Standard (conventional) mathematics is understood - in formal terms - as an exclusively rational discipline. The starting point for Holistic Mathematics is the recognition that true mathematical understanding is far more subtle, involving both reason and intuition in an inherently dynamic interaction.
Thus all quantities, operations and relationships
- with absolute static meanings in standard mathematics - have corresponding
interpretations in Holistic Mathematics which are dynamic and relative.
(Indeed conventional mathematics represents a reduced interpretation of a richer and more comprehensive mathematical understanding).
Thus the great use of Holistic Mathematics is in providing a coherent scientific basis for the integration of all dynamic systems (physical and psychological).
A key axiom is the complementarity of physical
and psychological reality. This entails that the underlying mathematical
structure of both are themselves complementary. Thus for example one can
attempt to derive - as I am presently doing - a knowledge of the fundamental
(holistic) mathematical structures of physical reality (at all levels)
from a knowledge of the complementary psychological structures.
Holistic Mathematics has enormous potential as a truly scientific approach to consciousness. Starting with the psychological aspect of experience, the full Spectrum of Consciousness can be precisely translated in mathematical format. Its structure is perfectly represented by a qualitative number system (which is the dynamic counterpart in Holistic Mathematics to the quantitative number system of standard mathematics).
This then provides the means to create a complementary Number Spectrum for Physics fully integrated with consciousness.
Holistic Mathematics can be used to bring dynamic integration to many fields. Thus we can have Holistic Psychology (Holochology), Holistic Physics (Holophysics), Holistic Philosophy (Holosophy), Holistic Biology (Holobiology), Holistic Economics (Holonomics) etc. Of course as Holistic Mathematics leads to the harmonious integration of these fields, they are all ultimately understood as aspects of the same unified system.
Holistic Mathematics provides an exciting new
way of looking at reality which is basically very simple. We will see again
and again that three fundamental symmetries apply to all dynamic relationships;
horizontal symmetry of external and internal (objective and subjective);
vertical symmetry of whole and part (qualitative and quantitative); and
diagonal symmetry of form and emptiness (actual and potential). When
translated in dynamic mathematical terms these poles are - in relative
terms - positive and negative, real and imaginary and finite and infinite
respectively. The mathematical directions in turn are derived from
a simple circular number system represented geometrically by the
eight roots of unity. So quite literally, reality - at all levels - can
be mathematically expressed as a reduced expression of unity!
The Theory of Everything, physically and psychologically, can be convincingly explained in terms of these eight directions.
On this site I have provided the full text of
"Transforming Voyage" which is a contemporary mapping of the Spectrum of
Consciousness and serves as an appropriate introduction to Holistic Mathematics.
In addition a key chapter from "The Number Paradigms" - which translates
this spectrum explicitly in Holistic Mathematical terms - is online. I
have also included the introductory chapter of "Original Vision" which
further develops key ideas in Holistic Mathematics and provides a more
subtle reading of the Spectrum in complementary psychological and physical
As well as other material I have posted the contents
of a discussion on the Ken Wilber Forum which may help to further clarify
the nature of Holistic Mathematics.