This brief glossary of terms has been provided to facilitate understanding of the qualitative mathematical approach I have been employing on this Forum (for 15 months).
 

BI-DIRECTIONAL UNDERSTANDING

From a rational perspective it is paradoxical as it affirms the equal validity of apparently opposite statements. It prepares the mind for an intuitive transformation where such paradox is reconciled.
 

BINARY SYSTEM

This has three forms:

Quantitative Binary. This is the conventional interpretation and provides the basis for the (digital) encoding of information. (It uses either/or logic).

Qualitative Binary. This is the corresponding holistic interpretation and provides the basis for the (digital) encoding of transformation. (It uses the both/and logic).

Double Binary. This combines both quantitative and qualitative systems and provides the basis for encoding of both information and transformation. (It uses both forms of logic).
 

CIRCULAR LEVEL

This is the qualitative understanding of the complementarity of opposites in horizontal terms (objective and subjective). It corresponds to HL1 and LL1 (subtle realm). The end points of a horizontal line (with positive and negative directions) lie on a circumscribed circle. The circular level is the qualitative counterpart of this relationship.
 

COMPLEX REALITY

This involves the translation of reality in "real" (quantitative) and "imaginary" (qualitative) terms. The scientific "real" world entails the reduction of reality in merely quantitative terms.

Complex Paradigm. This is a scientific paradigm that combines "real" (quantitative) and "imaginary" (qualitative) understanding.
 

DIFFERENTIATION

This requires the separation of opposite poles (the either/or logical system).It is the basis of conventional (i.e. quantitative) science.The greatest confusion in science is the reduction of the qualitative to its quantitative aspect.
 

DIRECTIONS

Each Level of the Spectrum (which relates to both physical and psychological structures of reality) is defined in terms of directions (which are the dynamic mathematical interpretation of dimensions).

L0 (the rational linear level has one direction (positive).

H1 and L1 have two directions (i.e. bi-directional in horizontal terms).

H2 and L2 have four directions (bi-directional in horizontal and vertical terms).

H3 and L3 are eight-directional (bi-directional in horizontal, vertical and diagonal terms). In each case the lower level represents a confused understanding of these directions.
 

HOLISTIC

This is always used to refer to qualitative type understanding based on the both/and logical system of complementary opposites. It is associated with the lower levels (in a confused fashion) and the higher levels (in an integrated manner).

Holistic Mathematics (Holomatics) is the qualitative interpretation of mathematical relationships based on the both/and logical system (of complementarity of opposites).

Holistic Mathematics 1 (Holomatics 1) is based on the complementarity of (horizontal) opposites.

Holistic Mathematics 2 (Holomatics 2) is based on the complementarity of (horizontal and vertical) opposites.

Holistic Mathematics 3 (Holomatics 3) is based on the complementarity of (horizontal, vertical and diagonal) opposites.

Holistic Science (Holoscience) is the qualitative interpretation of scientific relationships based on the both/and logic (of complementarity of opposites). Again we have Holoscience 1, Holoscience 2 and Holoscience 3. The ultimate structure of this science is provided by Holistic Mathematics.

Holistic Physics (Holophysics) represents one important aspect of this scientific approach.

Holophysics 1 (for example) is a qualitative (integrative) approach to physics based on the complementarity of (horizontal) opposites.
 

INTEGRATION

This requires the complementarity of opposites (i.e. the both/and logical system).It is the true basis for a qualitative holistic approach to science.
 

LINEAR LEVEL

This is the understanding of reality in one-dimensional (i.e. one-directional) terms (L0). Opposite poles are clearly separated with only the positive pole recognised. Conventional science is based on linear understanding. It is geared to understanding in objective terms (horizontal); quantitative terms (vertical)and finite terms (diagonal).
 

LOGICAL SYSTEMS

There are two main systemsEither/or logic. This is conventional logic based on the separation of opposites. It is the logic of differentiation. Both/and logic. This is based on the complementarity of opposites. It is the logic of integration.
 

MIRROR UNDERSTANDING

This is the negative direction of understanding and involves the dynamic negation (undoing) of conscious understanding. It is the means by which holistic (intuitive) awareness is developed.
 

