Abstract.  This paper makes a holistic move in addressing the Matrix potential for examining word/meaning relationships so essential to effective communication and to all related thinking processes.  It displays a complete set of dominant paradigms covering the whole Matrix landscape. The Matrix, a conceptual framework which integrates the four elements feel/think/act/time into a single holistic landscape of values and entities, provides the all inclusive background which the set of displayed paradigms fully covers.
The word paradigm captures the need to retain appropriate flexibility in dealing with word/meaning relationships.  The definition, etymology as well as the current usage of paradigm provide some protection against a partial, biased, non-holistic interpretation of key words. The Matrix expression for paradigms is a radical with zero fractal which combines identity with flexibility.
Each of the selected paradigms represents a basic key word or entity. The complete paradigm set is grouped in 5 visual displays which both separate the structural Matrix components and dovetail into each other. The main focus is visualisation and completeness.
Visual displays offer a very valuable methodology for presenting ideas and concepts which can influence ways of thinking. They operate in line with the well established notion that seeing is believing, adding that visual exposure will always give common sense a better chance to prevail. Apart from visual displays for the main title, a number of supportive displays are given illustrating the pattern configuration of Matrix projections and their ability to identify and separate values by polarity, thereby enhancing and promoting positive choices. In this regard, the holistic approach is seen as a mathematical enhancer leading to valuable breakthroughs.

1. Introduction

This paper takes another step in exploring the Matrix potential for examining word/meaning relationships so essential to effective communication and to all related thinking processes. It considers a complete set of dominant paradigms covering the whole Matrix landscape.

The selected paradigms represent basic key entities. The complete set is grouped in 5 visual displays which both separate the structural Matrix components and dovetail into each other. Visualisation and completeness are the main focus.

Additional visual displays are included to further demonstrate the useful and coherent power of separation between and within various key entities when projected on the Matrix landscape.

The Matrix provides the conceptual framework within which all concepts and entities are projected.  It is a framework which integrates the four elements feel/think/act/time into a single holistic landscape of values and entities, allowing visualisation of conceptual notions and relationships graphically and numerically.  Of modular construct with decimal continuity, it forms a universal framework accommodating conceptual totality and functional flexibility.

 A 4-page Matrix Statement giving details of the Matrix construction, its rationale and a number of associated corollaries is readily available.  It can be downloaded from the Internet, Web site http://www.ozemail.com.au/~bayerben/

2.1 Matrix expressions

They are numerical codes allocated to concepts and entities, in accordance with perception, to achieve the best fit on the Matrix landscape.

The decimal point in the expression separates the “Radical” on its left which is the selected starting position, from the “Fractal” on its right which is the decimal emphasis representing the direction of change.

For example, leadership (59.86) and consensus (59.75) share the radical 59 (choice/optimisation) but differ in the decimal emphasis, 86 (design) and 75 (reason) respectively.

The determination of a Matrix expression relating to an entity gets its validation from tests of perception (25.45), equivalence (55.383/55.386) and coherence (49.55).  For this reason, the Matrix expressions presented in this paper should be considered as a first draft, open to and inviting debate.

The word paradigm is chosen because it seems to capture the need to retain appropriate flexibility in dealing with word/meaning relationships. The definition and etymology of paradigm include the words: example, pattern, underlying, inflexion, for and against. Its current usage appears to provide some protection against a partial, biased, non-holistic interpretation of key words.

The Matrix expression for paradigms is a radical with zero fractal.  It combines identity with flexibility.  When fractals are added to the paradigms, new entities are formed with new identity at further levels of complexity.

3.1 The First Tier (visual display 1)
 

11.0    The edge 11.0    Isolation 12.0    Suppression 13.0    Hurt 14.0    Ego 15.0    Vigilance 16.0    Renewal 17.0    Intimacy 18.0    Decency 19.0    Purity

41.0    Weak 42.0    Deprived 43.0    Struggle 43.0    Gender 44.0    Roots 45.0    Acceptance 46.0    Effort 47.0    Relationship 48.0    Interest 49.0    Belief

71.0    Self Indulgence 72.0    Self Interest 73.0    Fun 74.0    Alter Ego 74.0    Investment 75.0    Reason 76.0    Contribution 77.0    Empathy 78.0    Care 79.0    Love

 3.2 The First Stage (visual display 2)
 

11.0    The edge 11.0    Isolation 12.0    Suppression 13.0    Hurt 14.0    Ego 15.0    Vigilance 16.0    Renewal 17.0    Intimacy 18.0    Decency 19.0    Purity

21.0    Fear 21.0    Uncertainty 22.0    Darkness 23.0    Error 24.0    Message 25.0    Logic 26.0    Bid 27.0    Opinion 28.0    Presentation 29.0    Validation

31.0    Mistake 32.0    Disregard 32.00  Excess 33.0    Aggression 34.0    Separation 35.0    Protection 36.0    Expression 37.0    Request 38.0    Consultation 39.0    Negotiation

3.3 The Second Tier (visual display 3)
 

21.0    Fear 21.0    Uncertainty 22.0    Darkness 23.0    Error 24.0    Message 25.0    Logic 26.0    Bid 27.0    Opinion 28.0    Presentation 29.0    Validation

