© BAYER 1997
THE TENSORIAL POWER OF WORDS
Ben Bayer
Adelaide, Australia
Abstract. Language is, on balance,
one of our most powerful means of expression and communication. Its building
tools are words and this paper examines their tensorial power. 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 perspective
background against which this power and the way it operates can be demonstrated.
The word/meaning nexus is captured in the Matrix expressions, usually in
numerical form with radicals and fractals. The emerging lexicon of key
words supports meaningful coherent relationships in the Matrix landscape
both in focus and perspective.
A tensorial integration relationship is postulated to provide a link between
three basic parameters: Quality, Entity and Quantity. The dynamic concept
of Tensors reflects the dynamic qualities of words clarifying and putting
in focus their potential.
The faceted format for articulating definitions provides a valuable series/parallel
continuum which helps comprehension through clarity. Language, through
its key words, single words, polar words, provides the tensorial power
which energises the thinking and communication processes. The polarised
concepts of covariance and contravariance and in particular the sensitive
concept of Equivalence help the harnessing of this power towards the positive
high ground. Critical versus creative thinking is examined and extended
to include logic (25.0), reason (75.0), rationality (55.0), legitimacy
(77.58), morality (97.58) and metricity (99.55).
Merging their tensorial strength, Analysis (82.25), Balance (55.55) and
Creativity (86.85) combine in partnership to achieve Optimisation (59.96),
the fairest and most effective pathway for the promotion of human progress
and harmony.
1. Introduction
This paper examines the power of words in terms of the mathematical
concept of tensors. There is no mathematical treatment intended, just the
concept of WORDS as dynamic entities operating in multiple directions at
varying magnitudes and, through these defining attributes, wielding a real
or perceived power that becomes an intrinsic part of the thinking process.
The framework of reference against which this notion of tensorial power
can be demonstrated in visual form is the Matrix.
2. The Framework
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 The Matrix coverage
The full spread of the Matrix coverage lends itself to a basic lexicon
of key words and meanings which could be associated with each of the Squares.
Such linkage would present a general first order of relationships as the
flexibility of the Matrix, through its mobility to suit purpose, allows
other patterns to be projected.
The following tabulation is intended only as a draft open ended display
of some of this lexicon, covering elements within a third of the Matrix
landscape.
|
39.9 agreement
39.5 accommodation
39.0 negotiation
35.9 liberation
35.5 freedom
35.0 protection
33.9 disruption
33.5 conflict
33.0 aggression |
69.9 achievement
69.5 success
69.0 status
68.9 leadership
68.5 skill
68.0 ability
66.9 authority
66.5 strength
66.0 power |
99.9 fulfilment
99.5 order
99.0 vision
96.9 excellence
96.5 merit
96.0 accomplishment
95.9 harmony
95.5 happiness
95.0 quality |
|
25.9 security
25.5 clarity
25.0 logic
23.9 misleading
23.5 misguided
23.0 error
21.9 confusion
21.5 fear
21.0 uncertainty |
59.9 commitment
59.5 will
59.0 optimisation
55.9 choice
55.5 comprehension
55.0 balance
54.9 emergence
54.5 accretion
54.0 retention |
89.9 ideals
89.5 hope
89.0 values
86.9 creation
86.5 concept
86.0 design
85.9 inspiration
85.5 talent
85.0 opportunity |
|
15.9 safety
15.5 awareness
15.0 vigilance
13.9 cruelty
13.5 punishment
13.0 hurt
12.9 oblivion
12.5 silence
12.0 suppression |
49.9 certainty
49.5 confidence
49.0 belief
48.9 involvement
48.5 motivation
48.0 interest
45.9 comfort
45.5 fairness
45.0 acceptance |
77.9 joy
77.5 indulgence
77.0 empathy
75.9 well being
75.5 sanity
75.0 reason
73.9 delight
73.5 excitement
73.0 fun |
2.2 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 (55.386) 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.
3 Tensorial integration
The relationship
is
postulated to provide a linkage between three basic parameters:
Quantity (q) which is a measurement
Entity (E) which is a concept
Quality (Q) which is a perception
n is the number of multiple entities associated with a given situation
and generally indicates the degree of dimensional complexity. Semantic
ambivalence which results in differing perceptions can often be traced
to elements of the above relationship.
The mathematical concepts of scalar (magnitude, no direction), vector
(magnitude, one direction) and tensor (magnitude, more than one direction)
are helpful in visualising the above process. Quantities are scalars, Entities
are tensors, and Quality, also a tensor, is the aggregate "bottom
line". In somehow remarkable fashion, the "right" words
can provide the correct fit for these complex realities. Conversely, the
"wrong" words can throw the whole edifice out of kilter.
Another mathematical assistance flowing on from Newton’s work allows
a process of “corrective iterations” increasing accuracy at each step of
the iteration. An analogous process takes place in individuals reflecting
and groups negotiating, offering opportunities to advance problems towards
their optimum or natural solutions.
4. Definitions
Facets are a key element of the Facet technique developed by Professor
Louis Guttman and used with high effectiveness in applied social research.
