, 8 is the Rejecting Object Relations Triad
the center column 9, 5, 4 is the Hornevian Withdrawing Triad
the diagonal is 6, 5, 7 is the Head Triad (Center)
the cross diagonal is 1, 5, 3 is the Competency (Work) Triad

Another pattern should also be apparent. All numbers in each of the columns and diagonals add up to and then reduced to number of 9. For the Center Column, 9+5+4 = 18 = 1+8 = 9. This pattern holds true for all the columns and all the diagonals, 6 + 5 + 7 = 18 = 1+8 = 9; cross diagonal 1+ 5 + 3 = 9.

The rows are also consistent in that for the types on the mental plane always adds up to and reduced to the number 9. For rows on the spiritual plane always add up to and reduce to the number 6. For rows on the physical plane always add up to and reduce to the number 3.

The Quad-Cube for Enneagram Core Type 1

GO GETTERS--- NETWORKERS----INTROSPECTIVES

___8__________ 2__________ 5 ______Spiritual Plane (8+2+5 = 15 = 1+5 = 6)

___7__________ 1 __________4 ______Physical Plane (7+1+4 = 12 = 1+2 = 3)

___3__________ 6__________ 9 ______Mental Plane (3+6+9 = 18 = 1+8 = 9)

Note that every column, row, and diagonal that includes "1" corresponds to one of four special Groups associated with Type 1

Center row 7, 1, 4 is the Frustrating Object Relations Triad
Center column 2, 1, 6 is the Compliant (Networker) Hornevian Triad
Diagonal 8, 1, 9 is the Gut Triad (Center)
Cross Diagonal 3, 1, 5 is the Competency (Work) Triad.

Another pattern should also be apparent. All numbers in each of the columns and diagonals add up to the reduced number of 9. Example for the Center Column, 2 +1 + 6 = 9
This pattern holds true for all the columns and all the diagonals, 8 + 1 + 9 = 18 = 1 + 8 = 9; cross diagonal 3 + 1 + 5 = 9

The rows are also consistent in that for the types on the mental plane, that row always adds up to and reduced to the number 9. For rows on the spiritual plane, the rows add up to and reduce to the number 6. For rows on the physical plane, the rows add up to and reduce to the number 3.

This is pattern for all 9 matrices where the Enneatype of interest is the center square of the magic cube.

Example of Matrix Solution for Type 1

Type 1 is a Networker who needs to develop the abilities of Introspective Group: Types 9, 5, and 4.

Type 1 is also on the Physical Plane with Types 4 and 7 and all together comprise the Frustrating Object Relation Group. By moving in the clockwise direction, Type 1 develops the positive qualities of Type 4 of its Dominant Affective Group.

So, I suggest after your move initially towards Type 4, and then to move towards the other members of the Introspective Group: Type 5 and Type 9. Type 1's are energetic, busy and productive people and have a hard time "wasting time" or "goofing off". The prolonged thinking processes of Type 5, the prolonged emotional recollections of Type 4 and the inactivity, sloth or lazy of Type 9 are extremely difficult for Type 1's to accept, yet master. They want to remain busy and organized. Yet, the diplomatic gifts of Type 9, the creative gifts of Type 4 and the penetrating insights of Type 5 will remain out of their reach until they do.

It is so important to realize that we have been developing the natural strengths of our specific Enneatype since an early age, and by middle age, we have probably nearly maximized our abilities to exploit this natural asset. Further competence at this stage of life comes from developing other talents that lay dormant in us. In fact, we may well believe that we do not possess these other talents as we have failed to develop them. I have met Perfectionist Type 1 who never thought that they possessed any artistic abilities, who late in life bloomed as artists. We have all 9 energies and essences in all of us. Some are obvious to us and others are not. Others need to be addressed or they remain our Achilles heel and trip us up over and over again.

The Quad-Cube for Enneagram Core Type 2

GO GETTERS--- NETWORKERS----INTROSPECTIVES

___3__________ 6__________ 9______ Mental Plane (3+6+9 = 18 = 1+8 = 9)

___8__________ 2 __________5 ______Spiritual Plane (8+2+5 = 15 = 1+5 = 6)

___7__________ 1__________ 4 ______Physical Plane (7+1+4 = 12 = 1+2 = 3)

Note that every column, row, and diagonal that includes "2" corresponds to one of four special Groups associated with Type 2

Center row 8, 2, 5 is the Rejecting Object Relations Triad
Center column 6, 2, 1 is the Compliant (Networker) Hornevian Triad
Diagonal 3, 2, 4 is the Heart Triad (Center)
Cross Diagonal 7, 2, 9 is the Positive Outlook (Optimistic) Harmonic Triad.

Another pattern should also be apparent. All numbers in each of the columns and diagonals add up to the reduced number of 9. Example for the Center Column, 6 +2 + 1 = 9
This pattern holds true for all the columns and all the diagonals, 3 + 2 + 4 = 9 and cross diagonal 7 + 2 + 9 = 18 = 1 + 8 = 9

The rows are also consistent. For rows on the mental plane, the row adds up to and reduced to the number 9. For rows on the spiritual plane, the rows add up to and reduce to the number 6. For rows on the physical plane, the rows add up to and reduce to the number 3.