51.0    Regression 52.0    Observation 53.0    Interpretation 54.0    Retention 55.0    Balance 55.00  Comprehension 56.0    Attitude 57.0    Partnership 58.0    Right 59.0    Optimisation

81.0    Myth 82.0    Search 83.0    Complexity 84.0    Information 85.0    Opportunity 86.0    Design 87.0    Belonging 88.0    Light 88.00  Truth 89.0    Values

3.4 The Second Stage (visual display 3)
 

41.0    Weak 42.0    Deprived 43.0    Struggle 43.0    Gender 44.0    Roots 45.0    Acceptance 46.0    Effort 47.0    Relationship 48.0    Interest 49.0    Belief

51.0    Regression 52.0    Observation 53.0    Interpretation 54.0    Retention 55.0    Balance 55.00  Comprehension 56.0    Attitude 57.0    Partnership 58.0    Right 59.0    Optimisation

61.0    Trail 62.0    Cope 63.0    Fight 64.0    Administration 65.0    Ability 65.0    Management 66.0    Power 67.0    Alliance 68.0    Skill 69.0    Status

3.5 The Third Stage (visual display 4)
 

71.0    Self Indulgence 72.0    Self Interest 73.0    Fun 74.0    Alter Ego 74.0    Investment 75.0    Reason 76.0    Contribution 77.0    Empathy 78.0    Care 79.0    Love

81.0    Myth 82.0    Search 83.0    Complexity 84.0    Information 85.0    Opportunity 86.0    Design 87.0    Belonging 88.0    Light 88.00  Truth 89.0    Values

91.0    Miss 92.0    Stumble 92.0    Quantum 93.0    Win 94.0    Assets 95.0    Quality 96.0    Accomplishment 97.0    Kindness 98.0    Worth 99.0    Vision

3.6 The Third Tier (visual display 5)
 

31.0    Mistake 32.0    Disregard 32.00  Excess 33.0    Aggression 34.0    Separation 35.0    Protection 36.0    Expression 37.0    Request 38.0    Consultation 39.0    Negotiation

61.0    Trail 62.0    Cope 63.0    Fight 64.0    Administration 65.0    Ability 65.0    Management 66.0    Power 67.0    Alliance 68.0    Skill 69.0    Status

91.0    Miss 92.0    Stumble 92.0    Quantum 93.0    Win 94.0    Assets 95.0    Quality 96.0    Accomplishment 97.0    Kindness 98.0    Worth 99.0    Vision

3.7 The Matrix Dominant Paradigms tabulated (visual display 5a)

This display conveniently tabulates all the Matrix Dominant Paradigms.  It groups and relates at a glance the Paradigms for all the Tiers and Stages.

On the Matrix,  the circle inscribed in a square shares its centre  and the equivalence potential attached to it.  Viewed from this central point , the circle is the Observer's "local horizon".

One element of basic import when considering equivalence is the direction (or arrow) of time. For instance regression (51.0) refers to a perception of moving back in time while elsewhere the time flows on.

Polarity, the notion of perceived positive and negative, is obviously linked (among other factors) to the direction of time flow. The more complicated the situation, the higher the potential for controversy about the sign of polarity in that particular situation..

1. Matrix Dominant Paradigms , First Tier
2.      "            "               "       , First Stage
3.      "            "               "       , Second Tier / Second Stage
4.      "            "               "       , Third Stage
5.      "            "               "       , Third Tier
5a.    "            "               "       , tabulated
6. The Broad Divisions
7. Achievement determinants
8. Behaviour determinants
9. Energy: the Vertical thrust
10. Intelligence: the Horizontal pull
11. Interactive social groups
12. From Perception to Choice
13. Information handling
14. Tooling up benefits
15. Approval v/s Disapproval
16. Priorities
17. Three golden Beliefs
18. Real v/s Virtual
19. Misguided passion
20. Reality, Potential, Propensity
21. Vision, Ideology, Metricity
22. Partnership
23. May and Can
24. Fear / Failure v/s Hope / Success

The 90 paradigms presented as providing a full coverage of the Matrix are qualified as dominant. They form a holistic set of basic entities defined by perception, which recognise polarity, equivalence and coherence. These entities combine with each other to form further entities captured by more complex Matrix expressions containing radicals and fractals.

The object of this tooling up is the convenience of a universal short hand to communicate objectively across cultural groupings without the word/meaning relationships causing hindrance but rather promoting enhancement to the thought processes and the problem solving optimisation.

The visual displays provided also facilitate open debate about universal values at the value level. The very wide acceptance of value levels confirms that polarity is a fact of life. Thinking must be encouraged into rejecting regressive modes and engaging in progressive pathways. This is not a new thought but well worth remembering at the start of the new Millennium.

Finally it is felt that the holistic approach is a mathematical enhancer leading to valuable breakthroughs . It helps provide not only windows of opportunity but also gates of delivery – hopefully for the benefit of all mankind.

The following short selection stands for both acknowledgement and reference:
1. Stephen Hawking: A brief history of time (1989)
2. Paul Davies: The mind of God (1992)
3. Edward de Bono: Simplicity (1998)