NATURAL

This is the qualitative counterpart of natural number quantities. It represents a state where the prime objects and dimensions (having been separated) are now combined to generate a multitude of distinct phenomena.
 

NULL LEVEL

This equates well with nondual reality (H3 and L3). It derives from the qualitative interpretation of null lines (i.e. lines in the complex plane of zero length).
 

NUMBER

The qualitative interpretation of number is of central importance in Holistic Mathematics.

The Number Spectrum is a holistic mapping of the Spectrum (physical and psychological) in terms of the qualitative number system.

The Number Paradigms are based directly on qualitative number types.Each of the major levels (and transitions) between level are associated with distinct number paradigms.

The rational paradigm is based on the qualitative interpretation of rational numbers (corresponding to L0).It is the appropriate paradigm for (conventional) science.

The negative paradigm (mirror understanding) is based on the transition from L0 to HL1.

The irrational paradigm is based on HL1. (It is the appropriate paradigm for Holoscience 1).

The imaginary paradigm (virtual understanding) is based on the transition from HL1 to HL2.

The transcendental paradigm is based on HL2. (It is the appropriate paradigm for Holoscience 2).

The complex paradigm is based on the transition from HL2 to HL3.

The transfinite paradigm is based on HL3. (It is the appropriate basis for Holoscience 3 together with the refined complex paradigm).

The comprehensive paradigm involves the differentiated (and integrated) combination of all partial paradigms. It is the appropriate paradigm for Radial Science.
 

ONE-DIRECTIONAL UNDERSTANDING

This is conventional either/or understanding where unambiguous polar distinctions are made. Thus to say that a proposition is either true or false is one-directional. Likewise the view that cause leads to effect in physical terms is one-directional.
 

POINT LEVEL

This represents understanding based on the complementarity of opposites (in both horizontal and vertical terms). It corresponds to HL2 and LL2 (causal realm).The intersection of horizontal and vertical axes (circumscribed by circle) is a point.This is the centre of both lines and circumscribed circle.In qualitative terms, the point represents the spiritual centre of personality and harmonises both linear and circular understanding.
 

PRIME

This is the qualitative interpretation of prime number quantities and represents a state where object phenomena are confused with space-time dimensions. So we have at this level prime objects and prime space-time which are inextricably linked.
 

RADIAL

This is another key term. It is based on the geometrical notion of a radius which involves both point (centre of circle) line and circumference (of circle). Radial interpretation therefore combines linear (analytic), circular (holistic) and point (spiritual) understanding.

Radial Reality represents the most mature stage of development involving (refined) dual and nondual understanding (differentiation and integration).

Radial Mathematics is the most comprehensive approach to Mathematics. It combines analytic (quantitative) and holistic (qualitative) aspects.

Radial Science likewise represents the most comprehensive approach to science again combining analytic and holistic aspects.
 

SPECTRUM

This represents the various levels of reality. The term has both a psychological and physical interpretation. Thus we have a physical spectrum (the different levels of manifest reality) and a psychological spectrum (the corresponding understanding of these levels). Physical and psychological interpretations of the spectrum are complementary in horizontal, vertical and diagonal terms).Each level of the spectrum has a precise (holistic) mathematical structure.The full mapping of the Spectrum involves life stages (or journeys), levels, sub-levels, directions, stages and phases.

The Spectrum of Consciousness is the mapping of the psychological aspect of the spectrum.
 

THEORY OF EVERYTHING

This is the explanation of the underlying symmetrical nature of reality based on the three sets of polarities (horizontal, vertical and diagonal). All relationships in reality (symmetrical and asymmetrical) can be explained in terms of both the separation and complementarity of these polarities.The Theory of Everything has an extremely simple algebraic structure (as the qualitative interpretation of the eight roots of unity). This can equally be expressed in geometric terms as a circle of unit radius divided into eight equal sectors by horizontal, vertical and diagonal lines. (This pattern is replicated in many mandalas).
 

VIRTUAL UNDERSTANDING

When a phenomenon is projected from the unconscious it becomes an indirect (conscious) expression of this holistic source. This is virtual understanding and in qualitative imaginary terms is "imaginary". The dynamic interaction of wholes and parts (e.g. concepts and perceptions) in understanding always involves virtual understanding (though this is rarely recognised).