Type 2 is a Networker who needs to develop the abilities of Introspective Group: Types 4, 5, and 9.

Type 2 is also on the Spiritual Plane with Type 5 and 8 and all together comprise the Rejecting Object Relation Triad. By moving in the direction of integration, Type 2 develops the positive qualities of Type 5. Type 2 has no need to focus on the direction of stress and movement towards Type 8, as this will happen naturally when Type 2's coping skills are overwhelmed.

So, I suggest you move initially towards Type 5, then take your first step out of your Comfort Zone towards your opposite type (-2 wing), Type 9. Type 2's have strong relationship to others and their network of family and friends is extremely important to them. They are motivated by their relationships with people, not inanimate objects or ideas. Hence, purely academic pursuits and independent scholarship are experienced as isolating and boring to them. It is their Achilles' heel. Type 2's feel more at homes in groups than in solitary pursuits. But, after reaching a mature age, that is where they need to focus and develop their ability to think, act and feel independently and look deep within themselves. They don't need to always agree, do for, please or cater to others. You will get 80% of the results of working the entire Hidden Path by just completing three steps towards this inherent weakness and develop the abilities of the Introspective Types: Type 5, Type 9 and then Type 4.

Remember, you have probably spend most of your life depending on and developing your "networker" strengths. You probably will not get much more by focusing on your Type 2 strengths. There comes a time in life will progress is measured by addressing your weaknesses and overcoming them.

The Quad-Cube for Enneagram Core Type 3

Introspectives----Go Getters--- Networkers

___4__________ 7__________ 1 ________ Physical Plane

___9__________ 3 __________6 ________ Mental Plane

___5__________ 8__________ 2 ________ Spiritual Plane

Note that every column, row, and diagonal that includes "3" corresponds to one of four special Groups associated with Type 3.

Center row 9, 3, 6 is the Accepting Object Relations Triad
Center column 7, 3, 8 is the Assertive (Go Getter) Hornevian Triad
Diagonal 4, 3, 2 is the Heart Triad (Center)
Cross Diagonal 5, 3, 1 is the Competency (Work) Triad.

Another pattern should also be apparent. All numbers in each of the columns and diagonals add up to the reduced number of 9. Example for the Center Column, 7 +3 + 8 = 18 = 1 + 8 = 9
This pattern holds true for all the columns and all the diagonals, 4 + 3 + 2 = 9; cross diagonal 5 + 3 + 1 = 9

The rows are also consistent in that for the types on the mental plane, that row always adds up to and reduced to the number 9. For rows on the spiritual plane, the rows add up to and reduce to the number 6. For rows on the physical plane, the rows add up to and reduce to the number 3.

This is pattern for all 9 matrices where the Enneatype of interest is the center square of the magic cube.

Example of Matrix Solution for Type 3

Type 3 is a Go Getter who needs to develop the abilities of Networker Group: Types 6, 2, and 1.

Type 3 is also on the Mental Plane with Type 6 and 9 and all together comprise the Accepting Object Relation Group. By moving in the direction of integration, Type 3 develops the positive qualities of Type 6. Type 3 has no need to focus on the direction of stress and movement towards Type 9, as this will happen naturally when Type 3's coping skills are overwhelmed.

So, I suggest you move initially towards Type 6, then take your first step out of your Comfort Zone towards your opposite type, Type 1. Type 3's are strongly independent Doers and have difficulty maintaining emotional bonds, particularly if these binds bind them. It is their Achilles' heel. Organizational Types like Types 6, 1 and 2 feel at homes in groups without the need to dominate, lead or head the group. You will get 80% of the results of working the entire Hidden Path by just completing three steps towards this inherent weakness and develop the abilities of the Networker Types: Type 6, Type 1 and then Type 2.

Remember, you have probably spend most of your life depending on and developing your "go getter" strengths. You probably will not get much more by focusing on your Type 3 strengths. There comes a time in life will progress is measured by addressing your weaknesses and overcoming them.

The Quad-Cube for Enneagram Core Type 4

2__5__8
1__4__7
6__9__3

The number 4 is at the center of this diagram and every column, row and diagonal that includes the number 4 corresponds to one of four special Groups associated with Type 4

the center row 1, 4, 7 is the Frustrating Object Relations Triad
the center column 5, 4, 9 is the Hornevian Withdrawing Triad
the diagonal is 2, 4, 3 is the Heart Triad (Center)
the cross diagonal is 6, 4, 8 is the Emotionally Intense Harmonic Triad

All numbers in each of the columns and diagonals add up to and then reduced to number of 9.

Example of Matrix Solution for Type 4

TYPE 4 IS AN INTROSPECTIVE OR WITHDRAWING HARMONIC TYPE WHO NEEDS TO DEVELOP THE ABILITIES OF ASSERTIVE HORVERIAN GO GETTER GROUP: TYPES 8, 7, AND 3.