By grouping a number of elemental words vertically between bracketing lines
in the horizontal flow of a sentence, facets achieve a functional and compact
form which allows a large number of permutations to be presented at a glance,
simply and clearly.
Facets are most valuable in formulating definitions because they allow
complex meanings to be presented in a sequence of simple structures where
the qualities of clarity and acceptability can be readily verified.
5. Language
Language is, on balance, one of our most powerful means of expression
and communication. Its building tools are words and hence their critical
importance in shaping the communication process.
Words are defining.
Single words can, with benefit to efficiency and effectiveness, substitute
for rambling descriptions. Clarity is enhanced when the right single words
are selected. It may not lead to consensus but it presents a focused picture
for meaningful debate. An example is the issue of affirmative action based
on need (41.37) rather than race (44.87).
Polar words are single words with emphasis placed on polarity. Polar
words at once suggest a scale of values with two or more polarities.
Instant access to the lexicon of key words and their corresponding Matrix
expressions is facilitated by sorting them out ordinally in two registers,
one alphabetical (dictionary fashion) and the other numerical.
The numerical register allows the chromatic changes to be viewed at
short range, facilitating the evaluating role of perception.
The word/meaning nexus is a dynamic relationship which responds to changing
needs, changing times, fast developing technology and ever increasing sophistication.
Existing words get redefined, new words and new structures are created.
It is important, at the key word level, to retain coherence and continuity.
I would like to float the word Metricity (99.55) as the proactive word
integrating optimally logic (25.0), reason (75.0), rationality (55.0),
legitimacy (77.58) and morality (97.58).
6. Relationships
6.1 Equivalence
Equivalence (55.386) is possibly the most critical and powerful element
of relationship. While Equivalence is not Equality (55.55), it postulates
the equating between entities in a well defined context.
Equivalence recognises - as equivalent - causes producing the same effect
or effects producing the same perception. The Matrix horizontal and vertical
lines provide alignments of Equivalence which accord with common perception.
One element of basic import when considering equivalence is the direction
or arrow of time.
The words transformation, projection, conversion, correspondence, coalescence
are related to equivalence.
6.2 Polarity
Polarity is generally qualified by the words positive (58.89), negative
(22.23), neutral, different.
Covariance and contravariance are polarity relationships between entities
moving in-phase or out-of-phase with each other. Correlations investigate
the magnitude aspect of these entity relationships.
Entropy (33.512) is a natural negative mechanistic universal energy
polarity which it is interesting to compare to its positive opposite (33.596)
and the forces of creativity (86.85).
6.3 Association and Analogy
They are very important relationship tools. Association (45.45) is passive,
triggered by proximity, contiguity or similarity of form. Analogy (85.85)
is proactive and recognises similarity of internal relationships between
two systems or two complex entities.
The basic process is self organising (25.56) mental patterns. These
patterns end up perceived as close neighbours in association, and recognised
as linked by similar mechanisms in analogy. To some extent the two processes
are partial elemental forms of Equivalence.
6.4 Analysis and Synthesis
Analysis (82.25) and Synthesis (82.86) are two aspects of the thinking
process which frequently follow each other in that order. Analysis separates
and relates elements of a context situation along logical lines (25) and
synthesis projects a desired new situation from this preceding analytical
work along creative lines (86). Without the constructive synthesis the
analysis can remain a job half done.
6.5 Balance and Creativity
Balance corresponds to square 55, to the central square in all the blocks
and to cell 5 in all the squares. It is always a powerful catalyst towards
the right direction (59). It extends analysis by lifting the dissected
context situation to a more complete, more inclusive, more holistic level
which would satisfy the demands of reason, but not yet necessarily the
opportunities of optimisation. The potential to stretch that extra mile
is left to Creativity.
Creativity (86.85) is the driving force in the Design paradigm (86.0).
The forum for creativity is Block 8. It is at the centre right of the Matrix,
about the future, the new, the innovative, the valuable, the cultural,
the useful, the beautiful. To stand the test of polarities, it must be
recognised not only by the author/creator (8), but as importantly by his
contemporaries, the market (6). Achieving both is a measure of real success
(69) and fulfilment (99).
7. Optimisation
Optimisation (59.96) as opposed to maximisation (64.66) is the best
choice (59) focusing on accomplishment (96). As the process outcome is
a tensorial integration of factors and parts, the relationship at section
3 can be expressed as:
(i) Optimisation is maximisation in the right direction.
(ii) Optimising the whole is by sub-optimising the parts.
8. Displays
9. Conclusion
Words are only a tool but their critical role in communication as well
as the various thinking processes gives them a corresponding critical importance,
especially at the level of key, single and polar words.
The Matrix, by providing a unified holistic framework of reference for
meanings and entities, allows the characteristics of words to be defined
and recognised to their full dynamic potential.
If we consider the quality of life in terms of human progress and harmony
as the worthwhile goal to aim for, Optimisation appears as the fairest
and most effective pathway to achieve it. A familiar combination operating
in partnership to achieve optimisation is Critical and Creative thinking.
Looking at other defining words and their tensorial potential, one could
also suggest Analysis (82.25), Balance (55.55) and Creativity (86.85).
