- a quantitative rational aspect suited to the partial analysis of systems. This is conventional mathematics and represents a horizontal approach where understanding takes place extensively within one fixed paradigm (i.e. rational).
- a qualitative (intuitive) aspect suited to the holistic synthesis of systems. Though implicit in the Pythagorean outlook and more recently Jungian psychology, this is a largely undeveloped form of mathematics. It represents essentially a vertical approach where understanding takes place intensively within different paradigms and is inseparable from transpersonal psychology.

- This is a follow-up letter on "Holistic
Mathematics" (again with minor editing) that I sent to Ken recently. It
complements my posting (on the same subject) earlier this week.

Dear Ken,

I was interested to check out the contents of your "Eye of the Spirit" on the forum and sample its first chapter. I look forward to reading the full book when published.

I have followed with admiration your writings for many years and have derived much benefit from them.

As I share a common interest in the spectrum of consciousness, I am writing to you regarding - what I consider - a highly fruitful approach, which has not been explicitly addressed in your books.

My thesis is briefly this:

The marriage of Western and Eastern wisdom entails a corresponding marriage of both reason and intuition.

Conventional mathematics (so important to western science) represents the most specialized expression of reason whereas mystical spirituality (esp. of the Eastern tradition) is the essence of transpersonal psychology and represents the most specialized expression of intuition.

A comprehensive synthesis of reason and intuition therefore entails the marriage of mathematics with transpersonal psychology.

For the past number of years I have been working on a new integral mathematics which has dual complementary poles:

Quite simply every mathematical relationship quantitatively understood, has a complementary qualitative interpretation which in essence is psychological. This provides a remarkably efficient mode for translating the entire spectrum of consciousness.

Of special relevance here is the number concept.

Specific numbers - quantitatively understood - are of course extremely valuable for ordering physical data. However complementary holistic numbers i.e. number types or sets - qualitatively understood - are equally valuable for ordering psychological data.

Let me explain:

There are many different number types (representing quantities) in mathematics.

We have the binary numbers (0 and 1).

We also have prime numbers and natural numbers (which are uniquely derived from prime numbers) and the integers (which include negative numbers). Then we have the rational numbers which involve fractions.

We also have irrational numbers (algebraic and transcendental), imaginary, transfinite and complex numbers. Corresponding to the conventional mathematical understanding of each number type as representing specific quantities, is a complementary psychological understanding of each number type as representing a holistic quality. In other words each qualitative number type represents a distinct manner of interpreting and ordering reality (i.e. paradigm) in the spectrum of consciousness.

In conventional mathematics though many differing number types as quantities are recognized, they are all interpreted within the understanding of just one number type as quality or paradigm. This is of course the rational paradigm and is the unquestioned basis of Western science. Indeed expressed more precisely it is the real positive rational paradigm. It is real in that it is based on conscious (rather than unconscious understanding). It is positive in that it recognizes solely the external objective (rather than the internal subjective) direction of experience. Finally it is rational in the sense that is based on a cognitive logic of clear separation (rather than mutual complementarity) of opposites. However just as the set of real positive rational numbers represents just one limited subset of the entire set of number quantities, likewise the real positive rational paradigm, represents just one of the entire set of possible paradigms.

Thus there are many other number paradigms possible all offering important and differing - though necessarily limited - interpretations of reality.

For example we can identify a real negative rational paradigm. What this entails is that every positive interpretation in conventional science is balanced by a corresponding negative interpretation. Just as physical matter in physics is complemented by anti-matter, likewise psychic matter is equally complemented by anti-matter. Thus every perception, concept and hypothesis used in science is complemented by a corresponding anti-perception, anti-concept and anti-hypothesis. In absolute reduced static terms positive and negative interpretations are formally identical. However in dynamic relative terms, they are opposite and paradoxical.

This helps to explain the changing nature of science when viewed from a historical perspective.

As conventional science is so tied to just one limited paradigm, there is enormous potential for vertical expansion into both "higher" and "lower" alternative number paradigms. Many of the findings of modern physics appear non-intuitive, because we attempt to explain them within the (real positive) rational paradigm which is no longer appropriate. From the perspective of an alternative number paradigm these findings become fully intuitive. However this involves an approach to science which includes transpersonal psychology as an integral component.

The first step however is to satisfactorily map out the entire spectrum of consciousness in this transrational fashion, making explicit the startling complementarity of (static) mathematical and (dynamic) psychological notions.

Though I stumbled unexpectedly on these insights six years ago and am a full convert at this stage, I still have some difficulty in accepting their implications, requiring nothing less than a complete revolution in the customary scientific world-view .

Therefore I am not surprised when attempting to communicate such insights to meet with skepticism from others.

Because Ken of your own enormous contribution to the field of consciousness I am confident that if you take the time to carefully read this letter that you will appreciate the potential power of this psycho-mathematical approach and place it on the agenda in future along with more traditional approaches

Indeed Ken it is already implicit in your most recent offerings. In your "Brief History of Everything" you outline "The Four Corners of the Kosmos" where every holon has both an individual and collective identity with external and internal facets.

In (conventional) mathematics the complex number system is the most comprehensive available with real and imaginary quantities in both positive and negative format.

Therefore in complementary (holistic) mathematics the most comprehensive paradigm is also complex and four directional with - in relative terms - real (individual) and imaginary (collective) aspects with positive (external) and negative (internal) directions. Your treatment of holons is therefore perfectly consistent with this complex paradigm.

The scientific belief that we live in a "real" world is an unfortunate form of reductionism where wholes are simply reduced to parts. In dynamic mathematical terms, in any context if the parts are "real", then in relative terms the wholes are "imaginary".

Therefore in correct dynamic terms we live in a "complex" rather than a "real" world.

I have written to you Ken on two previous occasions and trust that you received my letters. I appreciate that as a successful as highly respected writer that you probably receive a great deal of unwanted correspondence at times when you would rather concentrate on relevant research. However I believe that I have come up with an original and valuable approach which could fruitfully be included in such research.

Regards,

Peter Collins