Type 4 is also on the Physical Plane with Types 1 and 7 and all together comprise the Frustrating Object Relation Group. By moving in the clockwise direction, Type 4 develops the positive qualities of Type 7 of its Dominant Affective Group.

So, I suggest after your move initially towards Type 7, and then to move towards the other members of the Go Getter Group: Type 3 and Type 8. Type 4's are deep, emotional, introspective people and have a hard time "initiating action quickly". The prolonged introspective emotional thinking processes and memories of Type 4 make it extremely difficult for Type 4's to jump into action.

It is so important to realize that we have been developing the natural strengths of our specific Enneatype strengths since an early age, and by middle age, we have probably nearly maximized our abilities to exploit this natural asset. Further competence at this stage of life comes from developing other talents that lay dormant in us. In fact, we may well believe that we do not possess these other talents as we have failed to develop them. I have met Artistic Type 4's who never thought that they possessed any other abilities, who later in life bloomed as business men and women. We have all 9 energies and essences in all of us. Some are obvious to us and others are not. Others need to be addressed or they remain our Achilles heel and trip us up over and over again.

The Quad-Cube for Enneagram Core Type 5

The Lo Shu or Magic Square and the Enneagram have some sort of relationship according to some people. Certainly, the famous lo shu is a perfect model for all the Triad associations of Type 5.

The QuadType Cube for Enneagram Core Type 5 is as follows.

6__9__3
2__5__8
1__4__7

The number 5 is at the center of this Cube. Every column, row and diagonal that includes the number 5 corresponds to one of four special Groups associated with Type 5

the center row 2, 5, 8 is the Rejecting Object Relations Triad
the center column 9, 5, 4 is the Hornevian Withdrawing Triad
the diagonal is 6, 5, 7 is the Head Triad (Center)
the cross diagonal is 1, 5, 3 is the Competency (Work) Triad

Another pattern should also be apparent. All numbers in each of the columns and diagonals add up to and then reduced to number of 9. For the Center Column, 9+5+4 = 18 = 1+8 = 9. This pattern holds true for all the columns and all the diagonals, 6 + 5 + 7 = 18 = 1+8 = 9; cross diagonal 1+ 5 + 3 = 9.

The rows are also consistent in that for the types on the mental plane always adds up to and reduced to the number 9. For rows on the spiritual plane always add up to and reduce to the number 6. For rows on the physical plane always add up to and reduce to the number 3.


I can show this for all 9 Enneatypes with an associated Lo Shu with its number at its center that reduces mathematically for each row, column or diagonal of matrices to 3, 6 or 9.

The Quad-Cube for Enneagram Core Type 6

7__1__4
3__6__9
8__2__5

The number 6 is at the center of this lo shu and every column, row and diagonal that includes the number 6 corresponds to one of four special Groups associated with Type 6

the center row 3, 6, 9 is the Accepting Object Relations Triad
the center column 1, 6, 2 is the Hornevian Compliant Triad
the diagonal is 7, 6, 5 is the Head Triad (Center)
the cross diagonal is 8, 6, 4 is the Emotionally Intense Harmonic Triad

All numbers in each of the columns and diagonals add up to and then reduced to number of 9.

The Quad-Cube for Enneagram Core Type 7

5__8__2
4__7__1
9__3__6

The number 7 is at the center of this lo shu and every column, row and diagonal that includes the number 7 corresponds to one of four special Groups associated with Type 7

the center row 4, 7, 1 is the Frustrating Object Relations Triad
the center column 8, 7, 3 is the Hornevian Assertive Go Getter Triad
the diagonal is 5, 7, 6 is the Head Triad (Center)
the cross diagonal is 9, 7, 2 is the Positive Outlook (Optimistic) Harmonic Triad

All numbers in each of the columns and diagonals add up to and then reduced to number of 9.

The Quad-Cube for Enneagram Core Type 8

9__3__6
5__8__2
4__7__1

The number 8 is at the center of this lo shu and every column, row and diagonal that includes the number 8 corresponds to one of four special Groups associated with Type 8

the center row 5, 8, 2 is the Rejecting Object Relations Triad
the center column 3, 8, 7 is the Hornevian Assertive Go Getting Triad
the diagonal is 9, 8, 1 is the Gut Triad (Center)
the cross diagonal is 4, 8, 6 is the Emotionally Intense Harmonic Triad

All numbers in each of the columns and diagonals add up to and then reduced to number of 9.

The Quad-Cube for Enneagram Core Type 9

1__4__7
6__9__3
2__5__8

The number 9 is at the center of this lo shu and every column, row and diagonal that includes the number 9 corresponds to one of four special Groups associated with Type 9

the center row 6, 9, 3 is the Accepting Object Relations Triad
the center column 4, 9, 5 is the Hornevian Withdrawing Introspective Triad
the diagonal is 1, 9, 8 is the Gut Triad (Center)
the cross diagonal is 2, 9, 7 is the Positive Outlook Optimistic Harmonic Triad

All numbers in each of the columns and diagonals add up to and then reduced to number of 9.

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