mathematics is understood - in formal terms - as an exclusively rational
discipline and is based on the somewhat rigid cognitive type appreciation
of the middle of the psychological spectrum. Such understanding by its
very nature is well suited for the specialised analytic interpretation
of symbols and is associated with our conventional notions of science.
However beyond the middle level lie several "higher" spiritual levels of
understanding. Here a more dynamic and refined cognition unfolds where
reason and (spiritual) intuition increasingly interpenetrate in experience.
This understanding in turn enables an entirely new scientific appreciation
which is inherently suited for a truly integral - as opposed to merely
analytic - interpretation of reality.
So the starting point for Holistic Mathematics is the subtle interactive cognitive understanding associated with the "higher" levels of the spectrum. When mathematical symbols are interpreted - in the light of this understanding - in their original dynamic sense, they provide the appropriate basis for an exciting new vision of integral science.
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 can be seen to represent 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 reality - from both perspectives - can be fruitfully interpreted as being made up of a number of key levels (the fundamental structure of which can be precisely encoded in holistic mathematical terms). Because the underlying mathematical structure of levels, with repect to both aspects (physical and psychological) is complementary, one for example can thus derive knowledge of the fundamental (holistic) mathematical structures of physical reality (at all levels) from a knowledge of their complementary psychological structures. So with integral science the physical and psychological domains display remarkable unity and are ultimately indivisible. And when Holistic Mathematics is appropriately understood it has the power to awaken us - in scientific terms - to the nature of this unity.
Holistic Mathematics thus 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 an exact 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 (Holopsychology), Holistic Physics (Holophysics), Holistic Philosophy (Holophilsophy), Holistic Biology (Holobiology), Holistic Economics (Holoeconomics) etc. Of course as Holistic Mathematics can greatly assist the harmonious integration of these fields, they are then more easily 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 polar relationships apply to all dynamic relationships. In each case these can be given both an asymmetrical (linear) interpretation (suited to the differentiated aspect of reality) and a symmetrical (circular) interpretation (directly suited to the integrated aspect). So briefly we have the horizontal poles of external and internal (objective and subjective); vertical poles of whole and part (qualitative and quantitative); and diagonal poles of form and emptiness (actual and potential). Remarkably, these poles have an original holistic mathematical interpretation which encapsulate - in dynamic manner - the most fundamental notions of number. In dynamic mathematical terms the horizontal poles are - in relative terms - positive and negative (with respect to each other); the vertical poles are real and imaginary and the diagonal poles finite and infinite (with respect to each other). These polar directions (horizontal, vertical and diagonal) in turn are derived from a simple circular number system (represented geometrically by the basic roots of unity). So quite literally, reality - at all levels - can be mathematically expressed - in dynamic fashion - as a reduced expression of unity!
Indeed a holistic "Theory of Everything" (physically and psychologically) which applies in principle to any dynamic system, can be convincingly derived from these three fundamental poles of reality when interpreted in both a (linear) asymmetric and (circular) symmetric fashion.
for example that all the stages of development - even to a considerable
level of detail - can be remarkably encoded in this precise integral scientific
fashion (which simply reflects the holistic mathematical interpretation
of this "Theory of Everything")
Indeed underlying this TOE is dynamic binary system. So the binary digits of 1 and 0 have holistic mathematical interpretations as oneness and nothingness, reflecting ultimately (linear) form and (circular) emptiness respectively.
So just as
the analytic interpretation of the binary digits paves the way for the
potential encoding of all information processes, likewise the appropriate
holistic interpretation of these same digits equally paves the way for
the potential encoding of all transformation processes.
In particular the full spectrum of development (with respect to both its psychological and physical aspects) can be precisely encoded - to any desired level of detail - in a holistic digital fashion.
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. As this was written some years ago it does not
adequately represent my most recent thinking (which has considerably developed
since that time). However it has perhaps the benefit of being initially
more accessible than my recent work. In addition the full text of "The
Number Paradigms" - which provides a holistic mathematical interpretation
of "Transforming Voyage" is provided.
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 fashion.
(It is my intention in the near future to start on a more precise and much more comprehensive account of what is contained in those books).
As well as
much other material designed to clarify the nature and applications of
Holistic Mathematics, I have posted several articles and contents of a
discussion from the Ken Wilber Forum which may help to further clarify
the nature of my approach.